Dimensionality reduction of massive sparse datasets using coresets
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6596-dimensionality-reduction-of-massive-sparse-datasets-using-coresets.pdf
Description
Published version
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487.06 KB
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Adobe PDF
Checksum (MD5)
c5fa308847b256dca57d33ad344fb99a
Author(s)
Rus, Daniela
Feldman, Dan
Volkov, Mikhail
Date Issued
2016
Citation
Rus, Daniela, Feldman, Dan and Volkov, Mikhail. 2016. "Dimensionality reduction of massive sparse datasets using coresets."
Version
Final published version
Abstract
© 2016 NIPS Foundation - All Rights Reserved. In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any n × d matrix, using one pass over the stream of its rows. Our solution uses coresets: a scaled subset of the n rows that approximates their sum of squared distances to every k-dimensional affine subspace. An open theoretical problem has been to compute such a coreset that is independent of both n and d. An open practical problem has been to compute a non-trivial approximation to the PCA of very large but sparse databases such as the Wikipedia document-term matrix in a reasonable time. We answer both of these questions affirmatively. Our main technical result is a new framework for deterministic coreset constructions based on a reduction to the problem of counting items in a stream.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://papers.nips.cc/paper/6596-dimensionality-reduction-of-massive-sparse-datasets-using-coresets
