Kernel Information Embeddings

Abstract

We describe a family of embedding algorithms that are based on nonparametric estimates of mutual information (MI). Using Parzen window estimates of the distribution in the joint (input, embedding)-space, we derive a MI-based objective function for dimensionality reduction that can be optimized directly with respect to a set of latent data representatives. Various types of supervision signal can be introduced within the framework by replacing plain MI with several forms of conditional MI. Examples of the semi-(un)supervised algorithms that we obtain this way are a new model for manifold alignment, and a new type of embedding method that performs 'conditional dimensionality reduction'.