  A bipartite graph contains inter-set edges between two disjoint vertex sets,
and is widely used to model real-world data, such as user-item purchase
records, author-article publications, and biological interactions between drugs
and proteins. k-Bipartite Graph Clustering (k-BGC) is to partition the target
vertex set in a bipartite graph into k disjoint clusters. The clustering
quality is important to the utility of k-BGC in various applications like
social network analysis, recommendation systems, text mining, and
bioinformatics, to name a few. Existing approaches to k-BGC either output
clustering results with compromised quality due to inadequate exploitation of
high-order information between vertices, or fail to handle sizable bipartite
graphs with billions of edges.
  Motivated by this, this paper presents two efficient k-BGC solutions, HOPE
and HOPE+, which achieve state-of-the-art performance on large-scale bipartite
graphs. HOPE obtains high scalability and effectiveness through a new k-BGC
problem formulation based on the novel notion of high-order perspective (HOP)
vectors and an efficient technique for low-rank approximation of HOP vectors.
HOPE+ further elevates the k-BGC performance to another level with a judicious
problem transformation and a highly efficient two-stage optimization framework.
Two variants, HOPE+ (FNEM) and HOPE+ (SNEM) are designed when either the
Frobenius norm or spectral norm is applied in the transformation. Extensive
experiments, comparing HOPE and HOPE+ against 13 competitors on 10 real-world
datasets, exhibit that our solutions, especially HOPE+, are superior to
existing methods in terms of result quality, while being up to orders of
magnitude faster. On the largest dataset MAG with 1.1 billion edges, HOPE+ is
able to produce clusters with the highest clustering accuracy within 31
minutes, which is unmatched by any existing solution for k-BGC.
