{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/82057"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/82057","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Local Optima in K-Means Clustering","abstract":"\"The study of the properties of local optimality in K-means clustering is pursued. In doing so, it is shown that several of the commercial software packages prove to be inadequate in their treatment of the K-means algorithm, resulting in the proposal of an alternative method based on several thousand initializations, which is imbedded in a MATLAB m-file. The further developments of this dissertation are four-fold: (a) a comprehensive cluster generation method based on distributional theory and probability is developed; (b) the properties of local optimality are related to a cluster recovery criterion to develop a test that is able to distinguish between \"\"good\"\" and \"\"bad\"\" cluster solutions; (c) a method of consensus analysis for K-means clustering is proposed and extended to within-cluster standardization; and (d) a lower bound for the K -means criterion function is derived, and based on the lower bound, another (more powerful) test is developed to determine the quality of a given cluster solution.\"","abstract_html":""The study of the properties of local optimality in K-means clustering is pursued. In doing so, it is shown that several of the commercial software packages prove to be inadequate in their treatment of the K-means algorithm, resulting in the proposal of an alternative method based on several thousand initializations, which is imbedded in a MATLAB m-file. The further developments of this dissertation are four-fold: (a) a comprehensive cluster generation method based on distributional theory and probability is developed; (b) the properties of local optimality are related to a cluster recovery criterion to develop a test that is able to distinguish between ""good"" and ""bad"" cluster solutions; (c) a method of consensus analysis for K-means clustering is proposed and extended to within-cluster standardization; and (d) a lower bound for the K -means criterion function is derived, and based on the lower bound, another (more powerful) test is developed to determine the quality of a given cluster solution."","abstract_has_math":false,"creators":["Steinley, Douglas Lee"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Psychology","degree_department":null,"school":null,"contributors":["Hubert, Lawrence J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:38:57Z","date_published":"2015-09-25T20:38:57Z","updated_at":"2026-07-22T22:26:17Z","subjects":["Psychology, Psychometrics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3131029"],"render_values":[{"text":"(MiAaPQ)AAI3131029","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/82057","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hubert, Lawrence J."]},{"key":"dc:creator","label":"Author","values":["Steinley, Douglas Lee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:38:57Z","10000-01-01","2004"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Psychology"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Psychology, Psychometrics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/82057","(MiAaPQ)AAI3131029"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"The study of the properties of local optimality in K-means clustering is pursued. In doing so, it is shown that several of the commercial software packages prove to be inadequate in their treatment of the K-means algorithm, resulting in the proposal of an alternative method based on several thousand initializations, which is imbedded in a MATLAB m-file. The further developments of this dissertation are four-fold: (a) a comprehensive cluster generation method based on distributional theory and probability is developed; (b) the properties of local optimality are related to a cluster recovery criterion to develop a test that is able to distinguish between \"\"good\"\" and \"\"bad\"\" cluster solutions; (c) a method of consensus analysis for K-means clustering is proposed and extended to within-cluster standardization; and (d) a lower bound for the K -means criterion function is derived, and based on the lower bound, another (more powerful) test is developed to determine the quality of a given cluster solution.\"","Made available in DSpace on 2015-09-25T20:38:57Z (GMT). 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In doing so, it is shown that several of the commercial software packages prove to be inadequate in their treatment of the K-means algorithm, resulting in the proposal of an alternative method based on several thousand initializations, which is imbedded in a MATLAB m-file. The further developments of this dissertation are four-fold: (a) a comprehensive cluster generation method based on distributional theory and probability is developed; (b) the properties of local optimality are related to a cluster recovery criterion to develop a test that is able to distinguish between \"\"good\"\" and \"\"bad\"\" cluster solutions; (c) a method of consensus analysis for K-means clustering is proposed and extended to within-cluster standardization; and (d) a lower bound for the K -means criterion function is derived, and based on the lower bound, another (more powerful) test is developed to determine the quality of a given cluster solution.\"","Made available in DSpace on 2015-09-25T20:38:57Z (GMT). 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