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GitHub - Robotmurlock/Deepwalk-and-Node2vec: Implementation of Word2Vec, DeepWalk and Node2vec papers.
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8.351a1.312 1.312 0 0 1-1.146 1.954H1.33A1.313 1.313 0 0 1 .183 9.058ZM7 7V3H5v4Zm-1 3a1 1 0 1 0 0-2 1 1 0 0 0 0 2Z"></path> </svg> </span> <span></span> </div> </div> <div data-target="query-builder.screenReaderFeedback" aria-live="polite" aria-atomic="true" class="sr-only"></div> </query-builder></form> <div class="d-flex flex-row color-fg-muted px-3 text-small color-bg-default search-feedback-prompt"> <a target="_blank" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax" data-view-component="true" class="Link color-fg-accent text-normal ml-2"> Search syntax tips </a> <div class="d-flex flex-1"></div> </div> </div> </div> </div> </modal-dialog></div> </div> <div data-action="click:qbsearch-input#retract" class="dark-backdrop position-fixed" hidden data-target="qbsearch-input.darkBackdrop"></div> <div class="color-fg-default"> <dialog-helper> <dialog data-target="qbsearch-input.feedbackDialog" data-action="close:qbsearch-input#handleDialogClose cancel:qbsearch-input#handleDialogClose" id="feedback-dialog" aria-modal="true" aria-labelledby="feedback-dialog-title" aria-describedby="feedback-dialog-description" data-view-component="true" class="Overlay Overlay-whenNarrow Overlay--size-medium Overlay--motion-scaleFade Overlay--disableScroll"> <div data-view-component="true" class="Overlay-header"> <div class="Overlay-headerContentWrap"> <div class="Overlay-titleWrap"> <h1 class="Overlay-title " id="feedback-dialog-title"> Provide feedback </h1> </div> <div class="Overlay-actionWrap"> <button data-close-dialog-id="feedback-dialog" aria-label="Close" type="button" data-view-component="true" class="close-button Overlay-closeButton"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 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class=\"heading-element\" dir=\"auto\"\u003eDeep learning graph shallow encoders - DeepWalk and node2vec\u003c/h1\u003e\u003ca id=\"user-content-deep-learning-graph-shallow-encoders---deepwalk-and-node2vec\" class=\"anchor\" aria-label=\"Permalink: Deep learning graph shallow encoders - DeepWalk and node2vec\" href=\"#deep-learning-graph-shallow-encoders---deepwalk-and-node2vec\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDescription\u003c/h2\u003e\u003ca id=\"user-content-description\" class=\"anchor\" aria-label=\"Permalink: Description\" href=\"#description\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis repository provides from-the-ground-up implementations of both \u003ca href=\"https://arxiv.org/abs/1403.6652\" rel=\"nofollow\"\u003eDeepWalk\u003c/a\u003e\nand \u003ca href=\"https://arxiv.org/abs/1607.00653\" rel=\"nofollow\"\u003enode2vec\u003c/a\u003e. It also encompasses a handcrafted version of\n\u003ca href=\"http://arxiv.org/abs/1301.3781\" rel=\"nofollow\"\u003eword2vec\u003c/a\u003e\nwith \u003ca href=\"http://arxiv.org/abs/1310.4546\" rel=\"nofollow\"\u003enegative sampling\u003c/a\u003e,\nfundamental to the workings of DeepWalk and node2vec.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTable of Contents\u003c/h2\u003e\u003ca id=\"user-content-table-of-contents\" class=\"anchor\" aria-label=\"Permalink: Table of Contents\" href=\"#table-of-contents\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#introduction\"\u003eIntroduction\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#experiments\"\u003eExperiments\u003c/a\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#word2vec-1\"\u003eWord2vec\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#deepwalk-and-node2vec\"\u003eDeepWalk and Node2vec\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#usage\"\u003eUsage\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#references\"\u003eReferences\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eIntroduction\u003c/h2\u003e\u003ca id=\"user-content-introduction\" class=\"anchor\" aria-label=\"Permalink: Introduction\" href=\"#introduction\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis section briefly explains word2vec, DeepWalk and node2vec.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWord2vec\u003c/h3\u003e\u003ca id=\"user-content-word2vec\" class=\"anchor\" aria-label=\"Permalink: Word2vec\" href=\"#word2vec\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWord2Vec is a technique to represent words as continuous vector spaces.\nThe primary intuition is that words appearing in similar contexts in a sentence\ntend to have similar meanings. This task can be approached in two ways:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eBased on the observed word, predict context words - SkipGram.\u003c/li\u003e\n\u003cli\u003eBased on the observed context, predict missing word - CBOW (Continuous Bag Of Words).\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eConsider sentence \"Cats are similar to dogs in many ways.\". Goal for SkipGram would\nbe to predict context words \"Cats\", \"are\", \"similar\", \"to\", \"in\", \"many\", \"ways\" based\non the observed word \"dogs\". For CBOW it would be opposite.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/word2vec_architecture.png\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/word2vec_architecture.png\" alt=\"word2vec_architecture.png\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eEach word is encoded using \u003ca href=\"https://en.wikipedia.org/wiki/One-hot\" rel=\"nofollow\"\u003eone-hot\u003c/a\u003e encoding to\nobtain its one-hot vector. Afterward, each vector is projected to the embedding space\nusing a projection matrix. This operation can be performed more efficiently through a word index lookup\n(check: \u003ca href=\"https://pytorch.org/docs/stable/generated/torch.nn.Embedding.html\" rel=\"nofollow\"\u003ePytorch Embedding\u003c/a\u003e).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor the SkipGram model, it is trained to predict if another word\n(represented as an embedding) occurs in the context (refer to the image above on the right).\nFor CBOW, the process is similar, expect\ninstead of using embedding vector of a single observed word, a context representation vector\nis obtained by averaging over all context embedding vectors (refer to the image above on the left).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe cross-entropy function is utilized for model training. Using it directly results in an intractable computation.\nInstead, hierarchical softmax (\u003ca href=\"https://arxiv.org/abs/1301.3781\" rel=\"nofollow\"\u003eoriginal word2vec paper\u003c/a\u003e)\nor negative sampling (\u003ca href=\"https://proceedings.neurips.cc/paper_files/paper/2013/file/9aa42b31882ec039965f3c4923ce901b-Paper.pdf\" rel=\"nofollow\"\u003efollow-up paper\u003c/a\u003e)\nis employed. In short, cross-entropy compute time depends on the vocabulary size\nwhich can be huge (e.g. 1 million tokens). Executing that many operations per word\nis computationally unfeasible. Hierarchical softmax and negative samplings are remedy for this.\nIn this implementation, negative sampling is the chosen method.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWe use separate embedding weights for input and context words.\nAlthough it's theoretically acceptable to use the same weights for both input and context words,\nthe model becomes more expressive when two different embedding matrices are used.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDeepWalk\u003c/h3\u003e\u003ca id=\"user-content-deepwalk\" class=\"anchor\" aria-label=\"Permalink: DeepWalk\" href=\"#deepwalk\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWe possess a tool to learn word embeddings from a given corpus. In case of graphs we\ncan generate \"sentences\" using graph \u003ca href=\"https://en.wikipedia.org/wiki/Random_walk\" rel=\"nofollow\"\u003erandom walks\u003c/a\u003e.\nBasically, we start from a particular node and traverse through graph by choosing random neighbor\nfor \u003cem\u003eN-1\u003c/em\u003e steps where \u003cem\u003eN\u003c/em\u003e is random walk length. For every node we can generate multiple\nrandom walks. Once we obtain enough random walks we can form a \"node corpus\" and use\nword2vec to train learn node embeddings. Three hyperparameters can be observed here:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNumber of random walks per node for each epoch.\u003c/li\u003e\n\u003cli\u003eRandom walk length.\u003c/li\u003e\n\u003cli\u003eContext radius (length) for each node.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eNote that in this implementation we generate new random walks for each epoch.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eNode2vec\u003c/h3\u003e\u003ca id=\"user-content-node2vec\" class=\"anchor\" aria-label=\"Permalink: Node2vec\" href=\"#node2vec\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNode2vec is extension of the DeepWalk algorithm. It presents three main contributions compared to the\noriginal paper:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eIt uses \u003ca href=\"http://arxiv.org/abs/1310.4546\" rel=\"nofollow\"\u003enegative sampling\u003c/a\u003e instead of\n\u003ca href=\"https://arxiv.org/abs/1301.3781\" rel=\"nofollow\"\u003ehierarchical softmax\u003c/a\u003e\nthat was also used in the original word2vec paper\n(follow-up paper used negative sampling instead).\u003c/li\u003e\n\u003cli\u003eIt introduces more flexible algorithm for random walk generation.\u003c/li\u003e\n\u003cli\u003eIt defines a way to obtain edge embeddings from node embeddings. Edge embeddings\ncan be used for link prediction task - predicting if an edge exists between two nodes.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRandom walk generation\u003c/h4\u003e\u003ca id=\"user-content-random-walk-generation\" class=\"anchor\" aria-label=\"Permalink: Random walk generation\" href=\"#random-walk-generation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAssume that \u003cem\u003ev\u003c/em\u003e is current node in the random walk generation algorithm and\nwe have to choose next node that will be added to the walk. Node \u003cem\u003et\u003c/em\u003e is the previous\nnode in the walk, and \u003cem\u003ex\u003c/em\u003e is the candidate node (potential next node).\nWeights for each node are modified following rules:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eby \u003ccode\u003e1/p\u003c/code\u003e if \u003ccode\u003eshortest_path(t, x) == 0\u003c/code\u003e (i.e. x == t)\u003c/li\u003e\n\u003cli\u003eby \u003ccode\u003e1\u003c/code\u003e if \u003ccode\u003eshortest_path(t, x) == 1\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eby \u003ccode\u003e1/q\u003c/code\u003e if \u003ccode\u003eshortest_path(t, x) == 2\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003ewhere \u003cem\u003ep\u003c/em\u003e (return parameter) and \u003cem\u003eq\u003c/em\u003e (in-out parameter) are random walk generation hyperparameters:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eHigher values for \u003cem\u003ep\u003c/em\u003e lowers chance of adding already explored node to the random walk.\u003c/li\u003e\n\u003cli\u003eLower values for \u003cem\u003ep\u003c/em\u003e increases chance of going back and keeps the walk \"local\".\u003c/li\u003e\n\u003cli\u003eHigher values for \u003cem\u003eq\u003c/em\u003e bias walks to move more towards node \u003cem\u003et\u003c/em\u003e (\"inwards\", BFS-like).\u003c/li\u003e\n\u003cli\u003eLower values for \u003cem\u003eq\u003c/em\u003e bias walks to move from node \u003cem\u003et\u003c/em\u003e (\"outwards\", DFS-like).\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/node2vec_rwg.png\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/node2vec_rwg.png\" alt=\"node2vec_rwg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEdge embeddings\u003c/h4\u003e\u003ca id=\"user-content-edge-embeddings\" class=\"anchor\" aria-label=\"Permalink: Edge embeddings\" href=\"#edge-embeddings\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eEdge embedding can be obtained from the node embeddings. We just need to define\na function \u003cem\u003ef\u003c/em\u003e (heuristic) that aggregates arbitrary nodes \u003cem\u003en1\u003c/em\u003e and \u003cem\u003en2\u003c/em\u003e:\n\u003ccode\u003evector(edge(n1, n2)) = f(vector(n1), vector(n2))\u003c/code\u003e. Examples:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eAverage: \u003ccode\u003ef(vector(n1), vector(n2)) = (vector(n1) + vector(n2)) / 2\u003c/code\u003e;\u003c/li\u003e\n\u003cli\u003eHadamard (point-wise multiplication): \u003ccode\u003ef(vector(n1), vector(n2)) = vector(n1) * vector(n2)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003epoint-wise L1 distance: \u003ccode\u003ef(vector(n1), vector(n2)) = |vector(n1) - vector(n2))|\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003epoint-wise L2 distance: \u003ccode\u003ef(vector(n1), vector(n2)) = (vector(n1) - vector(n2)))^2\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eExperiments\u003c/h2\u003e\u003ca id=\"user-content-experiments\" class=\"anchor\" aria-label=\"Permalink: Experiments\" href=\"#experiments\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWord2vec\u003c/h3\u003e\u003ca id=\"user-content-word2vec-1\" class=\"anchor\" aria-label=\"Permalink: Word2vec\" href=\"#word2vec-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eBoth Skip-Gram and CBOW implementation are supported.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSupported text-based datasets are:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eABCDE (custom test dataset)\u003c/li\u003e\n\u003cli\u003eShakespeare\u003c/li\u003e\n\u003cli\u003eWikiText-2\u003c/li\u003e\n\u003cli\u003eWikiText-103\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eToy example - ABCDE\u003c/h4\u003e\u003ca id=\"user-content-toy-example---abcde\" class=\"anchor\" aria-label=\"Permalink: Toy example - ABCDE\" href=\"#toy-example---abcde\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis dataset is used as an sanity test -\nchecks is custom implementation of the word2vec model works:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003ea b a b a b a b a b\u003c/code\u003e, \u003ccode\u003ea\u003c/code\u003e goes with \u003ccode\u003eb\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ea b a b a b\u003c/code\u003e,\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eb a b a\u003c/code\u003e,\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ea b a b a b a b\u003c/code\u003e,\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ec d c d c d c d\u003c/code\u003e, \u003ccode\u003ec\u003c/code\u003e goes with \u003ccode\u003ed\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ed c d c d c\u003c/code\u003e,\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ec d c d c d\u003c/code\u003e,\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ee e e e e e e e\u003c/code\u003e, \u003ccode\u003ee\u003c/code\u003e goes alone\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003ee e e\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe expected model should position the embeddings of words \"a\" and \"b\" close together,\nas well as \"c\" and \"d\". However, the word \"e\" should form its own isolated cluster.\nOn the other hand, even though vectors \"a\" and \"b\" are close,\nthey shouldn't \"match\" because they don't share the same tokens in their context. Results:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/abcde_projected_embeddings.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/abcde_projected_embeddings.jpg\" alt=\"abcde_projected_embeddings\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor this experiment embedding dimension 2 was used. Full experiment configuration\ncan be found here \u003ccode\u003econfigs/w2v_sg_abcde.yaml\u003c/code\u003e and \u003ccode\u003econfigs/w2v_cbow_abcde.yaml\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eShakespeare dataset\u003c/h4\u003e\u003ca id=\"user-content-shakespeare-dataset\" class=\"anchor\" aria-label=\"Permalink: Shakespeare dataset\" href=\"#shakespeare-dataset\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePlease note that minimal effort was invested in preprocessing the input sentences\nfor the Word2Vec case. These datasets were primarily analyzed to\nvalidate the Word2Vec implementation. Enhancing data preparation could potentially\nlead to significant improvements in the results. Additionally, in the original paper,\naggressive subsampling was used for very frequent words. This detail was omitted in this\nimplementation since our primary focus is on learning graph embeddings rather than word\nembeddings.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor this experiment embedding dimension 12 was used. Full experiment configuration\ncan be found here \u003ccode\u003econfigs/w2v_shakespeare.yaml\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eClosest word pairs\u003c/h5\u003e\u003ca id=\"user-content-closest-word-pairs\" class=\"anchor\" aria-label=\"Permalink: Closest word pairs\" href=\"#closest-word-pairs\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFinding the closest context words for the chosen input word is performed using\n\u003ca href=\"https://en.wikipedia.org/wiki/Cosine_similarity\" rel=\"nofollow\"\u003ecosine similarity\u003c/a\u003e\nbetween embedding vectors of the trained model.\nSome examples (\u003cem\u003einput word\u003c/em\u003e: \u003cem\u003eclosest context words\u003c/em\u003e):\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eking: king, young, duke\u003c/li\u003e\n\u003cli\u003equeen: young, queen, king\u003c/li\u003e\n\u003cli\u003eduke: duke, king, enter\u003c/li\u003e\n\u003cli\u003elord: young, king, lord\u003c/li\u003e\n\u003cli\u003elady: hear, lady, boy\u003c/li\u003e\n\u003cli\u003ekiss: about, leave, hand\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEmbedding visualization\u003c/h5\u003e\u003ca id=\"user-content-embedding-visualization\" class=\"anchor\" aria-label=\"Permalink: Embedding visualization\" href=\"#embedding-visualization\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eInput word embeddings visualization.\n\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/shakespeare-projected_embeddings_edited.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/shakespeare-projected_embeddings_edited.jpg\" alt=\"shakespeare_embedding_visualization\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOnly the most frequent words are selected, and this includes stopwords, which are typically not of primary interest.\nStill we can observe two interesting clusters:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eRoyalty cluster (red) - king, queen, prince, lord, etc.\u003c/li\u003e\n\u003cli\u003eRelationship cluster (blue) - son, friend, brother, wife, etc.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSemantic tests\u003c/h5\u003e\u003ca id=\"user-content-semantic-tests\" class=\"anchor\" aria-label=\"Permalink: Semantic tests\" href=\"#semantic-tests\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHere we perform simple semantic calculations and check if the \"model\" can answer properly.\nFor an example, it is ideal if vector \u003ccode\u003evector(\"king\") - vector(\"man\") + vector(\"woman\")\u003c/code\u003e\nis close to vector \u003ccode\u003evector(\"queen\")\u003c/code\u003e. Results:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eSimilarity between vector(\"king\") - vector(\"man\") + vector(\"woman\") and vector(\"queen\") is 0.59 (good)\u003c/li\u003e\n\u003cli\u003eSimilarity between vector(\"queen\") - vector(\"woman\") + vector(\"man\") and vector(\"king\") is 0.43 (good)\u003c/li\u003e\n\u003cli\u003eSimilarity between vector(\"king\") - vector(\"queen\") + vector(\"woman\") and vector(\"man\") is -0.05 (bad)\u003c/li\u003e\n\u003cli\u003eSimilarity between vector(\"queen\") - vector(\"king\") + vector(\"man\") and vector(\"woman\") is 0.23 (bad)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDeepWalk and node2vec\u003c/h3\u003e\u003ca id=\"user-content-deepwalk-and-node2vec\" class=\"anchor\" aria-label=\"Permalink: DeepWalk and node2vec\" href=\"#deepwalk-and-node2vec\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eDeepWalk and Node2Vec are implemented as extensions of the Word2Vec model.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSupported datasets are:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eGraph triplets (test dataset)\u003c/li\u003e\n\u003cli\u003eZachary's Karate club\u003c/li\u003e\n\u003cli\u003eCora\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eToy example - Graph Triplets\u003c/h4\u003e\u003ca id=\"user-content-toy-example---graph-triplets\" class=\"anchor\" aria-label=\"Permalink: Toy example - Graph Triplets\" href=\"#toy-example---graph-triplets\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis graph consists of 3 fully connected components consisting of three nodes. Model\nshould be able to learn to cluster these nodes together in embeddings space.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor this experiment embedding dimension 2 was used. Full experiment configuration\ncan be found here \u003ccode\u003econfigs/sge_sg_graph_triplets.yaml\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEmbedding visualization\u003c/h5\u003e\u003ca id=\"user-content-embedding-visualization-1\" class=\"anchor\" aria-label=\"Permalink: Embedding visualization\" href=\"#embedding-visualization-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph_triplets-projected_embeddings.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph_triplets-projected_embeddings.jpg\" alt=\"graph_triplets_embedings\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWe can observe that clusters are successfully formed. One can tune the training parameters to\neither increase or decrease the separation between these clusters,\nand to make the nodes within each cluster more or less merged. If we query\nfor the two closest context nodes for each input node, we always get two nodes\nfrom the same input node cluster, which is what we expect.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDownstream tasks\u003c/h5\u003e\u003ca id=\"user-content-downstream-tasks\" class=\"anchor\" aria-label=\"Permalink: Downstream tasks\" href=\"#downstream-tasks\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn order to additionally evaluate quality of these embeddings, two downstream tasks\nare performed:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNode classification: \u003ca href=\"https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html\" rel=\"nofollow\"\u003eA scikit-learn logistic regression model\u003c/a\u003e\nis trained to predict node's label based on its vector embedding.\nIf there are multiple classes then\n\u003ca href=\"https://scikit-learn.org/stable/modules/generated/sklearn.multiclass.OneVsRestClassifier.html\" rel=\"nofollow\"\u003eone-vs-rest\u003c/a\u003e\napproach is used. It is required that the dataset has label nodes.\u003c/li\u003e\n\u003cli\u003eEdge classification (link prediction more precisely): similar to \u003cem\u003enode classification\u003c/em\u003e, a model\nis trained to predict if edge exists between two nodes. More precisely, model\npredicts if edge exists based on the edge embedding. This embedding is obtained using a\nfunction \u003cem\u003ef\u003c/em\u003e that aggregates arbitrary nodes \u003cem\u003en1\u003c/em\u003e and \u003cem\u003en2\u003c/em\u003e:\n\u003ccode\u003evector(edge(n1, n2)) = f(vector(n1), vector(n2))\u003c/code\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe model is evaluated using [transduction](\u003ca href=\"https://en.wikipedia.org/wiki/Transduction_(machine_learning)\" rel=\"nofollow\"\u003ehttps://en.wikipedia.org/wiki/Transduction_(machine_learning)\u003c/a\u003e.\nThis means that during unsupervised learning - while training the shallow graph encoder\n(either DeepWalk or node2vec) —\nthe complete graph structure is known. For downstream tasks, we partition the data for\nboth training and evaluation of the node label classifier.\nExperiments are conducted multiple times to obtain an average metric result.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eResults:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNode classification accuracy (averaged over 10 experiments): 88.89% (best: 100.00%)\u003c/li\u003e\n\u003cli\u003eEdge classification accuracy (averaged over 10 experiments): 85.83% (best: 100.00%)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eVisualization of best node classification model:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-triplets_downstream-node-classification.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-triplets_downstream-node-classification.jpg\" alt=\"graph_triplets_node_classification\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eZachary's karate club\u003c/h4\u003e\u003ca id=\"user-content-zacharys-karate-club\" class=\"anchor\" aria-label=\"Permalink: Zachary's karate club\" href=\"#zacharys-karate-club\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://camo.githubusercontent.com/d6e19947f6a8801e1118e2984bf5073a92844aac8e3d63068aadc46cbea0a095/68747470733a2f2f75706c6f61642e77696b696d656469612e6f72672f77696b6970656469612f656e2f7468756d622f382f38372f5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e672f37353070782d5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e67\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/d6e19947f6a8801e1118e2984bf5073a92844aac8e3d63068aadc46cbea0a095/68747470733a2f2f75706c6f61642e77696b696d656469612e6f72672f77696b6970656469612f656e2f7468756d622f382f38372f5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e672f37353070782d5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e67\" alt=\"zachary_karate_club\" data-canonical-src=\"https://upload.wikimedia.org/wikipedia/en/thumb/8/87/Zachary_karate_club_social_network.png/750px-Zachary_karate_club_social_network.png\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAnother small dataset that can be used for model analysis is \u003ca href=\"https://en.wikipedia.org/wiki/Zachary%27s_karate_club\" rel=\"nofollow\"\u003eZachary's karate club\u003c/a\u003e.\nThis graph has weighted edges and random walks are sampled based on that. Probability\nof picking successor node based on the current node is proportional to edge weight. It\nis assumed that all weights are positive.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor this experiment embedding dimension 2 was used. Full experiment configuration\ncan be found here \u003ccode\u003econfigs/sge_sg_karate_club.yaml\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEmbeddings visualization\u003c/h5\u003e\u003ca id=\"user-content-embeddings-visualization\" class=\"anchor\" aria-label=\"Permalink: Embeddings visualization\" href=\"#embeddings-visualization\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-karate-club_projected_embeddings.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-karate-club_projected_embeddings.jpg\" alt=\"karate_club_embedings\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWe can observe that two groups of nodes are clustered almost perfectly. Only\nnode \u003cem\u003en09\u003c/em\u003e is outside the green (label 1) cluster but these groups can still be easily\nseparated using a line. In case dataset edge weights are not used\nthen these cannot be separated as distinctly.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDownstream tasks\u003c/h5\u003e\u003ca id=\"user-content-downstream-tasks-1\" class=\"anchor\" aria-label=\"Permalink: Downstream tasks\" href=\"#downstream-tasks-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eSimilar configuration as for graph triplets is used for the downstream tasks.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eResults:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNode classification accuracy (averaged over 10 experiments): 98.06% (best: 100.00%)\u003c/li\u003e\n\u003cli\u003eEdge classification accuracy (averaged over 10 experiments): 69.52% (best: 80.13%)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eVisualization of best node classification model:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-karate-club_downstream-node-classification.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-karate-club_downstream-node-classification.jpg\" alt=\"karate_club_node_classification\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCora dataset\u003c/h4\u003e\u003ca id=\"user-content-cora-dataset\" class=\"anchor\" aria-label=\"Permalink: Cora dataset\" href=\"#cora-dataset\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/cora-graph.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/cora-graph.jpg\" alt=\"cora_graph\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe Cora dataset consists of 2708 scientific publications classified into one of seven classes:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eCase_Based\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eGenetic_Algorithms\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eNeural_Networks\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eProbabilistic_Methods\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eReinforcement_Learning\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eRule_Learning\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eTheory\u003c/code\u003e\nEach node represents one scientific publication. Each edge represents citation.\nThe citation network consists of 5429 links. This is one of the standard dataset\nfor evaluating graph based machine learning algorithm.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eFor this experiment embedding dimension 8 was used. For 2D visualization we\nuse \u003ca href=\"https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding\" rel=\"nofollow\"\u003eT-SNE\u003c/a\u003e.\nFull experiment configuration can be found here \u003ccode\u003econfigs/sge_sg_cora.yaml\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEmbedding visualization\u003c/h5\u003e\u003ca id=\"user-content-embedding-visualization-2\" class=\"anchor\" aria-label=\"Permalink: Embedding visualization\" href=\"#embedding-visualization-2\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer\" href=\"/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-cora_projected_embeddings.jpg\"\u003e\u003cimg src=\"/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-cora_projected_embeddings.jpg\" alt=\"cora_embedings\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFrom the visualized embedding, we can observe that all subjects\nform clusters that overlap with few others. There is also a large cluster\ncomprised of mixed node labels. The model was not able to successfully separate these nodes,\nleading us to expect weaker results when using logistic regression for classification.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch5 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDownstream tasks\u003c/h5\u003e\u003ca id=\"user-content-downstream-tasks-2\" class=\"anchor\" aria-label=\"Permalink: Downstream tasks\" href=\"#downstream-tasks-2\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eSimilar configuration as for graph triplets is used for the downstream tasks. The main\ndifference is that for this task we also combine node features with embeddings as an input\nvector that is used for the prediction task. Each node has 1433 flags that\nrepresent word occurrences in the publication.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eResults:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNode classification accuracy (averaged over 10 experiments): 68.55% (best: 70.90%)\u003c/li\u003e\n\u003cli\u003eEdge classification accuracy (averaged over 10 experiments): 81.65% (best: 82.02%)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eLink prediction has decent accuracy while node classification has somewhat\nweaker accuracy. Playing with node2vec and logistic regression hyperparameters can improve\nthe accuracy.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage\u003c/h2\u003e\u003ca id=\"user-content-usage\" class=\"anchor\" aria-label=\"Permalink: Usage\" href=\"#usage\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis section explains installation and framework usage.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eInstallation\u003c/h3\u003e\u003ca id=\"user-content-installation\" class=\"anchor\" aria-label=\"Permalink: Installation\" href=\"#installation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCreate a virtual environment and run:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"pip3 install -r requirements.txt\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003epip3 install -r requirements.txt\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eTraining a model\u003c/h3\u003e\u003ca id=\"user-content-training-a-model\" class=\"anchor\" aria-label=\"Permalink: Training a model\" href=\"#training-a-model\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn order to train a model use next command:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"python3 tools/train.py --config-name=\u0026lt;config_name\u0026gt;\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003epython3 tools/train.py --config-name=\u0026lt;config_name\u0026gt;\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eStart Tensorboard:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"tensorboard --port \u0026lt;port\u0026gt; --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003etensorboard --port \u0026lt;port\u0026gt; --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eStart Tensorboard in background:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"nohup tensorboard --port \u0026lt;port\u0026gt; --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false \u0026amp;\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003enohup tensorboard --port \u0026lt;port\u0026gt; --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false \u0026amp;\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eOpen Tensorboard on \u003ccode\u003ehttp://localhost:\u0026lt;port\u0026gt;\u003c/code\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eModel analysis\u003c/h3\u003e\u003ca id=\"user-content-model-analysis\" class=\"anchor\" aria-label=\"Permalink: Model analysis\" href=\"#model-analysis\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eModel analysis supports graph and text datasets. Model analysis performs:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eclosest pairs analysis\u003c/li\u003e\n\u003cli\u003eVisualize embeddings (performs T-SNE in case embeddings are not 2D)\u003c/li\u003e\n\u003cli\u003eSemantics test (not supported for graphs)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"python3 tools/model_analysis.py --config-name=\u0026lt;config_name\u0026gt;\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003epython3 tools/model_analysis.py --config-name=\u0026lt;config_name\u0026gt;\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDownloading dataset\u003c/h3\u003e\u003ca id=\"user-content-downloading-dataset\" class=\"anchor\" aria-label=\"Permalink: Downloading dataset\" href=\"#downloading-dataset\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eDataset download is implemented for \"wiki-text-2\", \"wiki-text-103\", \"cora\" and \"ppi\" datasets. Command:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"./download_dataset.sh \u0026lt;name\u0026gt;\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e./download_dataset.sh \u0026lt;name\u0026gt;\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eGraph downstream tasks\u003c/h3\u003e\u003ca id=\"user-content-graph-downstream-tasks\" class=\"anchor\" aria-label=\"Permalink: Graph downstream tasks\" href=\"#graph-downstream-tasks\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePerforms downstream tasks (node classification and edge prediction) based\non the learned node embeddings and/or node features.\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"python3 tools/graph_model_downstream_classification.py --config-name=\u0026lt;config_name\u0026gt;\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003epython3 tools/graph_model_downstream_classification.py --config-name=\u0026lt;config_name\u0026gt;\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eReferences\u003c/h2\u003e\u003ca id=\"user-content-references\" class=\"anchor\" aria-label=\"Permalink: References\" href=\"#references\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eKey papers\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"http://arxiv.org/abs/1301.3781\" rel=\"nofollow\"\u003eEfficient Estimation of Word Representations in Vector Space\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"http://arxiv.org/abs/1310.4546\" rel=\"nofollow\"\u003eDistributed Representations of Words and Phrases and their Compositionality\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.jmlr.org/papers/volume13/gutmann12a/gutmann12a.pdf\" rel=\"nofollow\"\u003eNoise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"http://arxiv.org/abs/1403.6652\" rel=\"nofollow\"\u003eDeepWalk: Online Learning of Social Representations\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"http://arxiv.org/abs/1607.00653\" rel=\"nofollow\"\u003enode2vec: Scalable Feature Learning for Networks\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eBooks:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"https://www.cs.mcgill.ca/~wlh/grl_book/files/GRL_Book.pdf\" rel=\"nofollow\"\u003eGraph Representation Learning\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eVideos:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"https://www.youtube.com/watch?v=JAB_plj2rbA\u0026amp;list=PLoROMvodv4rPLKxIpqhjhPgdQy7imNkDn\" rel=\"nofollow\"\u003eStanford CS224W\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Deep learning graph shallow encoders - DeepWalk and node2vec","anchor":"deep-learning-graph-shallow-encoders---deepwalk-and-node2vec","htmlText":"Deep learning graph shallow encoders - DeepWalk and node2vec"},{"level":2,"text":"Description","anchor":"description","htmlText":"Description"},{"level":2,"text":"Table of Contents","anchor":"table-of-contents","htmlText":"Table of Contents"},{"level":2,"text":"Introduction","anchor":"introduction","htmlText":"Introduction"},{"level":3,"text":"Word2vec","anchor":"word2vec","htmlText":"Word2vec"},{"level":3,"text":"DeepWalk","anchor":"deepwalk","htmlText":"DeepWalk"},{"level":3,"text":"Node2vec","anchor":"node2vec","htmlText":"Node2vec"},{"level":4,"text":"Random walk generation","anchor":"random-walk-generation","htmlText":"Random walk generation"},{"level":4,"text":"Edge embeddings","anchor":"edge-embeddings","htmlText":"Edge embeddings"},{"level":2,"text":"Experiments","anchor":"experiments","htmlText":"Experiments"},{"level":3,"text":"Word2vec","anchor":"word2vec-1","htmlText":"Word2vec"},{"level":4,"text":"Toy example - ABCDE","anchor":"toy-example---abcde","htmlText":"Toy example - ABCDE"},{"level":4,"text":"Shakespeare dataset","anchor":"shakespeare-dataset","htmlText":"Shakespeare dataset"},{"level":5,"text":"Closest word pairs","anchor":"closest-word-pairs","htmlText":"Closest word pairs"},{"level":5,"text":"Embedding visualization","anchor":"embedding-visualization","htmlText":"Embedding visualization"},{"level":5,"text":"Semantic tests","anchor":"semantic-tests","htmlText":"Semantic tests"},{"level":3,"text":"DeepWalk and node2vec","anchor":"deepwalk-and-node2vec","htmlText":"DeepWalk and node2vec"},{"level":4,"text":"Toy example - Graph Triplets","anchor":"toy-example---graph-triplets","htmlText":"Toy example - Graph Triplets"},{"level":5,"text":"Embedding visualization","anchor":"embedding-visualization-1","htmlText":"Embedding visualization"},{"level":5,"text":"Downstream tasks","anchor":"downstream-tasks","htmlText":"Downstream tasks"},{"level":4,"text":"Zachary's karate club","anchor":"zacharys-karate-club","htmlText":"Zachary's karate club"},{"level":5,"text":"Embeddings visualization","anchor":"embeddings-visualization","htmlText":"Embeddings visualization"},{"level":5,"text":"Downstream tasks","anchor":"downstream-tasks-1","htmlText":"Downstream tasks"},{"level":4,"text":"Cora dataset","anchor":"cora-dataset","htmlText":"Cora dataset"},{"level":5,"text":"Embedding visualization","anchor":"embedding-visualization-2","htmlText":"Embedding visualization"},{"level":5,"text":"Downstream tasks","anchor":"downstream-tasks-2","htmlText":"Downstream tasks"},{"level":2,"text":"Usage","anchor":"usage","htmlText":"Usage"},{"level":3,"text":"Installation","anchor":"installation","htmlText":"Installation"},{"level":3,"text":"Training a model","anchor":"training-a-model","htmlText":"Training a model"},{"level":3,"text":"Model analysis","anchor":"model-analysis","htmlText":"Model analysis"},{"level":3,"text":"Downloading dataset","anchor":"downloading-dataset","htmlText":"Downloading dataset"},{"level":3,"text":"Graph downstream tasks","anchor":"graph-downstream-tasks","htmlText":"Graph downstream tasks"},{"level":2,"text":"References","anchor":"references","htmlText":"References"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2FRobotmurlock%2FDeepwalk-and-Node2vec"}},{"displayName":"LICENSE","repoName":"Deepwalk-and-Node2vec","refName":"main","path":"LICENSE","preferredFileType":"license","tabName":"MIT","richText":null,"loaded":false,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":null,"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2FRobotmurlock%2FDeepwalk-and-Node2vec"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-1583894afd38.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-67668e8c2caa.js","githubDevUrl":null,"enabled_features":{"code_nav_ui_events":false,"overview_shared_code_dropdown_button":false,"react_blob_overlay":false,"copilot_conversational_ux_embedding_update":false,"copilot_smell_icebreaker_ux":true,"copilot_workspace":false,"accessible_code_button":true}}}}</script> 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16 16" width="16" height="16" fill="currentColor" style="display:inline-block;user-select:none;vertical-align:text-bottom;overflow:visible"><path d="M5.75 2.5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5ZM2 14a1 1 0 1 1 0-2 1 1 0 0 1 0 2Zm1-6a1 1 0 1 1-2 0 1 1 0 0 1 2 0ZM2 4a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path></svg></button></div><div class="Box-sc-g0xbh4-0 QkQOb js-snippet-clipboard-copy-unpositioned" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Deep learning graph shallow encoders - DeepWalk and node2vec</h1><a id="user-content-deep-learning-graph-shallow-encoders---deepwalk-and-node2vec" class="anchor" aria-label="Permalink: Deep learning graph shallow encoders - DeepWalk and node2vec" href="#deep-learning-graph-shallow-encoders---deepwalk-and-node2vec"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Description</h2><a id="user-content-description" class="anchor" aria-label="Permalink: Description" href="#description"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This repository provides from-the-ground-up implementations of both <a href="https://arxiv.org/abs/1403.6652" rel="nofollow">DeepWalk</a> and <a href="https://arxiv.org/abs/1607.00653" rel="nofollow">node2vec</a>. It also encompasses a handcrafted version of <a href="http://arxiv.org/abs/1301.3781" rel="nofollow">word2vec</a> with <a href="http://arxiv.org/abs/1310.4546" rel="nofollow">negative sampling</a>, fundamental to the workings of DeepWalk and node2vec.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Table of Contents</h2><a id="user-content-table-of-contents" class="anchor" aria-label="Permalink: Table of Contents" href="#table-of-contents"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li><a href="#introduction">Introduction</a></li> <li><a href="#experiments">Experiments</a> <ul dir="auto"> <li><a href="#word2vec-1">Word2vec</a></li> <li><a href="#deepwalk-and-node2vec">DeepWalk and Node2vec</a></li> </ul> </li> <li><a href="#usage">Usage</a></li> <li><a href="#references">References</a></li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Introduction</h2><a id="user-content-introduction" class="anchor" aria-label="Permalink: Introduction" href="#introduction"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This section briefly explains word2vec, DeepWalk and node2vec.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Word2vec</h3><a id="user-content-word2vec" class="anchor" aria-label="Permalink: Word2vec" href="#word2vec"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Word2Vec is a technique to represent words as continuous vector spaces. The primary intuition is that words appearing in similar contexts in a sentence tend to have similar meanings. This task can be approached in two ways:</p> <ul dir="auto"> <li>Based on the observed word, predict context words - SkipGram.</li> <li>Based on the observed context, predict missing word - CBOW (Continuous Bag Of Words).</li> </ul> <p dir="auto">Consider sentence "Cats are similar to dogs in many ways.". Goal for SkipGram would be to predict context words "Cats", "are", "similar", "to", "in", "many", "ways" based on the observed word "dogs". For CBOW it would be opposite.</p> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/word2vec_architecture.png"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/word2vec_architecture.png" alt="word2vec_architecture.png" style="max-width: 100%;"></a></p> <p dir="auto">Each word is encoded using <a href="https://en.wikipedia.org/wiki/One-hot" rel="nofollow">one-hot</a> encoding to obtain its one-hot vector. Afterward, each vector is projected to the embedding space using a projection matrix. This operation can be performed more efficiently through a word index lookup (check: <a href="https://pytorch.org/docs/stable/generated/torch.nn.Embedding.html" rel="nofollow">Pytorch Embedding</a>).</p> <p dir="auto">For the SkipGram model, it is trained to predict if another word (represented as an embedding) occurs in the context (refer to the image above on the right). For CBOW, the process is similar, expect instead of using embedding vector of a single observed word, a context representation vector is obtained by averaging over all context embedding vectors (refer to the image above on the left).</p> <p dir="auto">The cross-entropy function is utilized for model training. Using it directly results in an intractable computation. Instead, hierarchical softmax (<a href="https://arxiv.org/abs/1301.3781" rel="nofollow">original word2vec paper</a>) or negative sampling (<a href="https://proceedings.neurips.cc/paper_files/paper/2013/file/9aa42b31882ec039965f3c4923ce901b-Paper.pdf" rel="nofollow">follow-up paper</a>) is employed. In short, cross-entropy compute time depends on the vocabulary size which can be huge (e.g. 1 million tokens). Executing that many operations per word is computationally unfeasible. Hierarchical softmax and negative samplings are remedy for this. In this implementation, negative sampling is the chosen method.</p> <p dir="auto">We use separate embedding weights for input and context words. Although it's theoretically acceptable to use the same weights for both input and context words, the model becomes more expressive when two different embedding matrices are used.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">DeepWalk</h3><a id="user-content-deepwalk" class="anchor" aria-label="Permalink: DeepWalk" href="#deepwalk"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">We possess a tool to learn word embeddings from a given corpus. In case of graphs we can generate "sentences" using graph <a href="https://en.wikipedia.org/wiki/Random_walk" rel="nofollow">random walks</a>. Basically, we start from a particular node and traverse through graph by choosing random neighbor for <em>N-1</em> steps where <em>N</em> is random walk length. For every node we can generate multiple random walks. Once we obtain enough random walks we can form a "node corpus" and use word2vec to train learn node embeddings. Three hyperparameters can be observed here:</p> <ul dir="auto"> <li>Number of random walks per node for each epoch.</li> <li>Random walk length.</li> <li>Context radius (length) for each node.</li> </ul> <p dir="auto">Note that in this implementation we generate new random walks for each epoch.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Node2vec</h3><a id="user-content-node2vec" class="anchor" aria-label="Permalink: Node2vec" href="#node2vec"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Node2vec is extension of the DeepWalk algorithm. It presents three main contributions compared to the original paper:</p> <ul dir="auto"> <li>It uses <a href="http://arxiv.org/abs/1310.4546" rel="nofollow">negative sampling</a> instead of <a href="https://arxiv.org/abs/1301.3781" rel="nofollow">hierarchical softmax</a> that was also used in the original word2vec paper (follow-up paper used negative sampling instead).</li> <li>It introduces more flexible algorithm for random walk generation.</li> <li>It defines a way to obtain edge embeddings from node embeddings. Edge embeddings can be used for link prediction task - predicting if an edge exists between two nodes.</li> </ul> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Random walk generation</h4><a id="user-content-random-walk-generation" class="anchor" aria-label="Permalink: Random walk generation" href="#random-walk-generation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Assume that <em>v</em> is current node in the random walk generation algorithm and we have to choose next node that will be added to the walk. Node <em>t</em> is the previous node in the walk, and <em>x</em> is the candidate node (potential next node). Weights for each node are modified following rules:</p> <ul dir="auto"> <li>by <code>1/p</code> if <code>shortest_path(t, x) == 0</code> (i.e. x == t)</li> <li>by <code>1</code> if <code>shortest_path(t, x) == 1</code></li> <li>by <code>1/q</code> if <code>shortest_path(t, x) == 2</code></li> </ul> <p dir="auto">where <em>p</em> (return parameter) and <em>q</em> (in-out parameter) are random walk generation hyperparameters:</p> <ul dir="auto"> <li>Higher values for <em>p</em> lowers chance of adding already explored node to the random walk.</li> <li>Lower values for <em>p</em> increases chance of going back and keeps the walk "local".</li> <li>Higher values for <em>q</em> bias walks to move more towards node <em>t</em> ("inwards", BFS-like).</li> <li>Lower values for <em>q</em> bias walks to move from node <em>t</em> ("outwards", DFS-like).</li> </ul> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/node2vec_rwg.png"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/node2vec_rwg.png" alt="node2vec_rwg" style="max-width: 100%;"></a></p> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Edge embeddings</h4><a id="user-content-edge-embeddings" class="anchor" aria-label="Permalink: Edge embeddings" href="#edge-embeddings"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Edge embedding can be obtained from the node embeddings. We just need to define a function <em>f</em> (heuristic) that aggregates arbitrary nodes <em>n1</em> and <em>n2</em>: <code>vector(edge(n1, n2)) = f(vector(n1), vector(n2))</code>. Examples:</p> <ul dir="auto"> <li>Average: <code>f(vector(n1), vector(n2)) = (vector(n1) + vector(n2)) / 2</code>;</li> <li>Hadamard (point-wise multiplication): <code>f(vector(n1), vector(n2)) = vector(n1) * vector(n2)</code></li> <li>point-wise L1 distance: <code>f(vector(n1), vector(n2)) = |vector(n1) - vector(n2))|</code></li> <li>point-wise L2 distance: <code>f(vector(n1), vector(n2)) = (vector(n1) - vector(n2)))^2</code></li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Experiments</h2><a id="user-content-experiments" class="anchor" aria-label="Permalink: Experiments" href="#experiments"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Word2vec</h3><a id="user-content-word2vec-1" class="anchor" aria-label="Permalink: Word2vec" href="#word2vec-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Both Skip-Gram and CBOW implementation are supported.</p> <p dir="auto">Supported text-based datasets are:</p> <ul dir="auto"> <li>ABCDE (custom test dataset)</li> <li>Shakespeare</li> <li>WikiText-2</li> <li>WikiText-103</li> </ul> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Toy example - ABCDE</h4><a id="user-content-toy-example---abcde" class="anchor" aria-label="Permalink: Toy example - ABCDE" href="#toy-example---abcde"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This dataset is used as an sanity test - checks is custom implementation of the word2vec model works:</p> <ul dir="auto"> <li><code>a b a b a b a b a b</code>, <code>a</code> goes with <code>b</code></li> <li><code>a b a b a b</code>,</li> <li><code>b a b a</code>,</li> <li><code>a b a b a b a b</code>,</li> <li><code>c d c d c d c d</code>, <code>c</code> goes with <code>d</code></li> <li><code>d c d c d c</code>,</li> <li><code>c d c d c d</code>,</li> <li><code>e e e e e e e e</code>, <code>e</code> goes alone</li> <li><code>e e e</code></li> </ul> <p dir="auto">The expected model should position the embeddings of words "a" and "b" close together, as well as "c" and "d". However, the word "e" should form its own isolated cluster. On the other hand, even though vectors "a" and "b" are close, they shouldn't "match" because they don't share the same tokens in their context. Results:</p> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/abcde_projected_embeddings.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/abcde_projected_embeddings.jpg" alt="abcde_projected_embeddings" style="max-width: 100%;"></a></p> <p dir="auto">For this experiment embedding dimension 2 was used. Full experiment configuration can be found here <code>configs/w2v_sg_abcde.yaml</code> and <code>configs/w2v_cbow_abcde.yaml</code>.</p> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Shakespeare dataset</h4><a id="user-content-shakespeare-dataset" class="anchor" aria-label="Permalink: Shakespeare dataset" href="#shakespeare-dataset"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Please note that minimal effort was invested in preprocessing the input sentences for the Word2Vec case. These datasets were primarily analyzed to validate the Word2Vec implementation. Enhancing data preparation could potentially lead to significant improvements in the results. Additionally, in the original paper, aggressive subsampling was used for very frequent words. This detail was omitted in this implementation since our primary focus is on learning graph embeddings rather than word embeddings.</p> <p dir="auto">For this experiment embedding dimension 12 was used. Full experiment configuration can be found here <code>configs/w2v_shakespeare.yaml</code>.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Closest word pairs</h5><a id="user-content-closest-word-pairs" class="anchor" aria-label="Permalink: Closest word pairs" href="#closest-word-pairs"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Finding the closest context words for the chosen input word is performed using <a href="https://en.wikipedia.org/wiki/Cosine_similarity" rel="nofollow">cosine similarity</a> between embedding vectors of the trained model. Some examples (<em>input word</em>: <em>closest context words</em>):</p> <ul dir="auto"> <li>king: king, young, duke</li> <li>queen: young, queen, king</li> <li>duke: duke, king, enter</li> <li>lord: young, king, lord</li> <li>lady: hear, lady, boy</li> <li>kiss: about, leave, hand</li> </ul> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Embedding visualization</h5><a id="user-content-embedding-visualization" class="anchor" aria-label="Permalink: Embedding visualization" href="#embedding-visualization"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Input word embeddings visualization. <a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/shakespeare-projected_embeddings_edited.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/shakespeare-projected_embeddings_edited.jpg" alt="shakespeare_embedding_visualization" style="max-width: 100%;"></a></p> <p dir="auto">Only the most frequent words are selected, and this includes stopwords, which are typically not of primary interest. Still we can observe two interesting clusters:</p> <ul dir="auto"> <li>Royalty cluster (red) - king, queen, prince, lord, etc.</li> <li>Relationship cluster (blue) - son, friend, brother, wife, etc.</li> </ul> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Semantic tests</h5><a id="user-content-semantic-tests" class="anchor" aria-label="Permalink: Semantic tests" href="#semantic-tests"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Here we perform simple semantic calculations and check if the "model" can answer properly. For an example, it is ideal if vector <code>vector("king") - vector("man") + vector("woman")</code> is close to vector <code>vector("queen")</code>. Results:</p> <ul dir="auto"> <li>Similarity between vector("king") - vector("man") + vector("woman") and vector("queen") is 0.59 (good)</li> <li>Similarity between vector("queen") - vector("woman") + vector("man") and vector("king") is 0.43 (good)</li> <li>Similarity between vector("king") - vector("queen") + vector("woman") and vector("man") is -0.05 (bad)</li> <li>Similarity between vector("queen") - vector("king") + vector("man") and vector("woman") is 0.23 (bad)</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">DeepWalk and node2vec</h3><a id="user-content-deepwalk-and-node2vec" class="anchor" aria-label="Permalink: DeepWalk and node2vec" href="#deepwalk-and-node2vec"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">DeepWalk and Node2Vec are implemented as extensions of the Word2Vec model.</p> <p dir="auto">Supported datasets are:</p> <ul dir="auto"> <li>Graph triplets (test dataset)</li> <li>Zachary's Karate club</li> <li>Cora</li> </ul> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Toy example - Graph Triplets</h4><a id="user-content-toy-example---graph-triplets" class="anchor" aria-label="Permalink: Toy example - Graph Triplets" href="#toy-example---graph-triplets"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This graph consists of 3 fully connected components consisting of three nodes. Model should be able to learn to cluster these nodes together in embeddings space.</p> <p dir="auto">For this experiment embedding dimension 2 was used. Full experiment configuration can be found here <code>configs/sge_sg_graph_triplets.yaml</code>.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Embedding visualization</h5><a id="user-content-embedding-visualization-1" class="anchor" aria-label="Permalink: Embedding visualization" href="#embedding-visualization-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph_triplets-projected_embeddings.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph_triplets-projected_embeddings.jpg" alt="graph_triplets_embedings" style="max-width: 100%;"></a></p> <p dir="auto">We can observe that clusters are successfully formed. One can tune the training parameters to either increase or decrease the separation between these clusters, and to make the nodes within each cluster more or less merged. If we query for the two closest context nodes for each input node, we always get two nodes from the same input node cluster, which is what we expect.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Downstream tasks</h5><a id="user-content-downstream-tasks" class="anchor" aria-label="Permalink: Downstream tasks" href="#downstream-tasks"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In order to additionally evaluate quality of these embeddings, two downstream tasks are performed:</p> <ul dir="auto"> <li>Node classification: <a href="https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html" rel="nofollow">A scikit-learn logistic regression model</a> is trained to predict node's label based on its vector embedding. If there are multiple classes then <a href="https://scikit-learn.org/stable/modules/generated/sklearn.multiclass.OneVsRestClassifier.html" rel="nofollow">one-vs-rest</a> approach is used. It is required that the dataset has label nodes.</li> <li>Edge classification (link prediction more precisely): similar to <em>node classification</em>, a model is trained to predict if edge exists between two nodes. More precisely, model predicts if edge exists based on the edge embedding. This embedding is obtained using a function <em>f</em> that aggregates arbitrary nodes <em>n1</em> and <em>n2</em>: <code>vector(edge(n1, n2)) = f(vector(n1), vector(n2))</code>.</li> </ul> <p dir="auto">The model is evaluated using [transduction](<a href="https://en.wikipedia.org/wiki/Transduction_(machine_learning)" rel="nofollow">https://en.wikipedia.org/wiki/Transduction_(machine_learning)</a>. This means that during unsupervised learning - while training the shallow graph encoder (either DeepWalk or node2vec) — the complete graph structure is known. For downstream tasks, we partition the data for both training and evaluation of the node label classifier. Experiments are conducted multiple times to obtain an average metric result.</p> <p dir="auto">Results:</p> <ul dir="auto"> <li>Node classification accuracy (averaged over 10 experiments): 88.89% (best: 100.00%)</li> <li>Edge classification accuracy (averaged over 10 experiments): 85.83% (best: 100.00%)</li> </ul> <p dir="auto">Visualization of best node classification model:</p> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-triplets_downstream-node-classification.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-triplets_downstream-node-classification.jpg" alt="graph_triplets_node_classification" style="max-width: 100%;"></a></p> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Zachary's karate club</h4><a id="user-content-zacharys-karate-club" class="anchor" aria-label="Permalink: Zachary's karate club" href="#zacharys-karate-club"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer nofollow" href="https://camo.githubusercontent.com/d6e19947f6a8801e1118e2984bf5073a92844aac8e3d63068aadc46cbea0a095/68747470733a2f2f75706c6f61642e77696b696d656469612e6f72672f77696b6970656469612f656e2f7468756d622f382f38372f5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e672f37353070782d5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e67"><img src="https://camo.githubusercontent.com/d6e19947f6a8801e1118e2984bf5073a92844aac8e3d63068aadc46cbea0a095/68747470733a2f2f75706c6f61642e77696b696d656469612e6f72672f77696b6970656469612f656e2f7468756d622f382f38372f5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e672f37353070782d5a6163686172795f6b61726174655f636c75625f736f6369616c5f6e6574776f726b2e706e67" alt="zachary_karate_club" data-canonical-src="https://upload.wikimedia.org/wikipedia/en/thumb/8/87/Zachary_karate_club_social_network.png/750px-Zachary_karate_club_social_network.png" style="max-width: 100%;"></a></p> <p dir="auto">Another small dataset that can be used for model analysis is <a href="https://en.wikipedia.org/wiki/Zachary%27s_karate_club" rel="nofollow">Zachary's karate club</a>. This graph has weighted edges and random walks are sampled based on that. Probability of picking successor node based on the current node is proportional to edge weight. It is assumed that all weights are positive.</p> <p dir="auto">For this experiment embedding dimension 2 was used. Full experiment configuration can be found here <code>configs/sge_sg_karate_club.yaml</code>.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Embeddings visualization</h5><a id="user-content-embeddings-visualization" class="anchor" aria-label="Permalink: Embeddings visualization" href="#embeddings-visualization"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-karate-club_projected_embeddings.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-karate-club_projected_embeddings.jpg" alt="karate_club_embedings" style="max-width: 100%;"></a></p> <p dir="auto">We can observe that two groups of nodes are clustered almost perfectly. Only node <em>n09</em> is outside the green (label 1) cluster but these groups can still be easily separated using a line. In case dataset edge weights are not used then these cannot be separated as distinctly.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Downstream tasks</h5><a id="user-content-downstream-tasks-1" class="anchor" aria-label="Permalink: Downstream tasks" href="#downstream-tasks-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Similar configuration as for graph triplets is used for the downstream tasks.</p> <p dir="auto">Results:</p> <ul dir="auto"> <li>Node classification accuracy (averaged over 10 experiments): 98.06% (best: 100.00%)</li> <li>Edge classification accuracy (averaged over 10 experiments): 69.52% (best: 80.13%)</li> </ul> <p dir="auto">Visualization of best node classification model:</p> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-karate-club_downstream-node-classification.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-karate-club_downstream-node-classification.jpg" alt="karate_club_node_classification" style="max-width: 100%;"></a></p> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Cora dataset</h4><a id="user-content-cora-dataset" class="anchor" aria-label="Permalink: Cora dataset" href="#cora-dataset"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/cora-graph.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/cora-graph.jpg" alt="cora_graph" style="max-width: 100%;"></a></p> <p dir="auto">The Cora dataset consists of 2708 scientific publications classified into one of seven classes:</p> <ul dir="auto"> <li><code>Case_Based</code></li> <li><code>Genetic_Algorithms</code></li> <li><code>Neural_Networks</code></li> <li><code>Probabilistic_Methods</code></li> <li><code>Reinforcement_Learning</code></li> <li><code>Rule_Learning</code></li> <li><code>Theory</code> Each node represents one scientific publication. Each edge represents citation. The citation network consists of 5429 links. This is one of the standard dataset for evaluating graph based machine learning algorithm.</li> </ul> <p dir="auto">For this experiment embedding dimension 8 was used. For 2D visualization we use <a href="https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding" rel="nofollow">T-SNE</a>. Full experiment configuration can be found here <code>configs/sge_sg_cora.yaml</code>.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Embedding visualization</h5><a id="user-content-embedding-visualization-2" class="anchor" aria-label="Permalink: Embedding visualization" href="#embedding-visualization-2"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer" href="/Robotmurlock/Deepwalk-and-Node2vec/blob/main/images/graph-cora_projected_embeddings.jpg"><img src="/Robotmurlock/Deepwalk-and-Node2vec/raw/main/images/graph-cora_projected_embeddings.jpg" alt="cora_embedings" style="max-width: 100%;"></a></p> <p dir="auto">From the visualized embedding, we can observe that all subjects form clusters that overlap with few others. There is also a large cluster comprised of mixed node labels. The model was not able to successfully separate these nodes, leading us to expect weaker results when using logistic regression for classification.</p> <div class="markdown-heading" dir="auto"><h5 tabindex="-1" class="heading-element" dir="auto">Downstream tasks</h5><a id="user-content-downstream-tasks-2" class="anchor" aria-label="Permalink: Downstream tasks" href="#downstream-tasks-2"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Similar configuration as for graph triplets is used for the downstream tasks. The main difference is that for this task we also combine node features with embeddings as an input vector that is used for the prediction task. Each node has 1433 flags that represent word occurrences in the publication.</p> <p dir="auto">Results:</p> <ul dir="auto"> <li>Node classification accuracy (averaged over 10 experiments): 68.55% (best: 70.90%)</li> <li>Edge classification accuracy (averaged over 10 experiments): 81.65% (best: 82.02%)</li> </ul> <p dir="auto">Link prediction has decent accuracy while node classification has somewhat weaker accuracy. Playing with node2vec and logistic regression hyperparameters can improve the accuracy.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage</h2><a id="user-content-usage" class="anchor" aria-label="Permalink: Usage" href="#usage"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This section explains installation and framework usage.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Installation</h3><a id="user-content-installation" class="anchor" aria-label="Permalink: Installation" href="#installation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Create a virtual environment and run:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="pip3 install -r requirements.txt"><pre class="notranslate"><code>pip3 install -r requirements.txt </code></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Training a model</h3><a id="user-content-training-a-model" class="anchor" aria-label="Permalink: Training a model" href="#training-a-model"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In order to train a model use next command:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="python3 tools/train.py --config-name=<config_name>"><pre class="notranslate"><code>python3 tools/train.py --config-name=<config_name> </code></pre></div> <p dir="auto">Start Tensorboard:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="tensorboard --port <port> --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false"><pre class="notranslate"><code>tensorboard --port <port> --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false </code></pre></div> <p dir="auto">Start Tensorboard in background:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="nohup tensorboard --port <port> --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false &"><pre class="notranslate"><code>nohup tensorboard --port <port> --host 0.0.0.0 --logdir runs/tb_logs --load_fast=false & </code></pre></div> <p dir="auto">Open Tensorboard on <code>http://localhost:<port></code></p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Model analysis</h3><a id="user-content-model-analysis" class="anchor" aria-label="Permalink: Model analysis" href="#model-analysis"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Model analysis supports graph and text datasets. Model analysis performs:</p> <ul dir="auto"> <li>closest pairs analysis</li> <li>Visualize embeddings (performs T-SNE in case embeddings are not 2D)</li> <li>Semantics test (not supported for graphs)</li> </ul> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="python3 tools/model_analysis.py --config-name=<config_name>"><pre class="notranslate"><code>python3 tools/model_analysis.py --config-name=<config_name> </code></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Downloading dataset</h3><a id="user-content-downloading-dataset" class="anchor" aria-label="Permalink: Downloading dataset" href="#downloading-dataset"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Dataset download is implemented for "wiki-text-2", "wiki-text-103", "cora" and "ppi" datasets. Command:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="./download_dataset.sh <name>"><pre class="notranslate"><code>./download_dataset.sh <name> </code></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Graph downstream tasks</h3><a id="user-content-graph-downstream-tasks" class="anchor" aria-label="Permalink: Graph downstream tasks" href="#graph-downstream-tasks"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Performs downstream tasks (node classification and edge prediction) based on the learned node embeddings and/or node features.</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="python3 tools/graph_model_downstream_classification.py --config-name=<config_name>"><pre class="notranslate"><code>python3 tools/graph_model_downstream_classification.py --config-name=<config_name> </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">References</h2><a id="user-content-references" class="anchor" aria-label="Permalink: References" href="#references"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Key papers</p> <ul dir="auto"> <li><a href="http://arxiv.org/abs/1301.3781" rel="nofollow">Efficient Estimation of Word Representations in Vector Space</a></li> <li><a href="http://arxiv.org/abs/1310.4546" rel="nofollow">Distributed Representations of Words and Phrases and their Compositionality</a></li> <li><a href="https://www.jmlr.org/papers/volume13/gutmann12a/gutmann12a.pdf" rel="nofollow">Noise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics</a></li> <li><a href="http://arxiv.org/abs/1403.6652" rel="nofollow">DeepWalk: Online Learning of Social Representations</a></li> <li><a href="http://arxiv.org/abs/1607.00653" rel="nofollow">node2vec: Scalable Feature Learning for Networks</a></li> </ul> <p dir="auto">Books:</p> <ul dir="auto"> <li><a href="https://www.cs.mcgill.ca/~wlh/grl_book/files/GRL_Book.pdf" rel="nofollow">Graph Representation Learning</a></li> </ul> <p dir="auto">Videos:</p> <ul dir="auto"> <li><a href="https://www.youtube.com/watch?v=JAB_plj2rbA&list=PLoROMvodv4rPLKxIpqhjhPgdQy7imNkDn" rel="nofollow">Stanford CS224W</a></li> </ul> </article></div></div></div></div></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" value="4tg/+qoPYZdn4GG52JWUpXczslmeX3DR/a0UkqW+wrUySMkD4h5GemK3noiMY5R9pZMyb2UPITPU2EmweOeZcg==" /> 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d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> <div class="octocat-spinner my-6 js-details-dialog-spinner"></div> </details-dialog> </details> </template> <div class="Popover js-hovercard-content position-absolute" style="display: none; outline: none;"> <div class="Popover-message Popover-message--bottom-left Popover-message--large Box color-shadow-large" style="width:360px;"> </div> </div> <template id="snippet-clipboard-copy-button"> <div class="zeroclipboard-container position-absolute right-0 top-0"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn js-clipboard-copy m-2 p-0" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>