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PubMed2005

Gene selection for microarray data analysis using principal component analysis.

Principal component analysis (PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. It has become a useful tool in microarray data analysis. For a typical microarray data set, it is often difficult to compare the overall gene expression difference between observations from different groups or conduct the classification based on a very large number of genes. In this paper, we propose a gene selection method based on the strategy proposed by Krzanowski. We demonstrate the effectiveness of this procedure using a cancer gene expression data set and compare it with several other gene selection strategies. It turns out that the proposed method selects the best gene subset for preserving the original data structure.

Gene Expression↗

PubMedDate not supplied

Attenuation coefficients of body tissues using principal-components analysis.

Principal-components analysis is used to obtain a set of parameters for dual-energy radiography that completely describes the attenuation coefficient of any tissue over a given energy range. These parameters are the weighted averages of the densities of the elements present in a substance. Principal-components (PC) parameters are calculated for several soft tissues from measured attenuation coefficients published by Phelps et al. The calculated PC parameters are compared to the more conventional dual-energy representations of the attenuation coefficient: (1) the electron density/effective atomic number (or Compton/photoelectric) representation and (2) the equivalent water/equivalent aluminum thickness representation. The principal-components parameters represent the attenuation coefficients more accurately, and are more stable than the currently used parameters. In addition, these new parameters are sensitive to differences in the chemical composition and density, whereas the previous representations are primarily sensitive to changes in the density. It is concluded that the principal-components method provides a more sensitive and accurate indicator of changes in tissue composition than previous characterizations of the linear attenuation coefficient. The principal-components method provides a means for improving the accuracy of the characterization of tissues in dual-energy computed tomographic imaging and in dual-energy digital radiography.

Body Composition↗

PubMedDate not supplied

Exploring northeast African metric craniofacial variation at the individual level: a comparative study using principal components analysis.

A principal components analysis was carried out on male crania from the northeast quadrant of Africa and selected European and other African series. Individuals, not predefined groups, were the units of study, while nevertheless keeping group membership in evidence. The first principal component seems to largely capture "size" variation in crania from all of the regions. The same general morphometric trends were found to exist within the African and European crania, although there was some broad separation along a cline. Anatomically, the second principal component captures predominant trends denoting a broader to narrower nasal aperture combined with a similar shape change in the maxilla, an inverse relation between face-base lengths ("projection") and base breadths, and a decrease in anterior base length relative to base breadth. The third principal component broadly describes trends within Africa and Europe: specifically, a change from a combination of a relatively narrower face and longer vault, to one of a wider face and shorter vault; it shows the northeast quadrant Africans along a cline with the other Africans. Stated in relative terms, the northeastern Africans tend to exhibit narrower bases in relationship to more projecting faces, and broader nasal areas than Europeans, although there is range of variation. Relative to the other African groups, they have narrower nasal areas and narrower faces in relationship to vault length. The crania from the northeast quadrant of Africa collectively demonstrate the greatest pattern of overlap with both Europeans and other Africans. Variation was found to be high in all series but greatest in the African material as a whole. Individuals from different geographical regions frequently plotted near each other, revealing aspects of variation at the level of individuals that is obscured by concentrating on the most distinctive facial traits once used to construct "types." The high level of African interindividual variation in craniometric pattern is reminiscent of the great level of molecular diversity found in Africa. These results, coupled with those of Y chromosome studies, may help generate hypotheses concerning the length of time over which recent craniometric variation emerged in Africa.

Africa↗

PubMed1987

Relationships between physico-chemical parameters and microbial groups in Manchego and Burgos cheeses studied by principal component analysis.

Principal component analysis was used to examine the correlations between two sets of variables, one representing physicochemical characteristics (pH, aw and NaCl, moisture and fat content) of Manchego (36 samples) and Burgos (36 samples) cheeses, and the other representing counts of several microbial groups (mesophiles, psychrotrophs, lactic acid bacteria, coliforms, enterococci, staphylococci and molds and yeasts). Thermonuclease content was also included. In addition to the expected relationships (NaCl content, moisture, aw, etc.), significant correlations between some compositional characteristics and levels of certain microorganisms were found. These correlations were dependent on the type of cheese. Thermonuclease content was positively related to enterococci and ripening (only in Manchego cheese). In contrast to former observations, no relationships were observed between coliforms and enterococci counts.

Cheese↗

PubMedDate not supplied

Interpretation of laboratory results using multidimensional scaling and principal component analysis.

Principal component analysis (PCA) and multidimensional scaling (MDS) are a set of mathematical techniques which uncover the underlying structure of data by examining the relationships between variables. Both MDS and PCA use proximity measures such as correlation coefficients or Euclidean distances to generate a spatial configuration (map) of points where distances between points reflect the relationship between individuals with their underlying set of data. Multidimensional scaling, when compared to PCA, gives more readily interpretable solutions of lower dimensionality and does not depend on the assumption of a linear relationship between variables. Both MDS and PCA were applied to electrolyte profiles of patients with acute renal failure and patients without apparent disease. The MDS was superior to PCA in separating renal patients from normal patients. The one-dimensional and two-dimensional solutions of MDS and PCA were compared.

Acute Kidney Injury↗

PubMed1996

Face processing: human perception and principal components analysis.

Principal components analysis (PCA) of face images is here related to subjects' performance on the same images. In two experiments subjects were shown a set of faces and asked to rate them for distinctiveness. They were subsequently shown a superset of faces and asked to identify those that had appeared originally. Replicating previous work, we found that hits and false positives (FPs) did not correlate: Those faces easy to identify as being "seen" were unrelated to those faces easy to reject as being "unseen." PCA was performed on three data sets: (1) face images with eye position standardized, (2) face images morphed to a standard template to remove shape information, and (3) the shape information from faces only. Analyses based on PCA of shape-free faces gave high predictions of FPs, whereas shape information itself contributed only to hits. Furthermore, whereas FPs were generally predictable from components early in the PCA, hits appeared to be accounted for by later components. We conclude that shape and "texture" (the image-based information remaining after morphing) may be used separately by the human face processing system, and that PCA of images offers a useful tool for understanding this system.

Adult↗

PubMed1999

Experimental comparison of data transformation procedures for analysis of principal components.

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

Computer Simulation↗

PubMed1999

Obstructive sleep apnea: a principal component analysis.

A principal component analysis was performed on the cephalometric variables of 100 male obstructive sleep apnea (OSA) patients. Thirty cephalometric variables of cervicocraniofacial skeletal morphology were reduced to 8 principal components (PCs), which described 83.2% of the total variance. Sixteen cephalometric variables of hyoid bone position and head posture were reduced to 4 PCs, which described 85.5% of the total variance. Twenty cephalometric variables of upper airway soft tissue were reduced to 7 PCs, which described 83.7% of the total variance. These PCs described the actual characteristics of the OSA patients examined. For further analysis of PCs, stepwise multiple regression analysis was chosen. Two dependent variables of interest are the minimal distance of posterior pharyngeal airway space (PASmin) and the Apnea-Hypopnea Index (AHI). Seven PCs accounted for 79.4% of the variance of PASmin and 3 PCs accounted for 37.6% of the variance of AHI. Both principal component analysis and multiple regression analysis provide multivariate data analysis that is very useful in sorting out and clarifying the complexity of the interrelated cervicocraniofacial skeletal morphology and upper airway soft tissue in OSA patients.

Adult↗

PubMed1994

Epidemiologic analysis of spatial clustering of bovine ephemeral fever outbreaks. II. Principal component analysis.

The principal component analysis (PCA) was applied to analyze a correlation matrix of three variables on epidemic data of bovine ephemeral fever (BEF) outbreaks. These original data were summarized from the official outbreak report of Fukuoka Prefecture. The first and the second principal components of the PCA were interpreted as the infectious potency due to BEF virus and the prevention against BEF virus infection, respectively. The BEF outbreak areas were able to be classified epidemically into 4 groups by using the two principal components. The valuable epidemiological insights can be reasonably obtained from an application of the PCA. The results provided an important information for a further BEF vaccination campaign in the western part of Japan.

Animals↗

PubMed2002

[Research into simultaneous spectrophotometric determination of components in cough syrup by principal component regression method].

Principal component regression (PCR) method is used to analyse five components: acetaminophen, p-aminophenol, caffeine, chlorphenamine maleate and guaifenesin. The basic principle and the analytical step of the approach are described in detail. The computer program of LHG is based on VB language. The experimental result shows that the PCR method has no systematical error as compared to classical method. The experimental result shows that the average recovery of each component is all in the range from 96.43% to 107.14%. Each component obtains satisfactory result without any pre-separation. The approach is simple, rapid and suitable for the computer-aid analysis.

Acetaminophen↗

PubMed2004

Increasing the sensitivity of the multifocal visual evoked potential (mfVEP) technique: incorporating information from higher order kernels using a principal component analysis method.

Principal component analysis (PCA) was employed to enhance the multifocal visual evoked potential (mfVEP) technique. First, by using four principal components, the separation of mfVEP signals from noises was improved. Second, two otherwise unused higher order kernels, the 2nd slice of the 2nd order kernel and the 4th order kernels, were utilized by combining information obtained from the PCA. The PCA-kernel method improves the efficiency of the mfVEP test. The false positive rate, based upon an analysis of a noise window, was decreased by a factor of about one-third and the improvement in sensitivity of detecting glaucomatous defects was nearly as good as a doubling of the recording time.

Diagnostic Techniques, Ophthalmological↗

PubMed1987

Comparison of principal components computed with principal factor analysis on the basis of averaged and single-trial ERPs using the Fischer-Roppert procedure.

Averaged and single-trial event-related potentials (ERPs) were analysed using the Principal Factor Analysis (PFA) with following varimax rotation, and the results were compared. The correspondence between the matrices of factor loadings was tested by means of the Fischer-Roppert-procedure. For the application of PFA, a preceding averaging to improve the signal to noise ratio is not necessary. If the group of subjects is homogeneous enough, the analysis of the single-trial ERPs provides results sufficient to investigate the component structure of the ERP. The ERPs from all subjects can be described with one common component structure.

Arousal↗

PubMed1997

[Computer technology of genogeographic study of the gene pool. IV. Population in the space of principal components].

On the basis of maps of principal components ("synthetic maps"), populations were arranged in the space of principal components. In terms of the applied model, nodes of a dense, uniform grid represented human populations. For each node, the frequency of a given gene was interpolated from these values for all original populations. Principal components were estimated and mapped on the basis of maps for all genes. Each population (grid node) was assigned a marker of an ethnic or some other group of populations and was positioned in the space of principal components according to the values from the original maps. The resultant "ethnic clouds" of populations and "ethnic centroids" of principal components provide some new possibilities for explaining the patterns of changes in gene pools. The maps of reliability of principal components allow the researcher to eliminate the information on populations which is unreliable and turn to the "reliable" space of principal components. The method was tested with the use of the maps of principal components for the gene pool of the East European population. Eastern Slavonic (Russians, Ukrainians, and Belarussians) and western and eastern Finno-Ugrian (Estonians and Mordovians, respectively) ethnic groups were mapped to the space of principal components. The relative positions of the populations of these ethnic groups was analyzed in the spaces of the first and the second, the first and the third, and the second and the third principal components of the East European gene pool.

Commonwealth of Independent States↗

PubMed2006

Classification of soil samples according to their geographic origin using gamma-ray spectrometry and principal component analysis.

A principal component analysis (PCA) was used for classification of soil samples from different locations in Serbia and Montenegro. Based on activities of radionuclides ((226)Ra, (238)U, (235)U, (40)K, (134)Cs, (137)Cs, (232)Th and (7)Be) detected by gamma-ray spectrometry, the classification of soils according to their geographical origin was performed. Application of PCA to our experimental data resulted in satisfactory classification rate (86.0% correctly classified samples). The obtained results indicate that gamma-ray spectrometry in conjunction with PCA is a viable tool for soil classification.

Geography↗

PubMed2003

Monitoring of a sequencing batch reactor using adaptive multiblock principal component analysis.

Multiway principal component analysis (MPCA) for the analysis and monitoring of batch processes has recently been proposed. Although MPCA has found wide applications in batch process monitoring, it assumes that future batches behave in the same way as those used for model identification. In this study, a new monitoring algorithm, adaptive multiblock MPCA, is developed. The method overcomes the problem of changing process conditions by updating the covariance structure recursively. A historical set of operational data of a multiphase batch process was divided into local blocks in such a way that the variables from one phase of a batch run could be blocked in the corresponding blocks. This approach has significant benefits because the latent variable structure can change for each phase during the batch operation. The adaptive multiblock model also allows for easier fault detection and isolation by looking at the relationship between blocks and at smaller meaningful block models, and it therefore helps in the diagnosis of the disturbance. The proposed adaptive multiblock monitoring method is successfully applied to a sequencing batch reactor for biological wastewater treatment.

Algorithms↗

PubMed2003

Comparing G matrices: are common principal components informative?

Common principal components (CPC) analysis is a technique for assessing whether variance-covariance matrices from different populations have similar structure. One potential application is to compare additive genetic variance-covariance matrices, G. In this article, the conditions under which G matrices are expected to have common PCs are derived for a two-locus, two-allele model and the model of constrained pleiotropy. The theory demonstrates that whether G matrices are expected to have common PCs is largely determined by whether pleiotropic effects have a modular organization. If two (or more) populations have modules and these modules have the same direction, the G matrices have a common PC, regardless of allele frequencies. In the absence of modules, common PCs exist only for very restricted combinations of allele frequencies. Together, these two results imply that, when populations are evolving, common PCs are expected only when the populations have modules in common. These results have two implications: (1) In general, G matrices will not have common PCs, and (2) when they do, these PCs indicate common modular organization. The interpretation of common PCs identified for estimates of G matrices is discussed in light of these results.

Data Interpretation, Statistical↗

PubMedDate not supplied

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices.

Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k+1)/2 to m(2k-m+1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.

Analysis of Variance↗

PubMedDate not supplied

Principal component analysis of nonlinear chromatography.

Principal component analysis (PCA) has been used for the modeling of nonlinear chromatography under overload conditions. A 10-fold range of crude erythromycin samples were loaded onto columns with different stationary-phase chemistries (2 polystyrene, 1 methacrylate) in direct proportion to the bed volumes. The elution profiles indicated slightly concave isotherms for the polystyrene supports and a convex Langmuirian isotherm for the methacrylic support used. The principal component models accounted for over 98% of the original variance in the data for all three columns and were able to give excellent models of complete chromatograms in the absence of first-principle models or physicochemical data. Correlations between sample mass and the principal component scores were made for each that were consistent for the column types despite the different geometries and stationary phases. Linear relationships with high correlation coefficients were observed when the scores of the same principal component were compared between columns. Such correlations offer considerable potential for modeling of nonlinear chromatography.

Chromatography↗