A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries
This addresses the challenge of dictionary learning in sparse coding, which is incremental as it builds on existing methods with a new algorithmic approach.
The paper tackles the problem of learning overcomplete dictionaries for sparse coding by proposing a clustering-style algorithm to approximately recover the dictionary, with potential for high accuracy through a second-stage cleanup using $\ell_1$-regularized regression.
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 $\ell_1$-regularized regression can be used for such a second stage.