Due to exponential growth of complex data, graph structure has become increasingly important to model various entities and their interactions, with many interesting applications including, bioinformatics, social network analysis, etc. Depending on the complexity of the data, the underlying graph model can be a simple directed undirected and or weighted un-weighted graph to a complex graph (aka multi-attributed graph) where vertices and edges are labelled with multi-dimensional vectors. In this paper, we present a novel weighted distance measure based on weighted Euclidean norm which is defined as a function of both vertex and edge attributes, and it can be used for various graph analysis tasks including classification and cluster analysis. The proposed distance measure has flexibility to increase decrease the weightage of edge labels while calculating the distance between vertex-pairs. We have also proposed a MAGDist algorithm, which reads multi-attributed graph stored in CSV files containing the list of vertex vectors and edge vectors, and calculates the distance between each vertex-pair using the proposed weighted distance measure. Finally, we have proposed a multi-attributed similarity graph generation algorithm, MAGSim, which reads the output of MAGDist algorithm and generates a similarity graph that can be analysed using classification and clustering algorithms. The significance and accuracy of the proposed distance measure and algorithms is evaluated on Iris and Twitter data sets, and it is found that the similarity graph generated by our proposed method yields better clustering results than the existing similarity graph generation methods.
It can be seen from the discussions mentioned above that most of the graph analysis approaches have considered only one aspect of the graph structure and ignored the other aspects, due to which the generated clusters either have loose intra-cluster structures or reflect a random vertex properties distribution within clusters. However, as stated in @cite_12 , an ideal graph clustering should generate clusters which have a cohesive intra-cluster structure with homogeneous vertex properties, by balancing the structural and attribute similarities". Therefore, considering both vertex attributes and links for calculating similarity distance between the pairs of vertices in a graph is one of basic requirements for clustering complex multi-attributed graphs. In this paper, we have proposed a weighted distance function that can transform a multi-attributed graph into a simple similarity graph on which existing graph clustering algorithms can be applied to identify densely connected components.
@cite_12
2165515835 2135827982 2941396384 2044400205
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. In recent years, many networks have become available for analysis, including social networks, sensor networks, biological networks, etc. Graph clustering has shown its effectiveness in analyzing and visualizing large networks. The goal of graph clustering is to partition vertices in a large graph into clusters based on various criteria such as vertex connectivity or neighborhood similarity. Many existing graph clustering methods mainly focus on the topological structures, but largely ignore the vertex properties which are often heterogeneous. Recently, a new graph clustering algorithm, SA-Cluster, has been proposed which combines structural and attribute similarities through a unified distance measure. SA-Cluster performs matrix multiplication to calculate the random walk distances between graph vertices. As the edge weights are iteratively adjusted to balance the importance between structural and attribute similarities, matrix multiplication is repeated in each iteration of the clustering process to recalculate the random walk distances which are affected by the edge weight update. In order to improve the efficiency and scalability of SA-Cluster, in this paper, we propose an efficient algorithm Inc-Cluster to incrementally update the random walk distances given the edge weight increments. Complexity analysis is provided to estimate how much runtime cost Inc-Cluster can save. Experimental results demonstrate that Inc-Cluster achieves significant speedup over SA-Cluster on large graphs, while achieving exactly the same clustering quality in terms of intra-cluster structural cohesiveness and attribute value homogeneity. 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. Graph clustering, also known as community detection, is a long-standing problem in data mining. In recent years, with the proliferation of rich attribute information available for objects in real-world graphs, how to leverage not only structural but also attribute information for clustering attributed graphs becomes a new challenge. Most existing works took a distance-based approach. They proposed various distance measures to fuse structural and attribute information and then applied standard techniques for graph clustering based on these distance measures. In this article, we take an alternative view and propose a novel Bayesian framework for attributed graph clustering. Our framework provides a general and principled solution to modeling both the structural and the attribute aspects of a graph. It avoids the artificial design of a distance measure in existing methods and, furthermore, can seamlessly handle graphs with different types of edges and vertex attributes. We develop an efficient variational method for graph clustering under this framework and derive two concrete algorithms for clustering unweighted and weighted attributed graphs. Experimental results on large real-world datasets show that our algorithms significantly outperform the state-of-the-art distance-based method, in terms of both effectiveness and efficiency.