计算机应用研究2024，Vol.41Issue(1)：72-75,158,5.DOI:10.19734/j.issn.1001-3695.2023.04.0219
面向矩阵秩函数准确估计的自表示子空间聚类方法
Low rank subspace clustering algorithm based on accurate estimation for matrix rank function
摘要
Abstract
Traditional subspace clustering methods usually replace the matrix rank function by the matrix kernel norm to re-cover the original low rank matrices.However,in the process of minimizing the matrix kernel norm,these algorithms pay too much attention to the calculation of the large singular values of the matrix,resulting in inaccurate estimation of the matrix rank.To this end,this paper analyzed the long tail distribution of matrix singular values and proposed a low rank subspace clustering model based on truncated Schatten-p norm.The proposed model fitted the long tail distribution of matrix singular va-lues well and toke full account of the contribution of small singular values to the process of low rank matrix recovery.The mo-del could make full use of small singular values to fit the long tail distribution of matrix singular values,ultimately achieved an accurate estimation of matrix rank function and improved the performance of subspace clustering.The experimental results show that,compared with the WNNM-LRR and BDR subspace clustering algorithms,the proposed method improves the cluste-ring accuracy by 11％and 8％on Extended Yale B dataset,respectively.The proposed method can better fit the distribution of data singular values and construct the similarity matrices more accurately.关键词
子空间聚类/长尾分布/小奇异值/截断Schatten-p范数/矩阵核范数Key words
subspace clustering/long-tailed distribution/small singular value/truncated Schatten-p norm/matrix norm分类
信息技术与安全科学引用本文复制引用
刘明明,羊远灿,杨研博,张海燕..面向矩阵秩函数准确估计的自表示子空间聚类方法[J].计算机应用研究,2024,41(1):72-75,158,5.基金项目
国家自然科学基金资助项目(61801198) （61801198）
江苏省自然科学基金资助项目(BK20180174) （BK20180174）
江苏省青蓝工程资助项目 （）
