Efficient metric representations for big data
Name
1227780734-MIT.pdf
Size
3.41 MB
Format
Adobe PDF
Checksum (MD5)
be0d381027a5eef3817058814161e284
Author(s)
Wagner, Tal.
Advisor(s)
Piotr Indyk.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
Contemporary datasets are often represented as points in a high-dimensional metric space. To deal with increasingly larger datasets, many algorithms rely on efficient or compressed representations of the induced metric. In this thesis, we study several fundamental aspects of efficient metric representations. Our results include: -- Fully determining the minimal number of bits required to represent all distances, up to a given precision, in a finite Euclidean or Manhattan metric space. -- A space-efficient data structure for Euclidean approximate nearest neighbor search in high dimensions. -- A sublinear time algorithm for low-rank approximation of distance matrices, which is optimal in the number of entries it reads of the input matrix. -- A fast algorithm for nearest neighbor search in the Optimal Transport distance. Previous bounds on Euclidean metric compression have been restricted to discretizing a classical dimensionality reduction theorem of Johnson and Lindenstrauss (1984). Our results improve over those bounds, thereby establishing an asymptotic advantage of generic sketching over dimension reduction. All of our algorithms are both proven analytically and implemented and validated empirically.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, September, 2020
Cataloged from student-submitted PDF of thesis.
Includes bibliographical references (pages 201-213).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
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