基于改进Trace Lasso范数和PALM算法的子空间聚类方法  

Subspace Clustering Based on Improved Trace Lasso Norm and PALM Algorithm

作　　者：药嘉怡 张文娟 黄姝娟[2] 袁薛程 YAO Jiayi;ZHANG Wenjuan;HUANG Shujuan;YUAN Xuecheng(College of Sciences,Xi'an Technological University,Xi'an 710016,China;College of Computer Science and Information Engineering,Xi'an Technological University,Xi'an 710016,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：《内蒙古师范大学学报(自然科学版)》2025年第1期92-100,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“面向视觉注意选择的复杂场景层次化语义理解建模研究”(62171361)。

摘　　要：子空间聚类是一类广泛应用的聚类方法,其中最关键的技术是表示矩阵的获取,为使表示矩阵更好地满足块对角结构,提出一种基于改进迹Lasso范数和PALM算法的子空间聚类方法。首先,将原始数据减去噪声所得干净数据作为数据自表示的字典,能够促使表示矩阵更接近块对角结构;其次,提出一种改进的迹Lasso范数,利用非凸FCP范数约束矩阵的奇异值向量,能更好促使矩阵满足低秩性;最后,由于提出模型的非凸非光滑性及约束条件的非线性,利用近端交替线性极小化算法求解模型,具有收敛性保证。在CFP人脸数据集和动物面部图像数据集上进行聚类的数值实验表明,提出的子空间聚类方法相比于普遍应用的K‐means聚类、谱聚类及稀疏子空间聚类有更好的聚类性能。Subspace clustering is a widely used clustering method,in which the most critical technology is representation matrix acquisition.To make the representation matrix better fit the block-diagonal structure,this study proposes a subspace clustering method based on an improved trace Lasso norm and the proximal alternating linearized minimization(PALM)algorithm.Firstly,the clean data obtained by subtracting the noise from the original data is used as the dictionary of data self-representation,which makes the representation matrix closer to the block-diagonal structure.Secondly,an improved trace Lasso norm is proposed.It utilizes a non-convex FCP norm to constrain the singular value vector of the matrix,so that the matrix can be better promoted to satisfy the low rank.Finally,due to the non-convexity and non-smoothness of the proposed model and the nonlinearity of the constraint conditions,the PALM algorithm is used to solve the model,which ensures convergence.Numerical experiments of clustering on the CFP face dataset and an animal face image dataset show that the proposed subspace clustering method outperforms the commonly used K-means clustering,spectral clustering,and sparse subspace clustering(SSC).

关 键 词：子空间聚类 迹Lasso范数 非凸FCP范数 近端交替线性最小化 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]