{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1532"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1532","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"Decision Theory Classification Of High-dimensional Vectors Based On Small Samples","abstract":"In this paper, we review existing classification techniques and suggest an entirely new procedure for the classification of high-dimensional vectors on the basis of a few training samples. The proposed method is based on the Bayesian paradigm and provides posterior probabilities that a new vector belongs to each of the classes, therefore it adapts naturally to any number of classes. Our classification technique is based on a small vector which is related to the projection of the observation onto the space spanned by the training samples. This is achieved by employing matrix-variate distributions in classification, which is an entirely new idea. In addition, our method mimics time-tested classification techniques based on the assumption of normally distributed samples. By assuming that the samples have a matrix-variate normal distribution, we are able to replace classification on the basis of a large covariance matrix with classification on the basis of a smaller matrix that describes the relationship of sample vectors to each other.","abstract_html":"In this paper, we review existing classification techniques and suggest an entirely new procedure for the classification of high-dimensional vectors on the basis of a few training samples. The proposed method is based on the Bayesian paradigm and provides posterior probabilities that a new vector belongs to each of the classes, therefore it adapts naturally to any number of classes. Our classification technique is based on a small vector which is related to the projection of the observation onto the space spanned by the training samples. This is achieved by employing matrix-variate distributions in classification, which is an entirely new idea. In addition, our method mimics time-tested classification techniques based on the assumption of normally distributed samples. By assuming that the samples have a matrix-variate normal distribution, we are able to replace classification on the basis of a large covariance matrix with classification on the basis of a smaller matrix that describes the relationship of sample vectors to each other.","abstract_has_math":false,"creators":["Bradshaw, David"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Pensky, Marianna"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-01-01T08:00:00Z","date_published":"2005-01-01T08:00:00Z","updated_at":"2026-07-24T05:08:59Z","subjects":["Support Vector Machine","decision theory","posterior probabilities","matrix-variate normal","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000753"],"render_values":[{"text":"CFE0000753","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/533","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pensky, Marianna"]},{"key":"dc:creator","label":"Author","values":["Bradshaw, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Doctoral Dissertation (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Support Vector Machine","decision theory","posterior probabilities","matrix-variate normal","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000753"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/533"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Doctor of Philosophy (Ph.D.)","College of Arts and Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we review existing classification techniques and suggest an entirely new procedure for the classification of high-dimensional vectors on the basis of a few training samples. 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