{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/80688"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/80688","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Localized Hierarchical Approximations for Data Reduction and Learning","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Shekhar, Prashant; 0000-0003-2353-6740"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Patra, Abani","Computational and Data Enabled Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-28T22:10:01Z","date_published":"2019-10-28T22:10:01Z","updated_at":"2026-07-27T19:05:23Z","subjects":["applied mathematics","computer science","remote sensing"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/80688","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Patra, Abani","Computational and Data Enabled Sciences"]},{"key":"dc:creator","label":"Author","values":["Shekhar, Prashant; 0000-0003-2353-6740"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-10-28T22:10:01Z","2019","2019-08-23 11:55:17"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["applied mathematics","computer science","remote sensing"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/80688"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","With more and more awareness about the effects of climate change (be it natural or man-made), it has become imperative for us to gain more insight into how these rapidly changing environmental conditions will effect us in the near future. For this, in the recent decades NASA has funded several satellite and flight based missions as a part of its Earth Observing system to study and analyze these natural dynamical systems. In this regard, the behavior of the polar ice sheets has been marked as a very crucial factor feeding into the other natural systems like Oceans and Atmosphere. However, to extract the full benefit of these remote sensing missions for understanding these ice-sheets, we need efficient data driven physics based methods that can intelligently learn from these very large remote sensing datasets. This dissertation is mainly motivated by this idea and provides some novel methods to handle such modeling problems efficiently.Starting with univariate time series modeling of land ice changes, we move on to proposing methodologies for making data dependent hierarchical approximations, crucial in inferring sparse representations at multiple levels for a variety of mutivariate datasets. Such an approach has been shown to be useful for modeling noiseless as well as noisy data from areas including cryospheric sciences and as emulators for numerical modeling approaches in other related domains. A detailed analysis of approximation properties, stability bounds and convergence behavior is also presented to establish the viability of the proposed approaches.The success of the proposed approaches on both synthetic and real datasets is expected to encourage similar research in this domain for not only solving existing modeling problems by state of the art existing approaches but also for development of the related theory that can facilitate better understanding."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Localized Hierarchical Approximations for Data Reduction and Learning"]}]}],"canonical_facts":{"dc:contributor":["Patra, Abani","Computational and Data Enabled Sciences"],"dc:creator":["Shekhar, Prashant; 0000-0003-2353-6740"],"dc:date":["2019-10-28T22:10:01Z","2019","2019-08-23 11:55:17"],"dc:description":["Ph.D.","With more and more awareness about the effects of climate change (be it natural or man-made), it has become imperative for us to gain more insight into how these rapidly changing environmental conditions will effect us in the near future. For this, in the recent decades NASA has funded several satellite and flight based missions as a part of its Earth Observing system to study and analyze these natural dynamical systems. In this regard, the behavior of the polar ice sheets has been marked as a very crucial factor feeding into the other natural systems like Oceans and Atmosphere. However, to extract the full benefit of these remote sensing missions for understanding these ice-sheets, we need efficient data driven physics based methods that can intelligently learn from these very large remote sensing datasets. This dissertation is mainly motivated by this idea and provides some novel methods to handle such modeling problems efficiently.Starting with univariate time series modeling of land ice changes, we move on to proposing methodologies for making data dependent hierarchical approximations, crucial in inferring sparse representations at multiple levels for a variety of mutivariate datasets. Such an approach has been shown to be useful for modeling noiseless as well as noisy data from areas including cryospheric sciences and as emulators for numerical modeling approaches in other related domains. A detailed analysis of approximation properties, stability bounds and convergence behavior is also presented to establish the viability of the proposed approaches.The success of the proposed approaches on both synthetic and real datasets is expected to encourage similar research in this domain for not only solving existing modeling problems by state of the art existing approaches but also for development of the related theory that can facilitate better understanding."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/80688"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["applied mathematics","computer science","remote sensing"],"dc:title":["Localized Hierarchical Approximations for Data Reduction and Learning"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:23Z"}