基于多样性和谱嵌入的张量多视图子空间聚类  

Tensor Multi-view Subspace Clustering Based onDiversity and Spectral Embedding

作　　者：张沙沙 王长鹏 ZHANG Shasha;WANG Changpeng(School of Sciences,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《吉林大学学报(理学版)》2025年第2期499-512,共14页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12471480);长安大学中央高校基本科研业务费专项基金(批准号:300102122101)。

摘　　要：针对如何有效利用多视图的多样性信息和高阶信息,并建立系数矩阵的学习过程与谱聚类之间联系的问题,提出一种基于多样性和谱嵌入的张量多视图子空间聚类算法.首先,在自表示张量部分采用张量自适应对数行列式正则化,从而能根据奇异值的大小自适应地选择逼近函数.其次,采用Hilbert-Schmidt独立准则衡量多样性,以确保不同视图的系数表示矩阵具有足够的多样性.再次,为避免谱聚类过程的独立进行,将其引入模型中联合学习,使低秩张量学习、多样性学习和谱嵌入学习在一个统一的框架内进行.最后,通过在5个真实数据集上与10种优秀算法进行比较,验证了该算法在提升聚类性能方面的有效性.Aiming at how to effectively utilize the diversity information and higher-order information of multi-views,and establish the connection between the learning process of coefficient matrices and spectral clustering,we proposed a tensor multi-view subspace clustering algorithm based on diversity and spectral embedding.Firstly,the algorithm used tensor adaptive log-determinant regularization in the self-representation tensor part,which could adaptively select the approximation function according to the size of the singular values.Secondly,the Hilbert-Schmidt independence criterion was used to measure diversity to ensure that the coefficient representation matrices from different views exhibited sufficient diversity.Thirdly,in order to avoid the spectral clustering process to be performed independently,it was introduced into the model for joint learning,so that the low-rank tensor learning,diversity learning and spectral embedding learning were performed in a unified framework.Finally,the effectiveness of the algorithm in improving the clustering performance was verified by comparing it with ten excellent algorithms on five real datasets.

关 键 词：多视图子空间聚类 张量自适应对数行列式 多样性 谱嵌入 Hilbert-Schmidt独立准则 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]