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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 .
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 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).
Principal component analysis [ edit ] Given an unlabeled set of n input data vectors, PCA generates p (which is much smaller than the dimension of the input data) right singular vectors corresponding to the p largest singular values of the data matrix, where the k th row of the data matrix is the k th input data vector shifted by the sample ...
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 .
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 .
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.
The 2014 guaranteed algorithm for the robust PCA problem (with the input matrix being = +) is an alternating minimization type algorithm. [12] The computational complexity is () where the input is the superposition of a low-rank (of rank ) and a sparse matrix of dimension and is the desired accuracy of the recovered solution, i.e., ‖ ^ ‖ where is the true low-rank component and ^ is the ...