A Topological Clustering of Individuals

Abstract

AbstractThe 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 Clustering of Individuals, or TCI, studies a homogeneous set of individual 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 a topological context of principal component analysis (PCA) or multiple correspondence analysis (MCA), depending on the type of variable, then classifies individuals into homogeneous group, relative to the structure of the variables considered. The proposed TCI method is presented and illustrated here using a real dataset with quantitative variables, but it can also be applied with qualitative or mixed variables.