Recovering PCA from Hybrid-$(\ell_1,\ell_2)$ Sparse Sampling of Data Elements
Abstract
This paper addresses how well we can recover a data matrix when only given a few of its elements. We present a randomized algorithm that element-wise sparsifies the data, retaining only a few its elements. Our new algorithm independently samples the data using sampling probabilities that depend on both the squares ( sampling) and absolute values ( sampling) of the entries. We prove that the hybrid algorithm recovers a near-PCA reconstruction of the data from a sublinear sample-size: hybrid-() inherits the -ability to sample the important elements as well as the regularization properties of sampling, and gives strictly better performance than either or on their own. We also give a one-pass version of our algorithm and show experiments to corroborate the theory.
Cite
@article{arxiv.1503.00547,
title = {Recovering PCA from Hybrid-$(\ell_1,\ell_2)$ Sparse Sampling of Data Elements},
author = {Abhisek Kundu and Petros Drineas and Malik Magdon-Ismail},
journal= {arXiv preprint arXiv:1503.00547},
year = {2015}
}