Bregman Bubble Co-clustering

Clustering problems often involve datasets where only a part of the data is relevant to the problem e.g. in microarray data analysis only a subset of the genes show interesting patterns within a subset of the conditions(features). On such datasets, in order to accurately identify meaningful clusters, the non-informative data points should be automatically detected and pruned and non-discriminative features should be simultaneously discarded. Additionally, since clusters could exist in different subspaces of the feature space, a clustering algorithm that is capable of identifying clusters along multiple axes is more suitable as compared to one that is restricted to traditional “one-sided” clustering. We propose Bregman Bubble coclustering (BBCC), an approach that generalizes both, Bregman bubble clustering [GG06] and Bregman co-clustering [BDG07] to a scalable and very versatile framework. BBCC works with a large variety of distance measures and different co-cluster definitions, making it applicable to a wide range of real life datasets. We also provide insights into a soft version of our algorithm and the underlying generative model. We further extend BBCC to address the problem of efficiently detecting arbitrarily positioned, possibly overlapping co-clusters in a dataset and combine it with a novel model selection strategy that also automatically determines the appropriate number of co-clusters. We highlight the effectiveness of our approach through extensive experimentation on synthetic as well as real datasets. We show that BBCC not only performs better than traditional approaches on microarray datasets but even improves upon human curated techniques in a completely unsupervised manner.