A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

Alekh Agarwal; Animashree Anandkumar; Praneeth Netrapalli

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arXiv · 1309.1952

A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

Alekh Agarwal·Animashree Anandkumar·Praneeth Netrapalli

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Abstract

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.

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Alekh Agarwal, Animashree Anandkumar, Praneeth Netrapalli. 2014-07-07. A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries. https://arxiv.org/abs/1309.1952

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