低秩张量分解的多视角谱聚类算法  

Multi-View Clustering by Low-Rank Tensor Decomposition

作　　者：程士卿 郝问裕 李晨[1] 张茁涵 曹容玮 CHENG Shiqing;HAO Wenyu;LI Chen;ZHANG Zhuohan;CAO Rongwei(School of Software Engineering,Xi’an Jiaotong University,Xi’an 710049,China;State Key Laboratory of Rail Transit Engineering Informatization(FSDI),Xi’an 710043,China)

机构地区：[1]西安交通大学软件学院,西安710049 [2]轨道交通工程信息化国家重点实验室(中铁一院),西安710043

出　　处：《西安交通大学学报》2020年第3期119-125,133,共8页Journal of Xi'an Jiaotong University

基　　金：轨道交通工程信息化国家重点实验室（中铁一院）资助项目（SKLK19-07）;国家自然科学基金资助项目（61573273）

摘　　要：针对传统多视角学习算法只关注从多视角中提取共享信息而忽略了各视角的特有信息和高阶关联的问题,提出了一种基于截断核范数的低秩张量分解的多视角谱聚类算法。计算各视角的样本相似度矩阵和转移概率矩阵,构建一个包含各视角马尔可夫转移概率矩阵的张量,从而保留各个视角的信息。采用基于张量奇异值分解的截断核范数约束目标张量的秩。通过最小化张量截断核范数,学习到一个既包含各个视角共享信息又具有高阶关联的张量。利用迭代最优化算法求解目标函数,将求得的目标张量输入谱聚类算法得到聚类结果。在4个不同类型数据集上进行实验并与传统聚类算法进行了对比,结果表明:所提算法在4个数据集上的标准互信息度量值比标准谱聚类算法的分别提高了7.9%、24.9%、29.5%、8.1%,比LT-MSC算法的分别提高了3.4%、18.1%、17.6%、6.6%。通过对非负平衡参数在0.000 1~100之间的测试发现,所提算法表现基本稳定,在非负平衡参数取0.1~1之间表现良好。与传统多视角聚类算法相比,所提算法可有效增强各视角之间的互补性和高阶关联,并且具有良好的准确性和鲁棒性。To solve the problem that the traditional multi-view learning methods cannot fully explore the consensus information among different views,a low-rank tensor decomposition multiview spectral clustering algorithm based on truncated nuclear norm is proposed.The similarity matrix and transition probability matrix of each view are firstly obtained,then a tensor based on multi-view transition probability matrices is constructed.Tensor singular value decomposition based tensor truncated nuclear norm is imposed to preserve the low-rank property of the common tensor.Minimizing the tensor truncated kernel norm,a tensor containing both shared information and high-order correlations can be obtained properly via learning.The proposed method can be efficiently optimized by the alternating direction method of multipliers.Experimental results on 4 datasets show that compared with standard spectral clustering,the value of normalized mutual information is enhanced by 7.9%,24.9%,29.5% and 8.1% respectively,and 3.4%,18.1%,17.6%and 6.6%respectively compared with LT-MSC.It is found that the performance of the proposed method only has small variations when trade-off parameter is chosen from 0.000 1 to100,and the best trade-off parameter is ranged from 0.1 to 1.The proposed method has good clustering effect and robustness,and can effectively enhance the complementarity between the various perspectives.

关 键 词：多视角谱聚类 张量 截断核范数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]