Bipartite graph partitioning and data clustering

Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming; Simon, Horst D.

doi:10.2172/816202

Cited by 143 publications

(116 citation statements)

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“…Another advantage lies in the objective function, which naturally corresponds to some models about noise in the data. Examples of applications include [7], where a reduction from consensus clustering to our problem is introduced, and [8] for an application of a related problem to large scale document-term relation analysis.…”

Section: Introductionmentioning

confidence: 99%

Improved Approximation Algorithms for Bipartite Correlation Clustering

Ailon

Avigdor-Elgrabli

Liberty³

et al. 2011

Algorithms – ESA 2011

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Abstract. In this work we study the problem of Bipartite Correlation Clustering (BCC), a natural bipartite counterpart of the well studied Correlation Clustering (CC) problem. Given a bipartite graph, the objective of BCC is to generate a set of vertex-disjoint bi-cliques (clusters) which minimizes the symmetric difference to it. The best known approximation algorithm for BCC due to Amit (2004) guarantees an 11-approximation ratio. 4 In this paper we present two algorithms. The first is an improved 4-approximation algorithm. However, like the previous approximation algorithm, it requires solving a large convex problem which becomes prohibitive even for modestly sized tasks. The second algorithm, and our main contribution, is a simple randomized combinatorial algorithm. It also achieves an expected 4-approximation factor, it is trivial to implement and highly scalable. The analysis extends a method developed by Ailon, Charikar and Newman in 2008, where a randomized pivoting algorithm was analyzed for obtaining a 3-approximation algorithm for CC. For analyzing our algorithm for BCC, considerably more sophisticated arguments are required in order to take advantage of the bipartite structure. Whether it is possible to achieve (or beat) the 4-approximation factor using a scalable and deterministic algorithm remains an open problem.

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Section: Introductionmentioning

confidence: 99%

Improved Approximation Algorithms for Bipartite Correlation Clustering

Ailon

Avigdor-Elgrabli

Liberty³

et al. 2011

Algorithms – ESA 2011

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“…While the strange behaviors have been documented across services ranging from telecommunication fraud [1] to deceptive Ebay's reviews [2] to ill-gotten Facebook's page-likes [3], we study here a complete graph of more than 117 million users and 3.33 billion edges in a popular microblogging service Tencent Weibo (Jan. 2011). Several recent studies have used social graph data to characterize connectivity patterns, with a focus on understanding the community structure [4][5][6] and the cluster property [7,8]. However, no analysis was presented to demonstrate what strange connectivity pattern we can infer strange behavior from and how.…”

Section: Introductionmentioning

confidence: 99%

Inferring Strange Behavior from Connectivity Pattern in Social Networks

Jiang

Cui

Beutel

et al. 2014

Lecture Notes in Computer Science

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Abstract. Given a multimillion-node social network, how can we summarize connectivity pattern from the data, and how can we find unexpected user behavior? In this paper we study a complete graph from a large who-follows-whom network and spot lockstep behavior that large groups of followers connect to the same groups of followees. Our first contribution is that we study strange patterns on the adjacency matrix and in the spectral subspaces with respect to several flavors of lockstep. We discover that (a) the lockstep behavior on the graph shapes dense "block" in its adjacency matrix and creates "ray" in spectral subspaces, and (b) partially overlapping of the behavior shapes "staircase" in the matrix and creates "pearl" in the subspaces. The second contribution is that we provide a fast algorithm, using the discovery as a guide for practitioners, to detect users who offer the lockstep behavior. We demonstrate that our approach is effective on both synthetic and real data.

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“…The Graph Partitioning Problem (GPP) is one of the fundamental combinatorial optimization problems which is notable for its applicability to a wide range of domains, such as VLSI design [1,43], data mining [49], image segmentation [42], etc. Since the general GPP is NP-complete, approximate methods constitute a natural and useful approach to address this problem.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Metaheuristics for the Graph Partitioning Problem

Benlic

Hao

2013

Hybrid Metaheuristics

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The Graph Partitioning Problem (GPP) is one of the most studied NPcomplete problems notable for its broad spectrum of applicability such as in VLSI design, data mining, image segmentation, etc. Due to its high computational complexity, a large number of approximate approaches have been reported in the literature. Hybrid algorithms that are based on adaptations of popular metaheuristic techniques have shown to provide outstanding performance in terms of partition quality. In particular, it is the hybrids between well-known metaheuristics and multilevel strategies that report partitions of the minimal cut-size value. However, metaheuristic hybrids generally require more computing time than those based on greedy heuristics which can generate partitions of acceptable quality in a matter of seconds even for very large graphs. This chapter is dedicated to a review on some representative hybrid metaheuristic approaches including genetic local search, basic multilevel search and recent development on hybrid multilevel search.

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Bipartite graph partitioning and data clustering

Cited by 143 publications

References 0 publications

Improved Approximation Algorithms for Bipartite Correlation Clustering

Improved Approximation Algorithms for Bipartite Correlation Clustering

Inferring Strange Behavior from Connectivity Pattern in Social Networks

Hybrid Metaheuristics for the Graph Partitioning Problem

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