K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance
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 +...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Association for Computing Machinery (ACM)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73011 https://orcid.org/0000-0002-7983-9524 |
| Summary: | 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. |
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