A Topological Approach of Clustering
Résumé
The clustering of objects-individuals is one of the most widely used
approaches to exploring multidimensional data. The two common
unsupervised clustering strategies are Hierarchical Ascending Clustering
(HAC) and k-means partitioning used to identify groups of similar
objects in a dataset to divide it into homogeneous groups. The proposed
topological approach of clustering, called Topological Clustering of
Individuals (TCI), studies a homogeneous set of individuals-rows
of a data table, based on the notion of neighborhood graphs; the
columns-variables are more-or-less correlated or linked according to
whether the variable is of a quantitative or qualitative type. It enables
topological analysis of the clustering of individual variables which can
be quantitative, qualitative or a mixture of the two. It first analyzes
the correlations or associations observed between the variables in the
topological context of principal component analysis (PCA) or multiple
correspondence analysis (MCA), depending on the type of variable, then
classifies individuals into homogeneous groups relative to the structure
of the variables considered. The proposed TCI method is presented and
illustrated here using a simple real dataset with quantitative variables;
however, it can also be applied with qualitative or mixed variables.