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A Clustering Approach to Learning Sparsely Used Overcomplete Dictionaries

Agarwal, Alekh and Anandkumar, Animashree and Netrapalli, Praneeth (2017) A Clustering Approach to Learning Sparsely Used Overcomplete Dictionaries. IEEE Transactions on Information Theory, 63 (1). pp. 575-592. ISSN 0018-9448. doi:10.1109/TIT.2016.2614684.

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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.

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Additional Information:© 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.
Funding AgencyGrant Number
Microsoft ResearchUNSPECIFIED
Army Research Office (ARO)W911NF-13-1-0084
Subject Keywords:Dictionary learning, sparse coding, overcomplete dictionaries, incoherence, lasso
Issue or Number:1
Record Number:CaltechAUTHORS:20170920-111802806
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Official Citation:A. Agarwal, A. Anandkumar and P. Netrapalli, "A Clustering Approach to Learning Sparsely Used Overcomplete Dictionaries," in IEEE Transactions on Information Theory, vol. 63, no. 1, pp. 575-592, Jan. 2017. doi: 10.1109/TIT.2016.2614684 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81620
Deposited By: Tony Diaz
Deposited On:20 Sep 2017 18:55
Last Modified:15 Nov 2021 19:44

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