Representation and analysis of soccer players' actions using principal components

This paper proposes the use of the Principal Components Analysis (PCA) method to represent and to analyse soccer players' actions distribution in the pitch. The seven games of the Brazilian National Team during the 2002 World Cup were analysed. The player's position actions were measured from videotapes in a computer interface. The results were: a) the graphical representation, given by two orthogonal segments in the two directions of maximal variability and centred at the mean of each player's actions position; b) the eccentricity measurement, given by the variability ratio and c) the actions zone area, given by variability product. The results showed that the individual characteristics of acting were well represented by the PCA, allowing comparisons among games and providing insights related to the tactical organisation of the team.

Non-linear principal components analysis: an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia, Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore. three geographical areas with unique environmental characteristics could be identified. Copyright (c) 2005 John Wiley & Sons, Ltd.

The use of multivariate methods in the identification of subtypes of Alzheimer's disease: a comparison of principal components and cluster analysis

Two contrasting multivariate statistical methods, viz., principal components analysis (PCA) and cluster analysis were applied to the study of neuropathological variations between cases of Alzheimer's disease (AD). To compare the two methods, 78 cases of AD were analyzed, each characterised by measurements of 47 neuropathological variables. Both methods of analysis revealed significant variations between AD cases. These variations were related primarily to differences in the distribution and abundance of senile plaques (SP) and neurofibrillary tangles (NFT) in the brain. Cluster analysis classified the majority of AD cases into five groups which could represent subtypes of AD. However, PCA suggested that variation between cases was more continuous with no distinct subtypes. Hence, PCA may be a more appropriate method than cluster analysis in the study of neuropathological variations between AD cases.

Fluorescence and reflectance spectroscopy for identification of atherosclerosis in human carotid arteries using principal components analysis

Objectives: The aim of this work was to verify the differentiation between normal and pathological human carotid artery tissues by using fluorescence and reflectance spectroscopy in the 400- to 700-nm range and the spectral characterization by means of principal components analysis. Background Data: Atherosclerosis is the most common and serious pathology of the cardiovascular system. Principal components represent the main spectral characteristics that occur within the spectral data and could be used for tissue classification. Materials and Methods: Sixty postmortem carotid artery fragments (26 non-atherosclerotic and 34 atherosclerotic with non-calcified plaques) were studied. The excitation radiation consisted of a 488-nm argon laser. Two 600-mu m core optical fibers were used, one for excitation and one to collect the fluorescence radiation from the samples. The reflectance system was composed of a halogen lamp coupled to an excitation fiber positioned in one of the ports of an integrating sphere that delivered 5 mW to the sample. The photo-reflectance signal was coupled to a 1/4-m spectrograph via an optical fiber. Euclidean distance was then used to classify each principal component score into one of two classes, normal and atherosclerotic tissue, for both fluorescence and reflectance. Results: The principal components analysis allowed classification of the samples with 81% sensitivity and 88% specificity for fluorescence, and 81% sensitivity and 91% specificity for reflectance. Conclusions: Our results showed that principal components analysis could be applied to differentiate between normal and atherosclerotic tissue with high sensitivity and specificity.

Cochineal, a precious source of red: cochineal dyes characterization by high performance liquid chromatography with diode array detection and principal component analysis

Presented at Faculdade de Ciências e Tecnologias, Universidade de Lisboa, to obtain the Master Degree in Conservation and Restoration of Textiles

Retaining principal components for discrete variables

The present study discusses retention criteria for principal components analysis (PCA) applied to Likert scale items typical in psychological questionnaires. The main aim is to recommend applied researchers to restrain from relying only on the eigenvalue-than-one criterion; alternative procedures are suggested for adjusting for sampling error. An additional objective is to add evidence on the consequences of applying this rule when PCA is used with discrete variables. The experimental conditions were studied by means of Monte Carlo sampling including several sample sizes, different number of variables and answer alternatives, and four non-normal distributions. The results suggest that even when all the items and thus the underlying dimensions are independent, eigenvalues greater than one are frequent and they can explain up to 80% of the variance in data, meeting the empirical criterion. The consequences of using Kaiser"s rule are illustrated with a clinical psychology example. The size of the eigenvalues resulted to be a function of the sample size and the number of variables, which is also the case for parallel analysis as previous research shows. To enhance the application of alternative criteria, an R package was developed for deciding the number of principal components to retain by means of confidence intervals constructed about the eigenvalues corresponding to lack of relationship between discrete variables.

Principal components analysis for quality evaluation of cooled banana 'Nanicão' in different packing

This work aims determinate the evaluation of the quality of 'Nanicão' banana, submitted to two conditions of storage temperature and three different kinds of package, using the technique of the Analysis of Principal Components (ACP), as a basis for an Analysis of Variance. The fruits used were 'Nanicão' bananas, at ripening degree 3, that is, more green than yellow. The packages tested were: "Torito" wood boxes, load capacity: 18 kg; "½ box" wood boxes, load capacity: 13 kg; and cardboard boxes, load capacity: 18 kg. The temperatures assessed were: room temperature (control); and (13±1ºC), with humidity controlled to 90±2,5%. Fruits were discarded when a sensory analysis determined they had become unfit for consumption. Peel coloration, percentages of imperfection, fresh mass, total acidity, pH, total soluble solids and percentages of sucrose were assessed. A completely randomized design with a 2-factorial treatment structure (packing X temperature) was used. The obtained data were analyzed through a multivariate analysis known as Principal Components Analysis, using S-plus 4.2. The conclusion was that the best packages to preserve the fruit were the ½ box ones, which proves that it is necessary to reduce the number of fruits per package to allow better ventilation and decreases mechanical injuries and ensure quality for more time.

Identifying the component structure of job satisfaction by principal components analysis among extension officers in North West Province, South Africa

The component structure of a 34-item scale measuring different aspects of job satisfaction was investigated among extension officers in North West Province, South Africa. A simple random sampling technique was used to select 40 extension officers from which data were collected. A structured questionnaire consisting of 34 job satisfaction and 10 personal characteristic items was administered to the extension officers. Items on job satisfaction were measured at interval level and analyzedwith Principal ComponentAnalysis. Most of the respondents (82.5%) weremales, between 40 to 45 years, 85% were married and 87.5% had a diploma as their educational qualification. Furthermore, 54% of the households size between 4 to 6 persons, whereas 75% were Christians. The majority of the extension officers lived in their job area (82.5), while 80% covered at least 3 communities and 3 farmer groups. In terms of number of farmers covered, only 40% of the extension officers covered more than 500 farmers and 45% travelled more than 40 km to reach their farmers. From the job satisfaction items 9 components were extracted to show areas for job satisfaction among extension officers. These were in-service training, research policies, communicating recommended practices, financial support for self and family, quality of technical help, opportunity to advance education, management and control of operations, rewarding system and sanctions. The results have several implications for motivating extension officers for high job performance especially with large number of clients and small number of extension agents.

Chemotaxonomic relationships in Celastraceae inferred from principal component analysis (PCA) and partial least squares (PLS)

This paper describes a chemotaxonomic analysis of a database of triterpenoid compounds from the Celastraceae family using principal component analysis (PCA). The numbers of occurrences of thirty types of triterpene skeleton in different tribes of the family were used as variables. The study shows that PCA applied to chemical data can contribute to an intrafamilial classification of Celastraceae, once some questionable taxa affinity was observed, from chemotaxonomic inferences about genera and they are in agreement with the phylogeny previously proposed. The inclusion of Hippocrateaceae within Celastraceae is supported by the triterpene chemistry.

Reduction capability of soil humic substances from the Rio Negro basin, Brazil, towards Hg(II) studied by a multimethod approach and principal component analysis (PCA)

This paper characterizes humic substances (HS) extracted from soil samples collected in the Rio Negro basin in the state of Amazonas, Brazil, particularly investigating their reduction capabilities towards Hg(II) in order to elucidate potential mercury cycling/volatilization in this environment. For this reason, a multimethod approach was used, consisting of both instrumental methods (elemental analysis, EPR, solid-state NMR, FIA combined with cold-vapor AAS of Hg(0)) and statistical methods such as principal component analysis (PCA) and a central composite factorial planning method. The HS under study were divided into groups, complexing and reducing ones, owing to different distribution of their functionalities. The main functionalities (cor)related with reduction of Hg(II) were phenolic, carboxylic and amide groups, while the groups related with complexation of Hg(II) were ethers, hydroxyls, aldehydes and ketones. The HS extracted from floodable regions of the Rio Negro basin presented a greater capacity to retain (to complex, to adsorb physically and/or chemically) Hg(II), while nonfloodable regions showed a greater capacity to reduce Hg(II), indicating that HS extracted from different types of regions contribute in different ways to the biogeochemical mercury cycle in the basin of the mid-Rio Negro, AM, Brazil. (c) 2007 Published by Elsevier B.V.

Principal components analysis of Alzheimer’s disease based on neuropathological data: A study of 79 patients

A Principal Components Analysis of neuropathological data from 79 Alzheimer’s disease (AD) cases was performed to determine whether there was evidence for subtypes of the disease. Two principal components were extracted from the data which accounted for 72% and 12% of the total variance respectively. The results suggested that 1) AD was heterogeneous but subtypes could not be clearly defined; 2) the heterogeneity, in part, reflected disease onset; 3) familial cases did not constitute a distinct subtype of AD and 4) there were two forms of late onset AD, one of which was associated with less senile plaque and neurofibrillary tangle development but with a greater degree of brain atherosclerosis.