Maximum biclique search at billion scale

Abstract

Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to the difficulty of the problem in graph theory, no practical solution has been proposed to solve the issue in large-scale real-world datasets. Existing techniques for maximum clique search on a general graph cannot be applied because the search objective of maximum biclique search is two-dimensional, i.e., we have to consider the size of both parts of the biclique simultaneously. In this paper, we divide the problem into several subproblems each of which is specified using two parameters. These subproblems are derived in a progressive manner, and in each subproblem we can restrict the search in a very small part of the original bipartite graph. We prove that a logarithmic number of subproblems is enough to guarantee the algorithm correctness. To minimize the computational cost, we show how to reduce significantly the bipartite graph size for each subproblem while preserving the maximum biclique satisfying certain constraints by exploring the properties of one-hop and two-hop neighbors for each vertex. We use several real datasets from various application domains, one of which contains over 300 million vertices and 1.3 billion edges, to demonstrate the high efficiency and scalability of our proposed solution. It is reported that 50% improvement on recall can be achieved after applying our method in Alibaba Group to identify the fraudulent transactions in their e-commerce networks. This further demonstrates the usefulness of our techniques in practice.

Cohesive Subgraph Identification in Weighted Bipartite Graphs

“…In [28], Robins et al resort to the (2, 2)-biclique to model the cohesion. In [10], a progressive method is proposed to speed up the computation of biclique. As we can see, the previous studies do not consider the weight factor for cohesive subgraph identification.…”

“…As a fundamental problem in graph analysis, cohesive subgraph identification is widely studied in the literature (e.g., [5][6][7][8]). For bipartite graphs, a variety of cohesive subgraph models have been proposed to identify important structures, such as (α, β)core [3], bitruss [9] and biclique [10]. Biclique is the most cohesive model, which requires the nodes inside to be fully connected.…”

On Problem of Finding all Maximal Induced Bicliques of Hypergraph

“…There are two variants of this problem: find a maximal biclique with maximal number of vertices and find a maximal biclique with maximal number of edges. These problems arise in detection of anomalies in data, in analysing gene structures and social structures [10]. Both variants are N P -hard for general graphs [17].…”

“…For example, in telecommunication networks maximal bicliques used for route organizing and defining subnets for marking them [3,7]. In metabolic and genetic networks maximal bicliques are used to represent the interrelation between organisms and different external conditions [8][9][10]. In marketing maximal bicliques allow one to form social recommendations and product bundling [8][9][10].…”

“…In metabolic and genetic networks maximal bicliques are used to represent the interrelation between organisms and different external conditions [8][9][10]. In marketing maximal bicliques allow one to form social recommendations and product bundling [8][9][10]. Maximal bicliques are used for clustering data in various fields [11].…”