Data Analysis and Applications 3, 3rd Edition

6Selection of Proximity Measures for a Topological Correspondence Analysis

In this chapter, we propose a new topological approach to analyze the associations between two qualitative variables in the context of correspondence analysis. It compares and classifies proximity measures to select the best one according to the data under consideration. Similarity measures play an important role in many domains of data analysis. The results of any investigation into whether association exists between variables, or any operation of clustering or classification of objects are strongly dependent on the proximity measure chosen. The user has to select one measure among many existing ones. Yet, according to the notion of topological equivalence chosen, some measures are more or less equivalent. The concept of topological equivalence uses the basic notion of local neighborhood. We define the topological equivalence between two proximity measures, in the context of association between two qualitative variables, through the topological structure induced by each measure. We compare proximity measures and propose a topological criterion for choosing the best association measure, adapted to the data considered, from among some of the most widely used proximity measures for qualitative data. The principle of the proposed approach is illustrated using a real data set with conventional proximity measures for qualitative variables.

6.1. Introduction

In order to understand and act on situations that ...