Spectral clustering with robust self-learning constraints

Abstract

Spectral clustering is a leading unsupervised classification algorithm widely used to capture complex clusters in unlabeled data. Additional prior information can further enhance the quality of spectral clustering results to satisfy users' expectations. However, it is challenging for users to find the prior information under unsupervised scenes. To get rid of the deficiency, we propose a spectral clustering model with robust self-learning constraints. In this model, we first extend the optimization problem of spectral clustering by seeing label constraints as variables to learn the constraints and the clustering result simultaneously. Furthermore, we add a robust term to the proposed model so that we can learn multiple groups of label constraints to guide the clustering process and find a robust self-constrained spectral clustering result. The robust term can reduce the impact of uncertainty in the quality of a single set of label constraints on the performance of the proposed model. An iterative strategy with update formulas for variables is proposed to solve the self-constrained spectral clustering problem. We provide the theoretical analysis to explain the importance of the learned constraints in spectral clustering. Furthermore, we analyze the convergence of our optimization scheme. Finally, we have done many experiments on benchmark data sets to illustrate the effectiveness of the proposed algorithm.