
Sousa, Áurea; BacelarNicolau, Helena; Silva, Osvaldo
In 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 threeway 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 threeway data...

Teixeira, Ricardo Emanuel Cunha; D'Almeida, Andre F.; Chalub, Fabio A. C. C.
Copyright © 2014 North American Journal of Pyschology.

Silva, Osvaldo; BacelarNicolau, 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...

Sousa, Áurea; Silva, Osvaldo; BacelarNicolau, Helena; Nicolau, Fernando C.
The affinity coefficient and its extensions have both been used in hierarchical and nonhierarchical 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...

Sousa, Áurea; Nicolau, Fernando C.; BacelarNicolau, Helena; Silva, Osvaldo
Complex Data Analysis is a relatively new field that provides a range of methods for analyzing complex/symbolic data, and can be defined as the extension of standard data analysis to more complex data tables. There are two steps in Complex or Symbolic Data Analysis: i) knowledge extraction from large databases as in Data Mining; and ii) application of new tools to the extracted knowledge in order to extend Data Mining to Knowledge Mining. The weighted generalized affinity coefficient appears to be an appropriate resemblance measure between elements (statistical data units or variables) in cases where we deal with complex data...

Sousa, Áurea; BacelarNicolau, Helena; Nicolau, Fernando C.; Silva, Osvaldo
In 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.

BacelarNicolau, Helena; Nicolau, Fernando C.; Sousa, Ãurea; BacelarNicolau, Leonor
Copyright Â© 2009 Polish Academy of Sciences.

Silva, Emiliana; Mendes, Armando B.
PRORURAL Azores Rural Development Plan  for 2007 to 2013, is the European Union rural development policy adjusted to the Azores Region and it is supported by European Agricultural Fund for Rural Development. The PRORURAL was approved by Commission Decision C (2007) 6162, on the 4th of December 2007. The PRORURAL has four center lines: 1) improving competitiveness of the agricultural and forestry sectors; 2) improvement of the environment and rural landscape; 3) quality of life in rural areas and diversification of economy; and 4) operation of LAGs, Acquisition of skills and entertainment in rural areas. The financial implementation rate...

Martins, Maria do Carmo; Martins, Francisco
This paper combines Calculus and Programming to solve constrained optimization problems common in many areas, notably in Economics. It uses Lagrange multipliers, a wellknown technique for maximizing (or minimizing) functions, and the free opensource mathematics software system Sage to compute the maximum (minimum) automatically. Moreover, Sage can be used interactively to work out the solution and to graphically interpret the results, which we find a valuable and practical approach in teaching such techniques to the undergraduate level. In this paper we carry out an exercise describing how these three interdisciplinary areas can work together.

Câmara, Maria Cristina; Martins, Maria do Carmo
The canonical generalized factorization of a class of 2×2 triangular matrix symbols associated to convolution operators on a finite interval is studied. A case is considered in which the nondiagonal entry is an almostperiodic trinomial whose spectrum consists of the point zero and two other points of different signs whose distance is less than 1. Explicit formulas for the factors of such a factorization are obtained.

Câmara, Maria Cristina; Santos, António Ferreira dos; Martins, Maria do Carmo
The factorization of almostperiodic triangular symbols, G, associated to finiteinterval convolution operators is studied for two classes of operators whose Fourier symbols are almost periodic polynomials with spectrum in the group αZ+βZ+ZαZ+βZ+Z (α,β∈]0,1[α,β∈]0,1[, α+β>1α+β>1, α/β∉Qα/β∉Q). The factorization problem is solved by a method that is based on the calculation of one solution of the RiemannHilbert problem GΦ+=Φ−GΦ+=Φ− in L∞(R)L∞(R) and does not require solving the associated corona problems since a second linearly independent solution is obtained by means of an appropriate transformation on the space of solutions to the RiemannHilbert problem. Some unexpected, but interesting, results are obtained concerning the...

Cabral, João
The importance of symbolic systems is that they give us the possibility of simplifying some dynamical systems. Our expectations is that our work can help to understand better the behavior, under iteration, of the Real Rational Map, f(x)=(x²a)/(x²b), with 0

Cabral, João
The introduction of advanced scientific modules to support teaching has an important fundamental in mathematics education. But this kind of introduction collides with the lack of time that the teachers of High School have to develop new strategies and implement them, because they are attached, in Portugal, to a bureaucratic machine that consumes valuable time that could be invested in education. Didactic concepts and scientific content must work together like a gear of knowledge. The didactic knowledge allows introducing concepts that are later explored scientifically enabling educational expansion, which will be reflected in the student's creativity. We assist to a...

Melo, Helena Sousa
Procurando o envolvimento de diversas áreas, tais como a Matemática, a Arte, a Arquitetura, a História, a Geologia, as Tecnologias, o Turismo e o Empreendedorismo, e possivelmente outras tantas mais, encontramos a temática dos passeios de Calçada Portuguesa. Este trabalho incidirá sobre uma das suas utilizações, a pavimentação de passeios, destacando o interesse que desperta em cada uma das áreas mencionadas, o seu conceito e a sua aplicabilidade.

Cabral, João
Sometimes the student only needs the teacher fires the spark that ignites a whole new set of ideas and will to do something different, giving their own contribution to the development of new concepts in knowledge. The author in this article shows how a simple discipline of Informatics for Tourism, with sometimes boring concepts to the students, with a scheduled change toward the application in Tourism changed the motivation and helped to implemented team work and development of new ideas in tourism in Azores. This results intend to be a beacon, and an help to improve the techniques of teaching,...

Cabral, João
This work is an attempt to study the dynamics of real rational maps f ab (x) = (x 2  a) / (x 2  b), using symbolic dynamics. It is given an example that illustrates how the topological entropy can be calculated using kneading theory and Markov partitions in this family of rational maps.

Frias, Armindo Dias da Silva; Cabral, João
The global market advent, with consumers, that requires speed, quality of service and respect for the environment came to dictate the change of some imposed paradigms. We are seeing the integration of internal and external supply chains following the customers concerns about the environment and social friendly processes, making it sustainable. The collection and treatment of waste in the islands have great economic, social and environmental importance. Several critical points, such as transport, storage and processing must be integrated. By its growing influence on the performance on the majority of economy sectors, freight transport is assumed to be one of...

Mendes, Armando B.; Cardoso, Margarida G.M.S.
This work is part of a supermarket chain expansion study and is intended to cluster the existent outlets in order to support the evaluation of outlet performance and new outlet site location. To overcome the curse of dimensionality (a large number of attributes for a very small number of existing outlets) experts' knowledge is considered in the clustering process. Three alternative approaches are compared for this end, the experts being required to: (1) a priori: provide values for perceived dissimilarities between pairs of outlets; (2) a posteriori: evaluate results from alternative regression trees; (3) interactively: help to select base variables...

Mendes, Armando B.; Themido, Isabel H.
One of the most important decisions a retailer can make is where to locate a retail outlet. Because convenience is so important to today's consumers, a retail store can prosper or fail solely based on its location. Recently, a changing retail environment is augmenting the location importance as retail economic groups develop multioutlet chains of small stores. The methods used in the development and calibration of location models for commercial spaces and sales forecast are multiple, varying from simple analogy forecast models to very complex spatial interactions models, which may incorporate dependence models in a gravitational or logit structure and...

Noncheva, Veska; Mendes, Armando B.; Silva, Emiliana
In the nonparametric framework of Data Envelopment Analysis the statistical properties of its estimators have been investigated and only asymptotic results are available. For DEA estimators results of practical use have been proved only for the case of one input and one output. However, in the real world problems the production process is usually well described by many variables. In this paper a machine learning approach to variable aggregation based on Canonical Correlation Analysis is presented. This approach is applied for efficiency estimation of all the farms in Terceira Island of the Azorean archipelago.