Discovering Substantial Distinctions among Incremental Bi-Clusters

Alqadah, Faris; Bhatnagar, Raj

doi:10.1137/1.9781611972795.18

Cited by 7 publications

(3 citation statements)

References 14 publications

(8 reference statements)

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“…3 Bandedness and Bi-clustering Bi-clustering (subspace clustering, co-clustering, closed itemsets, maximal bicliques) in binary data has been extensively studied [8,10,13,18,3,11]. In these works the model for the subspace cluster is derived either from graph theory or Formal Concept Analysis (FCA) [11] (both models are equivalent but have different roots).…”

Section: Problem Definitionmentioning

confidence: 99%

Mining Maximally Banded Matrices in Binary Data

Alqadah¹,

Bhatnagar²,

Jegga³

2010

Proceedings of the 2010 SIAM International Conference on Data Mining

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Binary data occurs often in several real world applications ranging from social networks to bioinformatics. Extracting patterns from such data has been a focus of fundamental data mining tasks including association rule analysis, sequence mining and bi-clustering. Recently, the utility of banded structures in binary matrices has been pointed out with applications in paleontology, bioinformatics and social networking. A binary matrix has a banded structure if both the rows and columns can be permuted so that the 1's exhibit a staircase pattern down the rows, along the leading diagonal. In this paper we show the correspondence between biclustering and banded structures in matrices; and the MMBS (Mine Maximally Banded Sub-matrices) algorithm is presented as a direct result of this correspondence. The current state of the art algorithm, MBS, only allows for the discovery of a single band and assumes a fixed column permutation. On the other hand MMBS facilitates the discovery of multiple bands that may possibly be overlapping or segmented. Our experimental results, presented here, clearly indicate the advantage of MMBS over MBS with both, synthetic and real data sets.

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Section: Problem Definitionmentioning

confidence: 99%

Mining Maximally Banded Matrices in Binary Data

Alqadah¹,

Bhatnagar²,

Jegga³

2010

Proceedings of the 2010 SIAM International Conference on Data Mining

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“…Biclustering, itemset mining, and association rules [9,10,[17][18][19][20][21] have all utilized FCA as an implicit theoretical basis. Specifically, under the FCA model, biclusters are viewed as maximal rectangles of 1s in the matrix under a suitable permutation of the rows and columns.…”

Section: Bandedness and Fcamentioning

confidence: 99%

A novel framework for detecting maximally banded matrices in binary data

Alqadah

Bhatnagar

Jegga

2010

Statistical Analysis

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Binary data occurs often in real-world applications ranging from social networks to bioinformatics. As such, extracting patterns from binary data has been a fundamental task of data mining. Recently, the utility of banded structures in binary matrices has been pointed out for applications such as paleontology, bioinformatics, and social networking. A binary matrix has a banded structure if both the rows and columns can be permuted so that the 1s exhibit a staircase pattern down the rows, along the leading diagonal. Natural interpretations of banded structures include overlapping communities in social networks, patterns of species occurring in spatially correlated sites, and overlapping roles of genes in various diseases. In this paper, we show the correspondence between formal concept analysis and banded structure; as a direct result of this correspondence a novel framework for discovering banded structures is presented. Utilizing the framework, the MMBS algorithm (mine maximally banded submatrices) is developed. The current state-of-the-art algorithm, MBS, only allows for the discovery of a single band and assumes a fixed-column permutation. On the other hand, MMBS facilitates the discovery of multiple bands that may possibly be overlapping or segmented. Our experimental results, presented here, clearly indicate the advantage of MMBS over MBS with both, synthetic and real datasets. 

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“…Zaki 1998) (Alqadah & Bhatnagar 2009) (Li et al 2007) , conceptual modeling (Priss 2006), software engineering (Tonella 2004), social networking (Snasel, Horák, & Abraham 2008) and the semantic web (Y. Ding 2002). However, one drawback of FCA is the fact that the set of concepts tends to be quite large in dense datasets making reasoning about the concepts difficult (Pfaltz 2007).…”

Section: Introductionmentioning

confidence: 99%

Similarity measures in formal concept analysis

Alqadah

Bhatnagar

2011

Ann Math Artif Intell

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Formal concept analysis (FCA) has been applied successively in diverse fields such as data mining, conceptual modeling, social networks, software engineering, and the semantic web. One shortcoming of FCA, however, is the large number of concepts that typically arise in dense datasets hindering typical tasks such as rule generation and visualization. To overcome this shortcoming, it is important to develop formalisms and methods to segment, categorize and cluster formal concepts. The first step in achieving these aims is to define suitable similarity and dissimilarity measures of formal concepts. In this paper we propose three similarity measures based on existent set-based measures in addition to developing the completely novel zeros-induced measure. Moreover, we formally prove that all the measures proposed are indeed similarity measures and investigate the computational complexity of computing them. Finally, an extensive empirical evaluation on real-world data is presented in which the utility and character of each similarity measure is tested and evaluated.

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Discovering Substantial Distinctions among Incremental Bi-Clusters

Cited by 7 publications

References 14 publications

Mining Maximally Banded Matrices in Binary Data

Mining Maximally Banded Matrices in Binary Data

A novel framework for detecting maximally banded matrices in binary data

Similarity measures in formal concept analysis

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