The application of principal component analysis on human development indicators: Temporal approach from 1999 to 2010

Background and Objective. Ever since the human development index was published in 1990 by the United Nations Development Programme (UNDP), many researchers started searching and corporative studying for more effective methods to measure the human development. Published in 1999, Lai’s “Temporal analysis of human development indicators: principal component approach” provided a valuable statistical way on human developmental analysis. This study presented in the thesis is the extension of Lai’s 1999 research. ^ Methods. I used the weighted principal component method on the human development indicators to measure and analyze the progress of human development in about 180 countries around the world from the year 1999 to 2010. The association of the main principal component obtained from the study and the human development index reported by the UNDP was estimated by the Spearman’s rank correlation coefficient. The main principal component was then further applied to quantify the temporal changes of the human development of selected countries by the proposed Z-test. ^ Results. The weighted means of all three human development indicators, health, knowledge, and standard of living, were increased from 1999 to 2010. The weighted standard deviation for GDP per capita was also increased across years indicated the rising inequality of standard of living among countries. The ranking of low development countries by the main principal component (MPC) is very similar to that by the human development index (HDI). Considerable discrepancy between MPC and HDI ranking was found among high development countries with high GDP per capita shifted to higher ranks. The Spearman’s rank correlation coefficient between the main principal component and the human development index were all around 0.99. All the above results were very close to outcomes in Lai’s 1999 report. The Z test result on temporal analysis of main principal components from 1999 to 2010 on Qatar was statistically significant, but not on other selected countries, such as Brazil, Russia, India, China, and U.S.A.^ Conclusion. To synthesize the multi-dimensional measurement of human development into a single index, the weighted principal component method provides a good model by using the statistical tool on a comprehensive ranking and measurement. Since the weighted main principle component index is more objective because of using population of nations as weight, more effective when the analysis is across time and space, and more flexible when the countries reported to the system has been changed year after year. Thus, in conclusion, the index generated by using weighted main principle component has some advantage over the human development index created in UNDP reports.^

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Selection of cowpea progenies with enhanced drought-tolerance traits using principal component analysis.

Vigna unguiculata (L.) Walp (cowpea) is a food crop with high nutritional value that is cultivated throughout tropical and subtropical regions of the world. The main constraint on high productivity of cowpea is water deficit, caused by the long periods of drought that occur in these regions. The aim of the present study was to select elite cowpea genotypes with enhanced drought tolerance, by applying principal component analysis to 219 first-cycle progenies obtained in a recurrent selection program. The experimental design comprised a simple 15 x 15 lattice with 450 plots, each of two rows of 10 plants. Plants were grown under water-deficit conditions by applying a water depth of 205 mm representing one-half of that required by cowpea. Variables assessed were flowering, maturation, pod length, number and mass of beans/pod, mass of 100 beans, and productivity/plot. Ten elite cowpea genotypes were selected, in which principal components 1 and 2 encompassed variables related to yield (pod length, beans/pod, and productivity/plot) and life precocity (flowering and maturation), respectively.

Runoff sources and land cover change in the Amazon: an end-member mixing analysis from small watersheds

The flowpaths by which water moves from watersheds to streams has important consequences for the runoff dynamics and biogeochemistry of surface waters in the Amazon Basin. The clearing of Amazon forest to cattle pasture has the potential to change runoff sources to streams by shifting runoff to more surficial flow pathways. We applied end-member mixing analysis (EMMA) to 10 small watersheds throughout the Amazon in which solute composition of streamwater and groundwater, overland flow, soil solution, throughfall and rainwater were measured, largely as part of the Large-Scale Biosphere-Atmosphere Experiment in Amazonia. We found a range in the extent to which streamwater samples fell within the mixing space determined by potential flowpath end-members, suggesting that some water sources to streams were not sampled. The contribution of overland flow as a source of stream flow was greater in pasture watersheds than in forest watersheds of comparable size. Increases in overland flow contribution to pasture streams ranged in some cases from 0% in forest to 27-28% in pasture and were broadly consistent with results from hydrometric sampling of Amazon forest and pasture watersheds that indicate 17- to 18-fold increase in the overland flow contribution to stream flow in pastures. In forest, overland flow was an important contribution to stream flow (45-57%) in ephemeral streams where flows were dominated by stormflow. Overland flow contribution to stream flow decreased in importance with increasing watershed area, from 21 to 57% in forest and 60-89% in pasture watersheds of less than 10 ha to 0% in forest and 27-28% in pastures in watersheds greater than 100 ha. Soil solution contributions to stream flow were similar across watershed area and groundwater inputs generally increased in proportion to decreases in overland flow. Application of EMMA across multiple watersheds indicated patterns across gradients of stream size and land cover that were consistent with patterns determined by detailed hydrometric sampling.

Biomimetic oxidative treatment of spruce wood studied by pyrolysis-molecular beam mass spectrometry coupled with multivariate analysis and (13)C-labeled tetramethylammonium hydroxide thermochemolysis: implications for fungal degradation of wood

In this work, pyrolysis-molecular beam mass spectrometry analysis coupled with principal components analysis and (13)C-labeled tetramethylammonium hydroxide thermochemolysis were used to study lignin oxidation, depolymerization, and demethylation of spruce wood treated by biomimetic oxidative systems. Neat Fenton and chelator-mediated Fenton reaction (CMFR) systems as well as cellulosic enzyme treatments were used to mimic the nonenzymatic process involved in wood brown-rot biodegradation. The results suggest that compared with enzymatic processes, Fenton-based treatment more readily opens the structure of the lignocellulosic matrix, freeing cellulose fibrils from the matrix. The results demonstrate that, under the current treatment conditions, Fenton and CMFR treatment cause limited demethoxylation of lignin in the insoluble wood residue. However, analysis of a water-extractable fraction revealed considerable soluble lignin residue structures that had undergone side chain oxidation as well as demethoxylation upon CMFR treatment. This research has implications for our understanding of nonenzymatic degradation of wood and the diffusion of CMFR agents in the wood cell wall during fungal degradation processes.

Visualization of learning in multilayer perceptron networks using principal component analysis

This paper is concerned with the use of scientific visualization methods for the analysis of feedforward neural networks (NNs). Inevitably, the kinds of data associated with the design and implementation of neural networks are of very high dimensionality, presenting a major challenge for visualization. A method is described using the well-known statistical technique of principal component analysis (PCA). This is found to be an effective and useful method of visualizing the learning trajectories of many learning algorithms such as back-propagation and can also be used to provide insight into the learning process and the nature of the error surface.

Analysis of genetic diversity within Australian lucerne cultivars and implications for future genetic improvement

Lucerne (Medicago sativa L.) is autotetraploid, and predominantly allogamous. This complex breeding structure maximises the genetic diversity within lucerne populations making it difficult to genetically discriminate between populations. The objective of this study was to evaluate the level of random genetic diversity within and between a selection of Australian-grown lucerne cultivars, with tetraploid M. falcata included as a possible divergent control source. This diversity was evaluated using random amplified polymorphic DNA (RAPDs). Nineteen plants from each of 10 cultivars were analysed. Using 11 RAPD primers, 96 polymorphic bands were scored as present or absent across the 190 individuals. Genetic similarity estimates (GSEs) of all pair-wise comparisons were calculated from these data. Mean GSEs within cultivars ranged from 0.43 to 0.51. Cultivar Venus (0.43) had the highest level of intra-population genetic diversity and cultivar Sequel HR (0.51) had the lowest level of intra-population genetic diversity. Mean GSEs between cultivars ranged from 0.31 to 0.49, which overlapped with values obtained for within-cultivar GSE, thus not allowing separation of the cultivars. The high level of intra- and inter-population diversity that was detected is most likely due to the breeding of synthetic cultivars using parents derived from a number of diverse sources. Cultivar-specific polymorphisms were only identified in the M. falcata source, which like M. sativa, is outcrossing and autotetraploid. From a cluster analysis and a principal components analysis, it was clear that M. falcata was distinct from the other cultivars. The results indicate that the M. falcata accession tested has not been widely used in Australian lucerne breeding programs, and offers a means of introducing new genetic diversity into the lucerne gene pool. This provides a means of maximising heterozygosity, which is essential to maximising productivity in lucerne.

Principal component analysis of the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Pair trading: Clustering based on principal component analysis

This study focuses on the implementation of several pair trading strategies across three emerging markets, with the objective of comparing the results obtained from the different strategies and assessing if pair trading benefits from a more volatile environment. The results show that, indeed, there are higher potential profits arising from emerging markets. However, the higher excess return will be partially offset by higher transaction costs, which will be a determinant factor to the profitability of pair trading strategies. Also, a new clustering approach based on the Principal Component Analysis was tested as an alternative to the more standard clustering by Industry Groups. The new clustering approach delivers promising results, consistently reducing volatility to a greater extent than the Industry Group approach, with no significant harm to the excess returns.

Multivariate Analysis for Animal Selection in Experimental Research

Background: Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective: To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods: The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results: The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion: The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemicalcomposition of archaeological material such as ceramic and glass artefacts. Data of thistype can be explored using a variety of techniques, from standard multivariate methodssuch as principal components analysis and cluster analysis, to methods based upon theuse of log-ratios. The general aim is to identify groups of chemically similar artefactsthat could potentially be used to answer questions of provenance.This paper will demonstrate work in progress on the development of a documentedlibrary of methods, implemented using the statistical package R, for the analysis ofcompositional data. R is an open source package that makes available very powerfulstatistical facilities at no cost. We aim to show how, with the aid of statistical softwaresuch as R, traditional exploratory multivariate analysis can easily be used alongside, orin combination with, specialist techniques of compositional data analysis.The library has been developed from a core of basic R functionality, together withpurpose-written routines arising from our own research (for example that reported atCoDaWork'03). In addition, we have included other appropriate publicly availabletechniques and libraries that have been implemented in R by other authors. Availablefunctions range from standard multivariate techniques through to various approaches tolog-ratio analysis and zero replacement. We also discuss and demonstrate a smallselection of relatively new techniques that have hitherto been little-used inarchaeometric applications involving compositional data. The application of the libraryto the analysis of data arising in archaeometry will be demonstrated; results fromdifferent analyses will be compared; and the utility of the various methods discussed

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principalcomponent analysis allow to model compositional changes compared with a reference point.The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

Increased audiovisual integration in cochlear-implanted deaf patients: independent components analysis of longitudinal positron emission tomography data.

It has been demonstrated in earlier studies that patients with a cochlear implant have increased abilities for audio-visual integration because the crude information transmitted by the cochlear implant requires the persistent use of the complementary speech information from the visual channel. The brain network for these abilities needs to be clarified. We used an independent components analysis (ICA) of the activation (H2 (15) O) positron emission tomography data to explore occipito-temporal brain activity in post-lingually deaf patients with unilaterally implanted cochlear implants at several months post-implantation (T1), shortly after implantation (T0) and in normal hearing controls. In between-group analysis, patients at T1 had greater blood flow in the left middle temporal cortex as compared with T0 and normal hearing controls. In within-group analysis, patients at T0 had a task-related ICA component in the visual cortex, and patients at T1 had one task-related ICA component in the left middle temporal cortex and the other in the visual cortex. The time courses of temporal and visual activities during the positron emission tomography examination at T1 were highly correlated, meaning that synchronized integrative activity occurred. The greater involvement of the visual cortex and its close coupling with the temporal cortex at T1 confirm the importance of audio-visual integration in more experienced cochlear implant subjects at the cortical level.