Instance-level constraint-based semisupervised learning with imposed space-partitioning

A new method for semisupervised learning from pairwise sample (must- and cannot-link) constraints is introduced. It addresses an important limitation of many existing methods, whose solutions do not achieve effective propagation of the constraint information to unconstrained samples. We overcome this limitation by constraining the solution to comport with a smooth (soft) class partition of the feature space, which necessarily entails constraint propagation and generalization to unconstrained samples. This is achieved via a parameterized mean-field approximation to the posterior distribution over component assignments, with the parameterization chosen to match the representation power of the chosen (generative) mixture density family. Unlike many existing methods, our method flexibly models classes using a variable number of components, which allows it to learn complex class boundaries. Also, unlike most of the methods, ours estimates the number of latent classes present in the data. Experiments on synthetic data and data sets from the UC Irvine machine learning repository show that, overall, our method achieves significant improvements in classification performance compared with the existing methods.