Showing papers on "Principal component analysis published in 1985"
473 citations
TL;DR: In this article, principal components of two LANDSAT MSS subscenes were separately calculated using both unstandardized and standardized variables, and the results indicate substantial improvement in signal-to-noise ratio and image enhancement by using standardized variables in the principal components analysis.
Abstract: In remote sensing, principal components analysis is usually performed using unstandardized variables. However, the use of standardized variables yields significantly different results. In this paper principal components of two LANDSAT MSS subscenes were separately calculated using both methods. The result indicate substantial improvement in signal-to-noise ratio and image enhancement by using standardized variables in the principal components analysis.
353 citations
TL;DR: In this paper, a procedure was developed for analyzing remote reflectance spectra, including multispectral images, that quantifies parameters such as types of mineral mixtures, the abundances of mixed minerals, and particle sizes.
Abstract: A procedure was developed for analyzing remote reflectance spectra, including multispectral images, that quantifies parameters such as types of mineral mixtures, the abundances of mixed minerals, and particle sizes. Principal components analysis reduced the spectral dimensionality and allowed testing the uniqueness and validity of spectral mixing models. By analyzing variations in the overall spectral reflectance curves, the type of spectral mixture was identified, mineral abundances quantified and the effects of particle size identified. The results demonstrate an advantage in classification accuracy over classical forms of analysis that ignore effects of particle-size or mineral-mixture systematics on spectra. The approach is applicable to remote sensing data of planetary surfaces for quantitative determinations of mineral abundances.
347 citations
TL;DR: In this paper, the statistical technique of principal components is used to analyze two sets of near-infrared spectra, wheat flour samples for which % moisture and % protein values are included, and milled barley samples for whose hot water extract values were included.
Abstract: The statistical technique of principal components is used to analyze two sets of near-infrared spectra, wheat flour samples for which % moisture and % protein values are included, and milled barley samples for which hot water extract values are included. The methodology and interpretation of this technique are described within the context of NIR data, and its advantages both in providing insight into the variation of the spectra, and as a method of avoiding the problems caused by highly correlated reflectance energy values in the derivation of calibration equations, are highlighted. In each set of samples the first principal component accounts for the vast majority of the variation. These components also have an almost identical shape, which is interpreted as reflecting particle size. The second wheat component and the third barley component are also almost identical, with a shape very similar to that of the spectrum of water. Both fourth components share peaks at points in the spectrum which are used by fixed-filter instruments to measure protein in cereals.
266 citations
TL;DR: In this paper, the perturbation theory of real symmetric matrices is used to detect influential observations in principal component analysis (PCA) and the influence function is used as a diagnostic tool.
Abstract: SUMMARY In linear regression, the theoretical influence function and the various sample versions of it have an established place as diagnostic tools. These same functions are developed here to provide methods for the detection of influential observations in principal components analysis. The perturbation theory of real symmetric matrices unifies this development. Some interesting points of contrast with the regression case are noted and explained theoretically.
175 citations
TL;DR: In this article, principal component analysis of eight-channel data sets consisting of multitemporal LANDSAT MSS image pairs often generates higher-order principal components that are related to changes in brightness and greenness.
Abstract: Principal components analysis of eight-channel data sets consisting of multitemporal LANDSAT MSS image pairs often generates higher-order principal components that are related to changes in ‘brightness’ and ‘greenness’. This is the expected result of such analysis in a wide variety of biological and geological environments where the original imagery is intrinsically two dimensional; the two dimensions are ‘brightness’ and ‘greenness’; and the change in land cover between images exceeds some threshold value.
111 citations
TL;DR: In this article, principal component analysis (PCA) is applied to /sup 13/C nuclear magnetic resonance spectra of the naphtha fraction of crude oil from wells located on the Norwegian shelf.
Abstract: Principal component analysis (PCA) is applied to /sup 13/C nuclear magnetic resonance spectra of the naphtha fraction of crude oil from wells located on the Norwegian shelf. Unsupervised PCA correlates oil samples from the same geographical area. The correlation follows from properties related to the composition of the oils, e.g., long-chained vs. short-chained alkanes, branching, cyclization, and aromatization. Several of the major constituents present in the oils are identified. The link between chemical composition of the crude oils and the geochemical processes of biodegradation water washing, and maturation suggests a simplified characterization of the oil samples. Also, by use of component scores the possibility of communication between the wells is uncovered. Separate modeling of replicated spectra of each sample by the use of supervised PCA (SIMCA) confirmed the results of the unsupervised classification. 39 references, 8 figures, 1 table.
67 citations
TL;DR: In this article, the authors used principal components of streamflow variation at 106 locations across the United States during the period 1931-1978 to define the frequency of above-or below-mean streamflow.
Abstract: Interannual modes of streamflow variation at 106 locations across the United States during the period 1931–1978 are defined by using principal components. Five statistically significant components are found to account for more than 56% of the total streamflow variance. The first principal component represents a nationwide tendency for either above- or below-mean streamflow. The second component represents a north-south opposition in departures from mean flow, and the third, an east-west opposition. Higher-order components (fourth and fifth) geographically depict regional patterns of opposition in the sign of streamflow departures between coastal-continental areas and between the northern and southern plains, respectively. Analyses using spatially and temporally modified data sets indicate that the first three components (which explain 45% of the variance) are quite stable spatially, while only the first component is stable temporally. Time series analysis of principal component scores indicates that all but the fourth component are first-order autoregressive processes, as is mean annual nationwide streamflow. The fourth component is an autoregressive (AR)(2) process. In general, the principal components of streamflow are found to exhibit more persistence over annual time scales than the mean annual flow data themselves.
56 citations
TL;DR: The canonical trend surface analysis method extracts that part of the character variation that is most nearly coincident with the geographic information, and leaves unresolved the other covariances.
Abstract: Characteristics of organisms often vary widely across geographic space as a result of natural selection, migration and environmental heterogeneity. I present canonical trend surface analysis as an approach to the study of this variation. The method is based on the canonical correlations between sets of orthogonal axes in the space defined by the characteristics of the organism and in the space defined by the coordinates of the localities (and their squares and crossproducts). I apply this method to simulated data sets of trends and patches; the basic patterns are recovered. Next, I analyze two real data sets: the distribution of 21 HLA human blood types at 58 localities in Europe; and the distribution of 26 species of Foraminifera in 61 sediment core top samples from the Atlantic and Indian oceans. The derived patterns are similar to those developed by other investigators using different methods on these same data. However, canonical trend surface analysis is shown to be less sensitive to geographically unpatterned data than the methods used in these earlier studies of the same data. The canonical trend surface method extracts that part of the character variation that is most nearly coincident with the geographic information, and leaves unresolved the other covariances. (Canonical correlation; trend surface analysis; geographic variation; principal components analysis; factor analysis.)
49 citations
TL;DR: Principal components derived from sets of real data with dimensions of 120 x 7, 120 x 4, 150 x 11, 150x 8, 150 X 5, 454 x 12, 4 54 x 8, and 454x 5 were compared to sets of randomly generated data of corresponding size.
Abstract: We compared principal components derived from sets of real data with dimensions of 120 x 7, 120 x 4, 150 x 11, 150 x 8, 150 x 5, 454 x 12, 454 x 8, and 454 x 5, to those from sets of randomly generated data of corresponding size. Principal components from subsets of 25, 50, 75, and 100 observations from the 120— and 150—observation data sets and those from subsets of 25, 50, 75, 100, 150, 200, 300, and 400 observations from the 454—observation data sets were compared. Percent variance association with components from real data was relatively constant over all sample sizes; percent variance decreased with larger samples of random data. A bootstrap method was used to develop standard error estimates on percent variance and percent of remaining variance associated with components from real data. Percent of remaining variance associated with the first four components from real data was significantly higher than analogous components from random data.
49 citations
TL;DR: The effects of normalization and weighting on principal component analysis (p.c.a.a.) of gas chromatographic data are investigated and logarithmic transformation of raw data seems preferable.
TL;DR: Experimental data were used to evaluate the effects of subjectivity on habitat analyses and found that classification success of discriminant models was impaired by observer bias.
Abstract: Experimental data were used to evaluate the effects of subjectivity on habitat analyses. Multivariate vegetation observations were made by four observers who independently and repeatedly sampled a series of sites in an oak-maple forest. The data were analyzed univariately using analysis of variance and multivariately using principal component and discriminant function analyses. Observers significantly differed in their measurements on 18 of 20 vegetation variables. Transformation of variables and use of non-parametric methods did not mitigate observer effects whatsoever. Separate principal component analyses (PCA) of each observer's data yielded four sets of axes which weighted variables quite differently. The angular distance between the PCI axes of different observers got as high as 42?. Observer-specific PC ordinations showed that the sizes, shapes and relative positions of site surfaces were all highly variable among observers. Discriminant function analysis (DFA) was shown to be even more observer-sensitive than PCA. This was deduced from fluctuating variable weights and the angles between DFs. Classification success of discriminant models was impaired by observer bias. Some suggestions for field and analytic improvements are presented.
TL;DR: The authors discuss the liminations of the second approach and point out that deletion solely on the basis of the magnitude of the eigenvalues ignores the potentials for bias, which is a weak criterion.
TL;DR: In this paper, two criteria for the adequacy of a component representation are developed and are shown to lead to different component solutions, and both criteria are generalized to allow weighting, the choice of weights determining the scale invariance properties of the resulting solution.
Abstract: Principal components analysis can be redefined in terms of the regression of observed variables upon component variables. Two criteria for the adequacy of a component representation in this context are developed and are shown to lead to different component solutions. Both criteria are generalized to allow weighting, the choice of weights determining the scale invariance properties of the resulting solution. A theorem is presented giving necessary and sufficient conditions for equivalent component solutions under different choices of weighting. Applications of the theorem are discussed that involve the components analysis of linearly derived variables and of external variables.
TL;DR: In this paper, principal component analysis has been used to group the European Mediterranean stations into homogeneous regions, where the most important component corresponds to a fairly uniform field, the second marks the climatological distribution of cyclonic disturbances, the third shows a gradient from north-east to south-west and the fourth exhibits the existence of two centres of anomalies with a negative ridge and a positive value on each side.
Abstract: Principal component analysis has been used to group the European Mediterranean stations into homogeneous regions. The annual rainfall records used were from 90 stations distributed all over the European Mediterranean countries.
Major components were selected by a dominant-variance selection rule, called rule N. The most important component corresponds to a fairly uniform field, the second marks the climatological distribution of cyclonic disturbances, the third shows a gradient from north-east to south-west and the fourth exhibits the existence of two centres of anomalies with a negative ridge and a positive value on each side.
A cluster analysis based on these major eigenvectors shows the existence of five climatic regions. A subjective method, using the zero-line characterizing the significant eigenvectors, shows similar results.
19 Jun 1985
TL;DR: In this paper, a new method of designing predictive controllers based on a singular value analysis of the process dynamics is developed that is particularly well on MIMO processes and tolerates changes in process scaling and output weighting.
Abstract: A new method of designing predictive controllers has been developed that is based on a singular value analysis of the process dynamics. The primary design parameter is the number of principal components of the system generalized inverse to retain in the approximate process inverse used by the controller. The effects of the individual components on closed-loop performance and robustness can be easily calculated. Choices of other controller design parameters have a minimal impact on the results of the new method. Explicit move suppression is not required. The method works particularly well on MIMO processes and tolerates changes in process scaling and output weighting. Application of the method to two distillation column models is illustrated.
TL;DR: The presentation of multichannel image information in terms of a false-colour composite can, in general, be achieved with less sacrifice of data if the three leading principal component images are ...
Abstract: The presentation of multichannel image information in terms of a false-colour composite can, in general, be achieved with less sacrifice of data if the three leading principal component images are ...
TL;DR: In this paper, a factorially designed experiment was carried out using mixtures of four pure chemicals to assess the effectiveness of several statistical techniques to detect the known structure of sample spectra.
Abstract: To assess the effectiveness of several statistical techniques to detect the known structure of sample spectra, a factorially designed experiment was carried out using mixtures of four pure chemicals. Analyses of the variation between spectra as expressed by correlation graphs and principal components are shown to be powerful techniques for relating the spectra of constituents to those of samples. A method of interpreting correlation graphs is proposed that identifies the existence of dominant effects such as particle size variation. For these samples, a standardisation algorithm was shown to reduce interference effects due to particle size and to allow easier interpretation of both correlation graphs and principal components.
TL;DR: In this paper, principal components analysis by alternating least squares optimal scaling (PCA-OLS) is used for improving the reliability and convergent and discriminant validity of measurement results.
Abstract: PRINCIPALS analysis (principal components analysis by alternating least squares optimal scaling) provides an approach for improving the reliability and convergent and discriminant validity of measu...
TL;DR: In this paper, the authors consider the problem of defining a reduced number of new variables or indicators which summarize the information contained in the set of original variables, and generalize the method of principal components by allowing for nonlinear relationships between the new indicators and the original variables.
Abstract: Suppose that several variables are defined for each element of a population. Here we consider the problem of defining a reduced number of new variables or indicators which summarize the information contained in the set of original variables. One way of dealing with this problem is through the method of principal components. This method, in its original version (Hotelling, 1933), consists of finding the linear combinations of the original variables with maximum variances. Rao (1964) and Darroch (1965) showed that the principal components may be interpreted in terms of recovering the information contained in the original variables through linear functions. In this paper we generalize the method of principal components by allowing for nonlinear relationships between the new indicators and the original variables. Henry and Lazarsfeld (1968, Chap. 8) and McDonald (1962, 1967) have also considered models where the relationship between factors and variables is nonlinear. The models considered in these works assume the structural hypothesis that the errors are independent of the factors, and may therefore be considered models of factor analysis. The present approach, on the contrary, is "data analytic", and there is no necessity to assume any a priori structure. Another approach to nonlinear components was suggested by Gnanadesikan (1977). However, this latter approach is useful primarily for adjusting hypersurfaces (surfaces of maximum dimension) to a set of data, while we are here concerned with adjusting curves (surfaces of dimension 1), or surfaces of small dimension.
TL;DR: In this paper, an external analysis of two-mode data is presented for exploring differences in the individuals' mappings of the attribute vectors in the fixed stimulus space, under conditions under which individual differences may be ignored.
Abstract: Through external analysis of two-mode data one attempts to map the elements of one mode (e.g., attributes) as vectors in a fixed space of the elements of the other mode (e.g., stimuli). This type of analysis is extended to three-mode data, for instance, when the ratings are made by more individuals. It is described how alternating least squares algorithms for three-mode principal component analysis (PCA) are adapted to enable external analysis, and it is demonstrated that these techniques are useful for exploring differences in the individuals' mappings of the attribute vectors in the fixed stimulus space. Conditions are described under which individual differences may be ignored. External three-mode PCA is illustrated with data from a person perception experiment, designed after two studies by Rosenberg and his associates whose results were used as external information.
TL;DR: The distribution of morph frequencies is not random but shows weak clines associated with certain climatic factors, which indicate the action of natural selection although very local variations in morph frequencies may result from selection and/or drift.
Abstract: Data on the frequencies of the main colour morphs (lineata, redimita and ovata) of Enoplognatha ovata have been collected from a total of 454 Ordnance Survey 10 km squares distributed throughout Great Britain. Only c. 0.5% of samples were monomorphic, for lineata in each case. Multiple regression analysis has been used to assess possible associations between morph frequencies and principal components derived from nine environmental variables. The distribution of morph frequencies is not random but shows weak clines associated with certain climatic factors. These large scale clines indicate the action of natural selection although very local variations in morph frequencies may result from selection and/or drift.
TL;DR: The authors examined the factorial validity of the decision-making style scales of the Assessment of Career Decision Making (ACDM-DMS), which are designed to measure rational, intuitive, and dependent decision making styles.
TL;DR: In this paper, the basic tool is the Karhunen-loeve decomposition for real-valued data and for categorical processes harmonic analysis is presented in terms of reciprocal averaging.
Abstract: Principal components analysis and correspondence analysis may be generalized to handle time-dependent data. For real-valued data the basic tool is the Karhunen-Loeve decomposition. For categorical processes harmonic analysis is presented in terms of reciprocal averaging. Details are given for approximated and interpolated solutions.
TL;DR: This paper showed how three-mode principal compo nents analysis can be useful for the analysis of seman tic differential ratings, in particular because no sum mation is necessary over any one mode.
Abstract: This paper shows how three-mode principal compo nents analysis can be useful for the analysis of seman tic differential ratings, in particular because no sum mation is necessary over any one mode The use of "joint plots" (a variant of the biplot) and sums-of- squares interpretations is explained and illustrated
TL;DR: Using a Monte Carlo simulation, the research addresses two key questions about the accuracy of cluster analysis in reproducing a known true cluster model and indicates that using principal components analysis is superior to not using it and that the choice of how to utilize the principal components results may be critical.
Abstract: Using a Monte Carlo simulation, the research in this article addresses two key questions about the accuracy of cluster analysis in reproducing a known true cluster model. First, how is the accuracy affected by different ways of measuring interunit similarity; in this case, different ways of using principal components analysis. Second, how is the accuracy affected by the quality of the characteristics data and by different procedures for handling missing information? The results indicate that using principal components analysis is superior to not using it and that the choice of how to utilize the principal components results may be critical. The results also indicate that the impact of data quality differences may be minimal, but that there are important differentials among the procedures for handling missing data.
TL;DR: In this article, a method similar to variable selection procedures in regression is presented for screening and simplifying linear combinations with extreme ratios of variances, that is, those defined by the eigenvectors associated with the extreme roots of Σ1 − 1 Σ2.
Abstract: If the covariance matrices Σ1 and Σ2 of two multivariate populations are not identical, insight into the differences between Σ1 and Σ2 can often be gained by analyzing the linear combinations with extreme ratios of variances—that is, those defined by the eigenvectors associated with the extreme roots of Σ1 −1 Σ2. This article gives a descriptive method, similar to variable selection procedures in regression, for screening and simplifying these linear combinations. A hypothesis of redundancy of variables is defined, and a statistic for testing this hypothesis is derived. The method is illustrated by an example.
TL;DR: This paper describes a method of disentangling different sources of variance contributing to component extraction in Principal Components Analysis (PCA) of event-related potentials, and shows advantages for the new methods.
Abstract: This paper describes a method of disentangling different sources of variance contributing to component extraction in Principal Components Analysis (PCA) of event-related potentials. Those sources not of interest for a given experiment may be easily discarded prior to component extraction. A real data example is presented for comparison of the different approaches, showing advantages for the new methods. They also exhibited more success in detecting experimental effects as shown in subsequent analysis of variance procedures on component scores. In the latter framework, various issues of validity of subsequent testing procedures for all principal component approaches are addressed theoretically as well as empirically by a split-sample cross-validation study. It is claimed that data-adaptive computation of component scores does not constitute a crucial issue. Finally, a bootstrap simulation provides evidence that the methods proposed are superior to the usual PCA approach in capability and relibility in the assessment of experimental effects.
TL;DR: The problems of preprocessing of 13C-n.m.r. spectra for hierarchical clustering are discussed and encoding of the spectra in nonequidistant intervals is proposed, using a Simplex method with variable-sized movements.
TL;DR: The exploratory role three-mode principal component analysis can play in analyzing multivariate longitudinal organizational data is outlined by an exposition of the technique itself, and by its application to organizational data from Dutch hospitals.
Abstract: The exploratory role three-mode principal component analysis can play in analyzing multivariate longitudinal organizational data is outlined by an exposition of the technique itself, and by its application to organizational data from Dutch hospitals. Relationships with some other techniques for such data are indicated.