DME - Parte ou Capítulo de um Livro / Part of Book or Chapter of Book
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Browsing DME - Parte ou Capítulo de um Livro / Part of Book or Chapter of Book by Subject "Affinity Coefficient"
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- Clustering Validation in the Context of Hierarchical Cluster Analysis: an Empirical StudyPublication . Silva, Osvaldo Dias Lopes da; Sousa, Áurea; Bacelar-Nicolau, HelenaABSTRACT: The evaluation of clustering structures is a crucial step in cluster analysis. This study presents the main results of the hierarchical cluster analysis of variables concerning a real dataset in the context of Higher Education. The goal of this research is to find a typology of some relevant items taking into account both the homogeneity and the isolation of the clusters.Two similarity measures, namely the standard affinity coefficient and Spearman’s correlation coefficient, were used, and combined with three probabilistic (AVL, AVB and AV1) aggregation criteria, from a parametric family in the scope of the VL (Validity Link) methodology. The best partitions were selected based on some validation indices, namely the global STAT levels statistics and the measures P(I2, Σ) and , adapted to the case of similarity coefficients. In order to evaluate the clusters and identify their most representative elements, the Mann and Whitney U statistics and the silhouette plot were also used.
- Probabilistic approach for comparing partitionsPublication . Silva, Osvaldo; Bacelar-Nicolau, Helena; Nicolau, Fernando C.; Sousa, ÁureaThe comparison of two partitions in Cluster Analysis can be performed using various classical coefficients (or indexes) in the context of three approaches (based, respectively, on the count of pairs, on the pairing of the classes and on the variation of information). However, different indexes usually highlight different peculiarities of the partitions to compare. Moreover, these coefficients may have different variation ranges or they do not vary in the predicted interval, but rather only in one of their subintervals. Furthermore, there is a great diversity of validation techniques capable of assisting in the choice of the best partitioning of the elements to be classified, but in general each one tends to favour a certain kind of algorithm. Thus, it is useful to find ways to compare the results obtained using different approaches. In order to assist this assessment, a probabilistic approach to comparing partitions is presented and exemplified. This approach, based on the VL (Validity Linkage) Similarity, has the advantage, among others, of standardizing the measurement scales in a unique probabilistic scale. In this work, the partitions obtained from the agglomerative hierarchical cluster analysis of a dataset in the field of teaching are evaluated using classical and probabilistic (of VL type) indexes, and the obtained results are compared.