Multiple Kernel Clustering With Global and Local Structure Alignment

Abstract

Multiple kernel clustering (MKC) based on global structure alignment (GSA) has unified many existing MKC algorithms, and shown outstanding clustering performance. However, we observe that most of existing GSA-based MKC algorithms only maximally align global structure of data with an ideal similarity matrix, while ignoring the local geometrical structure hidden in data, which is regarded to be important in improving the clustering performance. To address this issue, we propose a global and local structure alignment framework for MKC (GLSAMKC) which well considers both the alignment between the global structure and local structure of data with the same ideal similarity matrix. To illustrate the effectiveness of the proposed framework, we instantiate two specific GLSAMKC-based algorithms by exploiting the local structure with local linear embedding and locality preserving projection, respectively. A two-step alternate iterative and convergent optimization algorithm is developed to implement the resultant optimization problem. Extensive experimental results on five benchmark data sets demonstrate the superiority of proposed algorithms compared with the many state-of-the-art MKC algorithms, indicating the effectiveness of the proposed framework.