聚类分析
子空间拓扑
数学
张量(固有定义)
奇异值
矩阵范数
拉普拉斯矩阵
奇异值分解
规范(哲学)
拉普拉斯算子
人工智能
模式识别(心理学)
计算机科学
算法
特征向量
纯数学
数学分析
物理
量子力学
政治学
法学
作者
Qingjiang Xiao,Shiqiang Du,Yongping Yu,Yixuan Huang,Jinmei Song
出处
期刊:Journal of Intelligent and Fuzzy Systems
[IOS Press]
日期:2022-04-28
卷期号:42 (6): 5809-5822
被引量:2
摘要
In recent years, tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm has achieved remarkable progress in multi-view subspace clustering. However, most existing clustering methods still have the following shortcomings: (a) It has no meaning in practical applications for singular values to be treated equally. (b) They often ignore that data samples in the real world usually exist in multiple nonlinear subspaces. In order to solve the above shortcomings, we propose a hyper-Laplacian regularized multi-view subspace clustering model that joints representation learning and weighted tensor nuclear norm constraint, namely JWHMSC. Specifically, in the JWHMSC model, firstly, in order to capture the global structure between different views, the subspace representation matrices of all views are stacked into a low-rank constrained tensor. Secondly, hyper-Laplace graph regularization is adopted to preserve the local geometric structure embedded in the high-dimensional ambient space. Thirdly, considering the prior information of singular values, the weighted tensor nuclear norm (WTNN) based on t-SVD is introduced to treat singular values differently, which makes the JWHMSC more accurately obtain the sample distribution of classification information. Finally, representation learning, WTNN constraint and hyper-Laplacian graph regularization constraint are integrated into a framework to obtain the overall optimal solution of the algorithm. Compared with the state-of-the-art method, the experimental results on eight benchmark datasets show the good performance of the proposed method JWHMSC in multi-view clustering.
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