Hypergraph regularized multi-view subspace clustering with dual tensor log-determinant  

具有双张量对数行列式的超图正则化多视图子空间聚类

作　　者：HU Keyin LI Ting GE Hongwei 胡克寅;李婷;葛洪伟(江南大学人工智能与计算机学院,江苏无锡214122;江南大学康养智能化技术教育部工程研究中心,江苏无锡214122)

机构地区：[1]School of Artificial Intelligence and Computer Science,Jiangnan University,Wuxi 214122,China [2]Engineering Research Center of Intelligent Technology for Healthcare,Ministry of Education,Jiangnan University,Wuxi 214122,China

出　　处：《Journal of Measurement Science and Instrumentation》2024年第4期466-476,共11页测试科学与仪器（英文版）

基　　金：supported by National Natural Science Foundation of China(No.61806006);Priority Academic Program Development of Jiangsu Higher Education Institutions。

摘　　要：The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.基于张量奇异值分解的多视图子空间聚类算法,大多利用张量核范数探索同一样本视图内的相关性,而忽略了不同视图中样本之间的相关性,并且没有充分考虑张量核范数作为张量秩函数的凸近似,平等地对待不同的奇异值会导致张量表示次优。本文提出了一种具有双张量对数行列式的超图正则化多视图子空间聚类算法(HRMSC-DTL)。首先,通过在每个视图中使用子空间学习来研究一组特定的亲和矩阵,并引入非凸张量对数行列式函数来替代张量核范数,以更好地提高全局低秩性。其次,引入了超拉普拉斯正则化,以保持嵌入在高维空间中的局部几何结构。此外,还对原始张量进行旋转,并引入双张量机制,以充分利用原始张量的视图内相关性和旋转张量的视图间相关性。同时,还设计了一种乘子交替方法(ADMM)来求解非凸优化模型。在7个广泛使用的数据集上进行实验,并与几个主流算法进行比较,实验结果证明了HRMSC-DTL算法在聚类效果上具有一定的优越性和有效性。

关 键 词：multi-view clustering tensor log-determinant function subspace learning hypergraph regularization 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]