Non-linear iterative partial least squares
Encyclopedia
In statistics
, non-linear iterative partial least squares (NIPALS) is an algorithm for computing the first few components in a principal component or partial least squares analysis. For very high-dimensional datasets, such as those generated in the 'omics sciences (e.g., genomics
, metabolomics
) it is usually only necessary to compute
the first few principal components. The nonlinear iterative partial least squares (NIPALS) algorithm
calculates t1 and p1' from X. The outer product
, t1p1' can then be subtracted from X leaving the residual
matrix
E1. This can be then used to calculate subsequent PCs. This results in a dramatic reduction in computational time since calculation of the covariance matrix
is avoided.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, non-linear iterative partial least squares (NIPALS) is an algorithm for computing the first few components in a principal component or partial least squares analysis. For very high-dimensional datasets, such as those generated in the 'omics sciences (e.g., genomics
Genomics
Genomics is a discipline in genetics concerning the study of the genomes of organisms. The field includes intensive efforts to determine the entire DNA sequence of organisms and fine-scale genetic mapping efforts. The field also includes studies of intragenomic phenomena such as heterosis,...
, metabolomics
Metabolomics
Metabolomics is the scientific study of chemical processes involving metabolites. Specifically, metabolomics is the "systematic study of the unique chemical fingerprints that specific cellular processes leave behind", the study of their small-molecule metabolite profiles...
) it is usually only necessary to compute
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
the first few principal components. The nonlinear iterative partial least squares (NIPALS) algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
calculates t1 and p1' from X. The outer product
Outer product
In linear algebra, the outer product typically refers to the tensor product of two vectors. The result of applying the outer product to a pair of vectors is a matrix...
, t1p1' can then be subtracted from X leaving the residual
Errors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
E1. This can be then used to calculate subsequent PCs. This results in a dramatic reduction in computational time since calculation of the covariance matrix
Covariance matrix
In probability theory and statistics, a covariance matrix is a matrix whose element in the i, j position is the covariance between the i th and j th elements of a random vector...
is avoided.