A Topological Approach of Clustering

The clustering of objects-individuals is one of the most widely usedapproaches to exploring multidimensional data. The two commonunsupervised clustering strategies are Hierarchical Ascending Clustering(HAC) and k-means partitioning used to identify groups of similarobjects in a dataset to divide it into homogeneous groups. The proposedtopological approach of clustering, called Topological Clustering ofIndividuals (TCI), studies a homogeneous set of individuals-rowsof a data table, based on the notion of neighborhood graphs; thecolumns-variables are more-or-less correlated or linked according towhether the variable is of a quantitative or qualitative type. It enablestopological analysis of the clustering of individual variables which canbe quantitative, qualitative or a mixture of the two. It first analyzesthe correlations or associations observed between the variables in thetopological context of principal component analysis (PCA) or multiplecorrespondence analysis (MCA), depending on the type of variable, thenclassifies individuals into homogeneous groups relative to the structureof the variables considered. The proposed TCI method is presented andillustrated here using a simple real dataset with quantitative variables;however, it can also be applied with qualitative or mixed variables