Random projection method is one of the important tools for the dimensionality reduction of data which can be made efficient with strong error guarantees. In this thesis, we focus on linear transforms of high dimensional data to the low dimensional space satisfying the Johnson-Lindenstrauss lemma. In addition, we also prove some theoretical results relating to the projections that are of interest when applying them in practical applications. We show how the technique can be applied to synthetic data with probabilistic guarantee on the pairwise distance. The connection between dimensionality reduction and compressed sensing is also discussed.
","abstract_html":"<p>Random projection method is one of the important tools for the dimensionality reduction of data which can be made efficient with strong error guarantees. In this thesis, we focus on linear transforms of high dimensional data to the low dimensional space satisfying the Johnson-Lindenstrauss lemma. In addition, we also prove some theoretical results relating to the projections that are of interest when applying them in practical applications. We show how the technique can be applied to synthetic data with probabilistic guarantee on the pairwise distance. The connection between dimensionality reduction and compressed sensing is also discussed.</p>","abstract_has_math":false,"creators":["Vamulapalli, Harika Rao"],"institution":null,"degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Chen, Huimin","Li, X. Rong","Jilkov, Vesselin P."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-05T07:00:00Z","date_published":"2010-08-05T07:00:00Z","updated_at":"2026-07-24T05:29:15Z","subjects":["principal component analysis","dimensionality reduction","random projection","fast Johnson Lindenstrauss transform"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uno.edu/td/1211","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chen, Huimin","Li, X. Rong","Jilkov, Vesselin P."]},{"key":"dc:creator","label":"Author","values":["Vamulapalli, Harika Rao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["principal component analysis","dimensionality reduction","random projection","fast Johnson Lindenstrauss transform"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uno.edu/td/1211"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Random projection method is one of the important tools for the dimensionality reduction of data which can be made efficient with strong error guarantees. In this thesis, we focus on linear transforms of high dimensional data to the low dimensional space satisfying the Johnson-Lindenstrauss lemma. In addition, we also prove some theoretical results relating to the projections that are of interest when applying them in practical applications. We show how the technique can be applied to synthetic data with probabilistic guarantee on the pairwise distance. The connection between dimensionality reduction and compressed sensing is also discussed.
"]},{"key":"dc:title","label":"Title","values":["On Dimensionality Reduction of Data"]}]}],"canonical_facts":{"dc:contributor":["Chen, Huimin","Li, X. Rong","Jilkov, Vesselin P."],"dc:creator":["Vamulapalli, Harika Rao"],"dc:description.abstract":["Random projection method is one of the important tools for the dimensionality reduction of data which can be made efficient with strong error guarantees. In this thesis, we focus on linear transforms of high dimensional data to the low dimensional space satisfying the Johnson-Lindenstrauss lemma. In addition, we also prove some theoretical results relating to the projections that are of interest when applying them in practical applications. We show how the technique can be applied to synthetic data with probabilistic guarantee on the pairwise distance. The connection between dimensionality reduction and compressed sensing is also discussed.
"],"dc:identifier":["https://scholarworks.uno.edu/td/1211"],"dc:subject":["principal component analysis","dimensionality reduction","random projection","fast Johnson Lindenstrauss transform"],"dc:title":["On Dimensionality Reduction of Data"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."]},"updated_at":"2026-07-24T05:29:15Z"}