Automatic Objects Organization

This paper addresses the problem of the automatic building of classifications to organize knowledge. The goal is to generate the set of least general generalizations of the objects descriptions: the Generalization Space. An anytime algorithm to build conceptual classifications for complex objects (having sub-parts) represented as conceptual graphs is presented. It is based upon an iterative reformulation of the descriptions that allows one to use at each step a propositional algorithm to enrich the Generalisation Space. Introduction In Artificial Intelligence, the problem of automatically constructing classifications has been studied in the field of Conceptual Clustering and more recently in that of Knowledge Organisation. Most of the conceptual clustering approaches have defined this task as the search for a good classification that would best predict unknown features of new objects (Fisher 96, Fisher, Pazzani & Langley 91). This type of construction is guided by heuristics, which allow one to choose the best classes among the set of possible ones. The developed methods have proven their interest in various domains (Michalski & Stepp 81; Fisher & al. 91, Ketterlin, Gancarski & Korczak 95). More recent research concerns the construction of classifications that organize knowledge (Godin, Missaoui & Alaoui 91; Carpineto & Romano 93). In this task, the goal is not to build a subset of the possible classes but all the classes clustering similar objects: the “Generalization Space”. In these methods, the process of construction is not based on a numerical distance among descriptions and a function to be optimised but on a generalization language, i.e. a language to describe the classes. In an object oriented context, a knowledge organization tool may be useful in various ways (Ducournau, Huchard, Libourel & Napoli 99): it may be used during the problem analysis to define classes from a set of instances or to guide the definition of abstract classes from a set of concrete classes. It may also find generality relations between classes based on their coverage and could provide an help for the identification of super-classes factorising common properties of several classes. This paper presents an approach for knowledge organization of objects described using conceptual graphs (Sowa 84). The sequel of the paper is organized as follows. We first recall the definition of the Generalization Space. We then briefly present a propositional approach to build a GS – called COING – which is searching for partial matching between the graphs describing the objects (Bournaud 96). We introduce an extension of COING, called KIDS, which takes into account the structure of the descriptions in the Generalization Space. KIDS is based upon an iterative reformulation of the object descriptions allowing to use at each step the propositional algorithm COING to enrich the Generalization Space. The last section is dedicated to a discussion of KIDS application. 1 We use the term “Conceptual Clustering” to refer to both Conceptual Clustering and Concept Formation. 1 The Generalization Space Given a set of object descriptions and a generalization language L in which generalizations of object descriptions are described, the associated Generalization Space (GS) is the set of the least general generalization (LGG) of these object descriptions in L. In the GS, a node ni is a pair (ci, di). The element ci, called the coverage of ni, is the set of objects covered by ni; and di, called the description of ni, corresponds to the common features (it is a maximally specific conjunctive concept) of the objects of ci. In the GS, a node corresponds to a cluster of objects described in intension by its description di and in extension by its coverage ci. Nodes of the GS are partially ordered by a subsumption relation between concepts. Given a node ni with coverage ci, its ancestors are all the nodes nj, such that Cj ⊃ Ci. This partial order provided the GS with a pruned lattice structure, which may be represented by an inheritance network (Godin & al. 91). Indeed, GS nodes inherit the descriptions of the nodes which are more general. The Generalization Space may also be defined by the two isomorphic lattices: the Galois lattice of concept descriptions (partially ordered by the subsumption relation) and the lattice of objects (partially ordered by the inclusion relation) (Godin & al. 91, Ganascia 93). An example of a Generalization Space is given in the next section (fig.1). 2 The COING approach to build a Generalization Space 2.1. Searching for partial matching A main problem to build conceptual classifications of a set of objects described using conceptual graphs is to generalize these conceptual graphs. In order to deal with the problem of matching graphs, COING transforms the graph representation into an arc representation. In other words, each graph describing an object is broken down into a set of independent arcs. For example, each graph describing a house in figure 1 is decomposed into a set of 6 arcs. Instead of trying to match a graph G1 with a graph G2, COING only searches for a partial matching of an arc from G1 with an arc from G2. This restriction has been previously used in (Godin & al. 91). COING also allows to efficiently take into account background knowledge to build the GS (Bournaud & Ganascia 97). This knowledge is represented in a generalization hierarchy; for example in the domain of colours it expresses that both Grey and White are generalized by the concept Black and White (noted B&W on fig. 1). Figure 1 below presents the Generalization Space for three houses (h1, h2 and h3) described by their windows. It contains three generalizing nodes: n1 clustering h1 and h2, n2 clustering h2 and h3 and n3 clustering h1, h2 and h3. h1 h2 Grey colour Window h1 h3 h2 House has has Black colour Small size Window Grey colour Big size Window House has has Black colour Small size Window White colour Big size Window House has has Black colour Big size Window Grey colour Big size Window h1 h2 h3 Black colour Window