CRAFT: ClusteR-specific Assorted Feature selecTion

We present a hierarchical Bayesian framework for clustering with cluster-specific feature selection. We derive a simplified model, CRAFT, by analyzing the asymptotic behavior of the log posterior formulations in a nonparametric MAP-based clustering setting in this framework. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuitively appealing. The resulting algorithm is simple to implement and scales nicely, requires minimal parameter tuning, obviates the need to specify the number of clusters a priori, and compares favorably with other state-of-the-art methods on several datasets. We provide empirical evidence on carefully designed synthetic data sets to highlight the robustness of the algorithm to recover the underlying feature subspaces, even when the average dimensionality of the features across clusters is misspecified. Besides, the framework seamlessly allows for multiple views of clustering by interpolating between the two extremes of cluster-specific feature selection and global selection, and recovers the DP-means objective [14] under the degenerate setting of clustering without feature selection.