# 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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`.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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.