融合局部结构学习的大规模子空间聚类算法  

Large-scale subspace clustering algorithm with Local structure learning

作　　者：任奇泽 贾洪杰 陈东宇 REN Qize;JIA Hongjie;CHEN Dongyu(School of Computer Science and Communication Engineering,Jiangsu University,Zhenjiang Jiangsu 212013,China)

机构地区：[1]江苏大学计算机科学与通信工程学院,江苏镇江212013

出　　处：《计算机应用》2023年第12期3747-3754,共8页journal of Computer Applications

基　　金：国家自然科学基金资助项目(61906077)。

摘　　要：常规的大规模子空间聚类算法在计算锚点亲和矩阵时忽略了数据之间普遍存在的局部结构,且在计算拉普拉斯(Laplacian)矩阵的近似特征向量时存在较大误差,不利于数据聚类。针对上述问题,提出一种融合局部结构学习的大规模子空间聚类算法(LLSC)。所提算法将局部结构学习嵌入锚点亲和矩阵的学习,从而能够综合利用全局和局部信息挖掘数据的子空间结构;此外,受非负矩阵分解(NMF)的启发,设计一种迭代优化方法以简化锚点亲和矩阵的求解过程;其次,根据Nystr?m近似方法建立锚点亲和矩阵与Laplacian矩阵的数学联系,并改进Laplacian矩阵特征向量的计算方法以提升聚类性能。相较于LMVSC(Large-scale Multi-View Subspace Clustering)、SLSR(Scalable Least Square Regression)、LSC-k(Landmark-based Spectral Clustering using k-means)和k-FSC(k-Factorization Subspace Clustering),LLSC在4个广泛使用的大规模数据集上显示出明显的提升,其中,在Pokerhand数据集上,LLSC的准确率比k-FSC高28.18个百分点,验证了LLSC的有效性。The conventional large-scale subspace clustering methods ignore the local structure that prevails among the data when computing the anchor affinity matrix,and have large error when calculating the approximate eigenvectors of the Laplacian matrix,which is not conducive to data clustering.Aiming at the above problems,a Large-scale Subspace Clustering algorithm with Local structure learning(LLSC)was proposed.In the proposed algorithm,the local structure learning was embedded into the learning of anchor affinity matrix,which was able to comprehensively use global and local information to mine the subspace structure of data.In addition,inspired by Nonnegative Matrix Factorization(NMF),an iterative optimization method was designed to simplify the solution of anchor affinity matrix.Then,the mathematical relationship between the anchor affinity matrix and the Laplacian matrix was established according to the Nyström approximation method,and the calculation method of the eigenvectors of the Laplacian matrix was modified to improve the clustering performance.Compared to LMVSC(Large-scale Multi-View Subspace Clustering),SLSR(Scalable Least Square Regression),LSC-k(Landmark-based Spectral Clustering using k-means),and k-FSC(k-Factorization Subspace Clustering),LLSC demonstrates significant improvements on four widely used large-scale datasets.Specifically,on the Pokerhand dataset,the accuracy of LLSC is 28.18 points percentage higher than that of k-FSC.These results confirm the effectiveness of LLSC.

关 键 词：子空间聚类 局部结构学习 非负矩阵分解 大规模聚类 低秩近似 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] TP311.13[自动化与计算机技术—控制科学与工程]