prcomp_irlba {irlba}

Principal Components Analysis

Description

Efficient computation of a truncated principal components analysis of a given data matrix using an implicitly restarted Lanczos method from the irlba package.

Usage

prcomp_irlba(x, n = 3, retx = TRUE, center = TRUE, scale. = FALSE, ...)

Arguments

x

a numeric or complex matrix (or data frame) which provides the data for the principal components analysis.

n

integer number of principal component vectors to return, must be less than min(dim(x)).

retx

a logical value indicating whether the rotated variables should be returned.

center

a logical value indicating whether the variables should be shifted to be zero centered. Alternately, a centering vector of length equal the number of columns of x can be supplied.

scale.

a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is FALSE for consistency with S, but scaling is often advisable. Alternatively, a vector of length equal the number of columns of x can be supplied.

The value of scale determines how column scaling is performed (after centering). If scale is a numeric vector with length equal to the number of columns of x, then each column of x is divided by the corresponding value from scale. If scale is TRUE then scaling is done by dividing the (centered) columns of x by their standard deviations if center=TRUE, and the root mean square otherwise. If scale is FALSE, no scaling is done. See scale for more details.

...

additional arguments passed to irlba.

Value

A list with class "prcomp" containing the following components:

• sdev the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix).

• rotation the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors).

• x if retx is TRUE the value of the rotated data (the centred (and scaled if requested) data multiplied by the rotation matrix) is returned. Hence, cov(x) is the diagonal matrix diag(sdev^2).

• center, scale the centering and scaling used, or FALSE.

Note

The signs of the columns of the rotation matrix are arbitrary, and so may differ between different programs for PCA, and even between different builds of R.

NOTE DIFFERENCES WITH THE DEFAULT prcomp FUNCTION! The tol truncation argument found in prcomp is not supported. In place of the truncation tolerance in the original function, the prcomp_irlba function has the argument n explicitly giving the number of principal components to return. A warning is generated if the argument tol is used, which is interpreted differently between the two functions.

See Also

prcomp

Examples

set.seed(1)
x  <- matrix(rnorm(200), nrow=20)
p1 <- prcomp_irlba(x, n=3)
summary(p1)

# Compare with
p2 <- prcomp(x, tol=0.7)
summary(p2)