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In this paper, an exploratory hierarchical method to classify variables is introduced as an alternative to principal component analysis when dealing with stock-exchange price time-series. The method is based on a particular principal component analysis applied to pairs of variables, each one associated to a group to be merged. Applied to time-series, this method reveals advantageous, since it helps in defining the number of groups and their composition, while providing a factorial structure of both the hierarchy’s nodes and the partition groups. Moreover, all the issued factors, which are weighted sums of the original variables forming the groups, result in easily interpretable representative variables of them. As a case study, the method is applied to a set of Brazilian financial stock price time-series, providing representative series for each of the five groups of the proposed partition. This result complements the information on the data set provided by principal component analysis, limited to the usual orthogonal factors, each one representing an independent source of variation. It is likely that the use of such classification method may help both in deepening the knowledge of a market structure and the modelling of the different time-series, based on the modelling of their representative one.

The geomorphometric classifications of three groups of volcanoes situated in the Andes Cordillera, Central America, and Mexico are performed and compared. Input data are eight local topographic gradients (i.e. elevation differences) obtained by processing each volcano raster ASTER-GDEM data. The pixels of each volcano DEM have been classified into 17 classes through a K-means clustering procedure following principal component analysis of the gradients. The spatial distribution of the classes, representing homogeneous terrain units, is shown on thematic colour maps, where colours are assigned according to mean slope and aspect class values. The interpretation of the geomorphometric classification of the volcanoes is based on the statistics of both gradients and morphometric parameters (slope, aspect and elevation). The latter were used for a comparison of the volcanoes, performed through classes' slope/aspect scatterplots and multidimensional methods. In this paper, we apply the mentioned methodology on 21 volcanoes, randomly chosen from Mexico to Patagonia, to show how it may contribute to detect geomorphological similarities and differences among them. As such, both its descriptive and graphical abilities may be a useful complement to future volcanological studies.

The identification of a reduced dimensional representation of the data is among the main issues of exploratory multidimensional data analysis and several solutions had been proposed in the literature according to the method. Principal Component Analysis (PCA) is the method that has received the largest attention thus far and several identification methods—the so-called stopping rules—have been proposed, giving very different results in practice, and some comparative study has been carried out. Some inconsistencies in the previous studies led us to try to fix the distinction between signal from noise in PCA—and its limits—and propose a new testing method. This consists in the production of simulated data according to a predefined eigenvalues structure, including zero-eigenvalues. From random populations built according to several such structures, reduced-size samples were extracted and to them different levels of random normal noise were added. This controlled introduction of noise allows a clear distinction between expected signal and noise, the latter relegated to the non-zero eigenvalues in the samples corresponding to zero ones in the population. With this new method, we tested the performance of ten different stopping rules. Of every method, for every structure and every noise, both power (the ability to correctly identify the expected dimension) and type-I error (the detection of a dimension composed only by noise) have been measured, by counting the relative frequencies in which the smallest non-zero eigenvalue in the population was recognized as signal in the samples and that in which the largest zero-eigenvalue was recognized as noise, respectively. This way, the behaviour of the examined methods is clear and their comparison/evaluation is possible. The reported results show that both the generalization of the Bartlett’s test by Rencher and the Bootstrap method by Pillar result much better than all others: both are accounted for reasonable power, decreasing with noise, and very good type-I error. Thus, more than the others, these methods deserve being adopted.

Aphasia is called the loss of some abilities related to language production and/or comprehension. In the framework of aphasia studies, the ability of the patient to recognize and correctly verbalize a set of images is verified through suitable tests. Since the images are supposed to be easily and unequivocally recognized and named by every person, tailoring images taken from the Snodgrass and Vanderwarts (1980) original test to the Brazilian reality is necessary. We faced the following two issues: the selection of images that are easily recognizable, and the estimate of an index measuring the primitivity of the corresponding word, that is how early in life a person heard the word. To this aim, two surveys have been carried out, where the images were proposed to non-aphasic judges. We report in this paper the results of the exploratory multidimensional analyses carried out to select both images and judges and to define the primitivity index.

For the study of El Nino phenomenon, winds data collected from the Equator belt of Pacific ocean would be analyzed through PCA. In this paper, the 2-dimensional nature of winds is discussed in respect to the possible ways in which PCA may be implemented. Among others, complex PCA is proposed and compared on a small example to other methods based on real PCA. Then, the first results on a larger data table are illustrated.

In order to assess the response of the radial growth of Pinus pinea L. to climatic variability in Central Italy, dendrochronological and dendroclimatological analyses were carried out on five different populations scattered along the Tyrrhenian coasts of the peninsula. The aim of this study is to contribute to the understanding of the ecological demands of this species, particularly in the study area. For each site total ring, early-, and late-wood width chronologies were developed. Multidimensional analyses were performed for the three tree-ring datasets in order to analyze the relations between sites chronologies. Both Principal Component Analyses and hierarchical classifications highlighted an important difference of one site in respect to the other, probably due to site characteristics. Correlation functions were performed to infer the main climatic factors controlling the radial growth of the species. For a comparative study, we limited our attention to the common interval 1926-2003 (78 years) in which the response of the tree-ring chronologies to climate at both local and regional scale was investigated. Positive moisture balance in the late spring-summer period of the year of growth is the climatic driver of P. pinea radial growth in the study area. Moreover, this study shows how low summer temperatures strongly favor the radial growth of the species. Fil: Piraino, Sergio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mendoza. Instituto Argentino de Investigaciones de Zonas Aridas; Argentina Fil: Camiz, Sergio. Universita degli studi di Roma "Sapienza". Dipartimento di Matematica; Italia Fil: Di Filippo, Alfredo. Universita Degli Studi Della Tuscia. DendrologyLab; Italia Fil: Piovesan, Gianluca. Universita Degli Studi Della Tuscia. DendrologyLab; Italia Fil: Spada, Francesco. Universita degli studi di Roma "Sapienza". Dipartimento de biología ambientale; Italia

In this paper a three-step procedure is proposed to deal with ecological data, usually very complex in their treatment. The three steps – exploratory, confirmatory, and modelling phases – reflect the different methodological approaches necessary in each phase of the study. To illustrate the methodology, a case study is proposed, concerning the suitability of plants as pollution bioindicators. Samples of differently aged Pinus pinea L. needles were collected throughout 1 year in three different locations, whose human disturbance was known to be different. In the samples some morphological and functional parameters were measured, whose relation with the stress was already known. The exploratory analysis suggested pollution with human origin, the needle’s age, and the environmental conditions as the main factors of influence of damage. The confirmatory analysis confirmed both site and age as main factors and occasionally the sampling date. On this basis, some models were estimated separately for each site: models that best described the damage as function of age resulted non-linear and some of them with seasonal fluctuations. As a result, whereas the models described well enough the pollution temporal variation, the difference of pollution in the sites was best described by the different values of the models parameters in the different sites. In short, different pollution conditions are described better by the damage trend than by the individual measures. The three-step procedure resulted of high utility in outlining the most interesting relations to investigate through the modelling, the opportunity to model the indicators variation along time separately for each site, and to introduce the seasonal variation in some models.