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The principal components of a collection of points in a real coordinate space are a sequence of unit vectors, where the -th vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component analysis (PCA) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest.

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rdf:type	Thing anatomical structure
rdfs:label	Principal component analysis (en)
rdfs:comment	The principal components of a collection of points in a real coordinate space are a sequence of unit vectors, where the -th vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component analysis (PCA) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest. (en)
rdfs:seeAlso	Portfolio optimization
sameAs	Principal component analysis Principal component analysis
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Subject	Dimension reduction Matrix decompositions
gold:hypernym	Procedure
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Principal_component_analysis?oldid=1070303429&ns=0
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has abstract	The principal components of a collection of points in a real coordinate space are a sequence of unit vectors, where the -th vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component analysis (PCA) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest. PCA is used in exploratory data analysis and for making predictive models. It is commonly used for dimensionality reduction by projecting each data point onto only the first few principal components to obtain lower-dimensional data while preserving as much of the data's variation as possible. The first principal component can equivalently be defined as a direction that maximizes the variance of the projected data. The -th principal component can be taken as a direction orthogonal to the first principal components that maximizes the variance of the projected data. For either objective, it can be shown that the principal components are eigenvectors of the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value decomposition of the data matrix. PCA is the simplest of the true eigenvector-based multivariate analyses and 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. Robust and L1-norm-based variants of standard PCA have also been proposed. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Principal_component_analysis
is differentFrom of	Component analysis (statistics)
is rdfs:seeAlso of	Factor analysis
is Wikipage redirect of	Non-linear iterative partial least squares Nonlinear iterative partial least squares Principal Component Analysis Principal Components Analysis Principal components analysis Eigenimage Eigenvector analysis Hotelling transform KL transform Principal-component analysis Principal-components analysis Principal component Principal component analyses Principal components Principle Component Analysis Principle component analysis Principle components Principle components analysis Characteristic vector analysis NIPALS Conditional principal components analysis Probabilistic principal component analysis Proper Orthogonal Decomposition
is Link from a Wikipage to another Wikipage of	Flow cytometry bioinformatics Greeks List of statistics articles Load factor Local pixel grouping Locality-sensitive hashing Machine learning Machine learning in bioinformatics Mahalanobis distance Mark Burgess (computer scientist) Market segmentation Non-linear iterative partial least squares Non-negative matrix factorization Nonlinear dimensionality reduction Nonlinear system identification Numbers (season 2) Numbers (season 3) Numerical analysis 3D sound synthesis ADaMSoft ANOVA–simultaneous component analysis Achenbach System of Empirically Based Assessment Adaptive coordinate descent Additive synthesis Affinity propagation Ali Akansu Analyse-it Analysis Analytic hierarchy process Analytics Anatolian hunter-gatherers Animal cognition Annoyance factor Anoura Apache Spark Apache SystemDS Applicability domain Archimedes Palimpsest ArrayTrack

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