Triangle sparse regression and its application in robust face recognition
Zheng Wei1，2，Yang Wankou3，Shao Fei1*，Zhao Wei1
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1. School of Computer Engineering，Jinling Institute of Technology，Nanjing，211169，China； 2．School of Computer Science and Engineering，Nanjing University of Science and Technology，Nanjing，210094，China； 3．School of Automation，Southeast University，Nanjing，210096，China
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Published
2017-11-27
Issue Date
2017-11-27
Abstract
Regression－based classifiers(e.g.Sparse Representation Classifier)have shown the promising performances in several classification tasks with Gaussian noise.However，they are sensitive to the impacts from outlier points in the training data，and lead to underfitting or overfitting results.Exploring the insensitivity of trigonometry functions in one period，the cosine function is employed to measure the fitting residuals of regressions.Considering the non－convexity of the cosine function，directly optimizations are not able to achieve the global minimizer.Therefore，the proposed Triangle Sparse Regression Classifier(TSRC)is transformed to a convex problem by trigonometry and kernel tricks.Subsequently，Alternating Direction Method of Multipliers(ADMM)method is used to solve the proposed model.The provided calculations reveal the robustness of TSRC，and eliminate the complex numbers in optimizations，by virtue of the Euler－Equation.Hence the optimization is only operated in the real numbers field，and thus obtain the efficiency algorithm.Finally，experiments on AR，Extend－YaleB and NUST－RF datasets(with various occlusions and illumination changes)validate the accuracy of the proposed methods，and the running time is illustrated on the variations of samples size of Extend－YaleB dataset，compared with the state－of－the－art regression methods.
Zheng Wei1，2，Yang Wankou3，Shao Fei1*，Zhao Wei1.
Triangle sparse regression and its application in robust face recognition[J]. Journal of Nanjing University(Natural Sciences), 2017, 53(6): 1091
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References
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