Journal
IEEE SIGNAL PROCESSING LETTERS
Volume 20, Issue 12, Pages 1195-1198Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2013.2285218
Keywords
Dictionary learning; K-SVD; MOD; sparse representation
Categories
Funding
- Iran National Science Foundation (INSF) [91004600]
- European Project [2012-ERC-AdG-320684 CHESS]
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A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, Y, as the product of a dictionary, D, and a sparse coefficient matrix, X, as follows, Y similar or equal to DX. Current dictionary learning algorithms minimize the representation error subject to a constraint on D (usually having unit column-norms) and sparseness of X. The resulting problem is not convex with respect to the pair (D, X). In this letter, we derive a first order series expansion formula for the factorization, DX. The resulting objective function is jointly convex with respect to D and X. We simply solve the resulting problem using alternating minimization and apply some of the previously suggested algorithms onto our new problem. Simulation results on recovery of a known dictionary and dictionary learning for natural image patches show that our new problem considerably improves performance with a little additional computational load.
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