Projective dictionary pair learning for pattern classification.pdf

Projective dictionary pair learning for pattern classification Shuhang Gu1, Lei Zhang1, Wangmeng Zuo2, Xiangchu Feng3 1Dept. of Computing, The Hong Kong Polytechnic University, Hong Kong, China 2School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China 3Dept. of Applied Mathematics, Xidian University, Xi′an, China {cssgu, cslzhang}@.hk cswmzuo@, xcfeng@ Abstract Discriminative dictionary learning (DL) has been widely studied in various pattern classification problems. Most of the existing DL methods aim to learn a synthesis dictionary to represent the input signal while enforcing the representation coef- ficients and/or representation residual to be discriminative. However, the `0 or `1-norm sparsity constraint on the representation coefficients adopted in most DL methods makes the training and testing phases time consuming. We propose a new discriminative DL framework, namely projective dictionary pair learning (DPL), which learns a synthesis dictionary and an analysis dictionary jointly to achieve the goal of signal representation and discrimination. Compared with convention- al DL methods, the proposed DPL method can not only greatly reduce the time complexity in the training and testing phases, but also lead to very competitive accuracies in a variety of visual classification tasks. 1 Introduction Sparse representation represents a signal as the linear combination of a small number of atoms cho- sen out of a dictionary, and it has achieved a big success in various image processing and computer vision applications [1, 2]. The dictionary plays an important role in the signal representation process [3]. By using a predefined analytical dictionary (e.g., wavelet dictionary, Gabor dictionary) to rep- resent a signal, the representation coefficients can be produced by simple inner product operations. Such a fast and explicit coding makes analytical dictionary very attractive in image representation; however, it is less effective to model