基于Schatten-p范数的深度可学习子空间聚类方法  

Deep Learnable Subspace Clustering Method Based on Schatten-p Norm

作　　者：药嘉怡 张文娟 沈超 黄姝娟[2] 袁薛程 YAO Jiayi;ZHANG Wenjuan;SHEN Chao;HUANG Shujuan;YUAN Xuecheng(College of Sciences,Xi’an Technological University,Xi’an 710016,Shaanxi,China;College of Computer Science and Information Engineering,Xi’an Technological University,Xi’an 710016,Shaanxi,China)

机构地区：[1]西安工业大学基础学院,陕西西安710016 [2]西安工业大学计算机科学与工程学院,陕西西安710016

出　　处：《咸阳师范学院学报》2025年第2期6-12,共7页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(52302505)。

摘　　要：针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低秩正则项,使得子空间聚类系数矩阵更好地满足低秩结构;其次,利用Schatten-p范数的矩阵分解格式,避免了SVD计算代价大的不足;最后,针对传统优化算法须人为调整参数的问题,根据激活函数和稀疏正则项的对应关系,建立深度学习网络框架,通过数据自适应学习得到最优参数集。在MNIST手写数字、Amsterdam Library of Object Images和ORL人脸三个数据集上进行聚类的数值实验,结果表明:提出的子空间聚类算法相比于谱聚类、低秩子空间聚类和稀疏子空间聚类算法有更好的聚类性能。To solve the problem that nuclear norm regularized constraints result in insufficient low-rank property of the matrix,SVD decomposition incurs a high computational cost for large-scale data,and traditional optimization algorithms require manual tuning of optimal parameters,a deep learnable subspace clustering algorithm based on Schatten-p norm and PALM is proposed.Firstly,by adopting the Schatten-p norm as the low-rank regularization term,the coefficient matrix of subspace clustering can better conform to the low-rank structure.Secondly,the matrix decomposition property of the Schatten-p norm is exploited to overcome the high computational cost drawback associated with SVD.Finally,to address the problem of manual parameter adjustment in traditional optimization algorithms,a deep learning network framework is established by leveraging the correspondence between activation functions and sparse regularization terms,and the optimal parameter set is obtained through data-driven adaptive learning.Numerical experiments for clustering on three datasets,namely MNIST handwritten digits,Amsterdam Library of Object Images,and ORL faces,demonstrate that the proposed subspace clustering algorithm exhibits better clustering performance compared with spectral clustering,low-rank subspace clustering,and sparse subspace clustering algorithms.

关 键 词：子空间聚类 Schatten-p范数 近端交替线性最小化 深度学习 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]