Constrained Spectral Clustering with Distance Metric Learning

Spectral clustering is a flexible clustering technique that finds data clusters in the spectral embedding space of the data. It doesn’t assume convexity of the shape of clusters, and is able to find non-linear cluster boundaries. Constrained spectral clustering aims at incorporating user-defined pairwise constraints in to spectral clustering. Typically, there are two kinds of pairwise constraints, Must-Link constraint and Cannot-Link constraint. These constraints represent prior knowledge indicating whether two data objects should be in the same cluster or not; thereby aiding clustering. In this paper, we propose a novel approach that alternatively learns a distance metric from such constraints, and finds the clustering solution on the spectral embedding of the transformed data by the learned metric. Although our formulation is non-convex, empirically we observe the alternative optimization can effectively find the local optimum. We show that the proposed method outperforms both existing methods that only learns distance metric from constraints, and constrained spectral clustering method without distance metric learning.