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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.
Half of Liberia's total landmass is forest (4.9 million hectares) and 47% is arable land, although most of this is upland pasture. [14] The 'slash and burn' technique is used extensively to convert woodland into rice paddies, often at the expense of biodiversity. The nation consists of flat, coastal plains and dwarf mountains further inland in ...
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 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 ...
In ()-(), L1-norm ‖ ‖ returns the sum of the absolute entries of its argument and L2-norm ‖ ‖ returns the sum of the squared entries of its argument.If one substitutes ‖ ‖ in by the Frobenius/L2-norm ‖ ‖, then the problem becomes standard PCA and it is solved by the matrix that contains the dominant singular vectors of (i.e., the singular vectors that correspond to the highest ...
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.
Within the field of molecular biology, a protein-fragment complementation assay, or PCA, is a method for the identification and quantification of protein–protein interactions. In the PCA, the proteins of interest ("bait" and "prey") are each covalently linked to fragments of a third protein (e.g. DHFR, which acts as a "reporter").
The sodium salt of pyroglutamic acid—known either as sodium pyroglutamate, sodium PCA, or sodium pidolate—is used for dry skin and hair products, as it is a humectant. It has low toxicity and is not a skin irritant, but its use in products is limited by a high price. [7] [8] L-pyroglutamic acid is sold online as a nootropic dietary ...