Data analysis methods in optometry Part 8: Principal components analysis (PCA) and factor analysis (FA)

PCA/FA is a method of analyzing complex data sets in which there are no clearly defined X or Y variables. It has multiple uses including the study of the pattern of variation between individual entities such as patients with particular disorders and the detailed study of descriptive variables. In most applications, variables are related to a smaller number of ‘factors’ or PCs that account for the maximum variance in the data and hence, may explain important trends among the variables. An increasingly important application of the method is in the ‘validation’ of questionnaires that attempt to relate subjective aspects of a patients experience with more objective measures of vision.

Characterization of dynamic speckle sequences using principal component analysis and image descriptors

Speckle is being used as a characterization tool for the analysis of the dynamic of slow varying phenomena occurring in biological and industrial samples. The retrieved data takes the form of a sequence of speckle images. The analysis of these images should reveal the inner dynamic of the biological or physical process taking place in the sample. Very recently, it has been shown that principal component analysis is able to split the original data set in a collection of classes. These classes can be related with the dynamic of the observed phenomena. At the same time, statistical descriptors of biospeckle images have been used to retrieve information on the characteristics of the sample. These statistical descriptors can be calculated in almost real time and provide a fast monitoring of the sample. On the other hand, principal component analysis requires longer computation time but the results contain more information related with spatial-temporal pattern that can be identified with physical process. This contribution merges both descriptions and uses principal component analysis as a pre-processing tool to obtain a collection of filtered images where a simpler statistical descriptor can be calculated. The method has been applied to slow-varying biological and industrial processes

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.

Assessment of heavy metals in soils of a vineyard region with the use of principal component analysis.

Agricultural management with chemicals may contaminate the soil with heavy metals. The objective of this study was to apply Principal Component Analysis and geoprocessing techniques to identify the origin of the metals Cu, Fe, Mn, Zn, Ni, Pb, Cr and Cd as potential contaminants of agricultural soils. The study was developed in an area of vineyard cultivation in the State of São Paulo, Brazil. Soil samples were collected and GPS located under different uses and coverings. The metal concentrations in the soils were determined using the DTPA method. The Cu and Zn content was considered high in most of the samples, and was larger in the areas cultivated with vineyards that had been under the application of fungicides for several decades. The concentrations of Cu and Zn were correlated. The geoprocessing techniques and the Principal Component Analysis confirmed the enrichment of the soil with Cu and Zn because of the use and management of the vineyards with chemicals in the preceding decades.

Principal component and linkage analysis of cardiovascular risk traits in the Norfolk isolate

OBJECTIVE(S): An individual's risk of developing cardiovascular disease (CVD) is influenced by genetic factors. This study focussed on mapping genetic loci for CVD-risk traits in a unique population isolate derived from Norfolk Island. METHODS: This investigation focussed on 377 individuals descended from the population founders. Principal component analysis was used to extract orthogonal components from 11 cardiovascular risk traits. Multipoint variance component methods were used to assess genome-wide linkage using SOLAR to the derived factors. A total of 285 of the 377 related individuals were informative for linkage analysis. RESULTS: A total of 4 principal components accounting for 83% of the total variance were derived. Principal component 1 was loaded with body size indicators; principal component 2 with body size, cholesterol and triglyceride levels; principal component 3 with the blood pressures; and principal component 4 with LDL-cholesterol and total cholesterol levels. Suggestive evidence of linkage for principal component 2 (h(2) = 0.35) was observed on chromosome 5q35 (LOD = 1.85; p = 0.0008). While peak regions on chromosome 10p11.2 (LOD = 1.27; p = 0.005) and 12q13 (LOD = 1.63; p = 0.003) were observed to segregate with principal components 1 (h(2) = 0.33) and 4 (h(2) = 0.42), respectively. CONCLUSION(S): This study investigated a number of CVD risk traits in a unique isolated population. Findings support the clustering of CVD risk traits and provide interesting evidence of a region on chromosome 5q35 segregating with weight, waist circumference, HDL-c and total triglyceride levels.

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.

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.

Analysis of the build-up of semi and non volatile organic compounds on urban roads

Vehicular traffic in urban areas may adversely affect urban water quality through the build-up of traffic generated semi and non volatile organic compounds (SVOCs and NVOCs) on road surfaces. The characterisation of the build-up processes is the key to developing mitigation measures for the removal of such pollutants from urban stormwater. An in-depth analysis of the build-up of SVOCs and NVOCs was undertaken in the Gold Coast region in Australia. Principal Component Analysis (PCA) and Multicriteria Decision tools such as PROMETHEE and GAIA were employed to understand the SVOC and NVOC build-up under combined traffic scenarios of low, moderate, and high traffic in different land uses. It was found that congestion in the commercial areas and use of lubricants and motor oils in the industrial areas were the main sources of SVOCs and NVOCs on urban roads, respectively. The contribution from residential areas to the build-up of such pollutants was hardly noticeable. It was also revealed through this investigation that the target SVOCs and NVOCs were mainly attached to particulate fractions of 75 to 300 µm whilst the redistribution of coarse fractions due to vehicle activity mainly occurred in the >300 µm size range. Lastly, under combined traffic scenario, moderate traffic with average daily traffic ranging from 2300 to 5900 and average congestion of 0.47 was found to dominate SVOC and NVOC build-up on roads.

Non-invasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for non-invasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform non-invasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.

Internal and external motivation factors in virtual and collocated project environments : a principal component investigation

In this study, we explore motivation in collocated and virtual project teams. The literature on motivation in a project set.,ting reveals that motivation is closely linked to team performance. Based on this literature, we propose a set., of variables related to the three dimensions of ‘Nature of work’, ‘Rewards’, and ‘Communication’. Thirteen original variables in a sample size of 66 collocated and 66 virtual respondents are investigated using one tail t test and principal component analysis. We find that there are minimal differences between the two groups with respect to the above mentioned three dimensions. (p= .06; t=1.71). Further, a principal component analysis of the combined sample of collocated and virtual project environments reveals two factors- ‘Internal Motivating Factor’ related to work and work environment, and ‘External Motivating Factor’ related to the financial and non-financial rewards that explain 59.8% of the variance and comprehensively characterize motivation in collocated and virtual project environments. A ‘sense check’ of our interpretation of the results shows conformity with the theory and existing practice of project organization

A Near-Infrared Reflectance Spectroscopy Method for Direct Analysis of Several Chemical Components and Properties of Fruit, for Example, Chinese Hawthorn

Near-infrared spectroscopy (NIRS) calibrations were developed for the discrimination of Chinese hawthorn (Crataegus pinnatifida Bge. var. major) fruit from three geographical regions as well as for the estimation of the total sugar, total acid, total phenolic content, and total antioxidant activity. Principal component analysis (PCA) was used for the discrimination of the fruit on the basis of their geographical origin. Three pattern recognition methods, linear discriminant analysis, partial least-squares-discriminant analysis, and back-propagation artificial neural networks, were applied to classify and compare these samples. Furthermore, three multivariate calibration models based on the first derivative NIR spectroscopy, partial least-squares regression, back-propagation artificial neural networks, and least-squares-support vector machines, were constructed for quantitative analysis of the four analytes, total sugar, total acid, total phenolic content, and total antioxidant activity, and validated by prediction data sets.

A high performance liquid chromatography and electrospray ionization mass spectrometry method for the analysis of the natural medicine, Forsythia suspensa

Samples of Forsythia suspensa from raw (Laoqiao) and ripe (Qingqiao) fruit were analyzed with the use of HPLC-DAD and the EIS-MS techniques. Seventeen peaks were detected, and of these, twelve were identified. Most were related to the glucopyranoside molecular fragment. Samples collected from three geographical areas (Shanxi, Henan and Shandong Provinces), were discriminated with the use of hierarchical clustering analysis (HCA), discriminant analysis (DA), and principal component analysis (PCA) models, but only PCA was able to provide further information about the relationships between objects and loadings; eight peaks were related to the provinces of sample origin. The supervised classification models-K-nearest neighbor (KNN), least squares support vector machines (LS-SVM), and counter propagation artificial neural network (CP-ANN) methods, indicated successful classification but KNN produced 100% classification rate. Thus, the fruit were discriminated on the basis of their places of origin.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.