On-demand Relational Concept Analysis

Formal Concept Analysis and its associated conceptual structures have been used to support exploratory search through conceptual navigation. Relational Concept Analysis (RCA) is an extension of Formal Concept Analysis to process relational datasets. RCA and its multiple interconnected structures represent good candidates to support exploratory search in relational datasets, as they are enabling navigation within a structure as well as between the connected structures. However, building the entire structures does not present an efficient solution to explore a small localised area of the dataset, for instance to retrieve the closest alternatives to a given query. In these cases, generating only a concept and its neighbour concepts at each navigation step appears as a less costly alternative. In this paper, we propose an algorithm to compute a concept and its neighbourhood in extended concept lattices. The concepts are generated directly from the relational context family, and possess both formal and relational attributes. The algorithm takes into account two RCA scaling operators. We illustrate it on an example.

Average Size of Implicational Bases

Implicational bases are objects of interest in formal concept analysis and its applications. Unfortunately, even the smallest base, the Duquenne-Guigues base, has an exponential size in the worst case. In this paper, we use results on the average number of minimal transversals in random hypergraphs to show that the base of proper premises is, on average, of quasi-polynomial size.

Introducer Concepts in n-Dimensional Contexts

Concept lattices are well-known conceptual structures that organise interesting patterns-the concepts-extracted from data. In some applications, such as software engineering or data mining, the size of the lattice can be a problem, as it is often too large to be efficiently computed, and too complex to be browsed. For this reason, the Galois Sub-Hierarchy, a restriction of the concept lattice to introducer concepts, has been introduced as a smaller alternative. In this paper, we generalise the Galois Sub-Hierarchy to n-lattices, conceptual structures obtained from multidimensional data in the same way that concept lattices are obtained from binary relations.