Selection of proximity measures for a Topological Correspondence Analysis

Rafik Abdesselam (1, 2)

1 COACTIS - COnception de l'ACTIon en Situation
2 ERIC - Entrepôts, Représentation et Ingénierie des Connaissances

In this work, 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.

Domaines: Statistiques [stat]; Topologie générale [math.GN]

Rafik Abdesselam. Selection of proximity measures for a Topological Correspondence Analysis. Andreas Makrides Alex Karagrigoriou Christos H. Skiadas. Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods, Volume 5, Wiley, 2020, ⟨10.1002/9781119721871.ch6⟩. ⟨hal-02937343⟩