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PubMed1995

EP component identification and measurement by principal components analysis.

Between the acquisition of Evoked Potential (EP) data and their interpretation lies a major problem: What to measure? An approach to this kind of problem is outlined here in terms of Principal Components Analysis (PCA). An important second theme is that experimental manipulation is important to functional interpretation. It would be desirable to have a system of EP measurement with the following characteristics: (1) represent the data in a concise, parsimonous way; (2) determine EP components from the data without assuming in advance any particular waveforms for the components; (3) extract components which are independent of each other; (4) measure the amounts (contributions) of various components in observed EPs; (5) use measures that have greater reliability than measures at any single time point or peak; and (6) identify and measure components that overlap in time. PCA has these desirable characteristics. Simulations are illustrated. PCA's beauty also has some warts that are discussed. In addition to discussing the usual two-mode model of PCA, an extension of PCA to a three-mode model is described that provides separate parameters for (1) waveforms over time, (2) coefficients for spatial distribution, and (3) scores telling the amount of each component in each EP. PCA is compared with more traditional approaches. Some biophysical considerations are briefly discussed. Choices to be made in applying PCA are considered. Other issues include misallocation of variance, overlapping components, validation, and latency changes.

Brain↗
PubMed1992

[Classification of congenital superior oblique palsy based on principal component analysis].

An attempt was to classify unilateral congenital superior oblique palsy principal component analysis. Each principal component was calculated by taking a linear combination of an eigenvector of the correlation matrix with a standardized original variable. The variables selected for the analysis were vertical deviation in the nine diagnostic positions of 51 cases measured by a synoptometer. The cumulative contributive percent of principal components showed that 88.5% of the variation were accounted for by the first three principal components. The first principal component accounted for 56.7% of the variation in samples indicating the extent of superior oblique palsy in which vertical deviation increases or decreases proportionately. The second principal component accounted for 20.6% of the variation of samples indicating the extent of the incomitance of vertical deviation with a vertical change of gaze. The third principal component accounted for 11.1% of the variation in the sample indicating the extent of the vertical deviation with a horizontal change of gaze.

Adolescent↗
PubMed1997

Topographical characteristics and principal component structure of the hypnagogic EEG.

The purpose of the present study was to identify the dominant topographic components of electroencephalographs (EEG) and their behavior during the waking-sleeping transition period. Somnography of nocturnal sleep was recorded on 10 male subjects. Each recording, from "lights-off" to 5 minutes after the appearance of the first sleep spindle, was analyzed. The typical EEG patterns during hypnagogic period were classified into nine EEG stages. Topographic maps demonstrated that the dominant areas of alpha-band activity moved from the posterior areas to anterior areas along the midline of the scalp. In delta-, theta-, and sigma-band activities, the differences of EEG amplitude between the focus areas (the dominant areas) and the surrounding areas increased as a function of EEG stage. To identify the dominant topographic components, a principal component analysis was carried out on a 12-channel EEG data set for each of six frequency bands. The dominant areas of alpha 2- (9.6-11.4 Hz) and alpha 3- (11.6-13.4 Hz) band activities moved from the posterior to anterior areas, respectively. The distribution of alpha 2-band activity on the scalp clearly changed just after EEG stage 3 (alpha intermittent, < 50%). On the other hand, alpha 3-band activity became dominant in anterior areas after the appearance of vertex sharp-wave bursts (EEG stage 7). For the sigma band, the amplitude of extensive areas from the frontal pole to the parietal showed a rapid rise after the onset of stage 7 (the appearance of vertex sharp-wave bursts). Based on the results, sleep onset process probably started before the onset of sleep stage 1 in standard criteria. On the other hand, the basic sleep process may start before the onset of sleep stage 2 or the manually scored spindles.

Adult↗
PubMed1992

Measurement processes and spatial principal components analysis.

Spatial principal components analysis (SPCA) applied to the ongoing EEG yields factor loadings which, when mapped, consistently reveal symmetrical patterns resembling the spherical harmonics. In this paper, we consider the mechanisms responsible for these characteristic patterns. In doing so, we demonstrate that volume conduction is one of a family of processes capable of generating such patterns with SPCA. It is shown that any series of measurements on a sphere in which the covariance is only a function of measurement site angular separation (shift invariant processes) will yield the spherical harmonics as the eigenvectors or factor loadings of the covariance matrix. Simulations further indicate that this effect is robust and not determined by the geometry of the measurement sites. In situations where shift invariant signals coexist with those generated at specific sites (anatomically specific processes), such as evoked potentials and some artifacts, it is shown that the anatomically specific signals do not influence the eigenvectors of the covariance matrix in a uniform or random fashion. The factors most influenced are those whose symmetry is similar to that of the site specific signal.

Brain↗
PubMed2000

Topography of clonidine-induced electroencephalographic changes evaluated by principal component analysis.

BACKGROUND: Principal component analysis is a multivariate statistical technique to facilitate the evaluation of complex data dimensions. In this study, principle component analysis was used to reduce the large number of variables from multichannel electroencephalographic recordings to a few components describing changes of spatial brain electric activity after intravenous clonidine. METHODS: Seven healthy volunteers (age, 26 +/- 3 [SD] yr) were included in a double-blind crossover study with intravenous clonidine (1.5 and 3.0 microg/kg). A spontaneous electroencephalogram was recorded by 26 leads and quantified by standard fast Fourier transformation in the delta, theta, alpha, and beta bands. Principle component analysis derived from a correlation matrix calculated between all electroencephalographic leads (26 x 26 leads) separately within each classic frequency band. The basic application level of principle component analysis resulted in components representing clusters of electrodes positions that were differently affected by clonidine. Subjective criteria of drowsiness and anxiety were rated by visual analog scales. RESULTS: Topography of clonidine-induced electroencephalographic changes could be attributed to two independent spatial components in each classic frequency band, explaining at least 85% of total variance. The most prominent effects of clonidine were increases in the delta band over centroparietooiccipital areas and decreases in the alpha band over parietooccipital regions. Clonidine administration resulted in subjective drowsiness. CONCLUSIONS: Data from the current study supported the fact that spatial principle component analysis is a useful multivariate statistical procedure to evaluate significant signal changes from multichannel electroencephalographic recordings and to describe the topography of the effects. The clonidine-related changes seen here were most probably results of its sedative effects.

Adult↗
PubMed2002

Interpretation of the results of common principal components analyses.

Common principal components (CPC) analysis is a new tool for the comparison of phenotypic and genetic variance-covariance matrices. CPC was developed as a method of data summarization, but frequently biologists would like to use the method to detect analogous patterns of trait correlation in multiple populations or species. To investigate the properties of CPC, we simulated data that reflect a set of causal factors. The CPC method performs as expected from a statistical point of view, but often gives results that are contrary to biological intuition. In general, CPC tends to underestimate the degree of structure that matrices share. Differences of trait variances and covariances due to a difference in a single causal factor in two otherwise identically structured datasets often cause CPC to declare the two datasets unrelated. Conversely, CPC could identify datasets as having the same structure when causal factors are different. Reordering of vectors before analysis can aid in the detection of patterns. We urge caution in the biological interpretation of CPC analysis results.

Analysis of Variance↗
PubMed2006

Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis.

Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems.

Computer Simulation↗
PubMed2005

Identifying critical variables of principal components for unsupervised feature selection.

Principal components analysis (PCA) is probably the best-known approach to unsupervised dimensionality reduction. However, axes of the lower-dimensional space, ie., principal components (PCs), are a set of new variables carrying no clear physical meanings. Thus, interpretation of results obtained in the lower-dimensional PCA space and data acquisition for test samples still involve all of the original measurements. To deal with this problem, we develop two algorithms to link the physically meaningless PCs back to a subset of original measurements. The main idea of the algorithms is to evaluate and select feature subsets based on their capacities to reproduce sample projections on principal axes. The strength of the new algorithms is that the computaion complexity involved is significantly reduced, compared with the data structural similarity-based feature evaluation.

Algorithms↗
PubMed1990

Comparing principal components analyses of evoked potentials recorded from heterogeneous groups of subjects.

Principal components analysis of evoked potentials differing between groups presents an interpretive problem, particularly in psychiatric research. Two sets of principal components and associated factor scores may appear to differ. The issue is to determine the extent to which visually differing principal components and resultant factor scores span the same factor space. Sets of evoked potentials from controls and from schizophrenics were each subjected to principal components analysis, from which factor score coefficients were computed for all subjects. This allowed determination of the extent to which (1) the two sets of basis waves were similar and (2) the factor scores resulting from the set of basis waves derived from principal components analysis of the control subjects' evoked potential data adequately represented those of the schizophrenics and vice-versa. Canonical correlation analyses indicated substantial similarities between the principal component structures (sets of basis waves). Multiple correlational analyses confirmed that the basis waves from either group spanned the other group's factor space. Factor scores from either set of basis waves were highly correlated. These results suggest that principal component structures derived from evoked potentials of a control group may be used in computing evoked potential factor scores of psychiatrically diverse populations even though the average evoked potentials of the groups may differ in several ways.

Evoked Potentials↗
PubMed1990

Multivariate data reduction by principal components, with application to neurological scoring instruments.

Principal components analysis is widely used as a practical tool for the analysis of multivariate data. The aim of this analysis is to reduce the dimensionality of a multivariate data set to the smallest number of meaningful and independent dimensions. The analysis can also provide interpretable linear functions of the original measured variables that may serve as valuable indices of variation. A brief introduction to principal components analysis is given herein, followed by an examination of a particular set of multivariate data accruing from a study of acute brain injuries in a pediatric population, in which severity of brain injury had been assessed with the Glasgow Coma Scale (CGS). Principal components analysis reveals that the GCS sum score is a particularly inefficient summarizer of information in this cohort. The determination of an objective weighting of measured variables, as provided through principal components analysis, is essential in the construction of meaningful neurological scoring instruments.

Coma↗
PubMed1999

A principal-components approach based on heritability for combining phenotype information.

For many traits, genetically relevant disease definition is unclear. For this reason, researchers applying linkage analysis often obtain information on a variety of items. With a large number of items, however, the test statistic from a multivariate analysis may require a prohibitively expensive correction for the multiple comparisons. The researcher is faced, therefore, with the issue of choosing which variables or combinations of variables to use in the linkage analysis. One approach to combining items is to first subject the data to a principal components analysis, and then perform the linkage analysis of the first few principal components. However, principal-components analyses do not take family structure into account. Here, an approach is developed in which family structure is taken into account when combining the data. The essence of the approach is to define principal components of heritability as the scores with maximum heritability in the data set, subject to being uncorrelated with each other. The principal components of heritability may be calculated as the solutions to a generalized eigensystem problem. Four simulation experiments are used to compare the power of linkage analyses based on the principal components of heritability and the usual principal components. The first of the experiments corresponds to the null hypothesis of no linkage. The second corresponds to a setting where the two kinds of principal components coincide. The third corresponds to a setting in which they are quite different and where the first of the usual principal components is not expected to have any power beyond the type I error rate. The fourth set of experiments corresponds to a setting where the usual principal components and the principal components of heritability differ, but where the first of the usual principal components is not without power. The results of the simulation experiments indicate that the principal components of heritability can be substantially different from the standard principal components and that when they are different, substantial gains in power can result by using the principal components of heritability in place of the standard principal components in linkage analyses.

Computer Simulation↗
PubMed1992

Composite index of skeletal mass: principal components analysis of regional bone mineral densities.

Principal components analysis is a statistical method that is used to reduce and explore data to facilitate further analyses. This method was applied to bone mineral densities measured at seven sites in 109 black and 44 white women, ages 22-80, at an internal medicine clinic in urban Detroit. We excluded subjects with a history of diseases or drugs known to affect bone metabolism. Principal components analysis was used to summarize the interrelationship of the densities and yielded two major results. First, the seven site measurements were reduced to a single, composite index (PC1) of skeletal mass that accounted for 73% of the variation in density among subjects. PC1 had roughly equal weights among the sites. A second combination of the seven sites indicated that the contrast between axial and appendicular regional densities accounted for another 10% of the variation among subjects. In investigating the relationship of density to age, body mass index, and ethnic group, we found that the principal components composite index had a stronger correlation with age (r = -0.58) and with body mass index (r = 0.34) than almost all of the regional densities. Black-white differences were larger for the composite index than for any single site density. A multiple regression of the composite index on ethnicity, body mass index, and age yielded a larger R2 (0.46) than any of the individual site densities. The second principal component, although of theoretical interest, showed a minimal ability to discriminate among subjects using the three independent variables of this study.

Absorptiometry, Photon↗
PubMed2004

Time-oriented hierarchical method for computation of principal components using subspace learning algorithm.

Principal Component Analysis (PCA) and Principal Subspace Analysis (PSA) are classic techniques in statistical data analysis, feature extraction and data compression. Given a set of multivariate measurements, PCA and PSA provide a smaller set of "basis vectors" with less redundancy, and a subspace spanned by them, respectively. Artificial neurons and neural networks have been shown to perform PSA and PCA when gradient ascent (descent) learning rules are used, which is related to the constrained maximization (minimization) of statistical objective functions. Due to their low complexity, such algorithms and their implementation in neural networks are potentially useful in cases of tracking slow changes of correlations in the input data or in updating eigenvectors with new samples. In this paper we propose PCA learning algorithm that is fully homogeneous with respect to neurons. The algorithm is obtained by modification of one of the most famous PSA learning algorithms--Subspace Learning Algorithm (SLA). Modification of the algorithm is based on Time-Oriented Hierarchical Method (TOHM). The method uses two distinct time scales. On a faster time scale PSA algorithm is responsible for the "behavior" of all output neurons. On a slower scale, output neurons will compete for fulfillment of their "own interests". On this scale, basis vectors in the principal subspace are rotated toward the principal eigenvectors. At the end of the paper it will be briefly analyzed how (or why) time-oriented hierarchical method can be used for transformation of any of the existing neural network PSA method, into PCA method.

Algorithms↗
PubMed2004

Adverse effect of drug-induced emotional problems on work and daily activities. A principal component as an independent predictor of ADRs in Shanghai patients with osteo-arthropathy taking nabumetone.

OBJECTIVE: To discover principal components among assessed items from the WHO-SF36 survey by principal component analysis (PCA) and then to establish the relationship between the candidate principal component and the incidence of ADRs induced by nabumetone in Shanghai osteoarthropathy patients. METHOD: A total of 145 patients were interviewed using the WHO-SF36 questionnaire for quality of life (QOL) assessment before the administration of nabumetone. The sub-items of the questionnaire were analyzed using PCA and several comprehensive variables were established. Relationships between these newly formed variables and the overall incidence of adverse drug reactions (ADRs) caused by nabumetone were evaluated using univariate and multivariate analyses. RESULTS: Several principal components were identified and their linear parameters were estimated using PCA. Through univariate analysis, only 1 principal component--"adverse effect on work and daily activities as a result of emotional problems"--was found related to the incidence of ADRs. The odds ratio (OR) was 1.28 with 95% confidence intervals (CI) of 1.11 and 1.48, p = 0.0384. This result was validated using a multivariate logistic analysis performed on all the alternative candidate covariates, including family income, a history of ADRs on NSAIDs, the course of the disease, level of education, control of stress, coffee consumption and consumption of salty food. The covariate information was taken from other parts of the clinical report form (CRF) used in this research. The analysis proved that the principal component, adverse effect on work and daily activities as a result of emotional problems, was an independent factor related to the overall incidence of ADRs. The odds ratio (OR) from the logistic analysis was 1.34, with 95% confidence intervals (CI) of 1.16 and 1.55, p = 0.0309. CONCLUSIONS: The principal component identified can be applied to overcome some limitations in the WHO-SF36 questionnaire such as high correlation between variables, information overlaps and weak representation of variables and the statistical data analysis of QOL can therefore be made more effective. The study shows that the principal component "adverse effect on work and daily activities as a result of emotional problems" is an independent predictor of the overall incidence of ADRs induced by nabumetone.

Activities of Daily Living↗
PubMed1975

Selecting key parameters in pharmaceutical formulations by principal component analysis.

The role of principal component analysis in the selection of pharmaceutical formulations is presented. The objective and the procedure of the analysis are discussed in detail. The technique was successfully applied to a system consisting of 10 response variables (tablet properties). Analysis of the results showed that the first component (dissolution) and components one and two together (dissolution and disintegration) contributed 95.4 and 99.3%, respectively, to the overall information about the formulations and that eight of 10 response parameters contributed nothing further to the overall information. The results obtained from this method of analysis may be found useful for achieving economy in both cost and time of measuring response. Principal component analysis also provides a basis for understanding the underlying mechanism of the system under consideration.

Computers↗
PubMed2001

Evaluation of dissolution profiles using principal component analysis.

The performance of principal component analysis (PCA) for the evaluation of dissolution profiles is examined and compared with other methods such as the similarity factor and the calculation of the area under the curve. Both simulated and real data from the pharmaceutical industry are used. The PCA scores plots of the dissolution curves provide information about the between- and within-batch variations. Differences in level or shape can be observed in the first two principal components (PCs). Irrelevant irregularities, which have a strong influence on the similarity factor, are neglected in PC1/PC2. To detect outliers in a set of dissolution curves, PCA was preferred above Hotelling's T2 test. In general, PCA is found to be a useful technique to examine dissolution data visually, but however, it does not contain criteria to decide if batches are similar or not. This can be done by combining PCA with the resampling with replacement or bootstrap method to construct confidence limits.

Solubility↗
PubMed1991

Evaluation of a principal-components tactile aid for the hearing-impaired.

Principal component analysis, a statistical data reduction technique which can be used to eliminate redundant information, has shown promising results as a speech coding strategy in auditory perceptual studies. The present study describes the development, modification, and evaluation of a principal components-based tactile aid for speech perception by the hearing-impaired. In this device, the first two principal components of an input speech signal were displayed on two-dimensional arrays of vibrators contacting either the fingertip or the forearm. Initial testing of the device with closed-set recorded speech tokens showed fair recognition performance, reaching 57% for three consonants and 56% for four vowels. Modifications to the processor algorithm designed to improve vowel recognizability resulted in higher levels of performance (66% for eight vowels). A real-time prototype was constructed implementing the revised algorithm. Live-voice testing was conducted with six normal-hearing subjects, three of whom had previous training with the Queen's University vocoder, a multichannel tactile vocoder that has shown promising results. Performance of these "trained" subjects for both single-item and connected speech tasks was excellent, equalling levels obtained with the Queen's vocoder. These results suggest that a principal components design may be a promising alternative to a vocoder strategy for a tactile aid. Results for the "naive" subjects did not reach the levels attained by the trained subjects, a finding partially attributed to the short training period available to the naive subjects. The higher level of performance for the trained subjects, together with the similarity of performance for the principal components aid and the Queen's vocoder for these subjects, suggests that they were able to transfer previous learning with the Queen's vocoder to the principal components device.

Adult↗
PubMed2000

Similarities between principal components of protein dynamics and random diffusion

Principal component analysis, also called essential dynamics, is a powerful tool for finding global, correlated motions in atomic simulations of macromolecules. It has become an established technique for analyzing molecular dynamics simulations of proteins. The first few principal components of simulations of large proteins often resemble cosines. We derive the principal components for high-dimensional random diffusion, which are almost perfect cosines. This resemblance between protein simulations and noise implies that for many proteins the time scales of current simulations are too short to obtain convergence of collective motions.

Journal Article↗