Information Sciences 396 (2017) 202–217 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins A methodology for analysis of concept lattice reduction Sérgio M. Dias a,b,∗ , Newton J. Vieira a a Department of Computer Science, Federal University of Minas Gerais (UFMG), Av. Antônio Carlos 6627 - Pampulha Prédio do ICEx - Anexo U - sala 5309 - Belo Horizonte - Minas Gerais - Brazil - 31270-010 b Federal Service of Data Processing (SERPRO), Av. José Cândido da Silveira, 1.200 - Cidade Nova, Belo Horizonte 31.035-536, Minas Gerais, Brazil a r t i c l e i n f o Article history: Received 30 November 2015 Revised 13 December 2016 Accepted 15 February 2017 Available online 20 February 2017 Keywords: Formal concept analysis Lattice reduction Proper implications a b s t r a c t 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 iden- tified 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 as- sess 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 lat- tices. 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. © 2017 Elsevier Inc. All rights reserved. 1. Introduction Formal concept analysi s (FCA) is currently considered an important formalism for knowledge extraction, representation and analysis. FCA has been widely studied and applied in many diverse scientific fields [24,31,36,42,45,62]. However, even a small set of data can result in a very large number of formal concepts [4]. In fact, FCA induces a potentially high combinato- rial complexity and the structures obtained, even from a small dataset, may become prohibitively large [27]. Despite the fact that the worst case of the lattice size (2 min(|G|, |M|) ) is rarely found in practice, the computational cost is still too prohibitive for many applications. Furthermore, the resulting number of formal concepts and the topology of the relationships between concepts can make difficult an analysis of the final lattice [46]. In particular, key aspects, those that are indeed important, may be immersed in a maze of irrelevant details. Regardless of the number of formal concepts generated in the worst case, all relationships between concepts are present in the concept lattice. This feature is suitable in terms of completeness, but generally results in a large number of relationships overloading the lattice’s structure. The problem of obtaining a concept lattice of appropriate size and structure, which exposes the really relevant aspects, is one of the most important problems when using FCA. As a consequence, there are many techniques, with different ∗ Corresponding author at: Department of Computer Science, Federal University of Minas Gerais (UFMG), Av. Antônio Carlos 6627 - Pampulha Prédio do ICEx - Anexo U - sala 5309 - Belo Horizonte - Minas Gerais - Brazil - 31270-010. E-mail addresses: mariano@dcc.ufmg.br, sergio.dias@serpro.gov.br (S.M. Dias), nvieira@dcc.ufmg.br (N.J. Vieira). http://dx.doi.org/10.1016/j.ins.2017.02.037 0020-0255/© 2017 Elsevier Inc. All rights reserved.