Variant Of Principal Component Analysis Research Articles

Correlation of the Edinburgh Gait Score With the Gillette Gait Index, the Gillette Functional Assessment Questionnaire, and Dimensionless Speed

This study examines the correlation of the Edinburgh Gait Score (EGS) with the Gillette Gait Index (GGI; formerly the Normalcy Index), the Gillette Functional Assessment Questionnaire, and speed, all of which are used as measures of gait quality or function. Scores were computed for 58 subjects, all with a diagnosis of cerebral palsy. The correlation of the EGS with all of the other scores was found to be significant, with r2 ranging from 0.26 to 0.79. The strongest correlation was found with the GGI, which may reflect common features in the derivation of both of these scores, although the EGS was derived from observational gait analysis and the GGI from principal component analysis of variables from computerized 3-dimensional gait data. We conclude that the EGS shows good concurrent validity with alternative gait assessment scores.

Parameterization and R‐Peak Error Estimations of ECG Signals Using Independent Component Analysis

Principal component analysis (PCA) is used to reduce dimensionality of electrocardiogram (ECG) data prior to performing independent component analysis (ICA). A newly developed PCA variance estimator by the author has been applied for detecting true, actual and false peaks of ECG data files. In this paper, it is felt that the ability of ICA is also checked for parameterization of ECG signals, which is necessary at times. Independent components (ICs) of properly parameterized ECG signals are more readily interpretable than the measurements themselves, or their ICs. The original ECG recordings and the samples are corrected by statistical measures to estimate the noise statistics of ECG signals and find the reconstruction errors. The capability of ICA is justified by finding the true, false and actual peaks of around 25–50, CSE (common standards for electrocardiography) database ECG files. In the present work, joint approximation for diagonalization of the eigen matrices (Jade) algorithm is applied to 3‐channel ECG. ICA processing of different cases is dealt with and the R‐peak magnitudes of the ECG waveforms before and after applying ICA are found and marked. ICA results obtained indicate that in most of the cases, the percentage error in reconstruction is very small. The developed PCA variance estimator along with the quadratic spline wavelet gave a sensitivity of 97.47% before applying ICA and 98.07% after ICA processing.

Detecting functional nodes in large‐scale cortical networks with functional magnetic resonance imaging: A principal component analysis of the human visual system

This study aimed to demonstrate how a regional variant of principal component analysis (PCA) can be used to delineate the known functional subdivisions of the human visual system. Unlike conventional eigenimage analysis, PCA was carried out as a second-level analysis subsequent to model-based General Linear Model (GLM)-type functional activation mapping. Functional homogeneity of the functional magnetic resonance imaging (fMRI) time series within and between clusters was examined on several levels of the visual network, starting from the level of individual clusters up to the network level comprising two or more distinct visual regions. On each level, the number of significant components was identified and compared with the number of clusters in the data set. Eigenimages were used to examine the regional distribution of the extracted components. It was shown that voxels within individual clusters and voxels located in bilateral homologue visual regions can be represented by a single component, constituting the characteristic functional specialization of the cluster(s). If, however, PCA was applied to time series of voxels located in functionally distinct visual regions, more than one component was observed with each component being dominated by voxels in one of the investigated regions. The model of functional connections derived by PCA was in accordance with the well-known functional anatomy and anatomical connectivity of the visual system. PCA in combination with conventional activation mapping might therefore be used to identify the number of functionally distinct nodes in an fMRI data set in order to generate a model of functional connectivity within a neuroanatomical network.

Segmentation and morphology of open water bodies from multispectral images

A number of problems in remote sensing require the segmentation of specific spectral classes such as water bodies, clouds or forested areas. Further analysis of these classes may include the calculation of optical reflectance values such as chlorophyll concentration, absolute reflectivity or vegetation indices. To derive reliable measurements of these variables, a precise segmentation − from the rest of the image − of the spectral classes is needed. In this work, we propose a new methodology to segment open water bodies based on a variant of principal component analysis (PCA). In this variant, information about the spectral class model of the water bodies to be separated in the feature space is required. This information is input by means of a training field encircling a set of pixels representative of this spectral model. A training field for land cover is also defined. This PCA variant produces two sets of multispectral bands, one for water bodies and one for land cover types. The first two bands of each set are input into a fuzzy clustering procedure. By using a merging process, the clusters are merged into two classes: water bodies and the rest of the image. From this, a logic bitmap image is obtained. The pixels of the bitmap consist of ON for water bodies and OFF for the rest of the image. The bitmap is then used to obtain morphological parameters of the water bodies.

Karhunen-Loeve analysis for pattern description in phase separated lipid bilayer systems

Karhunen-Loeve analysis, a special variant of principal component analysis, is used to describe and analyze the dynamics of self-assembled pattern formation in a mixed phospholipid bilayer. The dominant modes of the evolving heterogeneities in density and dynamics are elucidated. At low temperatures the evolution of patterns can be followed by the principal modes of the systems. We find that the higher modes only evolve after the dominant modes have been established. At high temperatures no such dominant modes are found. So, a clear descriptor of an evolving self-assembled pattern can be identified and its time evolution can be monitored. This analysis suggests, additionally, a new way of determining the equilibration decision in complex systems.

Robust centroid method

This paper describes a robust centroid method, which is a variant of principal component analysis. A genetic local search algorithm is presented to perform the calculations. Simulations are carried out to appraise the performance of the genetic local search algorithm. A real data set with missing data and multiple outliers is analyzed.

Higher-Order Asymptotic Standard Error and Asymptotic Expansion in Principal Component Analysis

ABSTRACT Asymptotic expansions of the distributions of the estimators of unrotated and orthogonally rotated component loadings are given under non normality of observed variables in principal component analysis for sample covariance and correlation matrices. The expansions include those for the Studentized statistics of the estimators with unknown standard errors. The expansions with the adjustment of the higher-order asymptotic variance of estimators are also presented with weight for partial adjustment. The formula is applied to the estimators of the contributions of unrotated/rotated components as well as their loadings, which includes eigenvalues as special cases. Simulations were performed to see the accuracy of the asymptotic moments and the higher-order standard errors in samples with finite sample sizes.

Independent-component analysis for hyperspectral remote sensing imagery classification

We investigate the application of independent-component analysis (ICA) to remotely sensed hyperspectral image classification. We focus on the performance of two well-known and frequently used ICA algorithms: joint approximate diagonalization of eigenmatrices (JADE) and FastICA; but the proposed method is applicable to other ICA algorithms. The major advantage of using ICA is its ability to classify objects with unknown spectral signatures in an unknown image scene, i.e., unsupervised classification. However, ICA suffers from computational expensiveness, which limits its application to high-dimensional data analysis. In order to make it applicable or reduce the computation time in hyperspectral image classification, a data-preprocessing procedure is employed to reduce the data dimensionality. Instead of using principal-component analysis (PCA), a noise-adjusted principal-components (NAPC) transform is employed for this purpose, which can reorganize the original data with respect to the signal-to-noise ratio, a more appropriate image-ranking criterion than variance in PCA. The experimental results demonstrate that the major principal components from the NAPC transform can better maintain the object information in the original data than those from PCA. As a result, an ICA algorithm can provide better object classification.

Proteomic analysis of amniotic fluids using analysis of variance-principal component analysis and fuzzy rule-building expert systems applied to matrix-assisted laser desorption/ionization mass spectrometry

Amniotic fluids from 36 women who had premature or at term deliveries were studied using matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS) [F. Hillenkamp, M. Karas, R.C. Beavis, B.T. Chait, Matrix-assisted laser desorption ionization mass-spectrometry of biopolymers, Analytical Chemistry 63 (1991) A1193–A1202. [1]]. The effects of experimental factors of patient, uterine infection, sample preparation, sample handling, three different days and four different studies, were examined using analysis of variance-principal component analysis (ANOVA-PCA) [P.B. Harrington, N.E. Vieira, J. Espinoza, J.K. Nien, R. Romero, A.L. Yergey, Analysis of variance-principal component analysis: a soft tool for proteomic discovery, Analytica Chimica Acta (in press)]. Hotelling T 2 95% confidence intervals were introduced as a graphical tool for evaluating the statistical significance of the levels for each factor. ANOVA-PCA gave biomarkers that distinguished amniotic fluids with evidence of chorioamniotic infection from the other amniotic fluids. All women with intrauterine infection, except for one were identified from the MALDI-MS spectra of their amniotic fluids. After querying the clinic, it was discovered that the amniotic fluid of the misclassified patient was incorrectly identified as infected. The biomarkers obtained from ANOVA-PCA corresponded to those obtained from a fuzzy rule-building system (FuRES) [P.B. Harrington, Fuzzy multivariate rule-building expert systems—minimal neural networks. Journal of Chemometrics 5 (1991) 467–486]. The FuRES model was evaluated using 10 Latin-partitions that yielded a sensitivity of 92% and specificity of 100% for detecting patients with uterine inflammation from MALDI-MS measurements of the amniotic fluids. The specificity value contains a patient that was clinically misidentified as infected that was disclosed by querying the FuRES results. An ANOVA-PCA indicated that the solid phase extraction improved the precision of the analysis, but FuRES analysis showed that this procedure resulted in a lower prediction rate. Using the MALDI-MS data obtained from the amniotic fluids of patients who delivered at term or preterm without evidence of infection in the patients, could not be classified by ANOVA-PCA or predicted by FuRES into these groups.

Three‐way component analysis of interval‐valued data

AbstractVertices Principal Component Analysis (V‐PCA) and Centers Principal Component Analysis (C‐PCA) are variants of Principal Component Analysis (PCA) to deal with two‐way interval‐valued data. In this case the observation units are represented as hyperrectangles instead of points. Tucker3 and CANDECOMP/PARAFAC are component analysis techniques to analyze the underlying structure of three‐way data sets. In the present paper, after recalling the above mentioned methods, we extend the C‐PCA and V‐PCA methods to deal with three‐way interval‐valued data by means of Tucker3 and CANDECOMP/PARAFAC and we describe how to represent the observation units in the obtained low‐dimensional space. Furthermore, an application of the extended methods—called Three‐way Vertices Principal Component Analysis (3V‐PCA) and Three‐way Centers Principal Component Analysis (3C‐PCA)—to three‐way interval‐valued air pollution data is described. Copyright © 2004 John Wiley & Sons, Ltd.

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.

Feature selection in principal component analysis of analytical data

A feature selection method is proposed to select a subset of variables in principal component analysis (PCA) that preserves as much information present in the complete data as possible. The information is measured by means of the percentage of consensus in generalised Procrustes analysis. The best subset of variables is obtained by applying a genetic algorithm (GA) to optimise the consensus between the subset and the complete data set in order to avoid exhaustive searching. The method was evaluated on a standard data set known as the Alate data, and on a high-dimensional industrial gas chromatography (GC) data set. The results showed that the proposed method successfully identified structure-bearing variables in both data sets and that it leads to a better subset of variables than other studied feature selection methods.

Classification of rapeseed and soybean oils by use of unsupervised pattern-recognition methods and neural networks.

Unsupervised pattern-recognition methods and Kohonen neural networks have been applied to the classification of rapeseed and soybean oil samples according to their type and quality by use of chemical and physical properties (density, refractive index, saponification value, and iodine and acid numbers) and thermal properties (thermal decomposition temperatures) as variables. A multilayer feed-forward (MLF) neural network (NN) has been used to select the most important variables for accurate classification of edible oils. To accomplish this task different neural networks architectures trained by back propagation of error method, using chemical, physical, and thermal properties as inputs, were employed. The network with the best performance and the smallest root mean squared (RMS) error was chosen. The results of MLF network sensitivity analysis enabled the identification of key properties, which were again used as variables in principal components analysis (PCA), cluster analysis (CA), and in Kohonen self-organizing feature maps (SOFM) to prove their reliability.

Selection of Important Variables in Principal Component Analysis Using Measures of Multivariate Association

As part of Exploratory Analysis of Multivariate data, Principal Componet Analysis (PCA) is generally directed towards inspection and dimensionality reduction of the data such that most of the sample variation is preserved. Hence, to be able to identify the subsets of variables which contain the main features of the entire data and possibly reveal interesting patterns or relationships, constitutes one the major aims of PCA. New selection methods based on Canonical Correlation Analysis and Euclidean distances are proposed. While the criterion (M2) based on Procrustes Analysis, found in literature, identifies structure-bearing variables, particularly for grouped data, the proposed criteria retain those variables that preserve the maximum sample variation and carry whatever unknown multivariate structure, which may be present in the complete data. These methods are evaluated and compared on real as well as Monte Carlo simulation data. UNISWA Research Journal of Agriculture, Science and Technology Vol 3 (2) 2000: pp 22-31

An introduction to independent component analysis

SUMMARY This paper is an introduction to the concept of independent component analysis (ICA) which has recently been developed in the area of signal processing. ICA is a variant of principal component analysis (PCA) in which the components are assumed to be mutually statistically independent instead of merely uncorrelated. The stronger condition allows one to remove the rotational invariance of PCA, i.e. ICA provides a meaningful unique bilinear decomposition of two-way data that can be considered as a linear mixture of a number of independent source signals. The discipline of multilinear algebra offers some means to solve the ICA problem. In this paper we briefly discuss four orthogonal tensor decompositions that can be interpreted in terms of higher-order generalizations of the symmetric eigenvalue decomposition. Copyright © 2000 John Wiley & Sons, Ltd.

Mixtures of probabilistic principal component analyzers.

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

地方圏域における小売構造の変化に関する研究 鳥取県の事例

Large scale retail stores (LSRS) increased fast during the high economic growth period in Japan. From 1970's they started to locate even in small local towns and affected small scale retail stores in adjacent rural areas. By the 1980's their impact was very significant. This study examined this phenomena in Tottori Prefecture in 1979 and 1991. The objective is to examine changes in spatial structure of retail by analysing retail sales and sales floor area (SFA) in relation to location characteristics at local goverments level.First, Correlation Analysis (CA) was used to analyze the relationship between characteristics of cities and towns and sales of 3 types of commodities, i. e. food, cloths, and others. It was observed that the degree of urbanization and degree of commerce has strong correlation with sales, but the correlation was stronger in 1991 than in 1979. There is no big differences among the commodities examined. Parameters obtained with the CA were then used as variables in Principal Component Analysis (PCI.) . Three principal component (PC) were obtained, representing 97% of the original information. PC 1 is the correlation between degree of urbanization and sales. PC 2 is the correlation between degree of commerce and sales, and PC 3 is the correlation between degree of centrality of cities and towns, and sales. For PC 1, at both periods, food experienced decrease in sales, while the sales of other commodities increased. This means, sales of commodities other than food concentrated in the urban area, while food sales are distributed in wider area. For PC 2 all commodities' sales increased. All commodities' sales decreased in PC 3. It means sales are strongly correlated with degree of commerce and level of centrality of cities and towns. For the cities and towns which had high degree of urbanization, high degree of commerce and high level of centrality showed increasing trend in retail business and the reverse of the above is true. In the objective region cities and towns can be grouped into those with increasing and that with decreasing retail businesses.An equation to predict the size of the small scale retail store was formulated as follows: M3j = λPj - μΣiM1i/dbij - vΣiM2i/dbijwhere λ, μ, v, b are parameters. Pj is population of city or town j. dij road distance from city or town i to city or town j. M1i is SFA of LSRS type 1 in city or town i. M2i, is SFA of LSRS type 2 in city or town i. M3j is SFA of small scale retail store in city or town j. Along the classical Huff model, the b parameter was fixed as 2. Regression was used to calibratie the equation. R2 obtained with 1979 and 1991 data of O. 993 and O. 989, indicates relialiability of the model. Thus the scale of small retail store in a city or town is mostly proportional to the population of the city or town in which it is located, the floor areas of LSRS and the distances to the other cities or towns.

Discrete Classification with Principal Component Analysis: Discrimination of Giant and Dwarf Spectra in K Stars

view Abstract Citations (15) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Discrete Classification with Principal Component Analysis: Discrimination of Giant and Dwarf Spectra in K Stars Ibata, Rodrigo A. ; Irwin, Michael J. Abstract We demonstrate the use of a variant of Principal Component Analysis (PCA) for discrimination problems in astronomy. This variant of PCA is shown to provide the best linear discrimination between data classes. As a test case, we present the problem of discrimination between K giant and K dwarf stars from intermediate resolution spectra near the Mg `b' feature. The discrimination procedure is trained on a set of 24 standard K giants and 24 standard K dwarfs, and then used to perform giant - dwarf classification on a sample of ~ 1500 field K stars of unknown luminosity class which were initially classified visually. For the highest S/N spectra, the automated classification agrees very well (at the 90 - 95% level) with the visual classification. Most importantly, however, the automated method is found to classify stars in a repeatable fashion, and, according to numerical experiments, is very robust to signal to noise (S/N) degradation. Publication: The Astronomical Journal Pub Date: May 1997 DOI: 10.1086/118398 arXiv: arXiv:astro-ph/9704014 Bibcode: 1997AJ....113.1865I Keywords: Astrophysics E-Print: 16 pages, 4 figures, 2 tables. Accepted for publication in AJ full text sources arXiv | ADS | data products SIMBAD (26)

Correspondence Analysis of the Skin Sensitization Potential of Organic Chemicals

AbstractCorrespondence analysis is a variant of principal component analysis for use with categoric data. It has been applied to structural information describing the frequencies of certain molecular features and the skin sensitization potential of a database of organic compounds. Correspondence analysis allows the graphical study of the interrelationship between the relative frequency of structural features of non, weak, moderate and strong sensitizers and the individual class membership. Structural features resulting in protein reactivity are shown to be strongly associated with strong sensitizers; other features, not related to reactivity, are associated with non, or weak, sensitizers. The analysis also indicates structural features whose description is too vague and needs more refinement.

Classification of pulmonary-function tests by principal component analysis

The structure of pulmonary-function data obtained from 468 randomly selected subjects was analyzed. The subjects included patients with chronic bronchitis, bronchial asthma, chronic pulmonary emphysema, diffuse panbronchiolitis, and idiopathic interstitial pneumonitis, and normal health adults. From among the many possible indices of pulmonary function, 19 were chosen and were used as variables in principal component analysis. Six significant principal components (PCs) were extracted. The first three PCs accounted for 70% of the total information and were termed "ventilation," "volume," and "diffusion." The second three PCs accounted for 17% of the information and were termed "small airway," "lower airway," and "shape." Indices of ventilatory unevenness were not separated from indices of airway obstruction, and were included in the first PC. No other, unknown PC was detected with these pulmonary-function indices. The relationship among indices is displayed in a factor loading matrix, and pulmonary-function tests are classified statistically.