# principal components analysis

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**Principal components analysis**— Principal component analysis (PCA) is a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen Loève transform (KLT),… … Wikipedia**Principal Components Analysis**— a method of transforming the axes of multidimensional space in which data occur so that the first axis explains the maximum amount of variance, the second axis, which is orthogonal to the first, explains the maximum of the remaining variance, and … Dictionary of ichthyology**Principal component analysis**— PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by… … Wikipedia**Analysis**— (from Greek ἀνάλυσις , a breaking up ) is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle,… … Wikipedia**Principal axis theorem**— In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated to an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse. The principal axis theorem states… … Wikipedia**Principal component regression**— In statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients.In PCR instead of regressing the independent variables (the regressors) on the dependent… … Wikipedia**Analysis of variance**— In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of… … Wikipedia**Factor analysis**— is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in … Wikipedia**Latent semantic analysis**— (LSA) is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA was … Wikipedia**multivariate analysis**— Univariate analysis consists in describing and explaining the variation in a single variable. Bivariate analysis does the same for two variables taken together (covariation). Multivariate analysis (MVA) considers the simultaneous effects of many… … Dictionary of sociology