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.