Constrained clustering by spectral kernel learning

Clustering performance can often be greatly improved by leveraging side information. In this paper, we consider constrained clustering with pairwise constraints, which specify some pairs of objects from the same cluster or not. The main idea is to design a kernel to respect both the proximity structure of the data and the given pairwise constraints. We propose a spectral kernel learning framework and formulate it as a convex quadratic program, which can be optimally solved efficiently. Our framework enjoys several desirable features: 1) it is applicable to multi-class problems; 2) it can handle both must-link and cannot-link constraints; 3) it can propagate pairwise constraints effectively; 4) it is scalable to large-scale problems; and 5) it can handle weighted pairwise constraints. Extensive experiments have demonstrated the superiority of the proposed approach.