been adapted to modularity clustering. Section 4 details the single-level and multi-level refinement heuristics, and Section 5.3 compares them experimentally. Because the effectiveness of (particularly multi-level) refinement may depend on the coarsening algorithm, Section 5.4 examines various combinations of coarsening and refinement heuristics. Section 6 compares public implementations and benchmark results of modularity clustering heuristics, without a restriction to coarsening and refinement algorithms. While this is one of the most extensive comparisons in the literature, it is far from exhaustive, because implementations and sufficient experimental results have not been published for some proposed heurisarXiv:0812.4073v1

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.

Abstract—Network vulnerability assessment is an indispensable component of attack risk reduction and proactive response. However, traditional assessment methods simply assume the attacks only target at nodes with high degree or betweenness centrality, thus fail to capture the worst-case scenarios under simultaneous failures. In our previous work, we formulated assessing network vulnerability as optimization problems, socalled β-edge disruptor and β-vertex disruptor, to identify the minimum cost critical infrastructures that removal expose the network to a certain disruption level. Here, the disruption is measured as the fraction of node pairs with no paths between them in the residual network. In this paper, we present an exact analytical solution for the vulnerability assessment problems i.e. an exact branch-and-cut algorithm to solve the integer programming formulation of the β-vertex disruptor. The two intriguing aspects of the algorithms are an efficient Mixed Integer Programming (MIP) formulation, called sparse metric, and vertex-cut inequalities, a specialized cutting plane procedure that tightens the bound on the optimal solutions. Experiments on both synthetic and real-world networks suggest that our algorithm yields a significant improvement on a large variety of network instances, raising the size of the largest instance solved from several dozen to several hundred nodes. Our techniques can be easily extended to many graph partitioning and connectivity optimization problems. I.

Network community detection—the problem of dividing a network of interest into clusters for intelligent analysis—has recently attracted significant attention in diverse fields of research. To discover intrinsic community structure a quantitative measure called modularity has been widely adopted as an optimization objective. Unfortunately, modularity is inherently NP-hard to optimize and approximate solutions must be sought if tractability is to be ensured. In practice, a spectral relaxation method is most often adopted, after which a community partition is recovered from relaxed fractional values by a rounding process. In this paper, we propose an iterative rounding strategy for identifying the partition decisions that is coupled with a fast constrained power method that sequentially achieves tighter spectral relaxations. Extensive evaluation with this coupled relaxation-rounding method demonstrates consistent and sometimes dramatic improvements in the modularity of the communities discovered. 1

Densely interacting regions of biological networks often correspond to functional modules such as protein complexes. Most algorithms proposed to uncover modules, however, produce one clustering that only reveals a single view of how the cell is organized. We describe two new methods to find ensembles of provably near-optimal modularity partitions that lie within a heuristically constrained search space. We also show how to count the number of solutions in this space that exist within a bounded modularity range. We apply our algorithms to a protein interaction network for S. cerevisiae and show how fine-grained differences between near-optimal partitions can be used to define robust communities. We also propose a technique to find structurally diverse nearoptimal solutions and show that these different partitions are enriched for different biological functions. Our results indicate that near-optimal solutions can represent alternative and complementary views of the network’s structure.

Given a collection of documents, most of existing multidocument summarization methods automatically generate a static summary for all the users. However, different users may have different opinions on the documents, thus there is a necessity for improving users ’ interactions in the summarization process. In this paper, we propose an interactive document summarization system using information visualization 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.

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Traditional sentiment analysis mainly considers binary classifications of reviews, but in many real-world sentiment classification problems, nonbinary review ratings are more useful. This is especially true when consumers wish to compare two products, both of which are not negative. Previous work has addressed this problem by extracting various features from the review text for learning a predictor. Since the same word may have different sentiment effects when used by different reviewers on different products, we argue that it is necessary to model such reviewer and product dependent effects in order to predict review ratings more accurately. In this paper, we propose a novel learning framework to incorporate reviewer and product information into the text based learner for rating prediction. The reviewer, product and text features are modeled as a three-dimension tensor. Tensor factorization techniques can then be employed to reduce the data sparsity problems. We perform extensive experiments to demonstrate the effectiveness of our model, which has a significant improvement compared to state of the art methods, especially for reviews with unpopular products and inactive reviewers. 1

With the recent advances in information networks, the problem of community detection has attracted much attention in the last decade. While network community detection has been ubiquitous, the task of collecting complete network data remains challenging in many real-world applications. Usually the collected network is incomplete with most of the edges missing. Commonly, in such networks, all nodes with attributes are available while only the edges within a few local regions of the network can be observed. In this paper, we study the problem of detecting communities in incomplete information networks with missing edges. We first learn a distance metric to reproduce the link-based distance between nodes from the observed edges in the local information regions. We then use the learned distance metric to estimate the distance between any pair of nodes in the network. A hierarchical clustering approach is proposed to detect communities within the incomplete information networks. Empirical studies on real-world information networks demonstrate that our proposed method can effectively detect community structures within incomplete information networks.