A Topological Approach of Clustering

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.