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Observations on a principal components analysis of head-related transfer functions.

A recent principal components analysis (Kistler and Wightman, 1992) has shown that the transfer functions of the human external ear, for a wide range of source locations, can be expressed as weighted sums of a small number of basis vectors. Directional transfer functions obtained in this laboratory, using substantially different measurement techniques, yielded principal component basis vectors that are remarkably similar to those reported by Kistler and Wightman. When this subject population was divided in half according to the overall physical sizes of subjects, basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects.

Ear, External↗

Quantitative analysis of polymorphic mixtures of ranitidine hydrochloride by Raman spectroscopy and principal components analysis.

Ranitidine hydrochloride exists as two polymorphs, forms I and II, both of which are used to manufacture commercial tablets. Raman spectroscopy can be used to differentiate the two forms but univariate methods of quantitative analysis of one polymorph as an impurity in the other lack sensitivity. We have applied principal components analysis (PCA) of Raman spectra to binary mixtures of the two polymorphs and to binary mixtures prepared by adding one polymorph to powdered tablets of the other. Based on absorption measurements of seven spectral regions, it was found that >97% of the spectral variation was accounted for by three principal components. Quantitative calibration models generated by multiple linear regression predicted a detection limit and quantitation limit for either forms I or II in mixtures of the two of 0.6 and 1.8%, respectively. This study demonstrates that PCA of Raman spectroscopic data provides a sensitive method for the quantitative analysis of polymorphic impurities of drugs in commercial tablets with a quantitation limit of less than 2%.

Drug Evaluation, Preclinical↗

Principal component analysis of TOF-SIMS images of organic monolayers.

Principal component analysis (PCA) is a statistical method used to find combinations of variables or factors that describe the most important trends in the data. PCA has been combined with time-of-flight secondary ion mass spectrometry (TOF-SIMS) data to extract new information and find relations between species contained in complex systems. Monolayers of dipalmitoylphosphatidylcholine alone and mixed with palmitoyloleoylphosphatidylglycerol prepared using the Langmuir-Blodgett technique are discussed. PCA software provides image scores and corresponding loadings for each significant principal component. Image plots of the scores show the spatial distribution and intensity of the species defined by the loading plots (mass spectral features). The intensity and resolution of the image scores can result in substantial improvement over that of the regular TOF-SIMS images especially when static conditions are used for small analysis areas. Also, some of the effects of topography and matrix in the images can be removed, allowing for a better presentation of chemical variations.

Journal Article↗

Brain areas involved in medial temporal lobe seizures: a principal component analysis of ictal SPECT data.

The study describes brain areas involved in medial temporal lobe (mTL) seizures of 12 patients. All patients showed so-called oro-alimentary behavior within the first 20 s of clinical seizure manifestation characteristic of mTL seizures. Single photon emission computed tomography (SPECT) images of regional cerebral blood flow (rCBF) were acquired from the patients in ictal and interictal phases and from normal volunteers. Image analysis employed categorical comparisons with statistical parametric mapping and principal component analysis (PCA) to assess functional connectivity. PCA supplemented the findings of the categorical analysis by decomposing the covariance matrix containing images of patients and healthy subjects into distinct component images of independent variance, including areas not identified by the categorical analysis. Two principal components (PCs) discriminated the subject groups: patients with right or left mTL seizures and normal volunteers, indicating distinct neuronal networks implicated by the seizure. Both PCs were correlated with seizure duration, one positively and the other negatively, confirming their physiological significance. The independence of the two PCs yielded a clear clustering of subject groups. The local pattern within the temporal lobe describes critical relay nodes which are the counterpart of oro-alimentary behavior: (1) right mesial temporal zone and ipsilateral anterior insula in right mTL seizures, and (2) temporal poles on both sides that are densely interconnected by the anterior commissure. Regions remote from the temporal lobe may be related to seizure propagation and include positively and negatively loaded areas. These patterns, the covarying areas of the temporal pole and occipito-basal visual association cortices, for example, are related to known anatomic paths.

Adolescent↗

Principal-component analysis of macaque lateral geniculate nucleus chromatic data.

Principal-component analysis was used to find a set of orthonormal basis vectors that could span the chromatic space of neurons in the parvocellular layers of the macaque monkey lateral geniculate nucleus (LGN). A total of 441 spectral curves measured on 147 cells from a well-known study [R. L. De Valois, I. Abramov, and G. H. Jacobs, J. Opt. Soc. Am. 56, 966 (1966)] were used as the input data. The principal-component technique, in a completely objective manner, showed that 93% of the variance in the data could be accounted for by only three eigenvectors. An orthogonal Varimax rotation of the first two eigenvectors matched the mean spectra of the previously identified GR and YB opponent cell groups. A different rotation gave a photopic luminosity curve.

Animals↗

Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations.

Principal components analysis (PCA) was used to define the linearly dependent factors underlying sensory information processing in the vibrissal sensory area of the ventral posterior medial (VPM) thalamus in eight awake rats. Ensembles of up to 23 single neurons were simultaneously recorded in this area, either during long periods of spontaneous behavior (including exploratory whisking) or controlled deflection of single whiskers. PCA rotated the matrices of correlation between these n neurons into a series of n uncorrelated principal components (PCs), each successive PC oriented to explain a maximum of the remaining variance. The fact that this transformation is mathematically equivalent to the general Hebb algorithm in linear neural networks provided a major rationale for performing it here on data from real neuronal ensembles. Typically, most information correlated across neurons in the ensemble was concentrated within the first 3-8 PCs. Each of these was found to encode distinct, and highly significant informational factors. These factor encodings were assessed in two ways, each making use of fact that each PC consisted of a matrix of weightings, one for each neuron. First, the neurons were rank ordered according to the locations of the central whiskers in their receptive fields, allowing their weightings within different PCs to be viewed as a function of their position within the whisker representation in the VPM. Each PC was found to define a distinctly different topographic mapping of the cutaneous surface. Next, the PCs were used to weight-sum the neurons' simultaneous activities to create population vectors (PVs). Each PV consisted of a single continuous time series which represented the expression of each PC's 'magnitude' in response to stimulation of different whiskers, or during behavioral events such as active tactile whisking. These showed that each PC functioned as a feature detector capable of selectively predicting significant sensory or behavioral events with far greater statistical reliability than could any single neuron. The encoding characteristics of the first few PCs were remarkably consistent across all animals and experimental conditions, including both spontaneous exploration and direct sensory stimulation: PC1 positively weighted all neurons, mainly according to their covariance. Thus it encoded global magnitude of ensemble activity, caused either by combined sensory inputs or intrinsic network activity, such as spontaneous oscillations. PC2 encoded spatial position contrast, generally in the rostrocaudal dimension, across the whole cutaneous surface represented by the ensemble. PC3 more selectively encoded contrast in an orthogonal (usually dorsoventral) dimension. A variable number of higher numbered PCs encoded local position contrast within one or more smaller regions of the cutaneous surface. The remaining PCs typically explained residual 'noise', i.e. the uncorrelated variance that constituted a major part of each neuron's activity. Differences in behavioral or sensory experience produced relatively little in the PC weighting patterns but often changed the variance they explained (eigenvalues) enough to alter their ordering. These results argue that PCA provides a powerful set of tools for selectively measuring neural ensemble activity within multiple functionally significant 'dimensions' of information processing. As such, it redefines the 'neuron' as an entity which contributes portions of its variance to processing not one, but several tasks.

Animals↗

Use of principal component analysis to evaluate the partial organ tolerance of normal tissues to radiation.

PURPOSE: To describe a novel method of analyzing partial volume effects of normal tissues to radiation. With this approach, principal component analysis (PCA) is used to efficiently describe the variance in cumulative dose-volume histogram (cDVH) morphology. The independent features of cDVHs that describe the largest variance are then investigated regarding complication risk. METHODS AND MATERIALS: Principal component analysis was used to describe the variance in the morphology of normal tissue cDVHs, irrespective of complication, by summarizing the largest source of variation within the first principal component (PC), the next largest in the second PC, and so on. Plots relating the most meaningful PCs were constructed. Ideally, cDVHs associated with a complication would yield PC values that could be easily segregated from cDVHs without a complication. Two data sets were evaluated with this approach: 90 parotid gland cDVHs (36 with complications) and 203 liver cDVHs (19 with complications). RESULTS: Ninety-four percent and 80% of the variation in cDVH morphology was described with two PCs for the parotid gland and the liver data sets, respectively. Plots of the first and second PC values on a Cartesian plane for both data sets revealed "clusters." For the parotid gland, one cluster contained PCs from parotid gland cDVHs with complications, and the other primarily contained PCs from cDVHs without complications. The first PC value, corresponding to a larger volume treated with 10-60 Gy (2 Gy per fraction), was more likely to be larger in parotid gland cDVHs associated with complications than those without complications. In the plots of PC values of liver cDVHs, whole liver radiation cDVHs were segregated from the other cDVHs. There was a trend for cDVHs with a higher first PC, corresponding to increased volume treated with approximately 10-40 Gy (1.5 Gy b.i.d.), to be associated with increased risk of complication. For partial liver radiation cDVHs there was a trend for cDVHs with a higher first PC, corresponding to an increased volume treated with 5-50 Gy, to be associated with a complication. For each data set, logistic regression modeling revealed that the first PC was significantly associated with a complication developing (p < 0.02). CONCLUSIONS: Principal component analysis can be used to summarize the variance in parallel normal tissue cDVHs, and it can help segregate cDVHs at high or low risk for complications.

Adult↗

Principal components analysis of haematological data from F344 rats with bladder cancer fed N-(ethyl)-all-trans-retinamide.

Several multivariate statistical methods are available which can alleviate the problems of analysing the large volumes of data generated from toxicological experiments. One such technique, principal components analysis, provides a method for exploring the relationships between a number of variables (such as blood parameters) and for eliminating redundant data if strong correlations exist between the characters. It also provides a method for clustering individuals, which may reveal similarities between animals in a treatment group or highlight individual 'outliers'. The application of principal components analysis to a set of haematological data from a trial evaluating the efficacy of a synthetic retinoid against carcinogen-induced bladder cancer in the rat has clearly shown, in two bivariate plots, that while some animals in the carcinogen-treated groups were normal, others were anaemic and that animals fed the synthetic retinoid and killed at 1 year had a microcytic anaemia. A full exploration of the data using conventional univariate statistical analysis would have involved at least 28 graphic representations of the data, as well as the interpretation of more than 130 means and SDs. Principal components analysis provides a valuable additional tool for the statistical analysis and exploration of toxicological data, but it must be used in conjunction with univariate or other multivariate methods if hypothesis testing is required. The use of multivariate techniques in toxicology may best be assessed by their practical application to toxicological data, and this paper presents such an evaluation with the aim of encouraging further exploration of the usefulness of principal components analysis. The raw data on which most analyses have been carried out are given.

Analysis of Variance↗

Quantitative Golgi study of the rat cerebellar molecular layer interneurons using principal component analysis.

In this study, we applied for the first time a multivariate analysis to describe the anatomy of cerebellar molecular layer interneurons. Forty variables extending over a variety of morphological features (geometrical, topological, and metrical) were obtained from a three-dimensional reconstruction of 26 rat rapid Golgi-stained neurons. The subsequent principal component analysis showed that the first principal component was strongly correlated with variables related to the depth of each cell's soma in the molecular layer. The second principal component was strongly correlated with parameters describing axonal morphology. Finally, an analysis of the distribution of these anatomical features suggested that these cells cannot be classified into distinct groups but, instead, represent one continuously varying population. Thus, the classical division of molecular layer neurons into deep basket cells and superficial stellate cells is not supported by our analysis. These results have important implications for the development of the cerebellar cortex as well as for the expected patterns of Purkinje cell activity following activation of the granule cell layer.

Animals↗

Principal component analysis of lifting waveforms.

BACKGROUND: One limiting factor in lifting research design has been the inability to effectively analyze waveform data, especially when differences in body mass, height, and load magnitude influence the derived kinetic variables. The purpose of this study was to demonstrate the sensitivity of principal component analysis to quantify clinically relevant differences in kinetic lifting waveforms over three load magnitudes and between two separate populations. METHODS: Principal component analysis was applied to five kinetic lifting waveforms. The derived principal component scores were used as the dependent measures in a two-way (clinical status x load magnitude) MANOVA. FINDINGS: Significant low back pain group differences (P<0.05) were found for three of the principal component scores on extension moment generation in the sacral and thoracic regions and for trunk compression. Significant differences were found for each variable with respect to the magnitude across the entire lift time between the three load conditions, as well as four significant differences related to inferred mechanical changes that resulted from lifting increasingly heavier loads. INTERPRETATION: Principal component analysis of kinetic lifting waveforms was shown to be insensitive to a confounding factor of different load magnitudes when attempting to identify previously determined clinically relevant differences in the waveform trajectories. The analysis was able to partition the variability attributed to the direct influence of different external load magnitudes, versus those differences in spinal loading that arose from the variations in the lifting mechanics of increasing loads. The technique could be beneficial for other kinetic analyses where confounding magnitude modifiers like body size are present.

Adult↗

Principal component analysis for content-based image retrieval.

Most picture archiving and communication systems provide image search capabilities that support queries based on patient demographics and study descriptions. In a preliminary study, principal component analysis was used to represent and retrieve images on the basis of content. Principal component analysis reduces the dimensionality of the search to a basis set of prototype images that best describes the images. Each image is described by its projection on the basis set; a match to a query image is determined by comparing its projection vector on the basis set with that of the images in the database. The training image database consisted of 100 axial brain images from a three-dimensional T1-weighted magnetic resonance imaging study. The algorithm was evaluated by using 96 axial images from eight patients. Image retrieval was considered accurate if the automated algorithm returned the match section to within 3 mm of an expert-selected section; the retrieval accuracy was 83% when the images were preprocessed for uniformity in intensity and geometry. Principal component analysis can be applied to content-based retrieval of medical images. The algorithm is designed to be part of an automated image selection module that filters relevant images from an imaging study.

Algorithms↗

Two-step cluster procedure after principal component analysis identifies sperm subpopulations in canine ejaculates and its relation to cryoresistance.

A 2-step clustering procedure, using indexes derived from principal component analysis, was used to disclose sperm subpopulations within the canine ejaculate and its relationship to sperm cryoresistance. Semen from 4 dogs was frozen-thawed by a standard protocol: before freezing, computer-assisted sperm analysis of motility and morphometry were performed; after thawing, motility analysis was performed again; and cryoresistance was estimated as the percent changes in progressive motility and sperm velocities after thawing. We used indexes derived from principal component analysis (sperm velocity index [SVI] and sperm motility index [SMI]) and the SPSS 2-step cluster method to disclose sperm subpopulations. The 2-step clustering procedure revealed the existence of 6 subpopulations. Subpopulations 4 and 6 were characterized by high values of both SVI (>200 arbitrary units) and SMI (>90 arbitrary units), subpopulations 2 and 3 were characterized by medium values (SVI 100 to 130; and SMI 30 to 40), and subpopulations 1 and 5 were characterized by low values (SVI < 100; SMI < 30). The distribution of sperm subpopulations was completely different among dogs. Four sperm subpopulations based in morphometric parameters of the sperm head and midpiece were revealed. Models including SVI and SMI indexes explained curvilinear velocity (R(2) = 0.997; P < .001), straight-line velocity (R(2) = 0.98; P < .001), and average velocity (R(2) = 0.99; P < .0001) postthaw.

Animals↗

The usefulness of the Laplacian in principal component analysis and dipole source localization.

Evoked potentials are difficult to analyze because multiple sources are active simultaneously. Principal component analysis and dipole localization are two techniques that have been used to disentangle overlapping sources. Both of these techniques have problems. Principal component analysis suffers from a rotation ambiguity. Dipole localization suffers from biases when the model used to derive the sources from the scalp potentials is misspecified. Using computer simulations we demonstrate that by applying both of these techniques to the Laplacian of the voltages rather than to the raw voltages the problems associated with the two techniques are reduced. Computer programs for the analyses are presented in an Appendix.

Brain Mapping↗

[Detection of wall motion abnormality in old myocardial infarction with principal component analysis to body surface potential distribution].

The purpose of this study was to examine the correlation between body surface potential distribution and the extent of abnormally contracting segments (ACS) of the left ventricle in patients with old myocardial infarction (MI). Body surface potential distribution was quantitatively analyzed using principal component analysis. The first 6 principal components were extracted from data set obtained from both 25 normal subjects and 100 patients. The z scores were calculated at every 4 or 8 msec in another 81 patients with previous MI. In conclusion, the principal component analysis on body surface maps successfully condensed mapped data without significant loss of total variance and minute differences in the extent of ACS were sensitively detected on z scores of principal components.

Adolescent↗

Effect of washing on identification of Bacillus spores by principal-component analysis of fluorescence data.

The fluorescence spectra of Bacillus spores are measured at excitation wavelengths of 280, 310, 340, 370, and 400 nm. When cluster analysis is used with the principal-component analysis, the Bacillus globigii spores can be distinguished from the other species of Bacillus spores (B. cereus, B. popilliae, and B. thuringiensis). To test how robust the identification process is with the fluorescence spectra, the B. globigii is obtained from three separate preparations in different laboratories. Furthermore the fluorescence is measured before and after washing and redrying the B. globigii spores. Using the cluster analysis of the first two or three principal components of the fluorescence spectra, one is able to distinguish B. globigii spores from the other species, independent of preparing or washing the spores.

Algorithms↗

Enzyme specificity under dynamic control II: Principal component analysis of alpha-lytic protease using global and local solvent boundary conditions.

The contributions of conformational dynamics to substrate specificity have been examined by the application of principal component analysis to molecular dynamics trajectories of alpha-lytic protease. The wild-type alpha-lytic protease is highly specific for substrates with small hydrophobic side chains at the specificity pocket, while the Met190-->Ala binding pocket mutant has a much broader specificity, actively hydrolyzing substrates ranging from Ala to Phe. Based on a combination of multiconformation analysis of cryo-X-ray crystallographic data, solution nuclear magnetic resonance (NMR), and normal mode calculations, we had hypothesized that the large alteration in specificity of the mutant enzyme is mainly attributable to changes in the dynamic movement of the two walls of the specificity pocket. To test this hypothesis, we performed a principal component analysis using 1-nanosecond molecular dynamics simulations using either a global or local solvent boundary condition. The results of this analysis strongly support our hypothesis and verify the results previously obtained by in vacuo normal mode analysis. We found that the walls of the wild-type substrate binding pocket move in tandem with one another, causing the pocket size to remain fixed so that only small substrates are recognized. In contrast, the M190A mutant shows uncoupled movement of the binding pocket walls, allowing the pocket to sample both smaller and larger sizes, which appears to be the cause of the observed broad specificity. The results suggest that the protein dynamics of alpha-lytic protease may play a significant role in defining the patterns of substrate specificity. As shown here, concerted local movements within proteins can be efficiently analyzed through a combination of principal component analysis and molecular dynamics trajectories using a local solvent boundary condition to reduce computational time and matrix size.

Amino Acid Substitution↗

Principal component analysis of measured quantities during degradation of hydroperoxides in oxidized vegetable oils.

Decomposition of hydroperoxides in sunflower oil under strictly oxygen-free conditions was followed by measuring peroxide values against time, absorbance values at 232 and 268 nm, para-anisidine values, and by quantitative analyses of volatile products using various additives. The results were arranged in a matrix form and subjected to principal component analysis. Three principal components explained 89-97% of the total variance in the data. The measured quantities and the effect of additives were closely related. Characteristic plots showed similarities among the measured quantities (loading plots) and among the additives (score plots). Initial decomposition rate of hydroperoxides and the amount of volatile products formed were similar to each other. The outliers, the absorbance values, were similar to each other but carried independent information from the other quantities. Para-anisidine value (PAV) was a unique parameter. Since PAV behaved differently during the course of hydroperoxide degradation, it served as a kinetic indicator. Most additives were similar in their effects on the mentioned quantities, but two outliers were also observed. Rotation of the principal component axes did not change the dominant patterns observed. The investigations clearly showed which variables were worth measuring to evaluate different additives.

Analysis of Variance↗

Identification of distinct characteristics of postural sway in Parkinson's disease: a feature selection procedure based on principal component analysis.

We selected descriptive measures of the centre of pressure (CoP) displacement in quiet standing, by means of a procedure based on principal component analysis, in two groups particularly different in terms of postural behaviours, such as subjects with Parkinson's disease (PD) in the levodopa off and on states. We computed 14 measures of the CoP: 5 measures of CoP trajectory over the support surface, 3 measures that estimated the area covered by the CoP, 1 measure that estimated the principal CoP sway direction, 1 measure that quantified the CoP total power, 1 measure that estimated the variability of CoP frequency content and 3 measures of characteristic CoP frequencies [L. Rocchi, L. Chiari, A. Cappello, Feature selection of stabilometric parameters based on principal component analysis, Med. Biol. Eng. Comput. 42 (2004) 71-79; L. Rocchi, L. Chiari, F.B. Horak, Effects of deep brain stimulation and levodopa on postural sway in Parkinson's disease, J. Neurol. Neurosurg. Psychiatry, 73 (2002) 267-274]. The feature selection, independently applied to the measures obtained in the two groups, resulted in different principal component (PC) subspaces of the 14-dimension original data set (4 PCs in the off and 3 PCs in the on state to account for over 90% of the original variance), but in the same 5 CoP measures (selected features) needed to describe the different postural behaviours: root mean square distance; mean velocity; principal sway direction; centroidal frequency of the power spectrum; frequency dispersion. The five selected features were found to provide insight into the postural control mechanisms and to describe changes in postural strategies in the two groups of PD subjects, off and on levodopa. Thus, the five selected features may be recommended for use in clinical practice and in research, in the direction toward the definition of a standard protocol in quantitative posturography.

Aged↗