Document Type

Article

Publication Date

5-2017

Publication Title

IEEE Transactions on Information Theory

ISSN

0018-9448

Volume

63

Issue

5

DOI

https://doi.org/10.1109/TIT.2017.2672725

Abstract

We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore, the sampling is single-pass and applicable to streaming data. The sampling mechanism is a variant of previous methods proposed in the literature combined with a randomized preconditioning to smooth the data. We provide guarantees for PCA in terms of the covariance matrix, and guarantees for K-means in terms of the error in the center estimators at a given step. We present numerical evidence to show both that our bounds are nearly tight and that our algorithms provide a real benefit when applied to standard test data sets, as well as providing certain benefits over related sampling approaches.

Comments

© Copyright 2017 IEEE

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