Generalized weak sharp minima of variational inequality problems with functional constraints
Wenyan Zhang Shu Xu Shengji Li Xuexiang Huang
In this paper, the notion of generalized weak sharp minima is introduced for variational inequality problems with functional constraints in finite-dimensional spaces by virtue of a dual gap function. Some equivalent and necessary conditions for the solution set of the variational inequality problems to be a set of generalized weak sharp minima are obtained.
keywords: Robinson's constraint qualification. dual gap function Variational inequality problems generalized weak sharp minima
Weighted two-phase supervised sparse representation based on Gaussian for face recognition
Shuhua Xu Fei Gao
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.
keywords: face recognition. Gaussian kernel distance prior information local structure Sparse representation

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