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

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  • 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.
Date Issued
  • 2017-05-01
Academic Affiliation
Journal Title
Journal Issue/Number
  • 5
Journal Volume
  • 63
Last Modified
  • 2019-12-05
Resource Type
Rights Statement
  • 0018-9448