Approximate k-means clustering through random projections
Name
927412847-MIT.pdf
Description
Full printable version
Size
1.66 MB
Format
Adobe PDF
Checksum (MD5)
21130ff64ac0242f1626b37992e61882
Author(s)
Persu, Elena-Mădălina
Advisor(s)
Ankur Moitra.
Date Issued
2015
Publisher
Massachusetts Institute of Technology
Abstract
Using random row projections, we show how to approximate a data matrix A with a much smaller sketch à that can be used to solve a general class of constrained k-rank approximation problems to within (1 + [epsilon]) error. Importantly, this class of problems includes k-means clustering. By reducing data points to just O(k) dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For k-means dimensionality reduction, we provide (1+ [epsilon]) relative error results for random row projections which improve on the (2 + [epsilon]) prior known constant factor approximation associated with this sketching technique, while preserving the number of dimensions. For k-means clustering, we show how to achieve a (9 + [epsilon]) approximation by Johnson-Lindenstrauss projecting data points to just 0(log k/[epsilon]2 ) dimensions. This gives the first result that leverages the specific structure of k-means to achieve dimension independent of input size and sublinear in k.
Description
Thesis: S.M. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 39-41).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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