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This paper proposes the Latent Case Model (LCM), a Bayesian approach to clustering in which clusters are represented by a prototype (a specific sample from the data) and feature subspaces (a binary subset of the variables signifying those features that are relevant to the class). The approach is presented as being a Bayesian, trainable version of the Case-Based Reasoning approach popular in AI, and is motivated by the ways such models have proved highly effective in explaining human decision making. The generative model (Figure 1) represents each item as coming from a mixture of S clusters, where each cluster is represented by a prototype and subspace (as above) and a function \phi which generates features matching those of the prototype with high probability for features in the subspace, and uniform features outside it. The model is thus similar in functionality to LDA but quite different in terms of its representation. Experimental results are shown for "prediction accuracy" (more on this later) and unsupervised accuracy of the clusters vs. a baseline of LDA (Figure 2), and the results seem superior/comparable to LDA.