nipals {nipals} | R Documentation |
Principal component analysis by NIPALS, non-linear iterative partial least squares
Description
Used for finding principal components of a numeric matrix. Missing values in the matrix are allowed. Principal Components are extracted one a time. The algorithm computes x = TP', where T is the 'scores' matrix and P is the 'loadings' matrix.
Usage
nipals(
x,
ncomp = min(nrow(x), ncol(x)),
center = TRUE,
scale = TRUE,
maxiter = 500,
tol = 1e-06,
startcol = 0,
fitted = FALSE,
force.na = FALSE,
gramschmidt = TRUE,
verbose = FALSE
)
Arguments
x |
Numerical matrix for which to find principal compontents. Missing values are allowed. |
ncomp |
Maximum number of principal components to extract from x. |
center |
If TRUE, subtract the mean from each column of x before PCA. |
scale |
if TRUE, divide the standard deviation from each column of x before PCA. |
maxiter |
Maximum number of NIPALS iterations for each principal component. |
tol |
Default 1e-9 tolerance for testing convergence of the NIPALS iterations for each principal component. |
startcol |
Determine the starting column of x for the iterations of each principal component. If 0, use the column of x that has maximum absolute sum. If a number, use that column of x. If a function, apply the function to each column of x and choose the column with the maximum value of the function. |
fitted |
Default FALSE. If TRUE, return the fitted (reconstructed) value of x. |
force.na |
Default FALSE. If TRUE, force the function to use the method for missing values, even if there are no missing values in x. |
gramschmidt |
Default TRUE. If TRUE, perform Gram-Schmidt orthogonalization at each iteration. |
verbose |
Default FALSE. Use TRUE or 1 to show some diagnostics. |
Details
The R2 values that are reported are marginal, not cumulative.
Value
A list with components eig
, scores
, loadings
,
fitted
, ncomp
, R2
, iter
, center
,
scale
.
Author(s)
Kevin Wright
References
Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In Multivariate Analysis (Ed., P.R. Krishnaiah), Academic Press, NY, 391-420.
Andrecut, Mircea (2009). Parallel GPU implementation of iterative PCA algorithms. Journal of Computational Biology, 16, 1593-1599.
Examples
B <- matrix(c(50, 67, 90, 98, 120,
55, 71, 93, 102, 129,
65, 76, 95, 105, 134,
50, 80, 102, 130, 138,
60, 82, 97, 135, 151,
65, 89, 106, 137, 153,
75, 95, 117, 133, 155), ncol=5, byrow=TRUE)
rownames(B) <- c("G1","G2","G3","G4","G5","G6","G7")
colnames(B) <- c("E1","E2","E3","E4","E5")
dim(B) # 7 x 5
p1 <- nipals(B)
dim(p1$scores) # 7 x 5
dim(p1$loadings) # 5 x 5
B2 = B
B2[1,1] = B2[2,2] = NA
p2 = nipals(B2, fitted=TRUE)
# Two ways to make a biplot
# method 1
biplot(p2$scores, p2$loadings)
# method 2
class(p2) <- "princomp"
p2$sdev <- sqrt(p2$eig)
biplot(p2, scale=0)