A methodology for analysis of concept lattice reduction

Abstract

Formal concept analysis (FCA) is a mathematical theory of data analysis with applications in many areas. The problem of obtaining a concept lattice of an appropriate size was identified in several applications as one of the most important problems of FCA. In order to deal with this problem several techniques with different characteristics were proposed for concept lattice reduction. However, there are currently no adequate methods to assess what types of knowledge transformations can result from a reduction. A methodology for analysis of concept lattice reduction is presented here. It is based on the use of sets of proper implications holding in the original and reduced formal contexts or concept lattices. Working with both sets of implications, the methodology is able to show what is preserved, eliminated, inserted or transformed by a reduction technique. Three classes of reduction techniques are analyzed from the standpoint of the methodology in order to highlight techniques of each class have in common with respect to the transformations performed. Such analysis is followed by specific examples in each class.

Keywords

  • Formal concept analysis;
  • Lattice reduction;
  • Proper implications 

Dias, Sérgio M.; Vieira, N. J. A methodology for analysis of concept lattice reduction, Information Sciences, Volume 396, August 2017, Pages 202-217, ISSN 0020-0255, http://dx.doi.org/10.1016/j.ins.2017.02.037.

Concept lattices reduction: definition, analysis and classification

Abstract

Formal concept analysis (FCA) is currently considered an important formalism for knowledge representation, extraction and analysis with applications in different areas. A problem identified in several applications is the computational cost due to the large number of formal concepts generated. Even when that number is not very large, the essential aspects, those effectively needed, can be immersed in a maze of irrelevant details. In fact, the problem of obtaining a concept lattice of appropriate complexity and size is one of the most important problems of FCA. In literature, several different approaches to control the complexity and size of a concept lattice have been described, but so far they have not been properly analyzed, compared and classified. We propose the classification of techniques for concept lattice reduction in three groups: redundant information removal, simplification, and selection. The main techniques to reduce concept lattice are analyzed and classified based on seven dimensions, each one composed of a set of characteristics. Considerations are made about the applicability and computational complexity of approaches of different classes.

Keywords

  • Formal concept analysis;
  • Concept lattices;
  • Reduction

Dias, Sérgio M.; Vieira, N. J. Concept lattices reduction: Definition, analysis and classification. Expert Systems with Applications, v. 42, p. 7084-7097, 2015. DOI: http://dx.doi.org/10.1016/j.eswa.2015.04.044

Palestra técnica: Ciência de Dados com Software Livre

Os sistemas transacionais geram um volume gigantesco de dados e em meio a essa massa de dados, existem informações que passam despercebidas. É necessário explorar esses dados usando o processo Knowledge Discovery in Databases (descoberta de conhecimento em base de dados) para descobrir estas informações, que em muitos casos são de extrema relevância ao negócio e alavancam em muitos casos ações que geram um diferencial para o negócio. Com este objetivo podem ser aplicadas soluções de Big Data, Data Discovery e Data Mining, que possibilitam encontrar padrões ou tendências em grandes massas de dados. Sejam suas fontes sistemas transacionais, redes sociais, e-mails, sites, listas de discussão entre outras.

http://www.softwarelivre.gov.br/palestras-tecnicas-cisl/palestra-tecnica-palestra-sobre-ciencia-de-dados-com-software-livre