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• Principal_component_analysis abstract "Principal component analysis (PCA) is a statistical procedure that uses orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to (i.e., uncorrelated with) the preceding components. Principal components are guaranteed to be independent if the data set is jointly normally distributed. PCA is sensitive to the relative scaling of the original variables.Depending on the field of application, it is also named the discrete Karhunen–Loève transform (KLT) in signal processing, the Hotelling transform in multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (Golub and Van Loan, 1983), eigenvalue decomposition (EVD) of XTX in linear algebra, factor analysis (for a discussion of the differences between PCA and factor analysis see Ch. 7 of ), Eckart–Young theorem (Harman, 1960), or Schmidt–Mirsky theorem in psychometrics, empirical orthogonal functions (EOF) in meteorological science, empirical eigenfunction decomposition (Sirovich, 1987), empirical component analysis (Lorenz, 1956), quasiharmonic modes (Brooks et al., 1988), spectral decomposition in noise and vibration, and empirical modal analysis in structural dynamics.PCA was invented in 1901 by Karl Pearson, as an analogue of the principal axes theorem in mechanics; it was later independently developed (and named) by Harold Hotelling in the 1930s. The method is mostly used as a tool in exploratory data analysis and for making predictive models. PCA can be done by eigenvalue decomposition of a data covariance (or correlation) matrix or singular value decomposition of a data matrix, usually after mean centering (and normalizing or using Z-scores) the data matrix for each attribute. The results of a PCA are usually discussed in terms of component scores, sometimes called factor scores (the transformed variable values corresponding to a particular data point), and loadings (the weight by which each standardized original variable should be multiplied to get the component score).PCA is the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way that best explains the variance in the data. If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space (1 axis per variable), PCA can supply the user with a lower-dimensional picture, a projection or "shadow" of this object when viewed from its (in some sense; see below) most informative viewpoint. This is done by using only the first few principal components so that the dimensionality of the transformed data is reduced.PCA is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix.PCA is also related to canonical correlation analysis (CCA). CCA defines coordinate systems that optimally describe the cross-covariance between two datasets while PCA defines a new orthogonal coordinate system that optimally describes variance in a single dataset.".
• Principal_component_analysis thumbnail GaussianScatterPCA.png?width=300.
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• Principal_component_analysis subject Category:Data_analysis.
• Principal_component_analysis subject Category:Dimension_reduction.
• Principal_component_analysis subject Category:Matrix_decompositions.
• Principal_component_analysis subject Category:Multivariate_statistics.
• Principal_component_analysis type Abstraction100002137.
• Principal_component_analysis type Algebra106012726.
• Principal_component_analysis type Cognition100023271.
• Principal_component_analysis type Content105809192.
• Principal_component_analysis type Decomposition106013471.
• Principal_component_analysis type Discipline105996646.
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• Principal_component_analysis type Mathematics106000644.
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• Principal_component_analysis type PureMathematics106003682.
• Principal_component_analysis type Science105999797.
• Principal_component_analysis type VectorAlgebra106013298.
• Principal_component_analysis comment "Principal component analysis (PCA) is a statistical procedure that uses orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables.".
• Principal_component_analysis label "Analisi delle componenti principali".
• Principal_component_analysis label "Analiza głównych składowych".
• Principal_component_analysis label "Analyse en composantes principales".
• Principal_component_analysis label "Análise de Componentes Principais".
• Principal_component_analysis label "Análisis de componentes principales".
• Principal_component_analysis label "Hauptkomponentenanalyse".
• Principal_component_analysis label "Hoofdcomponentenanalyse".
• Principal_component_analysis label "Principal component analysis".
• Principal_component_analysis label "Метод главных компонент".
• Principal_component_analysis label "تحليل العنصر الرئيسي".
• Principal_component_analysis label "主成分分析".
• Principal_component_analysis label "主成分分析".
• Principal_component_analysis sameAs Analýza_hlavních_komponent.
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• Principal_component_analysis sameAs Análisis_de_componentes_principales.
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• Principal_component_analysis sameAs Analyse_en_composantes_principales.
• Principal_component_analysis sameAs Analisis_komponen_utama.
• Principal_component_analysis sameAs Analisi_delle_componenti_principali.
• Principal_component_analysis sameAs 主成分分析.
• Principal_component_analysis sameAs 주성분_분석.
• Principal_component_analysis sameAs Hoofdcomponentenanalyse.
• Principal_component_analysis sameAs Analiza_głównych_składowych.
• Principal_component_analysis sameAs Análise_de_Componentes_Principais.
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• Principal_component_analysis depiction GaussianScatterPCA.png.
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