SYMBOLIC OBJECTS - ORDER STRUCTURE AND PYRAMIDAL CLUSTERING

• Type: Article in International Scientific Journal
• Date: 1995

Authors

brito, p (Author) Other

Journal

Title: Annals of Operations Research

Vol. 55

Pages: 277-297

ISSN: 0254-5330

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 11 Citations

Other information

Authenticus ID: P-007-DM1

DOI: 10.1007/bf02030863

Abstract (EN): We recall a formalism based on the notion of symbolic object (Diday [15], Brito and Diday [8]), which allows to generalize the classical tabular model of Data Analysis. We study assertion objects, a particular class of symbolic objects which is endowed with a partial order and a quasi-order. Operations are then defined on symbolic objects. We study the property of completeness, already considered in Brito and Diday [8], which expresses the duality extension/intension. We formalize this notion in the framework of the theory of Galois connections and study the order structure of complete assertion objects. We introduce the notion of c-connection, as being a pair of mappings (f, g) between two partially ordered sets which should fulfil given conditions. A complete assertion object is then defined as a fixed point of the composed f o g; this mapping is called a ''completeness operator'' for it ''completes'' a given assertion object. The set of complete assertion objects forms a lattice and we state how suprema and infima are obtained. The lattice structure being too complex to allow a clustering study of a data set, we have proposed a pyramidal clustering approach [8]. The symbolic pyramidal clustering method builds a pyramid bottom-up, each cluster being described by a complete assertion object whose extension is the cluster itself. We thus obtain an inheritance structure on the data set. The inheritance structure then leads to the generation of rules.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21