Pyramidal Clustering Algorithms in ISO-3D Project

Pyramidal clustering method generalizes hierarchies by allowing non-disjointclasses at a given level instead of a partition. Moreover, the clusters of thepyramid are intervals of a total order on the set being clustered. [Diday1984], [Bertrand, Diday 1990] and [Mfoumoune 1998] proposed algorithms to builda pyramid starting with an arbitrary order of the individual. In this paper wepresent two new algorithms name {\tt CAPS} and {\tt CAPSO}. {\tt CAPSO} buildsa pyramid starting with an order given on the set of the individuals (orsymbolic objects) while {\tt CAPS} finds this order. These two algorithmsallows moreover to cluster more complex data than the tabular model allows toprocess, by considering variation on the values taken by the variables, in thisway, our method produces a symbolic pyramid. Each cluster thus formed isdefined not only by the set of its elements (i.e. its extent) but also by asymbolic object, which describes its properties (i.e. its intent). These twoalgorithms were implemented in C++ and Java to the ISO-3D project.