Name
Abstract | ||
|---|---|---|
Formal Concept Analysis (FCA) is an exploratory data analysis technique for boolean relations based on lattice theory. Its main result is the existence of a dual order isomorphism between two set lattices induced by a binary relation between a set of objects and a set of attributes. Pairs of dually isomorphic sets of objects and attributes, called formal concepts, form a concept lattice, but actually model only a conjunctive mode of conceptualisation. In this paper we augment this formalism in two ways: first we extend FCA to consider different modes of conceptualisation by changing the basic dual isomorphism in a modal-logic motivated way. This creates the three new types of concepts and lattices of extended FCA, viz., the lattice of neighbourhood of objects, that of attributes and the lattice of unrelatedness. Second, we consider incidences with values in idempotent semirings-concretely the completed max-plus or schedule algebra R@?"m"a"x","+-and focus on generalising FCA to try and replicate the modes of conceptualisation mentioned above. To provide a concrete example of the use of these techniques, we analyse the performance of multi-class classifiers by conceptually analysing their confusion matrices. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.ins.2010.04.014 | Inf. Sci. |
Keywords | Field | DocType |
dually isomorphic set,lattice theory,extended fca,basic dual isomorphism,formal concept analysis,generalised formal concept analysis,conceptualisation mode,concept lattice,boolean relation,dual order isomorphism,binary relation,generalising fca,confusion matrix,modal logic,exploratory data analysis | Discrete mathematics,Lattice (order),Binary relation,Lattice Miner,Isomorphism,Formalism (philosophy),Idempotence,Formal concept analysis,Order isomorphism,Mathematics | Journal |
Volume | Issue | ISSN |
181 | 10 | 0020-0255 |
Citations | PageRank | References |
25 | 1.43 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Francisco J. Valverde-Albacete | 1 | 116 | 20.84 |
| Carmen Peláez-moreno | 2 | 130 | 22.07 |