K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance
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Indyk_K-median clustering.pdf
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245.13 KB
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Author(s)
Indyk, Piotr
Price, Eric C.
Date Issued
June 2011
Journal
Proceedings of the 43rd annual ACM symposium on Theory of computing (STOC '11)
Publisher
Association for Computing Machinery (ACM)
Citation
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.
Version
Author's final manuscript
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 + 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1145/1993636.1993720
