Parametric Embedding for Class Visualization

Abstract

In this paper, we propose a new method, Parametric Embedding (PE), for visualizing the posteriors estimated over a mixture model. PE simultane- ously embeds both objects and their classes in a low-dimensional space. PE takes as input a set of class posterior vectors for given data points, and tries to preserve the posterior structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assump- tion that samples are generated by a Gaussian mixture with equal covari- ances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier’s be- havior in supervised, semi-supervised and unsupervised settings. The PE algorithm has a computational advantage over conventional embedding methods based on pairwise object relations since its complexity scales with the product of the number of objects and the number of classes. We demonstrate PE by visualizing supervised categorization of web pages, semi-supervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, Latent Dirichlet Allo- cation.