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class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122704610/Eigenvalues_of_discontinuous_Sturm_Liouville_problems_with_symmetric_potentials"><img alt="Research paper thumbnail of Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/117316573/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122704610/Eigenvalues_of_discontinuous_Sturm_Liouville_problems_with_symmetric_potentials">Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials</a></div><div class="wp-workCard_item"><span>Computers & mathematics with applications</span><span>, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with symmetric potentials. The ¢igcnvalues of the systems were determined using the classical fourth order Runge-Kutta method. These eigenvalues are used to reconstruct the potential function using an algorithm presented in Kobayashi [1, 2]. The results of our numerical experiments are discussed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="17f3260ca40bf95844bba80b5568ed4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117316573,"asset_id":122704610,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117316573/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122704610"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122704610"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122704610; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122704606"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122704606/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials"><img alt="Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/117316557/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122704606/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials">An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials</a></div><div class="wp-workCard_item"><span>Computers & Mathematics with Applications</span><span>, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6046381363c6815be9d677b868869baf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117316557,"asset_id":122704606,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117316557/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122704606"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122704606"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122704606; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121215149"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/121215149/Discontinuous_Inverse_Sturm_Liouville_Problems_with_Symmetric_Potentials"><img alt="Research paper thumbnail of Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/116153643/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/121215149/Discontinuous_Inverse_Sturm_Liouville_Problems_with_Symmetric_Potentials">Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric potential function with two interior discontinuities. In the introductory chapter we survey previous results on the existence and uniqueness of solutions to inverse Sturm-Liouville problems and discuss earlier numerical methods. In chapter 1 we present a uniqueness proof for the inverse Sturm-Liouville problem on a finite interval with a symmetric potential having two interior jump discontinuities. In chapter 2 we show that any absolutely continuous function can be expanded in terms of the eigenfunctions of a Sturm-Liouville problem with two discontinuities. In chapter 3 we consider two Sturm-Liouville problems with different symmetric potentials with two discontinuities satisfying symmetric boundary conditions and symmetric jump conditions. We find that if only a finite number of eigenvalues differ then a simple expression for the difference of the potentials can be established. In addition, the locations of the discontinuities are uniquely determined. Finally, in chapter 4 we derive an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically and present the results of numerical experiments.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8a5086b233b8778baa9017945450c49" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116153643,"asset_id":121215149,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116153643/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121215149"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121215149"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121215149; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121215147"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/121215147/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials"><img alt="Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/116153650/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/121215147/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials">An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials</a></div><div class="wp-workCard_item"><span>Computers & mathematics with applications</span><span>, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="660c4cbaa39e35a65262e3041cf6e713" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116153650,"asset_id":121215147,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116153650/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121215147"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121215147"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121215147; 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Novel features of our search and cluster mining engine are: discovery of both major and minor clusters, accommodation of cluster overlap, automatic labeling of clusters based on their document contents, and advanced visualization of search and mining results. 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window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96657528]").text(description); $(".js-view-count[data-work-id=96657528]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96657528; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96657528']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=96657528]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96657528,"title":"Wavelets and Digitized Images","internal_url":"https://www.academia.edu/96657528/Wavelets_and_Digitized_Images","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="96657527"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/96657527/Cultural_Differences_in_Social_Media_Trust_and_Authority"><img alt="Research paper thumbnail of Cultural Differences in Social Media: Trust and Authority" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/96657527/Cultural_Differences_in_Social_Media_Trust_and_Authority">Cultural Differences in Social Media: Trust and Authority</a></div><div class="wp-workCard_item"><span>Roles, Trust, and Reputation in Social Media Knowledge Markets</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Sociologists and psychologists study how humans evaluate trust and reputation of people, document...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Sociologists and psychologists study how humans evaluate trust and reputation of people, documents, institutions, etc. in the real-world. Their studies of interactions between people from different cultures have contributed to the appreciation of diverse viewpoints. While the sudden emergence and proliferation of the internet has altered the landscape of relationships and social interactions, there has not been sufficient time to revisit and study cultural and demographic differences in perceptions of trust and reputation in the cyberspace domain on a grand scale. Studies that have been conducted to-date have been limited in scope with respect to number of countries, types of behavior, and size of data sets. This chapter reviews studies on cultural differences in behavior in cyberspace, with particular attention to the concepts of expertise, quality, and trust. It discusses applications that can benefit from these studies, such as: targeted marketing, crowd sourcing applications, and enhancement of security systems. It concludes with a discussion on open data and how Wikipedia data provides an opportunity to examine behavioral differences in different communities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96657527"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96657527"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96657527; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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Wavelet Analysis for a Text-to-Speech (TTS) System" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/85507819/4_Wavelet_Analysis_for_a_Text_to_Speech_TTS_System">4. Wavelet Analysis for a Text-to-Speech (TTS) System</a></div><div class="wp-workCard_item"><span>Wavelets and Their Applications: Case Studies</span><span>, 1998</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85507819"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85507819"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85507819; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85507819]").text(description); $(".js-view-count[data-work-id=85507819]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85507819; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85507819']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=85507819]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85507819,"title":"4. Wavelet Analysis for a Text-to-Speech (TTS) System","internal_url":"https://www.academia.edu/85507819/4_Wavelet_Analysis_for_a_Text_to_Speech_TTS_System","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352612"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352612/Wavelet_Analysis_Applications_in_Industry"><img alt="Research paper thumbnail of Wavelet Analysis: Applications in Industry" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352612/Wavelet_Analysis_Applications_in_Industry">Wavelet Analysis: Applications in Industry</a></div><div class="wp-workCard_item"><span>Wavelet Analysis and Multiresolution Methods</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352612"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352612"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352612; 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Application domains include financial transactions, sensor network measurements, and telecommunication networks. A new generation of mining algorithms are needed for real-time analysis and query response for these applications since most conventional data mining algorithms can only be applied to static data sets that may be updated periodically in large chunks, but not to continuous streams of data. We examine how some classical tools from statistical and signal analysis have been modified and enhanced to solve real world problems involving data streams.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="367b7059b89a3b6be89fa1c05257faf8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83154547,"asset_id":75352611,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83154547/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352611"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352611"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352611; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352610"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352610/Exploring_overlapping_clusters_using_dynamic_re_scaling_and_sampling"><img alt="Research paper thumbnail of Exploring overlapping clusters using dynamic re-scaling and sampling" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352610/Exploring_overlapping_clusters_using_dynamic_re_scaling_and_sampling">Exploring overlapping clusters using dynamic re-scaling and sampling</a></div><div class="wp-workCard_item"><span>Knowledge and Information Systems</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Until recently, the aim of most text-mining work has been to understand major topics and clusters...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Until recently, the aim of most text-mining work has been to understand major topics and clusters. Minor topics and clusters have been relatively neglected even though they may represent important information on rare events. We present a novel method for exploring overlapping clusters of heterogeneous sizes, which is based on vector space modeling, covariance matrix analysis, random sampling, and dynamic</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352610"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352610"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352610; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75352610]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75352610,"title":"Exploring overlapping clusters using dynamic re-scaling and sampling","internal_url":"https://www.academia.edu/75352610/Exploring_overlapping_clusters_using_dynamic_re_scaling_and_sampling","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352609"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352609/Speech_synthesis_using_glottal_closure_instants_determined_from_adaptively_threshold_wavelet_transforms"><img alt="Research paper thumbnail of Speech synthesis using glottal closure instants determined from adaptively-threshold wavelet transforms" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352609/Speech_synthesis_using_glottal_closure_instants_determined_from_adaptively_threshold_wavelet_transforms">Speech synthesis using glottal closure instants determined from adaptively-threshold wavelet transforms</a></div><div class="wp-workCard_item"><span>The Journal of the Acoustical Society of America</span><span>, 1998</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize st...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize stable speech synthesis processing in which pitch shaking is negligible. The present invention is characterized in that glottal closure instants are used as reference points (pitch marks) for overlapping. Since the glottal closure instants can be extracted stably and accurately by using dyadic Wavelet conversion, speech in which pitch shaking is negligible and rumbling sounds are minimized can be synthesized stably. In addition, more flexible waveform separation becomes possible by setting the reference point for overlapping and the reference point for waveform separation to different positions. The extraction of glottal closure instants is performed by searching the local peaks of the dyadic Wavelet conversion, but preferably a threshold value for searching for the local peaks of the dyadic Wavelet conversion is adaptively controlled each time dyadic Wavelet conversion is obtained.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352609"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352609"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352609; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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</script> <div class="js-work-strip profile--work_container" data-work-id="75352608"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection"><img alt="Research paper thumbnail of Matrix computations for information retrieval and major and outlier cluster detection" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection">Matrix computations for information retrieval and major and outlier cluster detection</a></div><div class="wp-workCard_item"><span>Journal of Computational and Applied Mathematics</span><span>, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive database...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive databases based on vector space modeling and spectral analysis of the covariance matrix, for the document vectors, to reduce the scale of the problem. Since the dimension of the covariance matrix depends on the attribute space and is independent of the number of documents, COV can be applied to databases that are too massive for methods based on the singular value decomposition of the document-attribute matrix, such as latent semantic indexing (LSI). In addition to improved scalability, theoretical considerations indicate that results from our algorithm tend to be more accurate than those from LSI, particularly in detecting subtle differences in document vectors. We demonstrate the power and accuracy of COV through an important topic in data mining, known as outlier cluster detection. We propose two new algorithms for detecting major and outlier clusters in databases—the first is based on LSI, and the second on COV. Our implementation studies indicate that our cluster detection algorithms outperform the basic LSI and COV algorithm in detecting outlier clusters.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352608"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352608"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352608; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75352608]").text(description); $(".js-view-count[data-work-id=75352608]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75352608; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75352608']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75352608]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75352608,"title":"Matrix computations for information retrieval and major and outlier cluster detection","internal_url":"https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352607"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/75352607/Estimation_of_singular_values_of_very_large_matrices_using_random_sampling"><img alt="Research paper thumbnail of Estimation of singular values of very large matrices using random sampling" class="work-thumbnail" src="https://attachments.academia-assets.com/83491673/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/75352607/Estimation_of_singular_values_of_very_large_matrices_using_random_sampling">Estimation of singular values of very large matrices using random sampling</a></div><div class="wp-workCard_item"><span>Computers & Mathematics with Applications</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The singular value decomposition (SVD) has enjoyed a long and rich history. Although it was intro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The singular value decomposition (SVD) has enjoyed a long and rich history. Although it was introduced in the 1870s by Beltrami and Jordan for its own intrinsic interest, it has become an invaluable tool in applied mathematics and mathematical modeling. Singular value analysis has been applied in a wide variety of disciplines, most notably for least squares fitting of data. More recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. Recently, the dimensions of matrices which are used in many mathematical models are becoming so large that classical algorithms for computing the SVD cannot be used. We present a new method to determine the largest 10%-25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to the average user. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. Our method is a type of randomized algorithm, i.e., algorithms which solve problems using randomly selected samples of data which are too large to be processed by conventional means. These algorithms output correct (or nearly correct) answers most of the time as long as the input has certain desirable properties. We list these properties and show that matrices which appear in information retrieval are fairly well suited for processing using randomized algorithms. We note, however, that the probability of arriving at an incorrect answer, however small, is not naught since an unrepresentative sample may be drawn from the data.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cf1993d74a62817d8bad46e4058b0c51" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83491673,"asset_id":75352607,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83491673/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352607"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352607"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352607; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352606"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352606/Efficient_estimation_of_singular_values_for_searching_very_large_and_dynamic_web_databases"><img alt="Research paper thumbnail of Efficient estimation of singular values for searching very large and dynamic web databases" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352606/Efficient_estimation_of_singular_values_for_searching_very_large_and_dynamic_web_databases">Efficient estimation of singular values for searching very large and dynamic web databases</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. The dimensions of matrices which appear in these applications are becoming so large that classical algorithms for computing the SVD cannot always be used. We present a new method to determine the largest 10%{25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to most users. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. We demonstrate t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352606"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352606"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352606; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75352606]").text(description); $(".js-view-count[data-work-id=75352606]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75352606; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75352606']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75352606]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75352606,"title":"Efficient estimation of singular values for searching very large and dynamic web databases","internal_url":"https://www.academia.edu/75352606/Efficient_estimation_of_singular_values_for_searching_very_large_and_dynamic_web_databases","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="11222494" id="papers"><div class="js-work-strip profile--work_container" data-work-id="122704610"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122704610/Eigenvalues_of_discontinuous_Sturm_Liouville_problems_with_symmetric_potentials"><img alt="Research paper thumbnail of Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/117316573/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122704610/Eigenvalues_of_discontinuous_Sturm_Liouville_problems_with_symmetric_potentials">Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials</a></div><div class="wp-workCard_item"><span>Computers & mathematics with applications</span><span>, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with symmetric potentials. The ¢igcnvalues of the systems were determined using the classical fourth order Runge-Kutta method. These eigenvalues are used to reconstruct the potential function using an algorithm presented in Kobayashi [1, 2]. The results of our numerical experiments are discussed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="17f3260ca40bf95844bba80b5568ed4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117316573,"asset_id":122704610,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117316573/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122704610"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122704610"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122704610; 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In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6046381363c6815be9d677b868869baf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117316557,"asset_id":122704606,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117316557/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122704606"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122704606"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122704606; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121215149"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/121215149/Discontinuous_Inverse_Sturm_Liouville_Problems_with_Symmetric_Potentials"><img alt="Research paper thumbnail of Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/116153643/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/121215149/Discontinuous_Inverse_Sturm_Liouville_Problems_with_Symmetric_Potentials">Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric potential function with two interior discontinuities. In the introductory chapter we survey previous results on the existence and uniqueness of solutions to inverse Sturm-Liouville problems and discuss earlier numerical methods. In chapter 1 we present a uniqueness proof for the inverse Sturm-Liouville problem on a finite interval with a symmetric potential having two interior jump discontinuities. In chapter 2 we show that any absolutely continuous function can be expanded in terms of the eigenfunctions of a Sturm-Liouville problem with two discontinuities. In chapter 3 we consider two Sturm-Liouville problems with different symmetric potentials with two discontinuities satisfying symmetric boundary conditions and symmetric jump conditions. We find that if only a finite number of eigenvalues differ then a simple expression for the difference of the potentials can be established. In addition, the locations of the discontinuities are uniquely determined. Finally, in chapter 4 we derive an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically and present the results of numerical experiments.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8a5086b233b8778baa9017945450c49" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116153643,"asset_id":121215149,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116153643/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121215149"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121215149"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121215149; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121215147"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/121215147/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials"><img alt="Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials" class="work-thumbnail" src="https://attachments.academia-assets.com/116153650/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/121215147/An_algorithm_for_discontinuous_inverse_Sturm_Liouville_problems_with_symmetric_potentials">An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials</a></div><div class="wp-workCard_item"><span>Computers & mathematics with applications</span><span>, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="660c4cbaa39e35a65262e3041cf6e713" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116153650,"asset_id":121215147,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116153650/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121215147"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121215147"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121215147; 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Novel features of our search and cluster mining engine are: discovery of both major and minor clusters, accommodation of cluster overlap, automatic labeling of clusters based on their document contents, and advanced visualization of search and mining results. Implementation studies using adata set with over 100,000 news articles demonstrate the effectiveness of our system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="248aad50816c211be625721bcc747c95" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116153635,"asset_id":121215144,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116153635/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121215144"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121215144"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121215144; 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</script> <div class="js-work-strip profile--work_container" data-work-id="96657528"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/96657528/Wavelets_and_Digitized_Images"><img alt="Research paper thumbnail of Wavelets and Digitized Images" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/96657528/Wavelets_and_Digitized_Images">Wavelets and Digitized Images</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96657528"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96657528"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96657528; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96657528]").text(description); $(".js-view-count[data-work-id=96657528]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96657528; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96657528']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=96657528]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96657528,"title":"Wavelets and Digitized Images","internal_url":"https://www.academia.edu/96657528/Wavelets_and_Digitized_Images","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="96657527"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/96657527/Cultural_Differences_in_Social_Media_Trust_and_Authority"><img alt="Research paper thumbnail of Cultural Differences in Social Media: Trust and Authority" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/96657527/Cultural_Differences_in_Social_Media_Trust_and_Authority">Cultural Differences in Social Media: Trust and Authority</a></div><div class="wp-workCard_item"><span>Roles, Trust, and Reputation in Social Media Knowledge Markets</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Sociologists and psychologists study how humans evaluate trust and reputation of people, document...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Sociologists and psychologists study how humans evaluate trust and reputation of people, documents, institutions, etc. in the real-world. Their studies of interactions between people from different cultures have contributed to the appreciation of diverse viewpoints. While the sudden emergence and proliferation of the internet has altered the landscape of relationships and social interactions, there has not been sufficient time to revisit and study cultural and demographic differences in perceptions of trust and reputation in the cyberspace domain on a grand scale. Studies that have been conducted to-date have been limited in scope with respect to number of countries, types of behavior, and size of data sets. This chapter reviews studies on cultural differences in behavior in cyberspace, with particular attention to the concepts of expertise, quality, and trust. It discusses applications that can benefit from these studies, such as: targeted marketing, crowd sourcing applications, and enhancement of security systems. It concludes with a discussion on open data and how Wikipedia data provides an opportunity to examine behavioral differences in different communities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96657527"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96657527"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96657527; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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Wavelet Analysis for a Text-to-Speech (TTS) System" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/85507819/4_Wavelet_Analysis_for_a_Text_to_Speech_TTS_System">4. 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75352612]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75352612,"title":"Wavelet Analysis: Applications in Industry","internal_url":"https://www.academia.edu/75352612/Wavelet_Analysis_Applications_in_Industry","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352611"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/75352611/Data_Stream_Mining_selected_tools_and_algorithms_Numerical_Analysis_and_New_Information_Technology_"><img alt="Research paper thumbnail of Data Stream Mining: selected tools & algorithms (Numerical Analysis and New Information Technology)" class="work-thumbnail" src="https://attachments.academia-assets.com/83154547/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/75352611/Data_Stream_Mining_selected_tools_and_algorithms_Numerical_Analysis_and_New_Information_Technology_">Data Stream Mining: selected tools & algorithms (Numerical Analysis and New Information Technology)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Data stream mining, i.e., the on-line processing and analysis of rapidly and continuously arrivin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Data stream mining, i.e., the on-line processing and analysis of rapidly and continuously arriving large volumes of data, has emerged as an exciting new area of re search. Application domains include financial transactions, sensor network measurements, and telecommunication networks. A new generation of mining algorithms are needed for real-time analysis and query response for these applications since most conventional data mining algorithms can only be applied to static data sets that may be updated periodically in large chunks, but not to continuous streams of data. We examine how some classical tools from statistical and signal analysis have been modified and enhanced to solve real world problems involving data streams.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="367b7059b89a3b6be89fa1c05257faf8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83154547,"asset_id":75352611,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83154547/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352611"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352611"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352611; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352610"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352610/Exploring_overlapping_clusters_using_dynamic_re_scaling_and_sampling"><img alt="Research paper thumbnail of Exploring overlapping clusters using dynamic re-scaling and sampling" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352610/Exploring_overlapping_clusters_using_dynamic_re_scaling_and_sampling">Exploring overlapping clusters using dynamic re-scaling and sampling</a></div><div class="wp-workCard_item"><span>Knowledge and Information Systems</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Until recently, the aim of most text-mining work has been to understand major topics and clusters...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Until recently, the aim of most text-mining work has been to understand major topics and clusters. Minor topics and clusters have been relatively neglected even though they may represent important information on rare events. We present a novel method for exploring overlapping clusters of heterogeneous sizes, which is based on vector space modeling, covariance matrix analysis, random sampling, and dynamic</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352610"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352610"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352610; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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The present invention is characterized in that glottal closure instants are used as reference points (pitch marks) for overlapping. Since the glottal closure instants can be extracted stably and accurately by using dyadic Wavelet conversion, speech in which pitch shaking is negligible and rumbling sounds are minimized can be synthesized stably. In addition, more flexible waveform separation becomes possible by setting the reference point for overlapping and the reference point for waveform separation to different positions. The extraction of glottal closure instants is performed by searching the local peaks of the dyadic Wavelet conversion, but preferably a threshold value for searching for the local peaks of the dyadic Wavelet conversion is adaptively controlled each time dyadic Wavelet conversion is obtained.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352609"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352609"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352609; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); 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</script> <div class="js-work-strip profile--work_container" data-work-id="75352608"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection"><img alt="Research paper thumbnail of Matrix computations for information retrieval and major and outlier cluster detection" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection">Matrix computations for information retrieval and major and outlier cluster detection</a></div><div class="wp-workCard_item"><span>Journal of Computational and Applied Mathematics</span><span>, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive database...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive databases based on vector space modeling and spectral analysis of the covariance matrix, for the document vectors, to reduce the scale of the problem. Since the dimension of the covariance matrix depends on the attribute space and is independent of the number of documents, COV can be applied to databases that are too massive for methods based on the singular value decomposition of the document-attribute matrix, such as latent semantic indexing (LSI). In addition to improved scalability, theoretical considerations indicate that results from our algorithm tend to be more accurate than those from LSI, particularly in detecting subtle differences in document vectors. We demonstrate the power and accuracy of COV through an important topic in data mining, known as outlier cluster detection. We propose two new algorithms for detecting major and outlier clusters in databases—the first is based on LSI, and the second on COV. Our implementation studies indicate that our cluster detection algorithms outperform the basic LSI and COV algorithm in detecting outlier clusters.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352608"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352608"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352608; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75352608]").text(description); $(".js-view-count[data-work-id=75352608]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75352608; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75352608']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75352608]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75352608,"title":"Matrix computations for information retrieval and major and outlier cluster detection","internal_url":"https://www.academia.edu/75352608/Matrix_computations_for_information_retrieval_and_major_and_outlier_cluster_detection","owner_id":4945594,"coauthors_can_edit":true,"owner":{"id":4945594,"first_name":"Mei","middle_initials":null,"last_name":"Kobayashi","page_name":"MeiKobayashi","domain_name":"independent","created_at":"2013-07-24T16:02:54.941-07:00","display_name":"Mei Kobayashi","url":"https://independent.academia.edu/MeiKobayashi"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352607"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/75352607/Estimation_of_singular_values_of_very_large_matrices_using_random_sampling"><img alt="Research paper thumbnail of Estimation of singular values of very large matrices using random sampling" class="work-thumbnail" src="https://attachments.academia-assets.com/83491673/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/75352607/Estimation_of_singular_values_of_very_large_matrices_using_random_sampling">Estimation of singular values of very large matrices using random sampling</a></div><div class="wp-workCard_item"><span>Computers & Mathematics with Applications</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The singular value decomposition (SVD) has enjoyed a long and rich history. Although it was intro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The singular value decomposition (SVD) has enjoyed a long and rich history. Although it was introduced in the 1870s by Beltrami and Jordan for its own intrinsic interest, it has become an invaluable tool in applied mathematics and mathematical modeling. Singular value analysis has been applied in a wide variety of disciplines, most notably for least squares fitting of data. More recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. Recently, the dimensions of matrices which are used in many mathematical models are becoming so large that classical algorithms for computing the SVD cannot be used. We present a new method to determine the largest 10%-25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to the average user. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. Our method is a type of randomized algorithm, i.e., algorithms which solve problems using randomly selected samples of data which are too large to be processed by conventional means. These algorithms output correct (or nearly correct) answers most of the time as long as the input has certain desirable properties. We list these properties and show that matrices which appear in information retrieval are fairly well suited for processing using randomized algorithms. We note, however, that the probability of arriving at an incorrect answer, however small, is not naught since an unrepresentative sample may be drawn from the data.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cf1993d74a62817d8bad46e4058b0c51" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83491673,"asset_id":75352607,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83491673/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352607"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352607"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352607; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75352606"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/75352606/Efficient_estimation_of_singular_values_for_searching_very_large_and_dynamic_web_databases"><img alt="Research paper thumbnail of Efficient estimation of singular values for searching very large and dynamic web databases" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/75352606/Efficient_estimation_of_singular_values_for_searching_very_large_and_dynamic_web_databases">Efficient estimation of singular values for searching very large and dynamic web databases</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. The dimensions of matrices which appear in these applications are becoming so large that classical algorithms for computing the SVD cannot always be used. We present a new method to determine the largest 10%{25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to most users. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. We demonstrate t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75352606"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75352606"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75352606; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75352606]").text(description); $(".js-view-count[data-work-id=75352606]").attr('title', description).tooltip(); 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