Approximate Bicluster and Tricluster Boxes in the Analysis of Binary Data

Mirkin, Boris; Kramarenko, Andrey V.

doi:10.1007/978-3-642-21881-1_40

Cited by 18 publications

(28 citation statements)

References 8 publications

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“…Let us look at different maximizing criteria for related Mixed Integer Programming models. In papers (Ignatov et al, 2015;Mirkin and Kramarenko, 2011) dedicated to triclustering generation, K = (G, M, B, I) is a triadic context with G, the set of objects, M, the set of attributes, B, the set of conditions, and I ⊆ G × M × B, the ternary relation. The proposed triclustering algorithm searches for clusters that maximize the following criteria:…”

Section: Modelmentioning

confidence: 99%

Mixed Integer Programming for Searching Maximum Quasi-Bicliques

Ignatov¹,

Ivanova²,

Zamaletdinova³

2020

Springer Proceedings in Mathematics &Amp; Statistics

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This paper is related to the problem of finding the maximal quasi-bicliques in a bipartite graph (bigraph). A quasi-biclique in the bigraph is its "almost" complete subgraph. The relaxation of completeness can be understood variously; here, we assume that the subgraph is a γ-quasi-biclique if it lacks a certain number of edges to form a biclique such that its density is at least γ ∈ (0, 1]. For a bigraph and fixed γ, the problem of searching for the maximal quasi-biclique consists of finding a subset of vertices of the bigraph such that the induced subgraph is a quasi-biclique and its size is maximal for a given graph. Several models based on Mixed Integer Programming (MIP) to search for a quasi-biclique are proposed and tested for working efficiency. An alternative model inspired by biclustering is formulated and tested; this model simultaneously maximizes both the size of the quasi-biclique and its density, using the least-square criterion similar to the one exploited by triclustering T B .

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Section: Modelmentioning

confidence: 99%

Mixed Integer Programming for Searching Maximum Quasi-Bicliques

Ignatov¹,

Ivanova²,

Zamaletdinova³

2020

Springer Proceedings in Mathematics &Amp; Statistics

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“…The TriBox method (Mirkin and Kramarenko 2011) implements an optimization approach for tricluster generation. Suppose K = (G, M, B, I ) is a triadic context.…”

Section: Individual Tricluster Approximation Modelmentioning

confidence: 99%

“…For example, according to Mirkin and Kramarenko (2011) biclusters found at a dataset relating most popular movies and keywords according to Movies database are rather trivial; adding one more aspect, genre, makes the obtained clumps more sensible, see, for example, bicluster and tricluster containing movie "Twelve Angry Men" from (Mirkin and Kramarenko 2011) Table 1.…”

Section: Introduction and Related Workmentioning

confidence: 99%

“…Specifically, in this paper we consider the case of data on yes/no relation among three sets of entities and the concepts of tricluster and formal triconcept. This allows us to bring forward both lattice-based and linear algebraic approaches, Formal Concept Analysis using lattices of closed sets (see Ganter and Wille 1999;Lehmann and Wille 1995;Jäschke et al 2006) and density/approximation based methods from linear algebra (see Mirkin and Kramarenko 2011). The formal triconcepts refer to such subsets of each of the three sets of entities that all the within-triples are in "yes" relation, whereas the algebraic methods allow some of the triples be not related.…”

Section: Introduction and Related Workmentioning

confidence: 99%

“…We describe a set of triclustering techniques proposed by members of the team in different projects within Formal Concept Analysis and/or bicluster analysis perspectives (OAC-box (Ignatov et al 2011), Tribox (Mirkin andKramarenko 2011), SpecTric ) and a novel OAC-prime algorithm. This novel algorithm, OAC-prime, overcomes computational and substantive drawbacks of the earlier formal-concept-like algorithms.…”

Section: Introduction and Related Workmentioning

confidence: 99%

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Triadic Formal Concept Analysis and triclustering: searching for optimal patterns

et al. 2015

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This paper presents several definitions of "optimal patterns" in triadic data and results of experimental comparison of five triclustering algorithms on real-world and synthetic datasets. The evaluation is carried over such criteria as resource efficiency, noise tolerance and quality scores involving cardinality, density, coverage, and diversity of the patterns. An ideal triadic pattern is a totally dense maximal cuboid (formal triconcept). Relaxations of this notion under consideration are: OAC-triclusters; triclusters optimal with respect to the leastsquare criterion; and graph partitions obtained by using spectral clustering. We show that searching for an optimal tricluster cover is an NP-complete problem, whereas determining the number of such covers is #P-complete. Our extensive computational experiments lead us to a clear strategy for choosing a solution at a given dataset guided by the principle of Pareto-optimality according to the proposed criteria.

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