GenaneYouness

Co-authors :Gilbert Saporta, Chaire de StatistiqueAppliquée- CEDRIC, CNAM

Title :

Comparing partitions of different units based on same questionnaire

Abstract :

Comparing partitions is one of the open-ended questions in data analysis. The need to compare two partitions occurs during the study of two surveys of different units based on the same questionnaires but with the same structure. The goal of our work is to study this approach and to find formal procedures based on probabilistic models that are realistic under the null hypothesis that “the two partitions are close”.

We propose a method of projection partitions using linear discriminant analysis. For this purpose, for only two data sets we considered the partition from the first one as a reference; then, the individuals of the second data set are allocated according to both such a reference partition by projection and by the classical k-means algorithm. These two partitions are compared by well-known measures of association to evaluate the significance of their difference. The empirical distributions of the association measures are derived by simulation and on a real data set.

References :

chavent, m., lacomblez, c., patouille, b., 2001. Critère de Rand asymétrique, in Proceeding SFC 2001, 8eme rencontre de la Société Francophone de la Classification, pointe à pitre.

Hand, D.J., 1981.Discrimination and Classification, Wiley, London.

Hubert L., ArabieP., 1985. Comparing Partitions, Journal of Classification, 2 193-198,

Krieger A., Green P.,A 1999. Generalized Rand-Index Method for Consensus Clustering of Separate Partitions of the Same Data Base, Journal of Classification, 16 63-89.

Lazraq, A., Cleroux R., 2002. Inférence Robuste sur un Indice de Redondance, Revue de Statistique Appliquée, 4 39-54.

McLachlan, G.J. 2004.Discriminant Analysis and Statistical Pattern Recognition.Wiley-Interscience; New Edition.Stewart D., Love W., 1968. A General Canonical Correlation index, Psychological Bulletin, 70 160- 163.

Tomassone, R., Danzart, M., Daudin, J.J., Masson, J.P., 1988. Discrimination et Classement, Masson, Paris.Youness G., Saporta G., 2004.Une Méthodologie pour la Comparaison de Partitions, Revue de Statistique Appliquée, LII (1) 97-120.

Youness G., Saporta G., 2004.Some Measures of Agreement Between Close Partitions, Journal Student, 5(1) 1-12.