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Showing papers on "Principal component analysis published in 1974"


Journal ArticleDOI
TL;DR: In this paper, Fisher's canonical analysis of contingency tables is shown to be applicable to incidence data as well as to contingency tables, and is accordingly designated by another author's name “correspondence analysis”.
Abstract: R. A. Fisher's canonical analysis of contingency tables is shown to be applicable to incidence data as well as to contingency tables, and is accordingly designated by another author's name “correspondence analysis”. In a theoretical section, the method is shown to be equivalent to a special case of Hotelling's canonical correlation analysis and also to a scale‐free variant of principal components analysis. A practical example is examined, and a number of practical considerations discussed.

811 citations


Journal ArticleDOI
TL;DR: In this paper, a method for resolving additive mixtures of overlapping curves by combining nonlinear regression and principal component analysis is presented, which makes use of the postulated chemical reaction, and allows one to check the reaction and estimate chemical rate and equilibrium constants.
Abstract: The paper presents a method for resolving additive mixtures of overlapping curves by combining nonlinear regression and principal component analysis. The method can be applied to spectroscopy, chromatography, etc. The method makes use of the postulated chemical reaction, and allows one to check the reaction and estimate chemical rate and equilibrium constants.

147 citations


Journal ArticleDOI
TL;DR: This article considers the case in which the base consists of data vectors following a multivariate normal distribution, and proposes five screening procedures—a "one-at-a-time" test, the standard χ2 test, and three statistics derived from principal component analysis.
Abstract: Serious problems arise in the maintenance of reliability in large data bases, since it becomes difficult to verify incoming data manually. This article considers the case in which the base consists of data vectors following a multivariate normal distribution. Five screening procedures are proposed—a “one-at-a-time” test, the standard χ2 test, and three statistics derived from principal component analysis. From analysis of a practical example, it emerges that the statistics derived from principal component analysis have superior performance.

105 citations


Journal ArticleDOI
TL;DR: In this article, principal component analysis in the frequency domain is used to replace the input/output variables by some function of smaller dimensions without much "loss of information" and the analogy between the "factor analysis" of time series in frequency domain and the minimal realization of state space models is pointed out.
Abstract: The identification of a multivariable stochastic system, usually, involves the estimation of a transfer function matrix, which is a general function of frequency. This estimation involves inversion of a large Hermitian matrix, which sometimes may become unwieldly. In this paper we describe how "principal component analysis" in the frequency domain may be used to replace the input/output variables by some function of smaller dimensions without much "loss of information." The analogy between the "factor analysis" of time series in frequency domain and the minimal realization of state space models is pointed out. The principal component approach described in this paper is applied in the case of a simulated system.

59 citations


Journal ArticleDOI
Harvey F. Silverman1, N. Dixon
TL;DR: The parametrically controlled analyzer (PCA) is a large PL/I program which has been designed to perform spectral analysis of speech signals and features parametric selection of several analysis methods, including discrete Fourier transformation and linear predictive coding.
Abstract: The parametrically controlled analyzer (PCA) is a large PL/I program which has been designed to perform spectral analysis of speech signals. PCA features parametric selection of several analysis methods, including discrete Fourier transformation and linear predictive coding. Also, selection may be made among various smoothing, normalization, and interpolation methods. PCA develops high-quality spectrographic representations of speech for standard line printers and CRT displays. The PCA is described and numerous examples of various parameter settings are presented and discussed.

45 citations


Journal ArticleDOI
TL;DR: A relatively simple technique for assessing the convergence of sets of variables across method domains, empirically orthogonalizes each method domain into sets of components, and then analyzes convergence among components across domains.
Abstract: A relatively simple technique for .assessing the convergence of sets of variables across method domains is presented. The technique, two-step principal components analysis, empirically orthogonalizes each method domain into sets of components, and then analyzes convergence among components across domains. The proposed technique is directly compared with Jackson's (1969) multi-method factor analysis (which involves an a priori orthogonalization) in the analysis of data from personality, vocational interest and aptitude domains. While Jackson's technique focuses on individual variables, and the two-step procedure focuses on the components of variable domains, both techniques produced evidence of cross-domain convergence. However, Jackson's method was found t o have several undesirable mathematical and interpretational consequences, while the two-step procedure appears to be a promising technique for the systematic, empirical analysis of multitrait-multimethod matrices.

42 citations


Journal ArticleDOI
TL;DR: A simultaneous multiple regression method is presented in this paper for estimating missing observations in a data matrix for multivariate analysis of variance (MANOVA), and discriminant analysis.
Abstract: The objective of this study was to demonstrate the application of multivariate statistical techniques towards the understanding of variables affecting water quality. One of the major problems confronting an investigator in the application of statistical techniques to water quality data is missing observations. A simultaneous multiple regression method is presented in this paper for estimating missing observations in a data matrix. The major goals of using multivariate analysis are to facilitate interpretation and to prove hypotheses concerning the data. The techniques considered in this paper include principal components, canonical correlation, partial correlation, multivariate analysis of variance (MANOVA), and discriminant analysis. Examples are presented demonstrating the application of these methods.

36 citations


Journal ArticleDOI
TL;DR: Theoretical problems with the factor analysis model have resulted in increased interest in component analysis as an alternative as mentioned in this paper, and it is therefore of interest to assess empirically some of the assert...
Abstract: Theoretical problems with the factor analysis model have resulted in increased interest in component analysis as an alternative. It is therefore of interest to assess empirically some of the assert...

35 citations


Journal ArticleDOI
TL;DR: In this paper, three multivariate methods of analysis were applied to the problem of selecting the most important descriptions of tea from a list of 11 relevant ones, and the value of using more than one method of multivariate analysis is stressed.
Abstract: Three multivariate methods of analysis were applied to the problem of selecting the most important descriptions of tea from a list of 11 relevant ones. Principal component analysis gave useful information with data from homogeneous groups of experts but not with data from an heterogeneous group of non-experts. When cluster analysis was used to give homogeneous groups of non-experts from the heterogeneous one then principal component analysis again gave useful and similar information. Stepwise discriminant analysis gave different results from that of principal component analysis, a quite logical solution. The value of using more than one method of multivariate analysis is stressed.

17 citations


Journal ArticleDOI
TL;DR: In this article, sixteen hydromorphic variables, with observations grouped by stream order, were subjected to principal components analysis to investigate the manner in which variables interact in a downstream direction within a drainage basin.
Abstract: Sixteen hydromorphic variables, with observations grouped by stream order, were subjected to principal components analysis to investigate the manner in which variables interact in a downstream direction within a drainage basin. The degree of intercorrelation between variables in a fluvial system is influenced by geology, structure, and variation in the physical characteristics of stream basins. The contention here is that since the degree to which these factors are effective varies downstream in an orderly way, the intensity of interaction between variables should also be so ordered. The results of the analysis support this because the variance accounted for by the first and second principal components increased systematically downstream, whereas that associated with principal components three through six generally decreased. The structure of the data is also examined in the context of varimax rotated components, and the changes that occur between lower- and higher-order stream basins are identified.

16 citations


Journal ArticleDOI
27 Oct 1974-Heredity
TL;DR: The expected convergence of the quantitative traits in a poorer range of environments was confirmed since most of the genotypic and important g × e interaction comparisons were found to be positively associated with the first principal component in both the absence and presence of calcium.
Abstract: Orthogonal and principal components analysis of genotype-environmental interactions for multiple metrical traits

Journal ArticleDOI
TL;DR: Principal component analysis and factor analysis are statistical techniques which can define structural patterns within a set of observations and assign appropriate weights to the importance of each observed variable in contributing to each part of the pattern.
Abstract: Summary: Pattern recognition, which depends upon the perception of inter-relationships between separate observations, has a central role in medical science. Principal component analysis and factor analysis are statistical techniques which can define structural patterns within a set of observations and assign appropriate weights to the importance of each observed variable in contributing to each part of the pattern. The technique of principal component analysis is exemplified by the definition of a “disease activity index” which has been used in the assessment of response of systemic lupus erythematosus to immunosuppressive therapy. Factor analysis of responses to a computer-based questionnaire (SASH) has been used to define patterns of symptoms which correspond to gastrointestinal and cardiac syndromes. Both techniques allow a quantitative approach to the recognition of patterns of disease and should be more widely used in medicine.

Journal ArticleDOI
TL;DR: The use of principal component analysis, followed by rotation of a reduced number of component axes, and its role in the identification and interpretation of relationships between disorder and mineral content in apple research is described.
Abstract: The use of principal component analysis, followed by rotation of a reduced number of component axes, and its role in the identification and interpretation of relationships between disorder and mineral content in apple research is described. The relationship among bitter pit incidence, calcium deficiency and mean fruit weight per tree is illustrated by using data obtained on Jonathan apples from potted trees. Principal component analysis must be performed on unstructured data, and emphasis is placed upon the removal of treatment and block effects when constructing the correlation matrix upon which the analysis is performed. The mathematical techniques described are applicable to a wide range of agricultural experimentation.

Journal ArticleDOI
TL;DR: In this article, the advantages of cluster analysis are illustrated in comparison with the principal component analysis recommended by Slater, in that cluster scores are easily calculated, and their interpretation is directly meaningful in relation to the patient's progress.
Abstract: When intensity levels for several symptoms are obtained by use of a personal questionnaire on a series of occasions, it is convenient to reduce the scores to a smaller set of variables by grouping symptoms. Elementary cluster analysis is suitable for this purpose, in that cluster scores are easily calculated, and their interpretation is directly meaningful in relation to the patient's progress. The advantages of cluster analysis are illustrated in comparison with the principal component analysis recommended by Slater.

Journal ArticleDOI
TL;DR: The authors state that the 'technique' (correspondence analysis) is designed to extract the maximum of information from an array of positive numbers and also emphasize the saving of computer time and storage (and by inference money).
Abstract: David et al. (1974a, b) present a different approach to factor analysis and are to be commended for bringing to the attention of the geological community the existence of a method of data analysis called Correspondence Analysis. However, before the utility of the technique can be properly evaluated on the basis of the set of data used in the paper, a number of points should be clarified. Principal Components Analysis (PCA) is not synonymous with Ror Q-mode factor analysis (Mulaik 1972; Davis 1973). The usual procedure (Klovan 1968 ; Rummel 1970; Davis 1973) is to begin with a PCA and then rotate a subset of the principal component axes according to some substantive criterion (for example, simple structure: Harmon 1967; Rummel 1970). The most common method of orthogonal rotation is the varimax procedure (Kaiser 1958). Oblique rotational methods (Hakstian 1969; Rummel 1970; Mulaik 1972) where the orthogonality constraints of the varimax scheme are relaxed are also utilized (Hitchon et al. 1971). The authors state (p. 13 1) that the 'technique' (correspondence analysis) is designed to extract the maximum of information from an array of positive numbers. They also emphasize the saving of computer time and storage (and by inference money). The latter aspect may be the most redeeming quality of their Correspondence Analysis. The transformation which they employ (p. 134) is a bounding type of data matrix transformation (Rummel 1970) and not standardization. Standardization in the strict sense involves subtracting the mean of a variable from each original observation and dividing the resultant

Journal ArticleDOI
TL;DR: The authors used principal component analysis (PCA) to isolate and identify general factors in a cross-sectional regression equation, not as representing individual influences but as representing more general factors, and showed that PCA can be used to identify and identify some of these general factors.
Abstract: Robert J. Saunders [4] has demonstrated that, because of the high degree of linear interdependence among many of the variables commonly used in banking studies, it may be necessary to interpret explanatory variables in a cross-sectional regression equation, not as representing individual influences but as representing more general factors. He attempted to demonstrate how principal component analysis might be used to isolate and identify some of these general factors.

Journal ArticleDOI
TL;DR: In this paper, principal component analysis (PCA) is used to reduce the number of time series that have to be monitored for quality assurance. But the sensitivity of the analysis to changes in the statistical characteristics of the measurements is examined.
Abstract: This paper develops the use of principal component analysis as an aid to quality assurance. The sensitivity of the analysis to changes in the statistical characteristics of the measurements is examined. The analysis can reduce the number of time series that have to be monitored for quality assurance. The technique is to linearly combine groups of the measurements. This grouping of measurements excludes the use of the cusum as a quality assurance aid. A new quality monitoring process is proposed; the cumoderror, which enables the detection of mean level and variance changes in single or combined measurements.

21 Mar 1974
TL;DR: In this article, a critical evaluation of principal component analysis (PCA) is presented for the separation of the signal components of mixed signals observed at an array since the eigenvectors of the spectral matrix often resemble signal delay vectors.
Abstract: : Principal component analysis, eigenvalue-eigenvector decomposition of array spectral matrices, has been proposed by several authors as a technique for the separation of the signal components of mixed signals observed at an array since the eigenvectors of the spectral matrix often resemble signal delay vectors. This report is a critical evaluation of the method.

Journal ArticleDOI
TL;DR: Chiattello as mentioned in this paper provided additional empirical support for the suggestion that, because of the high degree of linear interdependence between many of the variables commonly used in banking regression studies, it may be necessary to interpret explanatory variables in a cross-sectional regression equation, not as representing individual influences, but as representing more general factors.
Abstract: Marion L. Chiattello [1] has provided additional empirical support for the suggestion that, because of the high degree of linear interdependence between many of the variables commonly used in banking regression studies, it may be necessary to interpret explanatory variables in a cross-sectional regression equation, not as representing individual influences, but as representing more general factors. Further, he has provided more empirical support for the suggestion that principal component analysis might be useful in helping to isolate and identify some of these general factors.