{"id":{"repo_id":"vilnius","oai_identifier":"oai:vu.lt:elaba:11747459"},"canonical_url":"https://search.dev.ndltd.org/etd/vilnius/oai:vu.lt:elaba:11747459","repository":{"repo_id":"vilnius","name":"Vilnius University","base_url":"https://epublications.vu.lt/oai"},"display":{"title":"Optimization algorithms for multidimensional scaling with city-block distances and their parallelization /","abstract":"In this dissertation, a problem related to a visualization of elements of a multidimensional data set is considered. Here, for the sake of simplicity, an element of a multidimensional data set is called a multidimensional element. There are many techniques for visualizing multidimensional elements. Multidimensional scaling (MDS) is one of them. In applying MDS, a certain real function has to be constructed and minimized. In order to construct the function, a desired distance function has to be selected. If city-block distances are selected, the problem of minimizing such a function becomes a complicated optimization problem. In this work, this complicated optimization problem is the main research problem. Here, we formulate a new optimization problem and we show that it is equivalent to the original optimization problem arising in MDS with city-block distances. Also, we propose two sequential algorithms and one parallel algorithm for the newly formulated problem. Finally, we present the results of numerical investigations of the proposed algorithms.","abstract_html":"In this dissertation, a problem related to a visualization of elements of a multidimensional data set is considered. Here, for the sake of simplicity, an element of a multidimensional data set is called a multidimensional element. There are many techniques for visualizing multidimensional elements. Multidimensional scaling (MDS) is one of them. In applying MDS, a certain real function has to be constructed and minimized. In order to construct the function, a desired distance function has to be selected. If city-block distances are selected, the problem of minimizing such a function becomes a complicated optimization problem. In this work, this complicated optimization problem is the main research problem. Here, we formulate a new optimization problem and we show that it is equivalent to the original optimization problem arising in MDS with city-block distances. Also, we propose two sequential algorithms and one parallel algorithm for the newly formulated problem. Finally, we present the results of numerical investigations of the proposed algorithms.","abstract_has_math":false,"creators":["Galiauskas, Nerijus,"],"institution":"Institutional Repository of Vilnius University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T05:55:35Z","subjects":["multidimensional scaling ; city-block distances ; optimization ; parallel computing"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.vu.lt/VU:ELABAETD11747459&prefLang=en_US","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Galiauskas, Nerijus,"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015"]},{"key":"dc:publisher","label":"Institution","values":["Institutional Repository of Vilnius University"]},{"key":"dc:relation","label":"Dc Relation","values":["https://epublications.vu.lt/object/elaba:11747459/11747459.pdf"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["multidimensional scaling ; city-block distances ; optimization ; parallel computing"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.vu.lt/VU:ELABAETD11747459&prefLang=en_US"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, a problem related to a visualization of elements of a multidimensional data set is considered. Here, for the sake of simplicity, an element of a multidimensional data set is called a multidimensional element. There are many techniques for visualizing multidimensional elements. Multidimensional scaling (MDS) is one of them. In applying MDS, a certain real function has to be constructed and minimized. In order to construct the function, a desired distance function has to be selected. If city-block distances are selected, the problem of minimizing such a function becomes a complicated optimization problem. In this work, this complicated optimization problem is the main research problem. Here, we formulate a new optimization problem and we show that it is equivalent to the original optimization problem arising in MDS with city-block distances. Also, we propose two sequential algorithms and one parallel algorithm for the newly formulated problem. Finally, we present the results of numerical investigations of the proposed algorithms."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Optimization algorithms for multidimensional scaling with city-block distances and their parallelization /","Optimizavimo algoritmai daugiamatėms skalėms su miesto kvartalo atstumais ir jų lygiagretinimas."]}]}],"canonical_facts":{"dc:creator":["Galiauskas, Nerijus,"],"dc:date":["2015"],"dc:description":["In this dissertation, a problem related to a visualization of elements of a multidimensional data set is considered. Here, for the sake of simplicity, an element of a multidimensional data set is called a multidimensional element. There are many techniques for visualizing multidimensional elements. Multidimensional scaling (MDS) is one of them. In applying MDS, a certain real function has to be constructed and minimized. In order to construct the function, a desired distance function has to be selected. If city-block distances are selected, the problem of minimizing such a function becomes a complicated optimization problem. In this work, this complicated optimization problem is the main research problem. Here, we formulate a new optimization problem and we show that it is equivalent to the original optimization problem arising in MDS with city-block distances. Also, we propose two sequential algorithms and one parallel algorithm for the newly formulated problem. Finally, we present the results of numerical investigations of the proposed algorithms."],"dc:format":["application/pdf"],"dc:identifier":["https://repository.vu.lt/VU:ELABAETD11747459&prefLang=en_US"],"dc:language":["eng"],"dc:publisher":["Institutional Repository of Vilnius University"],"dc:relation":["https://epublications.vu.lt/object/elaba:11747459/11747459.pdf"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:subject":["multidimensional scaling ; city-block distances ; optimization ; parallel computing"],"dc:title":["Optimization algorithms for multidimensional scaling with city-block distances and their parallelization /","Optimizavimo algoritmai daugiamatėms skalėms su miesto kvartalo atstumais ir jų lygiagretinimas."],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:55:35Z"}