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RELATIONAL TOPOLOGICAL MAP

LAZHAR LABIOD

LIPN UMR 7030, Université Paris 13, 99, Avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

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NISTOR GROZAVU

LIPN UMR 7030, Université Paris 13, 99, Avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

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YOUNÈS BENNANI

LIPN UMR 7030, Université Paris 13, 99, Avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

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https://doi.org/10.1142/S146902681000294XCited by:0 (Source: Crossref)

Abstract

This paper introduces a relational topological map model, dedicated to multidimensional categorial data (or qualitative data) arising in the form of a binary matrix or a sum of binary matrices. This approach is based on the principle of Kohonen's model (conservation of topological order) and uses the Relational Analysis formalism by maximizing a modified Condorcet criterion. This proposed method is developed from the classical Relational Analysis approach by adding a neighborhood constraint to the Condorcet criterion. We propose a hybrid algorithm, which deals linearly with large data sets, provides a natural clusters identification and allows a visualization of the clustering result on a two-dimensional grid while preserving the a priori topological order of this data. The proposed approach called Relational Topological Map (RTM) was validated on several databases and the experimental results showed very promising performances.

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