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Unsupervised Group Feature Selection Method for Graph Optimization Based on l_(2,0)-norm Sparsity and Fuzzy Similarity

MENG Tiantian;ZHOU Shuisheng;TIAN Xinrun;School of Mathematics and Statistics, Xidian University;  
Most graph-based unsupervised feature selection methods choose l_(2,1)-norm sparse regularization of the projection matrix instead of non-convex l_(2,0)-norm constraint. However, the l_(2,1)-norm regularization method selects features one by one according to the scores, without considering the correlation of features. Therefore, an unsupervised group feature selection method for graph optimization based on l_(2,0)-norm sparsity and fuzzy similarity is proposed, and it simultaneously performs graph learning and feature selection. In graph learning, the similarity matrix with exact connected components is learned. In the process of feature selection, the number of non-zero rows of projection matrix is constrained to realize group feature selection. To solve the non-convex l_(2,0)-norm constraint, the feature selection vector with elements of 0 or 1 is introduced to transform the l_(2,0)-norm constraint problem into 0-1 integer programming problem, and the discrete 0-1 integer constraint is transformed into two continuous constraints to solve the problem. Finally, fuzzy similarity factor is introduced to extend the method and learn more accurate graph structure. Experiments on real datasets show the effectiveness of the proposed method.
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