On finding the maximum edge biclique in a bipartite graph: a subspace clustering approach

Shaham, Eran; H, Yu; Li, Xiaoli

doi:10.1137/1.9781611974348.36

Cited by 24 publications

(15 citation statements)

References 18 publications

(48 reference statements)

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“…Maximum Biclique Search and its Variants. The maximum biclique problem has become increasingly popular in recent years [30,29,7]. [30] proposes an integer programming methodology to find the maximum biclique in general graphs.…”

Section: Related Workmentioning

confidence: 99%

“…However, it is not applicable for large scale graphs. [29] develops a Monte Carlo algorithm for extracting a list of maximal bicliques, which contains a maximum biclique with fixed probability. [7] studies the parameterized maximum biclique problem in bipartite graphs, that reports if there exists a biclique with at least k edges, where k is a given integer parameter.…”

Section: Related Workmentioning

confidence: 99%

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Maximum biclique search at billion scale

Lyu

Lin

et al. 2020

Proc. VLDB Endow.

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Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to the difficulty of the problem in graph theory, no practical solution has been proposed to solve the issue in large-scale real-world datasets. Existing techniques for maximum clique search on a general graph cannot be applied because the search objective of maximum biclique search is two-dimensional, i.e., we have to consider the size of both parts of the biclique simultaneously. In this paper, we divide the problem into several subproblems each of which is specified using two parameters. These subproblems are derived in a progressive manner, and in each subproblem we can restrict the search in a very small part of the original bipartite graph. We prove that a logarithmic number of subproblems is enough to guarantee the algorithm correctness. To minimize the computational cost, we show how to reduce significantly the bipartite graph size for each subproblem while preserving the maximum biclique satisfying certain constraints by exploring the properties of one-hop and two-hop neighbors for each vertex. We use several real datasets from various application domains, one of which contains over 300 million vertices and 1.3 billion edges, to demonstrate the high efficiency and scalability of our proposed solution. It is reported that 50% improvement on recall can be achieved after applying our method in Alibaba Group to identify the fraudulent transactions in their e-commerce networks. This further demonstrates the usefulness of our techniques in practice.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Maximum biclique search at billion scale

Lyu

Lin

et al. 2020

Proc. VLDB Endow.

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“…In [10,24], ILP formulations of MEB are proposed, which can find an MEB with ILP solver. Since the MEB problem is NP-hard to approximate within a factor of n 1−ε , algorithms that can find an MEB with high probability is proposed [23]. Besides, the MEB problems for special instances of bipartite graphs, i.e., convex bipartite graphs, bipartite permutation graphs and tree convex bipartite graphs, are studied in [20] [21] and [6] respectively.…”

Section: Related Workmentioning

confidence: 99%

Efficient Exact Algorithms for Maximum Balanced Biclique Search in Bipartite Graphs

Chen

Liu

Zhou

et al. 2020

Preprint

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Given a bipartite graph, the maximum balanced biclique (MBB) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has numerous applications. Despite the NP-hardness of the MBB problem, in this paper, we show that an exact MBB can be discovered extremely fast in bipartite graphs for real applications. We propose two exact algorithms dedicated for dense and sparse bipartite graphs respectively. For dense bipartite graphs, an O * (1.3803 n ) algorithm is proposed. This

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“…Algorithm 2 shows the steps of determining the domains with feature subset grouping. In general, the problem of finding maximum edge biclique in a bipartite graph is an NP-complete problem (Shaham, Yu, & Li, 2016). However, the…”

Section: Feature Subset Groupingmentioning

confidence: 99%

Data-driven Conceptual Spaces: Creating Semantic Representations For Linguistic Descriptions Of Numerical Data

Banaee¹,

Schaffernicht²,

Loutfi³

2018

jair

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There is an increasing need to derive semantics from real-world observations to facilitate natural information sharing between machine and human. Conceptual spaces theory is a possible approach and has been proposed as mid-level representation between symbolic and sub-symbolic representations, whereby concepts are represented in a geometrical space that is characterised by a number of quality dimensions. Currently, much of the work has demonstrated how conceptual spaces are created in a knowledge-driven manner, relying on prior knowledge to form concepts and identify quality dimensions. This paper presents a method to create semantic representations using data-driven conceptual spaces which are then used to derive linguistic descriptions of numerical data. Our contribution is a principled approach to automatically construct a conceptual space from a set of known observations wherein the quality dimensions and domains are not known a priori. This novelty of the approach is the ability to select and group semantic features to discriminate between concepts in a data-driven manner while preserving the semantic interpretation that is needed to infer linguistic descriptions for interaction with humans. Two data sets representing leaf images and time series signals are used to evaluate the method. An empirical evaluation for each case study assesses how well linguistic descriptions generated from the conceptual spaces identify unknown observations. Furthermore, comparisons are made with descriptions derived on alternative approaches for generating semantic models.

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On finding the maximum edge biclique in a bipartite graph: a subspace clustering approach

Cited by 24 publications

References 18 publications

Maximum biclique search at billion scale

Maximum biclique search at billion scale

Efficient Exact Algorithms for Maximum Balanced Biclique Search in Bipartite Graphs

Data-driven Conceptual Spaces: Creating Semantic Representations For Linguistic Descriptions Of Numerical Data

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