K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance
Author(s)Indyk, Piotr; Price, Eric C.
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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 + ε approximation factor, which matches the best achievable bound for other error measures, such as the l[subscript 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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 43rd annual ACM symposium on Theory of computing (STOC '11)
Association for Computing Machinery (ACM)
Piotr Indyk and Eric Price. 2011. K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance. In Proceedings of the 43rd annual ACM symposium on Theory of computing (STOC '11). ACM, New York, NY, USA, 627-636.
Author's final manuscript