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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.
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 .
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 .
The data transformation may be linear, as in principal component analysis (PCA), but many nonlinear dimensionality reduction techniques also exist. [ 4 ] [ 5 ] For multidimensional data, tensor representation can be used in dimensionality reduction through multilinear subspace learning .
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.
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 .
Historically, multilinear principal component analysis has been referred to as "M-mode PCA", a terminology which was coined by Peter Kroonenberg. [10] In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA [11] terminology as a way to better differentiate between multilinear tensor decompositions that computed 2nd order statistics associated with each data tensor mode, [1] [2] [3 ...
As its name hints, it's operating an Orthogonal Decomposition along with the Principal Components of the field. As such it is assimilated with the principal component analysis from Pearson in the field of statistics, or the singular value decomposition in linear algebra because it refers to eigenvalues and eigenvectors of a physical field.