A Correspondence Between Maximal Complete Bipartite Subgraphs and Closed Patterns

Li, Jinyan; Li, Haiquan; Soh, Donny; Wong, Limsoon

doi:10.1007/11564126_18

Cited by 34 publications

(15 citation statements)

References 17 publications

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“…To enumerate the complete set of α-quasi-bicliques, all maximal biclique subgraph are first enumerated by using any algorithm of [4], [5], [21], and then every maximal biclique subgraph (deemed as a 'core') is expanded to obtain α-quasi-bicliques. However, this approach cannot enumerate the complete set of our defined maximal quasi-bicliques.…”

Section: A Graphmentioning

confidence: 99%

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Mining maximal quasi‐bicliques: Novel algorithm and applications in the stock market and protein networks

Sim¹,

Li²,

Gopalkrishnan³

et al. 2009

Statistical Analysis

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Abstract-Several real world applications require mining of bicliques, as they represent correlated pairs of data clusters. However, the mining quality is adversely affected by missing and noisy data. Moreover, some applications only require strong interactions between data members of the pairs, but bicliques are pairs that display complete interactions. We address these two limitations by proposing maximal quasi-bicliques. Maximal quasibicliques tolerate erroneous and missing data, and also relax the interactions between the data members of their pairs. Besides, maximal quasi-bicliques do not suffer from skewed distribution of missing edges that prior quasi-bicliques have. We develop an algorithm MQBminer, which mines the complete set of maximal quasi-bicliques from either bipartite or non-bipartite graphs. We demonstrate the versatility and effectiveness of maximal quasibicliques to discover highly correlated pairs of data in two diverse real world datasets. Firstly, we propose to solve a novel financial stocks analysis problem by using maximal quasi-bicliques to cocluster stocks and financial ratios. Results show that the stocks in our co-clusters usually have significant correlations in their price performance. Secondly, we use maximal quasi-bicliques on a mining protein network problem and we show that pairs of protein groups mined by maximal quasi-bicliques are more significant than those mined by maximal bicliques.

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Section: A Graphmentioning

confidence: 99%

“…(2) A closed itemset and its transaction set form a biclique [21], but a AFI and its transaction set do not form a quasibiclique, due to its error tolerance characteristic. (4) The error tolerance of ETI and AFI are percentagebased, which means they do not have anti-monotone property.…”

Section: B the "Quasi" Conceptmentioning

confidence: 99%

Mining maximal quasi‐bicliques: Novel algorithm and applications in the stock market and protein networks

Sim¹,

Li²,

Gopalkrishnan³

et al. 2009

Statistical Analysis

Self Cite

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“…It is also known that the maximum clique problem is hard to approximate: there exists an > 0 such that no polynomial time algorithm can approximate the size within a factor of n 1− [9,4,14,5]). Clique and biclique detecting algorithms typically enumerate all clique/bicliques [6,8,20,1,18] making use of the fact that a subset of a clique/biclique is still a clique/biclique. These algorithms typically have high order complexity.…”

Section: Clique and Biclique Findingmentioning

confidence: 99%

“…In these cases, biclustering becomes biclique finding, because the simplest and most dense sub-blocks are bicliques. Li et al [18] show there is a correspondence between biclique and frequent closed itemset.…”

Section: Introductionmentioning

confidence: 99%

Biclustering Protein Complex Interactions with a Biclique Finding Algorithm

Ding

et al. 2006

Sixth International Conference on Data Mining (ICDM'06)

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“…Java et al [17] present methods for detecting communities among users in a microblogging platform through identifying dense structures in an evolving network representing connections among users. A sample of other applications of dense subgraph mining in networks include identification of communities in a social network [15], [23], identification of web communities [14], [32], [18], phylogenetic tree construction [11], [33], [41], communities in bipartite networks [19], genome analysis [28], and closed itemset mining [38], [20].…”

Section: Introductionmentioning

confidence: 99%

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

Das

Tirthapura

2018

IEEE Trans. Multi-Scale Comp. Syst.

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We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1)~Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2)~Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Experimental results show that its performance exceeds that of baseline implementations by orders of magnitude. RightsPersonal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract-We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1) Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2) Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Our algorithm is easy to implement, and experimental results show that its performance exceeds that of baseline implementations by orders of magnitude.

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A Correspondence Between Maximal Complete Bipartite Subgraphs and Closed Patterns

Cited by 34 publications

References 17 publications

Mining maximal quasi‐bicliques: Novel algorithm and applications in the stock market and protein networks

Mining maximal quasi‐bicliques: Novel algorithm and applications in the stock market and protein networks

Biclustering Protein Complex Interactions with a Biclique Finding Algorithm

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

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