empca: Principal component analysis by weighted EMPCA, expectation...

In nipals: Principal Components Analysis using NIPALS or Weighted EMPCA, with Gram-Schmidt Orthogonalization

Description

Used for finding principal components of a numeric matrix. Missing values in the matrix are allowed. Weights for each element of 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

empca(
  x,
  w,
  ncomp = min(nrow(x), ncol(x)),
  center = TRUE,
  scale = TRUE,
  maxiter = 100,
  tol = 1e-06,
  seed = NULL,
  fitted = FALSE,
  gramschmidt = TRUE,
  verbose = FALSE
)

Arguments

x	Numerical matrix for which to find principal components. Missing values are allowed.
w	Numerical matrix of weights.
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 EM iterations for each principal component.
tol	Default 1e-6 tolerance for testing convergence of the EM iterations for each principal component.
seed	Random seed to use when initializing the random rotation matrix.
fitted	Default FALSE. If TRUE, return the fitted (reconstructed) value of x.
gramschmidt	Default TRUE. If TRUE, perform Gram-Schmidt orthogonalization at each iteration.
verbose	Default FALSE. Use TRUE or 1 to show some diagnostics.

Value

A list with components eig, scores, loadings, fitted, ncomp, R2, iter, center, scale.

Author(s)

Kevin Wright

References

Stephen Bailey (2012). Principal Component Analysis with Noisy and/or Missing Data. Publications of the Astronomical Society of the Pacific. http://doi.org/10.1086/668105

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 <- empca(B)
dim(p1$scores) # 7 x 5
dim(p1$loadings) # 5 x 5

B2 = B
B2[1,1] = B2[2,2] = NA
p2 = empca(B2, fitted=TRUE)

nipals documentation built on Sept. 16, 2021, 1:07 a.m.