Chi CVPR 2013 - Block and Group Regularized Sparse Modeling for Dictionary Learning.pdf

Chi CVPR 2013 - Block and Group Regularized Sparse Modeling for Dictionary Learning.pdf

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Chi CVPR 2013 - Block and Group Regularized Sparse Modeling for Dictionary Learning

Block and Group Regularized Sparse Modeling for Dictionary Learning Yu-Tseh Chi?, Mohsen Ali?, Ajit Rajwade?, Jeffrey Ho? ?University of Florida, Gainesville, FL, U. S. A. ?Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India ?{ychi, moali, jho}@cise.ufl.edu, ?ajit rajwade@daiict.ac.in Abstract This paper proposes a dictionary learning framework that combines the proposed block/group (BGSC) or recon- structed block/group (R-BGSC) sparse coding schemes with the novel Intra-block Coherence Suppression Dictionary Learning (ICS-DL) algorithm. An important and distin- guishing feature of the proposed framework is that all dic- tionary blocks are trained simultaneously with respect to each data group while the intra-block coherence being ex- plicitly minimized as an important objective. We provide both empirical evidence and heuristic support for this fea- ture that can be considered as a direct consequence of in- corporating both the group structure for the input data and the block structure for the dictionary in the learning pro- cess. The optimization problems for both the dictionary learning and sparse coding can be solved efficiently using block-gradient descent, and the details of the optimization algorithms are presented. We evaluate the proposed meth- ods using well-known datasets, and favorable comparisons with state-of-the-art dictionary learning methods demon- strate the viability and validity of the proposed framework. 1. Introduction Sparse modeling and dictionary learning have emerged re- cently as an effective and popular paradigm for solving many important learning problems in computer vision. Its appeal stems from its underlying simplicity: given a col- lection of data X = {x1, · · · ,xl} ∈ Rn, learning can be formulated using an objective function of the form: Q(D,C;X) = ∑ g ‖X(g) ?DC(g)‖2F + λD Ψ(D) + λC Ω(C (g)), (1) where the X(g) are vectors/matrices generated from the data X, and Ψ,Ω are regularizers on the lear

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