A Local Algorithm for Structure-Preserving Graph Cut

Abstract

Nowadays, large-scale graph data is being generated in a variety of real-world applications, from social networks to co-authorship networks, from protein-protein interaction networks to road traffic networks. Many existing works on graph mining focus on the vertices and edges, with the first-order Markov chain as the underlying model. They fail to explore the high-order network structures, which are of key importance in many high impact domains. For example, in bank customer personally identifiable information (PII) networks, the star structures often correspond to a set of synthetic identities; in financial transaction networks, the loop structures may indicate the existence of money laundering. In this paper, we focus on mining user-specified high-order network structures and aim to find a structure-rich subgraph which does not break many such structures by separating the subgraph from the rest. A key challenge associated with finding a structure-rich subgraph is the prohibitive computational cost. To address this problem, inspired by the family of local graph clustering algorithms for efficiently identifying a low-conductance cut without exploring the entire graph, we propose to generalize the key idea to model high-order network structures. In particular, we start with a generic definition of high-order conductance, and define the highorder diffusion core, which is based on a high-order random walk induced by user-specified high-order network structure. Then we propose a novel High-Order Structure-Preserving LOcal Cut (HOS-PLOC) algorithm, which runs in polylogarithmic time with respect to the number of edges in the graph. It starts with a seed vertex and iteratively explores its neighborhood until a subgraph with a small high-order conductance is found. Furthermore, we analyze its performance in terms of both effectiveness and efficiency. The experimental results on both synthetic graphs and real graphs

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“…Crowdsourcing is a special sourcing model in which pieces of micro-tasks are distributed to a pool of online workers. It has become a popular research topic in the recent decades because of its widely commercial and academic adoption in areas, such as machine learning [22,29,47,49,56], computer vision [14,55], medical healthcare [25,30,45], and graph mining [6,7,42,48,50], and so on. Modern machine learning tools such as deep models require massive amount of labeled data.…”

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