Self-Constrained Spectral Clustering

As a leading graph clustering technique, spectral clustering is one of the most widely used clustering methods to capture complex clusters in data. Some additional prior information can help it to further reduce the difference between its clustering results and users' expectations. However, it is hard to get the prior information under unsupervised scene to guide the clustering process. To solve this problem, we propose a self-constrained spectral clustering algorithm. In this algorithm, we extend the objective function of spectral clustering by adding pairwise and label self-constrained terms to it. We provide the theoretical analysis to show the roles of the self-constrained terms and the extensibility of the proposed algorithm. Based on the new objective function, we build an optimization model for self-constrained spectral clustering so that we can simultaneously learn the clustering results and constraints. Furthermore, we propose an iterative method to solve the new optimization problem. Compared to other existing versions of spectral clustering algorithms, the new algorithm can discover a high-quality cluster structure of a data set without prior information. Extensive experiments on benchmark data sets illustrate the effectiveness of the proposed algorithm.