I/O Scalable bregman co-clustering

Abstract

Consider an MxN matrix, where the (i,j)th entry represents the affinity between the i_th entity of the first type and the j_th entity of the second type. Co-clustering is an approach to simultaneously cluster both types of entities, using the affinities as the information guiding the clustering. Co-clustering has been found to achieve clustering and dimensionality reduction at the same time, and therefore it is finding application in various problems. Bregman co-clustering algorithm, which has been recently proposed, converts the co-clustering task to the search for an optimal approximation matrix. It is much more scalable but memory-based implementations have a severe computational bottleneck. In this paper we show that a significant fraction of computations performed by the Bregman co-clustering algorithm naturally map to those performed by an on-line analytical processing (OLAP) engine, making the latter a well suited data management engine for the algorithm. Based on this observation, we have developed a version of Bregman co-clustering algorithm that works on top of OLAP. Our experiments show that this version is much more scalable, achieving an order of magnitude performance improvement over the memory-based implementation. We believe this unlocks the power of this novel technique for application to much larger datasets. © 2008 Springer-Verlag Berlin Heidelberg.