A method for automated construction of classifications called conceptual clustering is described and compared to methods used in numerical taxonomy. This method arranges objects into classes rep- resenting certain descriptive concepts, rather than into.classes defined solely by a similarity metric in some a priori defined attribute space. A specific form of the method is conjunctive conceptual clustering, in which descriptive concepts are conjunetive statements involving rela- tions on selected object attributes and optimized aeeording to an assumed global criterion of clustering quality. The method, implemented in program CLUSTER/2, is tested together with 18 numerical taxonomy methods on two exemplary problems: 1) a construction of a classification of popular microcomputers and 2) the reconstruction of a classification of selected plant disease categories. In both experiments, the majority of numerical taxonomy methods (14 out of 18) produced results which were difficult to interpret and seemed to be arbitrary. In contrast to this, the conceptual clustering method produced results that had a simple interpretation and corresponded well to solutions pre- ferred by people.

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Assume that a dissimilarity measure between elements and subsets of the set being clustered is given. We define the transformation of the set of subsets under which each subset is transformed into the set of all elements whose dissimilarity to its is not greater than a given threshold. Then the cluster is defined as fixed point of this transformation. Three well-known clustering strategies are considered from this point of view: hierarchical clustering, graph-theoretic methods, and conceptual clustering. For hierarchical clustering generalizations are obtained that allow for overlapping clusters and/or clusters not forming a cover. Three properties of dissimilarity are introduced which guarantee the existence of fixed points for each threshold. We develop the relation to the theory of quasi-concave set functions, to help give an additional interpretation of clusters.

The problem to solve is the development of tools that allows us the comparison between sets of objects (individual objects) by the intentional via. The concept of symbolic object was introduced by E. Diday (starting from the conceptual algorithms proposed by Michalski) and developed actually by their group and by the authors of this work. In a previous paper was introduced the concept of symbolic variable and all possible types of this variables including the most frequently used in the literature. Now we propose comparison functions between values of symbolic variables and on the basis of this definitions we introduce similarity functions between symbolic objects, and crisp and fuzzy clustering criteria for the structuralization of a conceptual space (of concepts) based on the logic combinatory approach to Pattern Recognition.

In this paper we present a new formalization of symbolic object concept such that constitute a solid base for a theory of symbolic objects that contain as particular case the classical theory of data analysis and the theory of symbolic data analysis of E. Diday.

The following is a comprehensive user's guide and reference for using CLUSTERJ2C++, the latest version of the CLUSlER12 program for constructing classifications of arbitrary objects. Given a set of object descriptions, in the form of attribute-value pairs, the program structures the objects into a hierarchy of classes. The program produces a conjunctive description of each class using selected object attributes. The program runs in a batch mode, with parameter and object descriptions input via relational tables; future versions will provide interactive and embeddable interfaces. This document contains the deftnitions of the relational table syntax and the values that can be entered. Also included and discussed