A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

09/08/2013

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by   Alekh Agarwal, et al.

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We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary using an efficient algorithm. Our algorithm is a clustering-style procedure, where each cluster is used to estimate a dictionary element. The resulting solution can often be further cleaned up to obtain a high accuracy estimate, and we provide one simple scenario where ℓ_1-regularized regression can be used for such a second stage.