Global and Local Structure Preservation for Nonlinear High-dimensional Spectral Clustering

• Published in: Computer journal Vol. 64; no. 7; pp. 993 - 1004
• Main Authors: Wen, Guoqiu, Zhu, Yonghua, Chen, Linjun, Zhan, Mengmeng, Xie, Yangcai
• Format: Journal Article
• Language: English
• Published: Oxford University Press 24.08.2021
• Subjects: similarity matrix learning; nonlinear learning; dimensionality reduction; spectral clustering
• ISSN: 0010-4620; 1460-2067
• DOI: 10.1093/comjnl/bxab020

Abstract Spectral clustering is widely applied in real applications, as it utilizes a graph matrix to consider the similarity relationship of subjects. The quality of graph structure is usually important to the robustness of the clustering task. However, existing spectral clustering methods consider either the local structure or the global structure, which can not provide comprehensive information for clustering tasks. Moreover, previous clustering methods only consider the simple similarity relationship, which may not output the optimal clustering performance. To solve these problems, we propose a novel clustering method considering both the local structure and the global structure for conducting nonlinear clustering. Specifically, our proposed method simultaneously considers (i) preserving the local structure and the global structure of subjects to provide comprehensive information for clustering tasks, (ii) exploring the nonlinear similarity relationship to capture the complex and inherent correlation of subjects and (iii) embedding dimensionality reduction techniques and a low-rank constraint in the framework of adaptive graph learning to reduce clustering biases. These constraints are considered in a unified optimization framework to result in one-step clustering. Experimental results on real data sets demonstrate that our method achieved competitive clustering performance in comparison with state-of-the-art clustering methods.