Pyramidal Clustering Algorithms in ISO-3D Project

TL;DR

This paper introduces two new pyramidal clustering algorithms, CAPS and CAPSO, capable of handling complex data and producing symbolic pyramids, thus extending hierarchical clustering methods to more flexible and detailed data representations.

Contribution

The paper presents novel algorithms CAPS and CAPSO for pyramidal clustering, enabling clustering of complex data with symbolic descriptions, implemented in C++ and Java for the ISO-3D project.

Findings

Algorithms successfully cluster complex data beyond tabular models.

Produced symbolic pyramids with clusters characterized by properties.

Implemented in C++ and Java for practical application.

Abstract

Pyramidal clustering method generalizes hierarchies by allowing non-disjoint classes at a given level instead of a partition. Moreover, the clusters of the pyramid are intervals of a total order on the set being clustered. [Diday 1984], [Bertrand, Diday 1990] and [Mfoumoune 1998] proposed algorithms to build a pyramid starting with an arbitrary order of the individual. In this paper we present two new algorithms name {\tt CAPS} and {\tt CAPSO}. {\tt CAPSO} builds a pyramid starting with an order given on the set of the individuals (or symbolic objects) while {\tt CAPS} finds this order. These two algorithms allows moreover to cluster more complex data than the tabular model allows to process, by considering variation on the values taken by the variables, in this way, our method produces a symbolic pyramid. Each cluster thus formed is defined not only by the set of its elements (i.e. its extent) but also by a symbolic object, which describes its properties (i.e. its intent). These two algorithms were implemented in C++ and Java to the ISO-3D project.