Biclustering and Boolean Matrix Factorization in Data Streams

TL;DR

This paper introduces a novel streaming algorithm for bipartite graph clustering and Boolean matrix factorization that operates in a single pass with sublinear space, achieving fast performance and near-optimal quality.

Contribution

The authors present the first one-pass streaming algorithm for bipartite clustering with sublinear space and extend it to Boolean matrix factorization, supported by theoretical analysis.

Findings

Algorithm recovers right-side clusters after one pass

Achieves near-baseline quality on real data

Scales linearly with number of edges

Abstract

We study the clustering of bipartite graphs and Boolean matrix factorization in data streams. We consider a streaming setting in which the vertices from the left side of the graph arrive one by one together with all of their incident edges. We provide an algorithm that, after one pass over the stream, recovers the set of clusters on the right side of the graph using sublinear space; to the best of our knowledge, this is the first algorithm with this property. We also show that after a second pass over the stream, the left clusters of the bipartite graph can be recovered and we show how to extend our algorithm to solve the Boolean matrix factorization problem (by exploiting the correspondence of Boolean matrices and bipartite graphs). We evaluate an implementation of the algorithm on synthetic data and on real-world data. On real-world datasets the algorithm is orders of magnitudes faster than a static baseline algorithm while providing quality results within a factor 2 of the baseline algorithm. Our algorithm scales linearly in the number of edges in the graph. Finally, we analyze the algorithm theoretically and provide sufficient conditions under which the algorithm recovers a set of planted clusters under a standard random graph model.