Fast Gaussian Pairwise Constrained Spectral Clustering

We consider the problem of spectral clustering with partial supervision in the form of must-link and cannot-link constraints. Such pairwise constraints are common in problems like coreference resolution in natural language processing. The approach developed in this paper is to learn a new representation space for the data together with a distance in this new space. The representation space is obtained through a constraint-driven linear transformation of a spectral embedding of the data. Constraints are expressed with a Gaussian function that locally reweights the similarities in the projected space. A global, non-convex optimization objective is then derived and the model is learned via gradient descent techniques. Our algorithm is evaluated on standard datasets and compared with state of the art algorithms, like [14,18,31]. Results on these datasets, as well on the CoNLL-2012 coreference resolution shared task dataset, show that our algorithm significantly outperforms related approaches and is also much more scalable.