nipals {mixOmics} | R Documentation

## Non-linear Iterative Partial Least Squares (NIPALS) algorithm

### Description

This function performs NIPALS algorithm, i.e. the singular-value decomposition (SVD) of a data table that can contain missing values.

### Usage

    nipals(X, ncomp = 2, max.iter = 500, tol = 1e-06)

### Arguments

`X` | a numeric matrix (or data frame) which provides the data for the principal components analysis. It can contain missing values in which case `center = TRUE` is used as required by the `nipals` function.
`ncomp` | Integer, if data is complete `ncomp` decides the number of components and associated eigenvalues to display from the `pcasvd` algorithm and if the data has missing values, `ncomp` gives the number of components to keep to perform the reconstitution of the data using the NIPALS algorithm. If `NULL`, function sets `ncomp = min(nrow(X), ncol(X))`
`max.iter` | Integer, the maximum number of iterations in the NIPALS algorithm.
`tol` | Positive real, the tolerance used in the NIPALS algorithm.

### Details

The NIPALS algorithm (Non-linear Iterative Partial Least Squares) has been developed by H. Wold at first for PCA and later-on for PLS. It is the most commonly used method for calculating the principal components of a data set. It gives more numerically accurate results when compared with the SVD of the covariance matrix, but is slower to calculate.

This algorithm allows to realize SVD with missing data, without having to delete the rows with missing data or to estimate the missing data.

### Value

An object of class 'mixo_nipals' containing slots:

`eig` | Vector containing the pseudo-singular values of `X`, of length `ncomp`.
`t` | Matrix whose columns contain the left singular vectors of `X`. Note that for a complete data matrix X, the return values `eig`, `t` and `p` such that `X = t * diag(eig) * t(p)`.

### Author(s)

Sébastien Déjean, Ignacio González, Kim-Anh Le Cao, Al J Abadi

### References

Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

Wold H. (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiah, P. R. (editors), Multivariate Analysis. Academic Press, N.Y., 391-420.

Wold H. (1975). Path models with latent variables: The NIPALS approach. In: Blalock H. M. et al. (editors). Quantitative Sociology: International perspectives on mathematical and statistical model building. Academic Press, N.Y., 307-357.

### See Also

`impute.nipals`, `svd`, `princomp`, `prcomp`, `eigen` and http://www.mixOmics.org for more details.

[Package mixOmics version 6.14.1 Index]