K-Median Clustering, Model-Based Compressive Sensing, and Sparse Recovery for Earth Mover Distance
Abstract
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. One construction yields m = O(k log(n/k)) and a 1 + epsilon approximation factor, which matches the best achievable bound for other error measures, such as the L_1 norm. Our algorithms are obtained by exploiting novel connections to other problems and areas, such as streaming algorithms for k-median clustering and model-based compressive sensing. We also provide novel algorithms and results for the latter problems.
Keywords
Cite
@article{arxiv.1104.4674,
title = {K-Median Clustering, Model-Based Compressive Sensing, and Sparse Recovery for Earth Mover Distance},
author = {Piotr Indyk and Eric Price},
journal= {arXiv preprint arXiv:1104.4674},
year = {2012}
}
Comments
21 pages. Appeared in STOC 2011. This version corrects a bug in the proof of Theorem B.5