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CORR
2010
Springer

CUR from a Sparse Optimization Viewpoint

10 years 11 months ago
CUR from a Sparse Optimization Viewpoint
The CUR decomposition provides an approximation of a matrix X that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of X. In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithmic approach, whereas most sparse PCA methods are framed as convex optimization problems. In this paper, we try to understand CUR from a sparse optimization viewpoint. We show that CUR is implicitly optimizing a sparse regression objective and, furthermore, cannot be directly cast as a sparse PCA method. We also observe that the sparsity attained by CUR possesses an interesting structure, which leads us to formulate a sparse PCA method that achieves a CUR-like sparsity.
Jacob Bien, Ya Xu, Michael W. Mahoney
Added 01 Mar 2011
Updated 01 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Jacob Bien, Ya Xu, Michael W. Mahoney
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