This paper discusses the evaluation of a clustering solution. Criteria based on the number of clusters and discrimination and classification processes are used to evaluate a clustering solution. The proposed approach is based on two paradigms: Statistics and Machine Learning. A multimethodological approach is advocated in the construction of models associating between properties and clusters, to provide a wider and richer set of analysis perspectives and a better knowledge discovery. Specifically, the construction of classification and discrimination logical models as a complement of quantitative statistical models is particularly useful when most of the available information is of a qualitative nature (nominal or ordinal variables). Both, the classification's global precision and the comprehension added by the discriminant model to the association between variables and clusters, are essential to evaluate a clustering solution. Depending on the dimension of the sample, descriptive analysis performed can be validated through the partition in two of the total sample-(one sub-sample for model build-up and another (holdout) for validation)-or by other procedures of cross-validation. The proposed evaluation approach is applied to a Marketing Tourism case study. The clustering solution is built upon a sample of more than 2500 Portuguese clients of Pousadas de Portugal Hotels. The database includes variables related to the evaluation of stay (per client) at the Pousadas and profiles of the surveyed clients on holidays, demographic and psychographic aspects. Measures of association, Chi-square tests, ANOVA, Discriminant Analysis, Logistic Regression, and Rule Induction (based on CN2 and C4.5 algorithms) are applied in evaluating the clustering solution built through a K-Means process.

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Clustering,Machine learning,Marketing and tourism,Multivariate statistics

• Mathematics - Natural Sciences
• Computer and Information Sciences - Natural Sciences