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# Topic: Principal components analysis

 PlanetMath: principal components analysis The principal axes and the variance along each of them are then given by the eigenvectors and associated eigenvalues of the dispersion matrix. Principal component analysis has in practice been used to reduce the dimensionality of problems, and to transform interdependent coordinates into significant and independent ones. This is version 3 of principal components analysis, born on 2002-01-19, modified 2006-05-29. planetmath.org /encyclopedia/PrincipleComponentsAnalysis.html   (330 words)

 NationMaster - Encyclopedia: Principal components analysis PCA involves the computation of the eigenvalue decomposition or Singular value decomposition of a data set, usually after mean centering the data for each attribute. Principal components analysis is a technique for finding a set of weighted linear composites of original variables such that each composite (a principal component) is uncorrelated with the others. PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. www.nationmaster.com /encyclopedia/Principal-components-analysis   (566 words)

 Principal components analysis - Wikipedia, the free encyclopedia It is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. PCA has the distinction of being the optimal linear transformation for keeping the subspace that has largest variance. en.wikipedia.org /wiki/Principal_components_analysis   (1412 words)

 Principal components analysis Principal components analysis is a technique for finding a set of weighted linear composites of original variables such that each composite (a principal component) is uncorrelated with the others. The first principal component is such a weighted linear composite of the original variables with weights chosen so that the composite accounts for the maximum variation in the original data. factor analysis partitions the variation into that which is common among the variables and that which is unique to a given variable (and finds factors of the common variation) while principal components analysis regards all variation as common. www.pcp-net.org /encyclopaedia/pca.html   (285 words)

 Principal components analysis The purpose of principal component analysis is to derive a small number of linear combinations (principal components) of a set of variables that retain as much of the information in the original variables as possible. Principal components are linear combinations of variables that retain maximal amount of information about the variables. In technical terms, a principal component for a given set of N-dimensional data, is a linear combination of the original variables with coefficients equal to the components of an eigenvector of the correlation or covariance matrix. www.statistics.com /resources/glossary/p/pca.php   (173 words)

 SAS Annotated Output: Principal Components Analysis Principal components analysis is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize. Because we conducted our principal components analysis on the correlation matrix, the variables are standardized, which means that the each variable has a variance of 1, and the total variance is equal to the number of variables used in the analysis, in this case, 12. Components with an eigenvalue of less than 1 account for less variance than did the original variable (which had a variance of 1), and so are of little use. www.ats.ucla.edu /stat/sas/output/principal_components.htm   (1516 words)

 Principal Components Analysis (PCA) The first principal component is defined as that direction that encodes the maximum possible variance, The second component is orthogonal to the first and encodes as much as possible of the remaining variance. Principal component analysis of stacked multi-temporal images for the monitoring of rapid urban …. Principal component analysis and the scaled subprofile model compared to intersubject averaging and …. www.stats.org.uk /pca   (2372 words)

 BioMed Central | Full text | Assessing newborn body composition using principal components analysis: differences in the ... Principal components analysis with varimax rotation was used to reduce these measurements to two independent components each for mother, father and baby: one highly correlated with measures of fat, the other with skeletal size. Factors associated with the fat component were largely those related to the intrauterine environment (Table 7) with parity and maternal glucose associated with fat in both boys and girls, and the strongest predictor of fat in the girls being maternal fat component (Table 7). Components representing skeletal size and fat were produced in the study by Evans et al[33] investigating the effect of frequent prenatal ultrasound examinations on birthweight. www.biomedcentral.com /1471-2431/6/24   (5349 words)

 PlanetMath: principal components analysis The principal axes and the variance along each of them are then given by the eigenvectors and associated eigenvalues of the dispersion matrix. Principal component analysis has in practice been used to reduce the dimensionality of problems, and to transform interdependent coordinates into significant and independent ones. This is version 2 of principal components analysis, born on 2002-01-19, modified 2005-07-13. www.planetmath.org /encyclopedia/HotellingTransform.html   (330 words)

 [No title]   (Site not responding. Last check: ) Science, of course, was one of the principal components of analysis, along with logic and mathematics. Principal components analysis attempts to determine a smaller set of synthetic variables that could explain the original set. PCA can be used for reducing dimensionality in a dataset while retaining those characteristics... www.worldhistory.com /wiki/P/Principal-components-analysis.htm   (599 words)

 Independent component analysis - Wikipedia, the free encyclopedia   (Site not responding. Last check: ) Independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents supposing the mutual statistical independence of the non-Gaussian source signals. Linear independent component analysis can be divided into noiseless and noisy cases, where noiseless ICA is a special case of noisy ICA. The general framework for independent component analysis was introduced by Jeanny Herault and Christian Jutten in 1986 and was most clearly stated by Pierre Comon in 1994. www.sciencedaily.com /encyclopedia/independent_components_analysis   (1151 words)

 Principal components analysis and alpha reliability coefficient Principal components analysis is most often used as a data reduction technique for selecting a subset of "highly predictive" variables from a larger group of variables. PCA does not assume any particular distribution of your original data but it is very sensitive to variance differences between variables. Factor analysis (FA) is a child of PCA, and the results of PCA are often wrongly labelled as FA. www.statsdirect.com /help/statsdirect/pca.htm   (1097 words)

 Principal Components Analysis   (Site not responding. Last check: ) PCA seeks to rotate the space such that this direction is parallel to the x-axis. PCA would seek to rotate the space such that this direction was the new x-axis. PCA isn't generally used in speech recognition systems but it is a useful technique to apply when studying speech acoustics. www.shlrc.mq.edu.au /speech/recognition/unit_notes/x470.html   (633 words)

 Principal Components Analysis The sum of the variances of the principal components is equal to the variance of the original variables. It becomes easier to interpret the principal components when the elements of the latent vectors are transformed to correlations of the variables with the particular principal components. The purpose of principal components analysis is to reduce the complexity of the multivariate data into the principal components space and then choose the first q principal component (q < p) that explain most of the variation in the original variables. www.unesco.org /webworld/idams/advguide/Chapt6_2.htm   (1116 words)

 Cannonical Correlation PCA is a type of factor analysis that is most often used as an exploratory tool. After extraction of the principal components variables, components that explain a small amount of variance in the data set may be discarded. It may be possible to interpret each principal component as a combination of a small number of the original variables, with which they are most highly correlated. userwww.sfsu.edu /~efc/classes/biol710/pca/CCandPCA2.htm   (2303 words)

 Principal Components Analysis (PCA) PCA is a bilinear modeling method which gives an interpretable overview of the main information in a multidimensional data table. The second principal component is orthogonal to the first and covers as much of the remaining variation as possible, and so on. PCA helps you find out in what respect one sample is different from another, which variables contribute most to this difference, and whether those variables contribute in the same way (i.e. www.camo.com /rt/Products/Multivariate/types_methods.html   (2062 words)

 6.5.5. Principal Components Principal component analysis aims at reducing a large set of variables to a small set that still contains most of the information in the large set. The technique of principal component analysis enables us to create and use a reduced set of variables, which are called principal factors. While these principal factors represent or replace one or more of the original variables, it should be noted that they are not just a one-to-one transformation, so inverse transformations are not possible. www.itl.nist.gov /div898/handbook/pmc/section5/pmc55.htm   (507 words)

 MMU - Bio. Sci., MSc Multivariate Statistics: Principal components analysis   (Site not responding. Last check: ) PCA is one of a family of related ordination or projection techniques that includes Factor Analysis and Principal Co-ordinates Analysis. Note: it is Principal ('first in rank or importance' Concise Oxford Dictionary) not Principle ('a fundamental truth or law as the basis of reasoning or action', Concise Oxford Dictionary). PCA and FA are two similar methods, indeed under certain circumstances (no rotation and number of factors = number of variables) they produce identical results (albeit with some rescaling of the eigen vectors). obelia.jde.aca.mmu.ac.uk /multivar/pca.htm   (223 words)

 The Individualist: Principal components analysis (PCA) Principle Components are a set of variables that define a projection that encapsulates the maximum amount of variation in a dataset and is orthogonal (and therefore uncorrelated) to the previous principle component of the same dataset. PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Principal components and related or derived methods are procedures for simplifying multivariate data with minimum loss of information. www.dadamo.com /wiki/wiki.pl/Principal_components_analysis_(PCA)   (1018 words)

 Principal Components Analysis - PCA Principal components analysis (PCA) was originally introduced as far back as 1901 by Karl Pearson and found its first use or rather misuse in the analysis of intelligence tests. The new variables are derived in decreasing order of importance so that, for example, the first principal component accounts for as much as possible of the variation in the original data. The objective of this analysis is usually to see whether the first few components account for most of the variation in the data. www.dcs.gla.ac.uk /~mc/1stYearReport/2.6_PCA.htm   (427 words)

 Analysis - Wikipedia, the free encyclopedia Analysis of variance, a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts Aura analysis, a technique in which supporters of the method claim that the body's aura, or energy field is "analyzed" Chemical analysis, the analysis of material samples to gain an understanding of their chemical composition and structure en.wikipedia.org /wiki/Analysis   (651 words)

 Anais da Academia Brasileira de Ciências - Identification of Tibicen cicada species by a Principal Components Analysis ...   (Site not responding. Last check: ) Then the cluster analysis of the PCA scores clearly separated each species and allocated the samples in the same way. Therefore, a Principal Components Analysis of the sound was used to aid identification. Principal Components Analysis was carried out using the peak and mean frequencies and the pulse rate as the variables. www.scielo.br /scielo.php?script=sci_arttext&pid=S0001-37652004000200038&lng=en&nrm=iso&tlng=en   (954 words)

 web page for principal components analysis - ed 710 spring Principal Components Analysis is a multi variate technique that is grounded in several fundamental regression concepts that you have previously considered. The method of principal components analysis is primarily that of data reduction. Since the other components have loadings of zero (0), each predictor also explains 100 percent of all the variance in each component that can be attributed to a single predictor. www2.widener.edu /~aad0002/710princi.html   (1084 words)

 GOG 485-585 A Principal Components Analysis (PCA) on a set of image bands produces a new set of images with components that are uncorrelated with each other and explain progressively less of the variance found in the original set of bands. This technique is used for data compression since the first two or three components explain 95 to 99 percent of the variance in the original set of bands. When the PCA was run on the h87tm1-7 images a new principal component image was created for each of the TM images, each with the prefix “h87cmp”. www.albany.edu /faculty/fmh06/agog485/GOG585LAB4.htm   (1040 words)

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