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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
L1-norm principal component analysis (L1-PCA) is a general method for multivariate data analysis. [1] L1-PCA is often preferred over standard L2-norm principal component analysis (PCA) when the analyzed data may contain outliers (faulty values or corruptions), as it is believed to be robust .
Simultaneous component analysis is mathematically identical to PCA, but is semantically different in that it models different objects or subjects at the same time. The standard notation for a SCA – and PCA – model is: = ′ + where X is the data, T are the component scores and P are the component loadings.
In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis. [1] The scree plot is used to determine the number of factors to retain in an exploratory factor analysis (FA) or principal components to keep in a principal component analysis (PCA).
In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). PCR is a form of reduced rank regression . [ 1 ] More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model .
This involves the development of direct connections between simple correspondence analysis, principal component analysis and MCA with a form of cluster analysis known as Euclidean classification. [3] Two extensions have great practical use. It is possible to include, as active elements in the MCA, several quantitative variables.
Sparse principal component analysis (SPCA or sparse PCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structures to the input variables.
In the field of multivariate statistics, kernel principal component analysis (kernel PCA) [1] is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space .