BiNeTClus: Bipartite Network Community Detection Based on Transactional Clustering

Abstract

ing with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Association for Computing Machinery. 2157-6904/2020/11-ART6 $15.00 https://doi.org/10.1145/3423067 ACM Transactions on Intelligent Systems and Technology, Vol. 12, No. 1, Article 6. Publication date: November 2020. 6:2 M. Bouguessa and K. Nouri Fig. 1. Example 1: A simple bipartite network with a relatively clear community structure. Left: The bipartite network. Right: The expected community structure. have been proposed for analyzing networks with a single type of entities (nodes) and links (edges) [3, 4]. Such a simple network representation is, however, not suitable for modelling some complex systems with entities of different types. In fact, many real-world systems are naturally described as heterogeneous graphs with several types of nodes and links. As an example of heterogeneous graphs, we find bipartite networks that contain two types of nodes in such a way that nodes having the same type are never connected to each other. Links exist only between nodes of different types. Many real-world applications can be modeled as bipartite networks such as a users-products purchase network like Amazon, a scientists-papers collaboration network like DBLP, a users-photos annotation network like Flickr, and so on. For the purpose of illustration, Figure 1 (left-hand side) depicts a user-product purchase graph (we use graph and network interchangeably) containing two types of nodes. Users are represented by nodes of type V1, while nodes of type V2 correspond to products. Links between nodes in V1 and V2 reflect purchasing transactions. In this article, we focus on this kind of network, that is, a bipartite network, for the specific problem of detecting community structures. Community discovery is one of the most important tasks in network analysis. In the particular context of bipartite networks, a number of approaches have been proposed. Here, it is worth noting that the concept of community in bipartite networks remains qualitatively intuitive as there is no single, universally accepted definition of a community. For instance, some bipartite network community detection algorithms simply adopt the standard definition of a community in plain graph, that is, simple homogenous networks. For example, References [5, 6] simplify the detection task by projecting a bipartite graph to homogeneous graphs. Then, the authors apply traditional community detection algorithms (Louvain [3], Fast Greedy [7], Walktrap [8], and LabelPropagation [9]) to identify community structures. In contrast, some approaches, such as References [10–12], simply consider the bipartite graph as a plain homogeneous graph without the use of projection. A community in a bipartite graph is thus defined like the one in a simple graph, namely, a group of nodes densely connected to each other and loosely linked with the nodes of the other groups. With such an approach, node heterogeneity in bipartite networks is simply ignored. Other methods [11, 13–16] have reached a consensus and consider a community in a bipartite graph as a set of nodes of the same type that share a lot of connections to nodes of the second type. In other words, a community is a group of V1 nodes that connects in a dense manner with otherV2 nodes and vice versa. To illustrate, let us go back again to Figure 1, which shows a simple example of a bipartite graph. In the right-hand side of this figure we can see that the bipartite graph can be divided into four communities: C1 = {A,B,C}; C2 = {D,E,F}; D1 = {1,2} and D2 = {3,4,5}. Nodes in C1 are densely connected with the nodes of its corresponding community D1 and vice versa. Likewise, nodes inC2 are densely connected with the nodes of its corresponding community D2 and vice versa. In general, the corresponding community (also called the co-cluster mate) of a ACM Transactions on Intelligent Systems and Technology, Vol. 12, No. 1, Article 6. Publication date: November 2020.