{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/82325"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/82325","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Tree Estimation Based on an L(1) Loss Criterion","abstract":"Five applications were carried out in this study. In Application 1, L1 ultrametrics under fixed constraints were fitted to gene frequency data of Cavalli-Sforza et al. (1994) using both the IRIP approach and a linear programming (LP) approach of Spath (1992, Chapter 5). When coded for ultrametric constraints, IRIP showed faster processing speeds and larger object set size capacity than the LP approach. Heuristic fitting of ultrametrics and additive trees were considered in Applications 2 and 3, using occupational data from the U.S. Department of Labor Employment and Training Administration's (1998) O*NET Content Model, and food data from Ross and Murphy (1999). Both the L2 iterative projection (IP) approach of Hubert and Arabie (1995) and the IRIP L1 approach were applied. Both methods identified very similar solutions when the best-fitting and the most frequently-occurring local optima were considered. In Applications 4 and 5, a series of Monte Carlo analyses were carried out to assess metric recovery of ultrametrics and additive trees under (1) typical data error conditions, and (2) extreme data error conditions. Under typical error conditions, the IP approach showed superior metric recovery, while under extreme data error conditions the IRIP approach showed superior metric recovery when a relatively large proportion of extreme data values were present within a smaller object set size. Under extreme data error conditions, metric recovery of additive trees was much higher than metric recovery of ultrametrics (with either method). Possible extensions to other representational structures, and the use of additive trees as resilient structures in the presence of data error are discussed.","abstract_html":"Five applications were carried out in this study. In Application 1, L1 ultrametrics under fixed constraints were fitted to gene frequency data of Cavalli-Sforza et al. (1994) using both the IRIP approach and a linear programming (LP) approach of Spath (1992, Chapter 5). When coded for ultrametric constraints, IRIP showed faster processing speeds and larger object set size capacity than the LP approach. Heuristic fitting of ultrametrics and additive trees were considered in Applications 2 and 3, using occupational data from the U.S. Department of Labor Employment and Training Administration's (1998) O*NET Content Model, and food data from Ross and Murphy (1999). Both the L2 iterative projection (IP) approach of Hubert and Arabie (1995) and the IRIP L1 approach were applied. Both methods identified very similar solutions when the best-fitting and the most frequently-occurring local optima were considered. In Applications 4 and 5, a series of Monte Carlo analyses were carried out to assess metric recovery of ultrametrics and additive trees under (1) typical data error conditions, and (2) extreme data error conditions. Under typical error conditions, the IP approach showed superior metric recovery, while under extreme data error conditions the IRIP approach showed superior metric recovery when a relatively large proportion of extreme data values were present within a smaller object set size. Under extreme data error conditions, metric recovery of additive trees was much higher than metric recovery of ultrametrics (with either method). Possible extensions to other representational structures, and the use of additive trees as resilient structures in the presence of data error are discussed.","abstract_has_math":false,"creators":["Smith, Thomas Jay"],"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":"2015-09-25T20:40:19Z","date_published":"2015-09-25T20:40:19Z","updated_at":"2026-07-22T22:26:18Z","subjects":["Statistics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9990147"],"render_values":[{"text":"(MiAaPQ)AAI9990147","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/82325","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":["Smith, Thomas Jay"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:40:19Z","10000-01-01","2000"]},{"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":["Statistics"]}]},{"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/2142/82325","(MiAaPQ)AAI9990147"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Five applications were carried out in this study. In Application 1, L1 ultrametrics under fixed constraints were fitted to gene frequency data of Cavalli-Sforza et al. (1994) using both the IRIP approach and a linear programming (LP) approach of Spath (1992, Chapter 5). When coded for ultrametric constraints, IRIP showed faster processing speeds and larger object set size capacity than the LP approach. Heuristic fitting of ultrametrics and additive trees were considered in Applications 2 and 3, using occupational data from the U.S. Department of Labor Employment and Training Administration's (1998) O*NET Content Model, and food data from Ross and Murphy (1999). Both the L2 iterative projection (IP) approach of Hubert and Arabie (1995) and the IRIP L1 approach were applied. Both methods identified very similar solutions when the best-fitting and the most frequently-occurring local optima were considered. In Applications 4 and 5, a series of Monte Carlo analyses were carried out to assess metric recovery of ultrametrics and additive trees under (1) typical data error conditions, and (2) extreme data error conditions. Under typical error conditions, the IP approach showed superior metric recovery, while under extreme data error conditions the IRIP approach showed superior metric recovery when a relatively large proportion of extreme data values were present within a smaller object set size. Under extreme data error conditions, metric recovery of additive trees was much higher than metric recovery of ultrametrics (with either method). Possible extensions to other representational structures, and the use of additive trees as resilient structures in the presence of data error are discussed.","Made available in DSpace on 2015-09-25T20:40:19Z (GMT). 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(1994) using both the IRIP approach and a linear programming (LP) approach of Spath (1992, Chapter 5). When coded for ultrametric constraints, IRIP showed faster processing speeds and larger object set size capacity than the LP approach. Heuristic fitting of ultrametrics and additive trees were considered in Applications 2 and 3, using occupational data from the U.S. Department of Labor Employment and Training Administration's (1998) O*NET Content Model, and food data from Ross and Murphy (1999). Both the L2 iterative projection (IP) approach of Hubert and Arabie (1995) and the IRIP L1 approach were applied. Both methods identified very similar solutions when the best-fitting and the most frequently-occurring local optima were considered. In Applications 4 and 5, a series of Monte Carlo analyses were carried out to assess metric recovery of ultrametrics and additive trees under (1) typical data error conditions, and (2) extreme data error conditions. Under typical error conditions, the IP approach showed superior metric recovery, while under extreme data error conditions the IRIP approach showed superior metric recovery when a relatively large proportion of extreme data values were present within a smaller object set size. Under extreme data error conditions, metric recovery of additive trees was much higher than metric recovery of ultrametrics (with either method). Possible extensions to other representational structures, and the use of additive trees as resilient structures in the presence of data error are discussed.","Made available in DSpace on 2015-09-25T20:40:19Z (GMT). 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