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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.
The PCA has its roots in theological controversies over liberalism in Christianity and neo-orthodoxy that had been a point of contention in the Presbyterian Church in the United States which had split from the mainline Presbyterian Church in the U.S.A along regional lines at the beginning of the Civil War.
Output after kernel PCA, with a Gaussian kernel. Note in particular that the first principal component is enough to distinguish the three different groups, which is impossible using only linear PCA, because linear PCA operates only in the given (in this case two-dimensional) space, in which these concentric point clouds are not linearly separable.
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. [2] [3] [4]
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 ...
Patient-controlled analgesia; Plate count agar in microbiology; Polymerase cycling assembly, for large DNA oligonucleotides; Posterior cerebral artery; Posterior cortical atrophy, a form of dementia
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.
The Professional Chess Association (PCA), which existed between 1993 and 1996, was a rival organisation to FIDE, the International Chess Federation. The PCA was created in 1993 by Garry Kasparov and Nigel Short for the marketing and organization of their Chess World Championship.