Minimum description length and psychological clustering models

Clustering is one of the most basic and useful methods of data analysis. This chapter describes a number of powerful clustering models, developed in psychology, for representing objects using data that measure the similarities between pairs of objects. These models place few restrictions on how objects are assigned to clusters,and allow for very general measures of the similarities between objects and clusters.Geometric Complexity Criteria (GCC) are derived for these models, and are used to fit the models to similarity data in a way that balances goodness-of-fit with complexity. Complexity analyses, based on the GCC, are presented for the two most widely used psychological clustering models, known as “additive clustering”and “additive trees”

Latent features in similarity judgments: A nonparametric Bayesian approach

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.

Regarding the complexity of additive clustering models

The additive clustering approach to modeling pairwise similarity of entities is a powerful tool for deriving featural stimulus representations. In a recent paper, Lee (2001) proposes a statistically principled measure for choosing between clustering models that accounts for model complexity as well as data fit. Importantly, complexity is understood to be a property, not merely of the number of clusters, but also their size and pattern of overlap. However, some caution is required when interpreting the measure, with regard to the applicability of the Hadamard inequality to the complexity matrix.

Latent Features in Similarity Judgments: A Nonparametric Bayesian Approach

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.