# American Institute of Mathematical Sciences

December  2015, 8(6): 1385-1400. doi: 10.3934/dcdss.2015.8.1385

## Weighted two-phase supervised sparse representation based on Gaussian for face recognition

 1 College of Computer Science & Technology, Zhejiang University of Technology, Hang Zhou, China, China

Received  April 2015 Revised  September 2015 Published  December 2015

As recently newly techniques, two-phase sparse representation algorithms have been presented, which achieve an excellent performance in face recognition via different phase sparse representation, capturing more local structural information of samples. However, there are some defects in these algorithms:1) The Euclidean distance metric applied in these algorithms fails to capture nonlinear structural information, leading to that the performance of these algorithms is sensitive to the geometric structure of facial images. 2) To select the m nearest neighbors of the test sample is achieved directly by applying sparse representation in training samples, which ignores prior information to construct the sparse representation model. In order to solve these problems, a Weighted Two-Phase Supervised Sparse Representation based on Gaussian (GWTPSSR) algorithm is proposed on basic of existing two-phase sparse representation algorithm, in which the nonlinear local information of samples is captured by exploiting effectively the Gaussian distance metric instead of the Euclidean distance metric. Besides, GWTPSSR recreates reconstruction set from training samples in the sparse representation model for each test sample, making full use of prior information to eliminate some training samples far from the test sample. Compared with existing two-phase sparse representation algorithms, experimental results on standard face datasets show that GWTPSSR has better robustness and classification performance.
Citation: Shuhua Xu, Fei Gao. Weighted two-phase supervised sparse representation based on Gaussian for face recognition. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1385-1400. doi: 10.3934/dcdss.2015.8.1385
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