A Clustering Approach to Learning Sparsely Used Overcomplete Dictionaries
We consider the problem of learning over complete 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.
© 2017 IEEE. Manuscript received July 6, 2014; revised June 6, 2016; accepted September 11, 2016. Date of publication September 30, 2016; date of current version December 20, 2016. A. Anandkumar was supported in part by the Microsoft Faculty Fellowship, in part by the NSF Career Award under Grant CCF1254106, in part by the NSF Award under Grant CCF-1219234, and in part by the ARO YIP Award under Grant W911NF-13-1-0084. This paper was presented at the 2014 COLT.
Submitted - 1309.1952.pdf