Simple and Scalable Constrained Clustering: a Generalized Spectral Method.

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem in which both matrices are graph Laplacians. The algorithm works in nearly-linear time and provides concrete guarantees for the quality of the clusters, at least for the case of 2-way partitioning. In practice this translates to a very fast implementation that consistently outperforms existing spectral approaches both in speed and quality.