{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1875"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1875","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Manifold Sculpting","abstract":"Manifold learning algorithms have been shown to be useful for many applications of numerical analysis. Unfortunately, existing algorithms often produce noisy results, do not scale well, and are unable to benefit from prior knowledge about the expected results. We propose a new algorithm that iteratively discovers manifolds by preserving the local structure among neighboring data points while scaling down the values in unwanted dimensions. This algorithm produces less noisy results than existing algorithms, and it scales better when the number of data points is much larger than the number of dimensions. 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Additionally, this algorithm is able to benefit from existing knowledge by operating in a semi-supervised manner.","abstract_has_math":false,"creators":["Gashler, Michael S."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:29Z","subjects":["manifold learning","dimensionality reduction","NLDR","Computer Sciences"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/876","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gashler, Michael S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-04-24T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["manifold learning","dimensionality reduction","NLDR","Computer Sciences"]}]},{"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":["https://scholarsarchive.byu.edu/etd/876","https://scholarsarchive.byu.edu/context/etd/article/1875/viewcontent/ETD_CISOPTR_999.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Computer Science"]},{"key":"dc:description.abstract","label":"Abstract","values":["Manifold learning algorithms have been shown to be useful for many applications of numerical analysis. Unfortunately, existing algorithms often produce noisy results, do not scale well, and are unable to benefit from prior knowledge about the expected results. We propose a new algorithm that iteratively discovers manifolds by preserving the local structure among neighboring data points while scaling down the values in unwanted dimensions. This algorithm produces less noisy results than existing algorithms, and it scales better when the number of data points is much larger than the number of dimensions. 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This algorithm produces less noisy results than existing algorithms, and it scales better when the number of data points is much larger than the number of dimensions. Additionally, this algorithm is able to benefit from existing knowledge by operating in a semi-supervised manner."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/876","https://scholarsarchive.byu.edu/context/etd/article/1875/viewcontent/ETD_CISOPTR_999.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["manifold learning","dimensionality reduction","NLDR","Computer Sciences"],"dc:title":["Manifold Sculpting"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:29Z"}