低秩表示和加权核范数最小化的子空间聚类  

Subspace clustering based on low rank representation and weighted nuclear norm minimization

作　　者：宋昱 孙文赟 SONG Yu;SUN Wenyun(College of Electronics and Information Engineering,Shenzhen University,Shenzhen 518060,China;Shenzhen Key Laboratory of Media Security,Shenzhen University,Shenzhen 518060,China;Guangdong Key Laboratory of Intelligent Information Processing,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]深圳大学电子与信息工程学院,广东深圳518060 [2]深圳大学深圳市媒体信息内容安全重点实验室,广东深圳518060 [3]深圳大学广东省智能信息处理重点实验室,广东深圳518060

出　　处：《华中科技大学学报（自然科学版）》2021年第1期63-67,92,共6页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：中国博士后科学基金资助项目(2019M663068);广东省基础与应用基础研究基金资助项目(2019A1515110425);广东省自然科学基金资助项目(2020A1515010563);深圳市科技计划资助项目(JCYJ20180305124550725)。

摘　　要：为了进一步提升基于核范数和F范数最小化的子空间聚类算法的性能,使用加权核范数扩展上述两种范数.提出的算法中含有一个参数γ,当γ=0时,可得到核范数;当γ=1时,可得到F范数;当0<γ<1时,可得到介于核范数和F范数之间的范数.采用交替方向乘子方法和线性交替方向乘子方法求解所提算法的目标函数,并由此得到了2个基于加权核范数最小化的低秩子空间聚类算法.利用Extended Yale B人脸数据集、MNIST手写字符数据集和USPS手写字符数据集进行实验.实验结果表明:和现有的子空间聚类方法相比,所提算法可以得到较高的聚类精度.To further improve the performance of existing subspace clustering algorithm based on nuclear norm or Frobenius norm minimization,the weighted nuclear norm is proposed to generalize the above two norms.There is a parameter in the proposed algorithm which is γ.When γ=0,the weighted nuclear norm becomes nuclear norm and when γ=1,the weight nuclear norm becomes Frobenius norm.When 0 <γ<1,a norm between nuclear norm and Frobenius norm can be obtained.The objective function of the proposed algorithm is solved by alternating direction method of multipliers and linearized alternating direction method of multipliers.Two low rank subspace clustering algorithms based on weighted nuclear norm minimization are thus obtained.The experiments are performed using the Extended Yale B face dataset,MNIST handwritten digit dataset and USPS handwritten digit dataset.Experimental results show that,compared to existing subspace clustering algorithms,the proposed algorithm can obtain the highest clustering accuracy.

关 键 词：子空间聚类 低秩表示 加权核范数最小化 线性交替方向乘子方法 奇异值分解 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]