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

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

31 Oct 2015arXiv:1511.00152archive 2025-07-28

Farhad Pourkamali-Anaraki, Stephen Becker

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.

PaperPDFCode

Code

stephenbeckr/SparsifiedKMeans officialmentioned in papermentioned on GitHub report
erickightley/sparseklearn mentioned on GitHub report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

PCA

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections