Bayesian Hierarchical Cross-Clustering
Dazhuo Li, Patrick Shafto; JMLR W&CP 15:443-451, 2011.
AbstractMost clustering algorithms assume that all dimensions of the data can be described by a single structure. Cross-clustering (or multi- view clustering) allows multiple structures, each applying to a subset of the dimen- sions. We present a novel approach to cross- clustering, based on approximating the so- lution to a Cross Dirichlet Process mixture (CDPM) model [Shafto et al., 2006, Mans- inghka et al., 2009]. Our bottom-up, de- terministic approach results in a hierarchi- cal clustering of dimensions, and at each node, a hierarchical clustering of data points. We also present a randomized approxima- tion, based on a truncated hierarchy, that scales linearly in the number of levels. Re- sults on synthetic and real-world data sets demonstrate that the cross-clustering based algorithms perform as well or better than the clustering based algorithms, our determinis- tic approaches models perform as well as the MCMC-based CDPM, and the randomized approximation provides a remarkable speed- up relative to the full deterministic approxi- mation with minimal cost in predictive error.