Abstract not found

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. 1.

The division of a protein interaction network into biologically meaningful modules can aid with automated complex detection and prediction of biological processes and can uncover the global organization of the cell. We propose a novel graph summarization (GS) technique, based on graph compression, to cluster protein interaction graphs into biologically relevant modules. The method is motivated by defining a biological module as a set of proteins that have similar sets of interaction partners. We show this definition, put into practice by a GS algorithm, reveals modules that are more biologically enriched than those found by other methods. We also apply GS to predict complex memberships, biological processes, and co-complexed pairs and show that in most settings GS is preferable over existing methods of protein interaction graph clustering. 1.

OLAP (On-Line Analytical Processing) is an important notion in data analysis. Recently, more and more graph or networked data sources come into being. There exists a similar need to deploy graph analysis from different perspectives and with multiple granularities. However, traditional OLAP technology cannot handle such demands because it does not consider the links among individual data tuples. In this paper, we develop a novel graph OLAP framework, which presents a multi-dimensional and multi-level view over graphs. The contributions of this work are two-fold. First, starting from basic definitions, i.e., what are dimensions and measures in the graph OLAP scenario, we develop a conceptual framework for data cubes on graphs. We also look into different semantics of OLAP operations, and classify the framework into two major subcases: informational OLAP and topological OLAP. Then, with more emphasis on informational OLAP (topological OLAP will be covered in a future study due to the lack of space), we show how a graph cube can be materialized by calculating a special kind of measure called aggregated graph and how to implement it efficiently. This includes both full materialization and partial materialization where constraints are enforced to obtain an iceberg cube. We can see that the aggregated graphs, which depend on the graph properties of underlying networks, are much harder to compute than their traditional OLAP counterparts, due to the increased structural complexity of data. Empirical studies show insightful results on real datasets and demonstrate the efficiency of our proposed optimizations.

The problem of connectivity is an extremely important one in the context of massive graphs. In many large communication networks, social networks and other graphs, it is desirable to determine the minimum-cut between any pair of nodes. The problem is well solved in the classical literature, since it is related to the maximum-flow problem, which is efficiently solvable. However, large graphs may often be disk resident, and such graphs cannot be efficiently processed for connectivity queries. This is because the minimum-cut problem is typically solved with the use of a variety of combinatorial and flow-based techniques which require random access to the underlying edges in the graph. In this paper, we propose to develop a connectivity index for massive-disk resident graphs. We will use an edgesampling based approach to create compressed representations of the underlying graphs. Since these compressed representations can be held in main memory, they can be used to derive efficient approximations for the minimum-cut problem. These compressed representations are then organized into a disk-resident index structure. We present experimental results which show that the resulting approach provides between two and three orders of magnitude more efficient query processing than a disk-resident approach at the expense of a small amount of accuracy. 1.

Large graph datasets are ubiquitous in many domains, including social networking and biology. Graph summarization techniques are crucial in such domains as they can assist in uncovering useful insights about the patterns hidden in the underlying data. One important type of graph summarization is to produce small and informative summaries based on userselected node attributes and relationships, and allowing users to interactively drill-down or roll-up to navigate through summaries with different resolutions. However, two key components are missing from the previous work in this area that limit the use of this method in practice. First, the previous work only deals with categorical node attributes. Consequently, users have to manually bucketize numerical attributes based on domain knowledge, which is not always possible. Moreover, users often have to manually iterate through many resolutions of summaries to identify the most interesting ones. This paper addresses both these key issues to make the interactive graph summarization approach more useful in practice. We first present a method to automatically categorize numerical attributes values by exploiting the domain knowledge hidden inside the node attributes values and graph link structures. Furthermore, we propose an interestingness measure for graph summaries to point users to the potentially most insightful summaries. Using two real datasets, we demonstrate the effectiveness and efficiency of our techniques.

Unveiling the modular structure of biological networks can reveal important organizational patterns in the cell. Many graph partitioning algorithms have been proposed towards this end. However, most approaches only consider a single, optimal decomposition of the network. In this work, we make use of the multitude of near-optimal clusterings in order to explore the dynamics of network clusterings and how those dynamics relate to the structure of the underlying network. We recast the modularity optimization problem as an integer linear program with diversity constraints. These constraints produce an ensemble of dissimilar but still highly modular clusterings. We apply our approach to four social and biological networks and show how optimal and near-optimal solutions can be used in conjunction to identify deeper community structure in the network, including inter-community dynamics, communities that are especially resilient to change, and core-and-peripheral community members. 1.

We consider extending decision support facilities toward large sophisticated networks, upon which multidimensional attributes are associated with network entities, thereby forming the so-called multidimensional networks. Data warehouses and OLAP (Online Analytical Processing) technology have proven to be effective tools for decision support on relational data. However, they are not well-equipped to handle the new yet important multidimensional networks. In this paper, we introduce Graph Cube, a new data warehousing model that supports OLAP queries effectively on large multidimensional networks. By taking account of both attribute aggregation and structure summarization of the networks, Graph Cube goes beyond the traditional data cube model involved solely with numeric value based group-by’s, thus resulting in a more insightful and structure-enriched aggregate network within every possible multidimensional space. Besides traditional cuboid queries, a new class of OLAP queries, crossboid, is introduced that is uniquely useful in multidimensional networks and has not been studied before. We implement Graph Cube by combining special characteristics of multidimensional networks with the existing well-studied data cube techniques. We perform extensive experimental studies on a series of real world data sets and Graph Cube is shown to be a powerful and efficient tool for decision support on large multidimensional networks.

Large graph databases are commonly collected and analyzed in numerous domains. For reasons related to either space efficiency or for privacy protection (e.g., in the case of social network graphs), it sometimes makes sense to replace the original graph with a summary, which removes certain details about the original graph topology. However, this summarization process leaves the database owner with the challenge of processing queries that are expressed in terms of the original graph, but are answered using the summary. In this paper, we propose a formal semantics for answering queries on summaries of graph structures. At its core, our formulation is based on a random worlds model. We show that important graph-structure queries (e.g., adjacency, degree, and eigenvector centrality) can be answered efficiently and in closed form using these semantics. Further, based on this approach to query answering, we formulate three novel graph partitioning/compression problems. We develop algorithms for finding a graph summary that least affects the accuracy of query results, and we evaluate our proposed algorithms using both real and synthetic data. 1

Consensus clustering has emerged as an important extension of the classical clustering problem. Given a set of input clusterings of a given dataset, consensus clustering aims to find a single final clustering which is a better fit in some sense than the existing clusterings. There is a significant drawback in generating a single consensus clustering since different input clusterings could differ significantly. In this paper, we develop a new framework, called Multiple Consensus Clustering (MCC), to explore multiple clustering views of a given dataset from a set of input clusterings. Instead of generating a single consensus, MCC organizes the different input clusterings into a hierarchical tree structure and allows for interactive exploration of multiple clustering solutions. A dynamic programming algorithm is proposed to obtain a flat partition from the hierarchical tree using the modularity measure. Multiple consensuses are finally obtained by applying consensus clustering algorithms to each cluster of the partition. Extensive experimental results on 11 real world data sets and a case study on a Protein-Protein Interaction (PPI) data set demonstrate the effectiveness of our proposed method. 1