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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. https://resolver.caltech.edu/CaltechAUTHORS:20170920-111802806

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TIT.2016.2614684DOIArticle
http://ieeexplore.ieee.org/document/7580653/PublisherArticle
https://arxiv.org/abs/1309.1952arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
Microsoft ResearchUNSPECIFIED
NSFCCF-1254106
NSFCCF-1219234
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170920-111802806
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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7580653&isnumber=7792231
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81620
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Sep 2017 18:55
Last Modified:03 Oct 2019 18:45

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