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Martin C. Rinard and Jonathan A. Kelner. Musco, Christopher Paul Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2015-11-09T19:53:22Z 2015-11-09T19:53:22Z 2015 2015 http://hdl.handle.net/1721.1/99856 927699160 Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. Cataloged from PDF version of thesis. Includes bibliographical references (pages 97-103). Dimensionality reduction has become a critical tool for quickly solving massive matrix problems. Especially in modern data analysis and machine learning applications, an overabundance of data features or examples can make it impossible to apply standard algorithms efficiently. To address this issue, it is often possible to distill data to a much smaller set of informative features or examples, which can be used to obtain provably accurate approximate solutions to a variety of problems In this thesis, we focus on the important case of dimensionality reduction for sparse and structured data. In contrast to popular structure-agnostic methods like Johnson-Lindenstrauss projection and PCA, we seek data compression techniques that take advantage of structure to generate smaller or more powerful compressions. Additionally, we aim for methods that can be applied extremely quickly - typically in linear or nearly linear time in the input size. Specifically, we introduce new randomized algorithms for structured dimensionality reduction that are based on importance sampling and sparse-recovery techniques. Our work applies directly to accelerating linear regression and graph sparsification and we discuss connections and possible extensions to low-rank approximation, k-means clustering, and several other ubiquitous matrix problems. by Christopher Paul Musco. S.M. 103 pages eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Dimensionality reduction for sparse and structured matrices Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="4b5e6c43-4ba2-4d15-9c62-5e1f03a5a6dd"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Dimensionality reduction for sparse and structured matrices</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2015</PublicationDate> <Authors> <Author> <DisplayName>Musco, Christopher Paul</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>Dimensionality reduction has become a critical tool for quickly solving massive matrix problems. Especially in modern data analysis and machine learning applications, an overabundance of data features or examples can make it impossible to apply standard algorithms efficiently. To address this issue, it is often possible to distill data to a much smaller set of informative features or examples, which can be used to obtain provably accurate approximate solutions to a variety of problems In this thesis, we focus on the important case of dimensionality reduction for sparse and structured data. In contrast to popular structure-agnostic methods like Johnson-Lindenstrauss projection and PCA, we seek data compression techniques that take advantage of structure to generate smaller or more powerful compressions. Additionally, we aim for methods that can be applied extremely quickly - typically in linear or nearly linear time in the input size. Specifically, we introduce new randomized algorithms for structured dimensionality reduction that are based on importance sampling and sparse-recovery techniques. Our work applies directly to accelerating linear regression and graph sparsification and we discuss connections and possible extensions to low-rank approximation, k-means clustering, and several other ubiquitous matrix problems.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>