How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view. The basic idea is to envision the graph clustering as a density-cut problem, such that the vertices in the same cluster are densely connected and the vertices between clusters are sparsely connected. To identify meaningful clusters (communities) in a graph, a density-connected tree is first constructed in a local fashion. Owing to the density-connected tree, Dcut allows partitioning a graph into multiple densely tight-knit clusters directly. We demonstrate that our method has several attractive benefits: (a) Dcut provides an intuitive criterion to evaluate the goodness of a graph clustering in a more natural and precise way; (b) Built upon the density-connected tree, Dcut allows identifying the meaningful graph clusters of densely connected vertices efficiently; (c) The density-connected tree provides a connectivity map of vertices in a graph from a local density perspective. We systematically evaluate our new clustering approach on synthetic as well as real data to demonstrate its good performance.
During the past several decades, many approaches have been proposed for graph clustering, such as @cite_14 , @cite_0 , @cite_1 etc. Due to space limitations, we can only review the closest approaches from the literature. For detailed reviews of graph clustering, please refer to @cite_7 .
@cite_0 @cite_14 @cite_1 @cite_7
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The goal of graph clustering is to partition vertices in a large graph into different clusters based on various criteria such as vertex connectivity or neighborhood similarity. Graph clustering techniques are very useful for detecting densely connected groups in a large graph. Many existing graph clustering methods mainly focus on the topological structure for clustering, but largely ignore the vertex properties which are often heterogenous. In this paper, we propose a novel graph clustering algorithm, SA-Cluster, based on both structural and attribute similarities through a unified distance measure. Our method partitions a large graph associated with attributes into k clusters so that each cluster contains a densely connected subgraph with homogeneous attribute values. An effective method is proposed to automatically learn the degree of contributions of structural similarity and attribute similarity. Theoretical analysis is provided to show that SA-Cluster is converging. Extensive experimental results demonstrate the effectiveness of SA-Cluster through comparison with the state-of-the-art graph clustering and summarization methods. Graph clustering is a fundamental problem in graph mining and network analysis. To group vertices of a graph into a series of densely knitted clusters with each cluster being well-separated from all the others, classic methods primarily consider the mere graph structure information in modeling and quantifying the proximity or distance of vertices for graph clustering. However, with the proliferation of rich, heterogeneous attribute information widely available in real-world graphs, such as user profiles in social networks, and GO (Gene Ontology) terms in protein interaction networks, it becomes essential to combine both structure and attribute information of graphs towards yielding better-quality clusters. In this chapter, we propose a new graph embedding approach for attributed graph clustering. We embed each vertex of a graph into a continuous vector space within which the local structure and attribute information surrounding the vertex can be jointly encoded in a unified, latent representation. Specifically, we quantify the vertex-wise attribute proximity into edge weights and leverage a group of truncated, attribute-aware random walks to learn the latent representations of vertices. This way, the challenging attributed graph clustering problem can be cast into the traditional problem of multidimensional data clustering, which has admitted efficient and cost-effective solutions. We apply our attribute-aware graph embedding algorithm in a series of real-world and synthetic attributed graphs and networks. The experimental studies demonstrate that our proposed method significantly outperforms the state-of-the-art attributed graph clustering techniques in terms of both clustering effectiveness and efficiency. Mining patterns in graphs has become an important issue in real applications, such as bioinformatics and web mining. We address a graph clustering problem where a cluster is a set of densely connected nodes, under a practical setting that 1) the input is multiple graphs which share a set of nodes but have different edges and 2) a true cluster cannot be found in all given graphs. For this problem, we propose a probabilistic generative model and a robust learning scheme based on variational Bayesian estimation. A key feature of our probabilistic framework is that not only nodes but also given graphs can be clustered at the same time, allowing our model to capture clusters found in only part of all given graphs. We empirically evaluated the effectiveness of the proposed framework on not only a variety of synthetic graphs but also real gene networks, demonstrating that our proposed approach can improve the clustering performance of competing methods in both synthetic and real data. Learning from graph data has been attracting much attention recently due to its importance in many scientific applications, where objects are represented as graphs. In this paper, we study the problem of multi-graph clustering i.e., clustering multiple graphs. We propose a multi-graph clustering approach MGCT based on the interior-node topology of graphs. Specifically, we extract the interior-node topological structure of each graph through a sparsity-inducing interior-node clustering. We merge the interior-node clustering stage and the multi-graph clustering stage into a unified iterative framework, where the multi-graph clustering will influence the interior-node clustering and the updated interior-node clustering results will be further exerted on multi-graph clustering. We apply MGCT on two real brain network data sets i.e., ADHD and HIV. Experimental results demonstrate the superior performance of the proposed model on multi-graph clustering.