基于加权张量低秩约束的多视图谱聚类

doi:10.19678/j.issn.1000-3428.0068270

计算机工程 ›› 2024, Vol. 50 ›› Issue (1): 129-137. doi: 10.19678/j.issn.1000-3428.0068270

基于加权张量低秩约束的多视图谱聚类

刘思慧¹, 高全学², 宋伟³, 谢德燕¹^,*()

1. 青岛农业大学理学与信息科学学院, 山东青岛 266109
2. 西安电子科技大学通信工程学院, 陕西西安 710071
3. 深圳大学微纳光电子学研究院, 广东深圳 518060

收稿日期:2023-08-21 出版日期:2024-01-15 发布日期:2023-12-19
通讯作者: 谢德燕
基金资助:
国家自然科学基金面上项目(61875130); 国家自然科学基金面上项目(62175159); 山东省自然科学基金面上项目(ZR202102180986); 广东省自然科学基金面上项目(2023A1515012888); 深圳市基础研究重点项目(JCYJ20200109113808048); 青岛农业大学人才启动项目(665/1120051); 青岛农业大学博士基金(663/1122014); 深圳大学医工交叉研究基金(86901/00000311)

Multiview Spectral Clustering Based on Weighted Tensor Low-Rank Constraint

Sihui LIU¹, Quanxue GAO², Wei SONG³, Deyan XIE¹^,*()

1. School of Science and Information Science, Qingdao Agricultural University, Qingdao 266109, Shandong, China
2. School of Telecommunications Engineering, Xidian University, Xi'an 710071, Shaanxi, China
3. Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, Guangdong, China

Received:2023-08-21 Online:2024-01-15 Published:2023-12-19
Contact: Deyan XIE

摘要/Abstract

摘要：

现有基于图的多视图聚类方法通常难以同时考虑不同视图的潜在高阶相关信息和每个视图内的全局几何结构，导致聚类性能受限。为此，提出一种基于加权张量低秩约束的多视图谱聚类方法(WTLR-MSC)。根据多视图数据构建概率转移矩阵，将所有的概率转移矩阵构建为三阶张量，并借助鲁棒主成分分析思想将其分解为目标张量和误差张量。使用加权张量核范数约束目标张量的旋转张量，利用奇异值先验信息准确挖掘多视图数据的潜在高阶相关信息，并利用核范数约束目标张量的每个正切片以刻画每个视图内的全局几何结构。基于此建立数学模型，并设计有效的求解算法。在BBCSport、BBC4View、COIL20、UCI Digits 4个常用数据集上的实验结果表明，WTLR-MSC较ERLRT、MCA²M、MGL-WTNN等聚类方法的性能有显著提升，准确率、标准化互信息、F1值、精确率、召回率相较于次优方法最高提升约1.3、1.0、1.2、1.6和0.8个百分点，大幅增强了多视图聚类的稳健性。

关键词: 加权张量核范数, 谱聚类, 多视图谱聚类, 图学习, 张量低秩

Abstract:

Many existing multiview clustering methods fail to simultaneously exploit the high-order correlations embedded in different views and the global geometric structure of each single view, resulting in inadequate clustering performance. A Weighted Tensor Low-Rank constraint-based Multiview Spectral Clustering (WTLR-MSC) method is proposed in this study to address this limitation. First, a set of transition probability matrices are constructed from each single view. Second, a three-order tensor, which is decomposed into object and error tensors, is constructed using these matrices. The object tensor is rotated and constrained using the weighted tensor nuclear norm.Thus, the high-order correlations can be investigated efficiently. Simultaneously, the nuclear norm is applied to regularize each frontal slice of the object tensor to obtain the global geometric structure of each view. This study proposes an efficient optimization algorithm to solve the challenged mathematical optimization problem.Experiments on four datasets (BBCSport, BBC4View, COIL20, and UCI Digits) indicate that WTLR-MSC outperforms many state-of-the-art multiview methods, such as ERLRT, MCA2M, and MGL-WTNN. In terms of Accuracy (ACC), Normalized Mutual Information (NMI), F1-score, Precision, and Recall, WTLR-MSC improves by approximately 1.3, 1.0, 1.2, 1.6, and 0.8 percentage points, demonstrating an enhanced robustness of multiview clustering.

Key words: weighted tensor nuclear norm, Spectral Clustering(SC), Multiview Spectral Clustering(MSC), graph learning, tensor low-rank

刘思慧, 高全学, 宋伟, 谢德燕. 基于加权张量低秩约束的多视图谱聚类[J]. 计算机工程, 2024, 50(1): 129-137.

Sihui LIU, Quanxue GAO, Wei SONG, Deyan XIE. Multiview Spectral Clustering Based on Weighted Tensor Low-Rank Constraint[J]. Computer Engineering, 2024, 50(1): 129-137.

http://www.ecice06.com/CN/Y2024/V50/I1/129

图/表 10

图1 WTLR-MSC方法框架

Fig.1 Framework of WTLR-MSC method

图2 BBC4view数据集的聚类结果可视化

Fig.2 Visualization of the clustering results on the BBC4view dataset

图3 ACC随参数

$ {\lambda } $

和

$ {\alpha } $

的变化

Fig.3 Variation of ACC with parameters

$ {\lambda } $

and

$ {\alpha } $

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