DME - Artigos em Revistas Internacionais / Articles in International Journals
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Browsing DME - Artigos em Revistas Internacionais / Articles in International Journals by Subject "Affinity Coefficient"
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- Cluster Analysis of Business DataPublication . Sousa, Áurea; Bacelar-Nicolau, Helena; Silva, OsvaldoIn this work, classical as well as probabilistic hierarchical clustering models are used to look for typologies of variables in classical data, typologies of groups of individuals in a classical three-way data table, and typologies of groups of individuals in a symbolic data table. The data are issued from a questionnaire on business area in order to evaluate the quality and satisfaction with the services provided to customers by an automobile company. The Ascendant Hierarchical Cluster Analysis (AHCA) is based, respectively, on the basic affinity coefficient and on extensions of this coefficient for the cases of a classical three-way data table and a symbolic data table, obtained from the weighted generalized affinity coefficient. The probabilistic aggregation criteria used, under the probabilistic approach named VL methodology (V for Validity, L for Linkage), resort essentially to probabilistic notions for the definition of the comparative functions. The validation of the obtained partitions is based on the global statistics of levels (STAT).
- Cluster analysis using affinity aoefficient in order to identify religious beliefs profilesPublication . Sousa, Áurea; Nicolau, Fernando C.; Bacelar-Nicolau, Helena; Silva, OsvaldoWe present an application of Ascendant Hierarchical Cluster Analysis (AHCA) to a dataset related to religion, in order to find a typology of religious beliefs profiles of individuals who live on São Miguel island (Azores) according to the frequency they go to the Mass. AHCA was based on the weighted generalized affinity coefficient for symbolic or complex data, and on classical and probabilistic aggregation criteria; the probabilistic ones belong to a parametric family of methods in the scope of the VL methodology. Additionally, we applied some validation measures (based on the values of the proximity matrix and adapted for the case of similarity measures) to evaluate the obtained results (clusters and partitions).
- Clustering of Symbolic Data based on Affinity Coefficient: Application to a Real Data SetPublication . Sousa, Áurea; Bacelar-Nicolau, Helena; Nicolau, Fernando C.; Silva, OsvaldoIn this paper, we illustrate an application of Ascendant Hierarchical Cluster Analysis (AHCA) to complex data taken from the literature (interval data), based on the standardized weighted generalized affinity coefficient, by the method of Wald and Wolfowitz. The probabilistic aggregation criteria used belong to a parametric family of methods under the probabilistic approach of AHCA, named VL methodology. Finally, we compare the results achieved using our approach with those obtained by other authors.
- Distribution of the Affinity Coefficient between Variables based on the Monte Carlo Simulation MethodPublication . Sousa, Áurea; Silva, Osvaldo; Bacelar-Nicolau, Helena; Nicolau, Fernando C.The affinity coefficient and its extensions have both been used in hierarchical and non-hierarchical Cluster Analysis. The purpose of the present empirical study on the distribution of the basic and the generalized affinity coefficients and on the distribution of the standardized affinity coefficient, by the method of Wald and Wolfowitz, under different assumptions, is to assess the effect of the statistical probability distributions of the variables (columns) of the initial data matrix, and of the respective parameters, in the distribution of the values of these coefficients. We present some results concerning the asymptotic distribution of the referred coefficients under the assumption that the variables (for which the values of these coefficients are calculated) are independent and have statistical probability distributions specified apriori. In this distributional study, based on the Monte Carlo simulation method, we considered ten well-known statistical probability distributions with different variations of the respective parameters. The simulation studies lead to the conclusion that the coefficients’ convergence for the normal distribution is quite fast and, in general, a good approximation is obtained for small sample sizes, that is for sample sizes above 20 and in many cases for sample sizes above 10.
- A global Approach to the Comparison of Clustering ResultsPublication . Silva, Osvaldo; Bacelar-Nicolau, Helena; Nicolau, Fernando C.The discovery of knowledge in the case of Hierarchical Cluster Analysis (HCA) depends on many factors, such as the clustering algorithms applied and the strategies developed in the initialstage of Cluster Analysis. We present a global approach for evaluating the quality of clustering results and making a comparison among different clustering algorithms using the relevant information available (e.g. the stability, isolation and homogeneity of the clusters). In addition, we present a visual method to facilitate evaluation of the quality of the partitions, allowing identification of the similarities and differences between partitions, as well as the behaviour of the elements in the partitions. We illustrate our approach using a complex and heterogeneous dataset (real horse data) taken from the literature. We apply HCA based on the generalized affinity coefficient (similarity coefficient) to the case of complex data (symbolic data), combined with 26 (classic and probabilistic) clustering algorithms. Finally, we discuss the obtained results and the contribution of this approach to gaining better knowledge of the structure of data.