number of principal components. Origin – Contains PCA in its Pro version. Qlucore – Commercial software for analyzing multivariate data with instant response using PCA. R – Free statistical package, the functions princomp and prcomp can be used for principal component analysis; prcomp uses singular value decomposition which generally gives better numerical accuracy. Some packages that implement PCA in R, include, but are not limited to: ade4, vegan, ExPosition, dimRed, and FactoMineR. SAS – Proprietary software; for example, see scikit-learn – Python library for machine learning which contains PCA, Probabilistic PCA, Kernel PCA, Sparse PCA and other techniques in the decomposition module. Scilab – Free and open-source, cross-platform numerical computational package, the function princomp computes principal component analysis, the function pca computes principal component analysis with standardized variables. SPSS – Proprietary software most commonly used by social scientists for PCA, factor analysis and associated cluster analysis. Weka – Java library for machine learning which contains modules for computing principal components. See also Correspondence analysis (for contingency tables) Multiple correspondence analysis (for qualitative variables) Factor analysis of mixed data (for quantitative and qualitative variables) Canonical correlation CUR matrix approximation (can replace of low-rank SVD approximation) Detrended correspondence analysis Directional component analysis Dynamic mode decomposition Eigenface Expectation–maximization algorithm Exploratory factor analysis (Wikiversity) Factorial code Functional principal component analysis Geometric data analysis Independent component analysis Kernel PCA L1-norm principal component analysis Low-rank approximation Matrix decomposition Non-negative matrix factorization Nonlinear dimensionality reduction Oja's rule Point distribution model (PCA applied to morphometry and computer vision) Principal component analysis (Wikibooks) Principal component regression Singular spectrum analysis Singular value decomposition Sparse PCA Transform coding Weighted least squares References Further reading Jackson, J.E. (1991). A User's Guide to Principal Components (Wiley). Husson François, Lê Sébastien & Pagès Jérôme (2009). Exploratory Multivariate Analysis by Example Using R. Chapman & Hall/CRC The R Series, London. 224p. Pagès Jérôme (2014). Multiple Factor Analysis by Example Using R. Chapman & Hall/CRC The R Series London 272 p External links A Tutorial on Principal Component Analysis (a video of less than 100 seconds.) See also the list of Software implementations Matrix decompositions Dimension reduction