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- Análise discriminante dos públicos do Centro Cultural de BelémPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaO trabalho apresentado refere-se ao uso de combinação de modelos em Análise Discriminante Discreta, no sentido de diferenciar classes de públicos do Centro Cultural de Belém. É efectuada uma análise de sensibilidade associada ao coeficiente da combinação linear dos modelos de Independência Condicional (MIC) e Gráfico Decomponível (MGD). São ainda utilizadas medidas alternativas para a avaliação dos erros de classificação.
- Avaliação do desempenho em análise discriminante discretaPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaA Análise Discriminante Discreta (ADD) está frequentemente associada a estudos nas áreas das ciências sociais e da saúde. Nestes domínios é comum dispor de classes a priori mal separadas e/ou amostras de pequenas dimensões. Neste contexto, muitos dos métodos de ADD revelam um fraco desempenho, impondo-se o desenvolvimento de outros métodos de classificação, nomeadamente por recurso à combinação de modelos. Neste trabalho iremos avaliar o desempenho de um método de ADD, usando uma abordagem de combinação de modelos, recorrendo à taxa de observações corretamente classificadas e a uma medida de associação entre as classes a priori e as classes previstas segundo a análise efetuada. Estas medidas serão determinadas em amostra de teste e/ou mediante validação cruzada.
- Classificação hierárquica de consensoPublication . Marques, AnabelaNeste trabalho apresenta-se a técnica Classificação segundo uma direcção, introduzida por Vichi, em 1995. Esta técnica tem por base a teoria da Análise Classificatória e dos Métodos de Consenso. Aplicando a Classificação segundo uma direcção a um conjunto de dados tridimensionais obtém-se uma classificação hierárquica única.
- Classification and combining modelsPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaIn the context of Discrete Discriminant Analysis (DDA) the idea of combining models is present in a growing number of papers aiming to obtain more robust and more stable models. This seems to be a promising approach since it is known that different DDA models perform differently on different subjects. Furthermore, the idea of combining models is particularly relevant when the groups are not well separeted, which often occurs in practice. Recently, we proposed a new DDA approach which is based on a linear combination of the First-order Independence Model (FOIM) and the Dependence Trees Model (DTM). In the present work we apply this new approach to classify consumers of a Portuguese cultural institution. We specifically focus on the performance of alternative models' combinations assessing the error rate and the Huberty index in a test sample. We use the R software for the algorithms' implementation and evaluation.
- Combining models in discrete discriminant analysisPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaDiverse Discrete Discriminant Analysis (DDA) models perform differently on different sample observations (Brito et al. (2006)). This fact has encouraged research in combined models for DDA. This research seems to be specially promising when the a priori classes are not well separated or 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 DDA models (Marques et al. (2008)): the First-Order Independence Model (FOIM) and the Dependence Trees Model (DTM) (Celeux and Nakache (1994). The pro- posed methodology also uses a Hierarchical Coupling Model (HIERM) when addressing multiclass classification problems, decomposing the multiclass problems into several bi-class problems, using a binary tree structure (Sousa Ferreira (2000)). The analysis is based both on simulated and real datasets. Results include measures of precision regarding a training set, a test set and cross-validation. The R software is used for the algorithm's implementation.
- Combining models in discrete discriminant analysis in the multiclass casePublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaThe idea of combining models in Discrete Discriminant Analysis (DDA) is present in a growing number of papers which aim to obtain more robust and more stable models than any of the competing ones. This seems to be a promising approach since it is known that different DDA models perform differently on different subjects (Brito et al.(2006)). In particular, this will be a more relevant issue if the groups are not well separated, which often occurs in practice. In the present work a new methodological approach is suggested which is based on DDA models' combination. The multiclass problem is decomposed into several dichotomous problems that are nested in a hierarchical binary tree (Sousa Ferreira (2000), Brito et al. (2006)) and at each level of the binary tree a new combining model is proposed to derive the decision rule. This combining model is based on two well known models in the literature - the First-order Independence Model (FOIM) and the Dependence Trees Model (DTM) (Celeux and Nakache (1994)). The MATLAB software is used for the algorithms' implementation and the proposed approach is illustrated in a DDA application.
- Combining models in supervised classification: New developmentsPublication . Ferreira, Ana Sousa; Marques, Anabela; Cardoso, MargaridaIn Discrete Discriminant Analysis dimensionality problems often occur. In this context, we propose a combining models approach, taking profit from several potential models. In the bi-class case, a single combination coefficient is considered and estimated using several strategies. In the multi-class case, the decomposition into several bi-class problems embedded in a binary tree is implemented. New developments of this approach are presented and their performances assessed on real or simulated data.
- Desempenho de uma abordagem de combinação de modelos em análise discriminante discretaPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaDeparamo-nos frequentemente nas mais diversas áreas da vida quotidiana com problemas de classificação onde vários modelos revelam um fraco desempenho, particularmente em presença de classes mal separadas e/ou amostras de pequena dimensão. A abordagem da combinação de modelos surgiu, então, naturalmente com o objectivo de encontrar novos métodos que se adaptassem melhor ao comportamento dos dados em estudo, usando a contribuição de vários modelos, minimizando assim o número de observações mal classificadas. Este trabalho insere-se no campo da Análise Discriminante Discreta, que tem vindo a despertar um interesse crescente, nomeadamente nas áreas das ciências sociais e da saúde. Neste trabalho, pretende-se avaliar o desempenho da combinação de modelos proposta por Marques et al. [3], sobre dados simulados com base no modelo de Bahadur.
- Discrete discriminant analysis: The performance of combining modelsPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, MargaridaThe idea of combinig models in Discrete Discriminant Analysis (DDA) is present in a growing number of papers which aim to obtain more robust and more stable models than any of the competing ones. This seems to be a promising approach since it is known that different DDA models perform differently on different subjects [1]. This is a particularly relevant issue when the groups are not well separeted, which often occurs in practice. recently, a new methodological approach was proposed based on a linear combination of the First-order Independence Model (FOIM) and the Dependence trees Model (DTM) ([3] and [2]). In the present work we further explore the referred approach. Since FOIM assumes that the P discrete predictive variables are independent in each group and DTM takes the predictors relationships into account, we think that the proposed approach could be sucessfully applied to many real situations. In order to evaluate its performance, we consider both real and simulated data. Furthermore we present comparisons with alternative models performance. According to the training sample size the leave-one-out approach, v-fold cross validation or assessing the error rate in a test sample are considered. The MATLAB software is used for the algorithms' implementation.
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