On Quantum Special Kaehler Geometry

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 2

Estabilidade de uma estrutura de agrupamento : segmentos de clientes de uma instituição cultural

Neste trabalho implementa-se, como meio de avaliação de estabilidade de um agrupamento, uma nova proposta de validação cruzada de agrupamentos que prescinde do uso de classificadores, recorrendo à utilização de amostras ponderadas de treino e teste (Cardoso, Faceli et al. 2009). Ilustra-se a metodologia proposta sobre um agrupamento de clientes do CCB - Centro Cultural de Belém. Este agrupamento é efetuado mediante estimação de um modelo de mistura finita. Na constituição dos grupos ou segmentos atende-se à natureza ordinal das variáveis base (medições em escala de tipo Likert), em alternativa à modelação habitual que consideraria as mesmas variáveis como métricas. Em complemento, são apontadas metodologias consideradas mais apropriadas para a interpretação e discriminação dos grupos obtidos.This work implements, as a means of assessing the stability of a cluster, a new proposal for crossvalidation of clusters that dispenses with the use of classifiers, resorting to the use of weighted samples of training and testing (Cardoso, Facel et al. 2009) We illustrate the proposed approach over a cluster of clients of CCB – Cultura Centre of Belem (Centro Cultural de Belém). The clustering is obtained by means of an estimation of a mixture finite model. In the constitution of the clusters or segments, it it taken in consideration the ordinal nature of the clustering base variables (measurements in Likert scale) in lieu of the usual modeling that would consider the same variables as metric. In addition, we point out to some methodologies that are considered more adequate to interpret and discriminate the segments obtained

Clustering stability and ground truth: numerical experiments

Stability has been considered an important property for evaluating clustering solutions. Nevertheless, there are no conclusive studies on the relationship between this property and the capacity to recover clusters inherent to data (“ground truth”). This study focuses on this relationship, resorting to experiments on synthetic data generated under diverse scenarios (controlling relevant factors) and experiments on real data sets. Stability is evaluated using a weighted cross-validation procedure. Indices of agreement (corrected for agreement by chance) are used both to assess stability and external validity. The results obtained reveal a new perspective so far not mentioned in the literature. Despite the clear relationship between stability and external validity when a broad range of scenarios is considered, the within-scenarios conclusions deserve our special attention: faced with a specific clustering problem (as we do in practice), there is no significant relationship between clustering stability and the ability to recover data clustersinfo:eu-repo/semantics/publishedVersio

Evaluation of clusters of credit cards holders

This work is focused on the evaluation of a clustering of credit card holders of a Portuguese financial organization, using a cross-validation procedure which is imported from supervised learning and used for evaluating results yielded by cluster analysis (an unsupervised technique). The proposed approach is conceived to deal with the particular sample characteristics – it handles a large data set and mixed (numerical and categorical) variables. This approach provides both the evaluation of the clustering solution and helps characterizing the clusters. Furthermore, it provides classification rules for new credit card holders. According to the obtained results, the internal stability is verified for a solution with five clusters. Finally, this work presents the profiles of the credit card holders’ clusters and suggests some possible strategies to study in each of them, in the business context

Evaluating discriminant analysis results

In discrete discriminant analysis (DDA) different models often exhibit different classification performances. Therefore, the idea of combining models has increasingly gained importance. In the present work we focus on the evaluation of alternative DDA models, including combined models. The proposed approach uses not only the classic indicators of classification precision but also indices of agreement that regard the relationship between the actual classes and the ones predicted by discriminant analysis. The performance of the DDA methods is analyzed based on simulated binary data, using small and moderate sample sizes. The results obtained illustrate the potential of combining DDA models, offering different evaluation perspectives.info:eu-repo/semantics/acceptedVersio

Retail clients latent segments

Latent Segments Models (LSM) are commonly used as an approach for market segmentation. When using LSM, several criteria are available to determine the number of segments. However, it is not established which criteria are more adequate when dealing with a specific application. Since most market segmentation problems involve the simultaneous use of categorical and continuous base variables, it is particularly useful to select the best criteria when dealing with LSM with mixed type base variables. We first present an empirical test, which provides the ranking of several information criteria for model selection based on ten mixed data sets. As a result, the ICL-BIC, BIC, CAIC and L criteria are selected as the best performing criteria in the estimation of mixed mixture models. We then present an application concerning a retail chain clients' segmentation. The best information criteria yield two segments: Preferential Clients and Occasional Clients.info:eu-repo/semantics/acceptedVersio

The performance of a combined distance between time series

This paper presents the comparison of a proposed measure of dissimilarity between time series (COMB) with three baseline measures. COMB is a convex combination of Euclidean distance, a Pearson correlation based distance, a Periodogram based measure and a distance between estimated autocorrelation structures. The comparison resorts to 1-Nearest Neighbour classifier (1NN) since the effectiveness of the dissimilarity measures is directly reflected on the performance of 1NN. Data considered is available in the University of California Riverside (UCR) Time-Series Archive which includes data sets from a wide variety of application domains and have been used in similar studies. The COMB measure shows promising results: a good trade-off performance-computation time when compared to the alternative distances considered.info:eu-repo/semantics/acceptedVersio

Selection of variables in Discrete Discriminant Analysis

In Discrete Discriminant Analysis one often has to deal with dimensionality problems. In fact, even a moderate number of explanatory variables leads to an enormous number of possible states (outcomes) when compared to the number of objects under study, as occurs particularly in the social sciences, humanities and health-related elds. As a consequence, classi cation or discriminant models may exhibit poor performance due to the large number of parameters to be estimated. In the present paper, we discuss variable selection techniques which aim to address the issue of dimensionality. We speci cally perform classi cation using a combined model approach. In this setting, variable selection is particularly pertinent, enabling the handling of degrees of freedom and reducing computational cost

Combining models in discrete discriminant analysis

When conducting discrete discriminant analysis, alternative models provide different levels of predictive accuracy which has encouraged the research in combined models. This research seems to be specially promising when small or moderate sized samples are considered, which often occurs in practice. In this work we evaluate the performance of a linear combination of two discrete discriminant analysis models: the first-order independence model and the dependence trees model. The proposed methodology also uses a hierarchical coupling model when addressing multi-class classification problems, decomposing the multi-class problems into several bi-class problems, using a binary tree structure. The analysis is based both on simulated and real datasets. Results of the proposed approach are compared with those obtained by random forests, being generally more accurate. Measures of precision regarding a training set, a test set and cross-validation are presented. The R software is used for the algorithms' implementation.info:eu-repo/semantics/submittedVersio