Sparsity Optimization Method And Its Applications

Nowadays sparse optimization methods attract a great deal of interest in computer vision, imageprocessing, bioinformatics, and other fields. According to the structure and sparse form of data onactual application background, choosing suitable sparse optimization models and constructing suitablealgorithms can fast and efficiently solve problems. In this paper, we propose sparse optimizationmodels of vectors and matrices, design relevant algorithms applied to the problems of gene expressionanalysis and face recognition.For gene expression analysis, this paper designs methods from the angles of vector and matrix.In terms of vector, this paper integrates vector sparse representation with two-samplestatistical t-test to construct features from high-dimensional microarray data for classification ofdiseases. In the aspect of matrix, this paper proposes two joint roust methods with l2, p(0<p≤1)-normminimization, namely the inverse iteration method and the improved gradient projection method forgene expression analysis. The two algorithms can consistently solve l2, p(0<p≤1)-norm minimizationproblem. The convergences of the two algorithms are proved. Both the vector and matrix sparseoptimization methods properly reflect the characteristics of high-dimensional gene expression data,reduce the dimension by sparse linear combination, as well as use the discriminative power genes forclassification. The experiment results on three gene datasets demonstrate the good numericalperformance of our methods.For face recognition, this paper proposes a matrix sparse representation model based on l2,p(0<p<2)-norm, designs a iterative quadratic algorithm to consistently solve the l2,p(0<p<2)-normminimization problem, combines the matrix sparse representation iterative quadratic algorithm andthe nearest neighbor method to get a new method for face recognition. It is a kind of global sparserepresentation classification method, which incorporates the information of all the samples both in thetraining set and testing set; categorizes all test samples quickly at the same time; improves the speedand accuracy of classification. For the problem of contiguous occlusion, we propose a modular facerecognition method, which joints the matrix sparse representation iterative quadratic algorithm andthe nearest neighbor method. Numerical experiments on three classical face datasets show that theproposed algorithm is effective.