Mining Bi-sets in Numerical Data

Besson, J.; Robardet, Céline; Raedt, Luc De; Boulicaut, Jean-François

doi:10.1007/978-3-540-75549-4_2

Cited by 13 publications

(29 citation statements)

References 16 publications

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“…In Besson et al (2006), the authors try to identify relevant pattern (bi-sets), which is defined similar to hyperrectangle in this paper, to mine numerical data. A bi-sets pattern is a Cartesian product between X rows and Y columns, in which each element has different numerical values.…”

Section: Data Descriptive Mining and Rectangle Coveringmentioning

confidence: 99%

Summarizing transactional databases with overlapped hyperrectangles

Xiang

Jin

Fuhry

et al. 2010

Data Min Knowl Disc

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Transactional data are ubiquitous. Several methods, including frequent itemset mining and co-clustering, have been proposed to analyze transactional databases. In this work, we propose a new research problem to succinctly summarize transactional databases. Solving this problem requires linking the high level structure of the database to a potentially huge number of frequent itemsets. We formulate this problem as a set covering problem using overlapped hyperrectangles (a concept generally regarded as tile according to some existing papers); we then prove that this problem and its several variations are NP-hard, and we further reveal its relationship with the Responsible editor: Bart Goethals. A preliminary version of this article appeared in 123 216 Y. Xiang et al.compact representation of a directed bipartite graph. We develop an approximation algorithm Hyper which can achieve a logarithmic approximation ratio in polynomial time. We propose a pruning strategy that can significantly speed up the processing of our algorithm, and we also propose an efficient algorithm Hyper+ to further summarize the set of hyperrectangles by allowing false positive conditions. Additionally, we show that hyperrectangles generated by our algorithms can be properly visualized. A detailed study using both real and synthetic datasets shows the effectiveness and efficiency of our approaches in summarizing transactional databases.

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Section: Data Descriptive Mining and Rectangle Coveringmentioning

confidence: 99%

Summarizing transactional databases with overlapped hyperrectangles

Xiang

Jin

Fuhry

et al. 2010

Data Min Knowl Disc

View full text Add to dashboard Cite

show abstract

“…Usually, the efficient algorithms for enumerating CTV biclusters of ones from binary data are based on the monotonicity and anti-monotonicity properties [12]. In fact, we do not know any efficient algorithm for this task that is not based on these properties.…”

Section: Maximality and Monotonicitymentioning

confidence: 99%

Enumerating all maximal biclusters in numerical datasets

Veroneze

Banerjee

Zuben

2017

Information Sciences

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“…A bicluster of similar values in a numerical object‐attribute data‐table is usually defined95–97 as a pair consisting of an inclusion‐maximal set of objects and an inclusion‐maximal set of attributes having similar values for the objects. Such a pair can be represented as an inclusion‐maximal rectangle in the numerical table, modulo rows and columns permutations.…”

Section: Relationships Of Fca To Models Of Knowledge Representation Amentioning

confidence: 99%

Knowledge representation and processing with formal concept analysis

Kuznetsov

Poelmans

2013

WIREs Data Min & Knowl

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During the last three decades, formal concept analysis (FCA) became a well‐known formalism in data analysis and knowledge discovery because of its usefulness in important domains of knowledge discovery in databases (KDD) such as ontology engineering, association rule mining, machine learning, as well as relation to other established theories for representing knowledge processing, like description logics, conceptual graphs, and rough sets. In early days, FCA was sometimes misconceived as a static crisp hardly scalable formalism for binary data tables. In this paper, we will try to show that FCA actually provides support for processing large dynamical complex (may be uncertain) data augmented with additional knowledge. © 2013 Wiley Periodicals, Inc. This article is categorized under: Fundamental Concepts of Data and Knowledge > Key Design Issues in Data Mining Fundamental Concepts of Data and Knowledge > Knowledge Representation Technologies > Computational Intelligence

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Mining Bi-sets in Numerical Data

Cited by 13 publications

References 16 publications

Summarizing transactional databases with overlapped hyperrectangles

Summarizing transactional databases with overlapped hyperrectangles

Enumerating all maximal biclusters in numerical datasets

Knowledge representation and processing with formal concept analysis

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