自适应张量奇异值收缩的多视角聚类  

Multi-View Clustering Based on Adaptive Tensor Singular Value Shrinkage

作　　者：钱罗雄 陈梅[1] 马学艳 张弛 张锦宏 Qian Luoxiong;Chen Mei;Ma Xueyan;Zhang Chi;Zhang Jinhong(School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070)

机构地区：[1]兰州交通大学电子与信息工程学院,兰州730070

出　　处：《计算机研究与发展》2025年第3期733-750,共18页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(62266029);甘肃省重点研发计划项目(21YF5GA053);甘肃省高等学校产业支撑计划项目(2022CYZC-36)。

摘　　要：现有多视角聚类算法存在:1)在学习低维表征的过程中无法准确捕获或忽略嵌入在多视角数据中的高阶信息和互补信息;2)未能准确捕获数据局部信息;3)信息捕获方法缺少对噪声点鲁棒性等问题.为解决上述问题,提出一种自适应张量奇异值收缩的多视角聚类(multi-view clustering based on adaptive tensor singular value shrinkage,ATSVS)算法.ATSVS首先提出一种符合秩特性的张量对数行列式函数对表示张量施加低秩约束,在张量奇异值分解(tensor singular value decomposition,t-SVD)过程中能够根据奇异值自身大小进行自适应收缩,更加准确地进行张量秩估计,进而从全局角度精准捕获多视角数据的高阶信息和互补信息.然后采用一种结合稀疏表示和流形正则技术优势的l_(1,2)范数捕获数据的局部信息,并结合l_(2,1)范数对噪声施加稀疏约束,提升算法对噪声点的鲁棒性.与11个对比算法在9个数据集上的实验结果显示,ATSVS的聚类性能均优于其他对比算法.因此,ATSVS是一个能够有效处理多视角数据聚类任务的优秀算法.The existing multi-view clustering algorithms exhibit limitations in accurately capturing the high-order information and complementary information embedded in multi-view data during the low-dimensional representations learning process. Meanwhile, these algorithms fail to capture the local information of data, and their information extraction methods lack robustness to noise and outliers. To address these challenges, an adaptive tensor singular value shrinkage multi-view clustering algorithm named ATSVS is proposed. ATSVS proposes a novel tensor log-determinant function to enforce the low-rank constraint on the representation tensor, which can adaptively enable adaptive shrinkage of singular values based on their magnitude. Consequently, ATSVS effectively captures high-order information and complementary information within multi-view data from the global perspective. Then, ATSVS captures the local information of the data by using the l_(1,2) norm that combines the advantages of sparse representation and manifold regularization technology, while improving the robustness of the algorithm to noisy points by combining with l_(2,1) norms to impose sparse constraints on the noise. The experimental results with eleven comparison algorithms on nine different types of datasets show that our proposed algorithm ATSVS has the superior clustering performance, outperforming state-of-the-art baselines significantly. Consequently, ATSVS is an excellent algorithm that can effectively handle the task of clustering multi-view data.

关 键 词：张量表示 聚类 低秩约束 多视角聚类 奇异值分解 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]