One of the central problems in cognitive science is determining the mental representations that underlie human inferences. Solutions to this problem often rely on the analysis of subjective similarity judgments, on the assumption that recognizing likenesses between people, objects, and events is crucial to everyday inference. One such solution is provided by the additive clustering model, which is widely used to infer the features of a set of stimuli from their similarities, on the assumption that similarity is a weighted linear function of common features. Existing approaches for implementing additive clustering often lack a complete framework for statistical inference, particularly with respect to choosing the number of features. To address these problems, this article develops a fully Bayesian formulation of the additive clustering model, using methods from nonparametric Bayesian statistics to allow the number of features to vary. We use this to explore several approaches to parameter estimation, showing that the nonparametric Bayesian approach provides a straightforward way to obtain estimates of both the number of features and their importance.

We propose a new method, parametric embedding (PE), that embeds objects with the class structure into a low-dimensional visualization space. PE takes as input a set of class conditional probabilities for given data points and tries to preserve the structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assumption that samples are generated by a gaussian mixture with equal covariances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier's behavior in supervised, semisupervised, 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, semisupervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, latent Dirichlet allocation.