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模式识别与人工智能  2023, Vol. 36 Issue (1): 34-48    DOI: 10.16451/j.cnki.issn1003-6059.202301003
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基于l2,0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
孟田田1, 周水生1, 田昕润1
1.西安电子科技大学 数学与统计学院 西安 710071
Unsupervised Group Feature Selection Method for Graph Optimization Based on l2,0-norm Sparsity and Fuzzy Similarity
MENG Tiantian1, ZHOU Shuisheng1, TIAN Xinrun1
1. School of Mathematics and Statistics, Xidian University, Xi'an 710071

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摘要 基于图的无监督特征选择方法大多选择投影矩阵的l2,1范数稀疏正则化代替非凸的l2,0范数约束,然而l2,1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l2,0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l2,0范数约束,引入元素为0或1的特征选择向量,将l2,0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.
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关键词 无监督特征选择0-1整数规划图优化稀疏学习    
Abstract:Most graph-based unsupervised feature selection methods choose l2,1-norm sparse regularization of the projection matrix instead of non-convex l2,0-norm constraint. However, the l2,1-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 l2,0-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 l2,0-norm constraint, the feature selection vector with elements of 0 or 1 is introduced to transform the l2,0-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.
Key wordsKey Words Unsupervised Feature Selection    0-1 Integer Programming    Graph Optimization    Sparse Learning   
收稿日期: 2022-10-23     
ZTFLH: TP391  
通讯作者: 周水生,博士,教授,主要研究方向为最优化理论与算法、模式识别及应用、智能信息处理、机器学习等.E-mail:sszhou@mail.xidian.edu.cn.   
作者简介: 孟田田,硕士研究生,主要研究方向为机器学习、最优化理论与算法.E-mail:mengtiatian7@163.com. 田昕润,硕士研究生,主要研究方向为最优化计算理论与算法、模式识别及应用.E?mail:xrtian_1@stu.xidian.edu.cn.
引用本文:   
孟田田, 周水生, 田昕润. 基于l2,0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[J]. 模式识别与人工智能, 2023, 36(1): 34-48. MENG Tiantian, ZHOU Shuisheng, TIAN Xinrun. Unsupervised Group Feature Selection Method for Graph Optimization Based on l2,0-norm Sparsity and Fuzzy Similarity. Pattern Recognition and Artificial Intelligence, 2023, 36(1): 34-48.
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