Relational topological clustering

This paper introduces a new topological clustering formalism, dedicated to categorical data arising in the form of a binary matrix or a sum of binary matrices. The proposed approach is based on the principle of the Kohonen´s model (conservation of topological order) and uses the Relational Analysis formalism by optimizing a cost function defined as a Condorcet criterion. We propose an hybrid algorithm, which deals linearly with large datasets, 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 the data. The proposed approach called RTC was validated on several datasets and the experimental results showed very promising performances.