Optimal compression for bipartite networks

Abstract

• We analytically derive the structure entropy, which is equivalent to the compression limit, for arbitrary random bipartite networks without node labeling. • We theoretically show that the compression length of random bipartite networks resulted from the compression algorithm, BSZIP, asymptotically achieves the theoretical limit. • The compression algorithm BSZIP for random bipartite networks outperforms the majority of compression algorithms in existence from perspectives including the encoding length and the computational time. Bipartite network is crucial for recommendation systems as user-product behaviors are thoroughly described by bipartite interactions. Almost all of the state-of-the-art network compression algorithms are designed for general networks without harnessing the unique bipartite structure. Until 2017, Basu and Varshney proposed a compression algorithm, BSZIP , selectively for bipartite networks. However, the performance of this algorithm is not clear. Here, we derive the structural entropy which is equivalent to the compression limit for unlabeled random bipartite networks. Theoretically, we show that BSZIP algorithm asymptotically achieves the analytical limit.