ZooM: a nested Galois lattices-based system for conceptual clustering

This paper deals with the representation of multi-valued data by clustering them in a small number of classes organized in a hierarchy and described at an appropriate level of abstraction. The contribution of this paper is three fold. First, we investigate a partial order, namely nesting, relating Galois lattices. A nested Galois lattice is obtained by reducing (through projections) the original lattice. As a consequence it makes coarser the equivalence relations defined on extents and intents. Second we investigate the intensional and extensional aspects of the languages used in our system ZooM. In particular we discuss the notion of α-extension of terms of a class language £. We also present our most expressive language £3, close to a description logic, and which expresses optionality or/and multi-valuation of attributes. Finally, the nesting order between the Galois lattices corresponding to various languages and extensions is exploited in the interactive system ZooM. Typically a ZooM session starts from a propositional language £2 and a coarse view of the data (through α-extension). Then the user selects two ordered nodes in the lattice and ZooM constructs a fine-grained lattice between the antecedents of these nodes. So the general purpose of ZooM is to give a general view of concepts addressing a large data set, then focussing on part of this coarse taxonomy.