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arXiv · 1511.00152

Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means

Farhad Pourkamali-Anaraki·Stephen Becker
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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.

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Farhad Pourkamali-Anaraki, Stephen Becker. 2016-09-20. Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means. https://doi.org/10.1109/tit.2017.2672725

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