Abstract Details
Activity Number:
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542
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Type:
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Invited
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Date/Time:
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Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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Abstract #310791
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View Presentation
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Title:
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Learning Sparsely Used Overcomplete Dictionaries
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Author(s):
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Alekh Agarwal*+ and Animashree Anandkumar and Prateek Jain and Praneeth Netrapalli and Rashish Tandon
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Companies:
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Microsoft and University of California, Irvine and Microsoft and University of Texas at Austin and University of Texas at Austin
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Keywords:
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Dictionary learning ;
Sparse coding ;
Alternating minimization ;
Sparse estimation
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Abstract:
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We consider the problem of learning sparsely used overcomplete dictionaries, where each observation consists of a sparse combination of the mutually incoherent dictionary elements. Our method consists of a clustering-based initialization step that gives a reasonably accurate initial estimate of the true dictionary. This estimate is further improved via an iterative algorithm with the following alternating steps: 1) estimation of the dictionary coefficients for each observation through $\ell_1$ minimization, given the dictionary estimate and 2) estimation of the dictionary elements through least squares, given the coefficient estimates. We establish that, under a set of sufficient conditions, our method converges at a linear rate to the true dictionary as well as the true coefficients for each observation.
[Joint work with Anima Anandkumar, Prateek Jain, Praneeth Netrapalli and Rashish Tandon]
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Authors who are presenting talks have a * after their name.
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