基于l_(2,0)范数稀疏性和模糊相似性的图优化无监督组特征选择方法

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

基于图的无监督特征选择方法大多选择投影矩阵的l_(2,1)范数稀疏正则化代替非凸的l_(2,0)范数约束,然而l_(2,1)范数正则化方法根据得分高低逐个选择特征,未考虑特征的相关性.因此,文中提出基于l_(2,0)范数稀疏性和模糊相似性的图优化无监督组特征选择方法,同时进行图学习和特征选择.在图学习中,学习具有精确连通分量的相似性矩阵.在特征选择过程中,约束投影矩阵的非零行个数,实现组特征选择.为了解决非凸的l_(2,0)范数约束,引入元素为0或1的特征选择向量,将l_(2,0)范数约束问题转化为0-1整数规划问题,并将离散的0-1整数约束转化为2个连续约束进行求解.最后,引入模糊相似性因子,拓展文中方法,学习更精确的图结构.在真实数据集上的实验表明文中方法的有效性.

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.