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PubMed1998

[Method of simulation and choice of factors in the analysis of principal components].

OBJECTIVE: There are many methods to determine how many components should be retained in principal components analysis. This choice can be made on the basis of arbitrary (Kaiser) or subjective (Interpretable factors) criteria. This work presents the simulation criteria of Lébart e Dreyfus. The method create a matrix of randomized numbers and a principal component analysis is performed on the basis of this matrix. The components extracted from this data represent the cut off values. Those that exceed this cut off value should be retained. As an example, a principal component analysis is performed with the Hamilton depression rating scale (17 items) on a sample of 130 subjects. RESULTS AND CONCLUSION: The Simulation method is compared with the Kaiser method and is shown that the Simulation method maintains the components clinically significant.

Depression↗
PubMed2005

Accounting for probe-level noise in principal component analysis of microarray data.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.

Algorithms↗
PubMed1989

[Principal component analysis of the masticatory motion path during gum chewing].

This study examined the characteristics of masticatory motion path using multivariate analysis. Principal component analysis was selected as the method and various important results were revealed as follows; Approximately 70% of the information describing gum chewing motion was explained by three principal components. From factor loading, the first principal component explains back and forth movement from the end of the opening phase to the closed position, the second principal component explains left to right movement at the onset of the mouth opening phase, and the third principal component explains left and right movement at about the position of maximum opening. Using scatter diagrams combining the first and second principal components, as well as the first and third principal components, we were able to recognize delicate differents among the subjects, but to the different strokes of any subject, characteristic patterns were emerged.

Chewing Gum↗
PubMed1995

Principal-component localization of the sources of the background EEG.

A method, based on principal components for localizing the sources of the background EEG, is presented which overcomes the previous limitations of this approach. The spatiotemporal source model of the EEG is assumed to apply, and the method involves attempting to fit the spatial aspects of this general model with an optimal rotation of a subset of the principal components of a particular EEG. The method is shown to be equivalent to the subspace scanning method, a special case of the MUSIC algorithm, which enables multiple sources to be localized individually rather than all at once. The novel aspect of the new method is that it offers a way of selecting the relevant principal components for the localization problem. The relevant principal components are chosen by decomposing the EEG using spatial patterns common with a control EEG. These spatial patterns have the property that they account for maximally different proportions of the combined variances in the two EEG's. An example is given using a particular EEG from a neurologic patient. Components containing spike and sharp wave potentials are extracted, with respect to a standard EEG derived from 15 normal volunteers. Spike and sharp wave potentials are identified visually using the common spatial patterns decomposition and an EEG reconstructed from these components. Four dipole sources are fitted to the principal components of the reconstructed EEG and these source account for over 88% of the temporal variance present in that EEG.

Action Potentials↗
PubMed2006

Classification of macular and optic nerve disease by principal component analysis.

In this study, pattern electroretinography (PERG) signals were obtained by electrophysiological testing devices from 70 subjects. The group consisted of optic nerve and macular diseases subjects. Characterization and interpretation of the physiological PERG signal was done by principal component analysis (PCA). While the first principal component of data matrix acquired from optic nerve patients represents 67.24% of total variance, the first principal component of the macular patients data matrix represents 76.81% of total variance. The basic differences between the two patient groups were obtained with first principal component, obviously. In addition, the graphic of second principal component vs. first principal component of optic nerve and macular subjects was analyzed. The two patient groups were separated clearly from each other without any hesitation. This research developed an auxiliary system for the interpretation of the PERG signals. The stated results show that the use of PCA of physiological waveforms is presented as a powerful method likely to be incorporated in future medical signal processing.

Adult↗
PubMed2002

Principal-component characterization of noise for infrared images.

Principal-component decomposition is applied to the analysis of noise for infrared images. It provides a set of eigenimages, the principal components, that represents spatial patterns associated with different types of noise. We provide a method to classify the principal components into processes that explain a given amount of the variance of the images under analysis. Each process can reconstruct the set of data, thus allowing a calculation of the weight of the given process in the total noise. The method is successfully applied to an actual set of infrared images. The extension of the method to images in the visible spectrum is possible and would provide similar results.

Journal Article↗
PubMed2003

A constrained EM algorithm for principal component analysis.

We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.

Algorithms↗
PubMed2005

[Classification of maxillary dental arches by correlation and principal component analyses].

PURPOSE: To evaluate the morphology of dental arches. METHODS: 62 (male: 36, female: 26) paired casts having normal dentitions and occlusion were selected from 396 (age: 18 to 26 years old; male: 257, female: 139) sets of dental study models. The maxillary dentitions were preliminarily classified as square, round-square, round and round V-shaped arches based on the conventional morphological descriptions. Midpoints of the incisor edge (I1(R), I1(L), I2(R), &I2(L)), summits of the cuspids (C(R) & C(L)), buccal cusps of the premolars (P1(R), P1(L), P2(R), & P2(L)), mesial buccal cusps of the first and second molars (M1(R), M1(L), M2(R), & M2(L)), and the midpoint (A) of line I1(R)-I1(L) were designated as reference points. From A, let a vertical line intersected line M2(R)-M2(L) at reference point B. The line A-B intersected CR-CL at reference point E. The following items were evaluated: (1) the protrusion of the cuspids by 1. angle I2(R)-C(R)-P1(R) (angle R) + angle I2(L)-C(L)-P1(L) (angle L); (2) the curvature of the anterior teeth by 2. A-B/C(R)-C(L), 3. 180 degrees-angle C(R)-A-C(L), and 4. A-E/C(R)-C(L); (3) the length to width ratio of the dental arch by 5. A-B/M2(R)-M2(L); (4) the degree of roundness of the maxillary arch by estimation of 6. (rtheta(5)-rtheta(4))(R)+(rtheta(5)-rtheta(4))(L); and (5) an item 7. for the differentiation of type I and type II round-square arches by relating the bilateral contour and position of break line P1-P2-M1-M2 (i) to line P1-M2 (ii). The data of items 1, 2, 3, 4, 5, and 6 were further standardized and summarized into three essential principal components: (1) the curvature of the anterior teeth, (2) the curvilinear contour of the dental arch, and (3) the length-to-width ratio of the dental arch. RESULTS: (1) 60% of the maxillary dentitions were round-square arches which showed no prominent principal component; (2) square maxillary arches distinctly showed a small 1. angle R+angle L; (3) round arches were characteristic by small 6 (rtheta(5)-rtheta(4))(R)+(rtheta(5)-rtheta(4))(L) values; and (4) round V-shaped arches had large 2, 3 and 4 values. CONCLUSIONS: We concluded that parameters 1, 2, 3, 4, 5, 6 and 7 were summarized into three principal components (first principal component, second principal component and third principal component). Through three principal component analysis, we can quickly evaluate the morphology of the dental arches clinically. This methods is simple and of validity. And we can also obtain the characteristics of maxillary dental arches.

Adolescent↗
PubMed1987

Principal-component amplitude compression for the hearing impaired.

Principal-component amplitude compression, a means for matching speech to the reduced dynamic range in sensorineural hearing impairments, is a multiband approach aimed at preserving details of spectral shape while reducing overall level variation. The effect of compression has been studied for the first and second principal components (PC1 an PC2) of the short-term speech spectrum, which are roughly representative of overall level and spectral tilt, respectively. Compression of PC1 roughly equalizes consonant and vowel levels while compression of PC2 provides time-varying high-frequency emphasis. The effect on speech intelligibility of sensorineural hearing-impaired listeners of two principal-component compression system implementations, compression of PC1 and compression of both PC1 and PC2, was compared to that of linear amplification (LA), independent compression of multiple bands (MBC), and wideband compression (WC). Results indicate that compression of overall level as provided by compression of PC1 and WC improved intelligibility relative to LA over a 10- to 15-dB range of input levels. While MBC was beneficial in some cases, it did not provide higher intelligibility than WC. Compression of PC2 did not benefit but rather degraded performance relative to LA. Error analyses and band-level measurements indicate that the highest intelligibility is obtained when audibility is improved and the relative spectral shapes of different speech sounds are preserved.

Auditory Threshold↗
PubMed1992

Morphology of the normal visual field in a population-based random sample: principal components analysis.

I applied principal components analysis to Humphrey central 24-2 threshold values from both eyes of 304 clinically normal persons selected by simple random sample from Barbados, WI. The first component, accounting for 62 per cent of the variation, is equivalent to the average threshold value within persons. The first eigenvector, when represented by grey scale maps depicting a pair of eyes, reveals that, as average threshold increases, the visual field rises and flattens, like an umbrella that, initially closed, is simultaneously opened and thrust upwards. I verify three numerical predictions based upon this umbrella description. Much less important sources of variation involve disparity between fellow eyes, and hemimeridional and other symmetric differences within eyes. I discuss briefly possible physiologic explanatory mechanisms.

Barbados↗
PubMed1995

Efficient calculation of the principal components of imaging data.

Principal components analysis (PCA) of images is important in many applications such as positron emission tomography and functional magnetic resonance imaging. PCA is difficult for image data because the correlation matrix is very large. We present a direct method of calculating the PCA of the voxels from the small matrix expressing the correlations between images, instead of the larger matrix representing the correlations between voxels. The method is fast and accurate. It is faster and requires less memory than a singular value decomposition, although it is less accurate. It is much faster and more accurate than iterative and other approximate methods developed for this problem.

Algorithms↗
PubMed2003

Exploring pleiotropy using principal components.

A standard multivariate principal components (PCs) method was utilized to identify clusters of variables that may be controlled by a common gene or genes (pleiotropy). Heritability estimates were obtained and linkage analyses performed on six individual traits (total cholesterol (Chol), high and low density lipoproteins, triglycerides (TG), body mass index (BMI), and systolic blood pressure (SBP)) and on each PC to compare our ability to identify major gene effects. Using the simulated data from Genetic Analysis Workshop 13 (Cohort 1 and 2 data for year 11), the quantitative traits were first adjusted for age, sex, and smoking (cigarettes per day). Adjusted variables were standardized and PCs calculated followed by orthogonal transformation (varimax rotation). Rotated PCs were then subjected to heritability and quantitative multipoint linkage analysis. The first three PCs explained 73% of the total phenotypic variance. Heritability estimates were above 0.60 for all three PCs. We performed linkage analyses on the PCs as well as the individual traits. The majority of pleiotropic and trait-specific genes were not identified. Standard PCs analysis methods did not facilitate the identification of pleiotropic genes affecting the six traits examined in the simulated data set. In addition, genes contributing 20% of the variance in traits with over 0.60 heritability estimates could not be identified in this simulated data set using traditional quantitative trait linkage analyses. Lack of identification of pleiotropic and trait-specific genes in some cases may reflect their low contribution to the traits/PCs examined or more importantly, characteristics of the sample group analyzed, and not simply a failure of the PC approach itself.

Blood Pressure↗
PubMed1990

Characterization of premotor interneurones by their input patterns--application of principal component analysis to cat cervical interneurones.

Principal component analysis of input patterns of cat C6-C8 interneurones (300 cells) revealed that identified premotor interneurones (11 cells) activated from skin afferents and projecting to T1 motoneurones possessed a special input pattern, characterized by restricted distribution on the plane of the first (Prin 1) versus second (Prin 2) principal component (high positive values of both components). These premotor neurones were located mostly in laminae V-VI. Among other laminae V-VI cells descending in the lateral funiculus to T1 similar to such premotor neurones, there were cells distributed similarly on the Prin 1-2 plane. Further, a majority of interneurones antidromically activated from the T1 motor nucleus at low thresholds also showed a distribution on the plane similar to the premotor neurones. We suggest that premotor neurones of this input pattern constitute a major group among laminae V-VI premotor neurones projecting to T1.

Animals↗
PubMed2003

Principal component regression analysis with SPSS.

The paper introduces all indices of multicollinearity diagnoses, the basic principle of principal component regression and determination of 'best' equation method. The paper uses an example to describe how to do principal component regression analysis with SPSS 10.0: including all calculating processes of the principal component regression and all operations of linear regression, factor analysis, descriptives, compute variable and bivariate correlations procedures in SPSS 10.0. The principal component regression analysis can be used to overcome disturbance of the multicollinearity. The simplified, speeded up and accurate statistical effect is reached through the principal component regression analysis with SPSS.

Regression Analysis↗
PubMed2000

Characterisation of three-dimensional anatomic shapes using principal components: application to the proximal tibia.

The objective of the research is to determine if principal component analysis (PCA) provides an efficient method to characterise the normative shape of the proximal tibia. Bone surface data, converted to analytical surface descriptions, are aligned, and an auto-associative memory matrix is generated. A limited subset of the matrix principal components is used to reconstruct the bone surfaces, and the reconstruction error is assessed. Surface reconstructions based on just six (of 1452) principal components have a mean root-mean-square (RMS) reconstruction error of 1.05% of the mean maximum radial distance at the tibial plateau. Surface reconstruction of bones not included in the auto-associative memory matrix have a mean RMS error of 2.90%. The first principal component represents the average shape of the sample population. Addition of subsequent principal components represents the shape variations most prevalent in the sample and can be visualised in a geometrically meaningful manner. PCA offers an efficient method to characterise the normative shape of the proximal tibia with a high degree of dimensionality reduction.

Adult↗
PubMed2006

Pattern classification using principal components of cortical thickness and its discriminative pattern in schizophrenia.

We proposed pattern classification based on principal components of cortical thickness between schizophrenic patients and healthy controls, which was trained using a leave-one-out cross-validation. The cortical thickness was measured by calculating the Euclidean distance between linked vertices on the inner and outer cortical surfaces. Principal component analysis was applied to each lobe for practical computational issues and stability of principal components. And, discriminative patterns derived at every vertex in the original feature space with respect to support vector machine were analyzed with definitive findings of brain abnormalities in schizophrenia for establishing practical confidence. It was simulated with 50 randomly selected validation set for the generalization and the average accuracy of classification was reported. This study showed that some principal components might be more useful than others for classification, but not necessarily matching the ordering of the variance amounts they explained. In particular, 40-70 principal components rearranged by a simple two-sample t-test which ranked the effectiveness of features were used for the best mean accuracy of simulated classification (frontal: (left(%)|right(%))=91.07|88.80, parietal: 91.40|91.53, temporal: 93.60|91.47, occipital: 88.80|91.60). And, discriminative power appeared more spatially diffused bilaterally in the several regions, especially precentral, postcentral, superior frontal and temporal, cingulate and parahippocampal gyri. Since our results of discriminative patterns derived from classifier were consistent with a previous morphological analysis of schizophrenia, it can be said that the cortical thickness is a reliable feature for pattern classification and the potential benefits of such diagnostic tools are enhanced by our finding.

Adult↗
PubMed2006

Comment on: "Energy landscape of a small peptide revealed by dihedral angle principal component analysis".

The dihedral angle principal component analysis method published recently by Mu, Nguyen, and Stock, is shown to produce distortions of the free energy landscape due to the neglect of constraints in the coordinates. It is further shown that these distortions can create artificial minima and energy barriers. The rugged energy landscape that the authors find for a small peptide chain might thus be an artifact of their method.

Energy Transfer↗
PubMed1999

Motor coordination in a multi-muscle system as revealed by principal components analysis of electromyographic variation.

The variation in electromyographic output of twelve trigeminal muscles of the rabbit was studied to test the hypothesis that they are under the control of a small number of independent neural factors. Jaw muscle electromyograms (EMGs) of eight animals were recorded in 95 chewing sequences, each consisting of 40-75 chewing cycles. The within-sequence correlations of the EMG burst amplitudes (integrated per cycle) and burst onsets were calculated between the muscles. The correlation matrix was subjected to a principal components analysis. This method aims at describing the variation in EMG amplitude and timing by means of the smallest possible set of newly defined variables, or principal components. Of the variation in EMG amplitude values of the twelve muscles, 75-90% could be accounted for by only three principal components. Each principal component was characterized by a group of muscles with high mutual positive correlations; they had zero correlation with other principal components. The first component represents the jaw closers: most of the bilateral masseter and the medial pterygoid muscles. The second represents the openers: the bilateral digastric and lateral pterygoid muscles. This demonstrates the tight control of both the jaw openers and closers, each by a single neural factor; these two factors are independent of one another. They most likely originate from the specific inputs from primary afferents to the opener and closer motoneurons. Unexpectedly, a third independent principal component appeared to control the closing activity of the non-chewing side, posterior deep masseter muscle. It was hypothesized that this muscle acts independently of the other closers to disengage the teeth and resets the jaw for a new chewing cycle. Principal components analysis of variation in timing of EMG onset revealed a grouping of all masticatory muscles in a single cluster, independent of EMG amplitude. This supports the hypothesis that timing and amplitude of masticatory EMG patterns are controlled independently.

Animals↗