GitHub - kwstat/nipals: Principal Component Analysis with missing data using NIPALS with Gram-Schmidt orthogonalization (original) (raw)

nipals

Homepage: https://kwstat.github.io/nipals

Repository: https://github.com/kwstat/nipals

The nipals package provides two functions to perform Principal Components Analysis of a matrix:

1. The nipals function uses Non-linear Iterative Partial Least Squares.
2. The empca function uses EM PCA.

NIPALS has been implemented several times in R packages. EMPCA has previously appeared in python, but is available in R here for the first time. This package strives to have the best (fast and accurate) R implementations.

The empca() function should be considered experimental. There is a problem using empca() on matrices that are both (1) non-full rank (2) have missing values.

Key features

• Missing values are allowed.
• Uses Gram-Schmidt to ensure orthogonal principal components.
• Carefully optimized for speed (nipals only, not empca).
• Flexible options.
• Vignettes and unit tests.
• Weights are allowed (empca only).

Installation

Install the released version from CRAN:

install.packages("nipals")

Install the development version from GitHub:

install.packages("devtools") devtools::install_github("kwstat/nipals")

Usage

require(nipals) data(uscrime, package = "nipals") dat <- uscrime dat <- as.matrix(dat[ , -1])

Gram-Schmidt corrected NIPALS

m3 <- nipals(dat)

Show that the Principal Components are orthogonal

round(crossprod(m3$loadings),3)

PC1 PC2 PC3 PC4 PC5 PC6 PC7

PC1 1 0 0 0 0 0 0

PC2 0 1 0 0 0 0 0

PC3 0 0 1 0 0 0 0

PC4 0 0 0 1 0 0 0

PC5 0 0 0 0 1 0 0

PC6 0 0 0 0 0 1 0

PC7 0 0 0 0 0 0 1

round(m3$loadings,3)

PC1 PC2 PC3 PC4 PC5 PC6 PC7

murder 0.296 -0.623 0.178 -0.241 0.540 -0.265 -0.270

rape 0.432 -0.171 -0.244 0.060 0.200 0.769 0.299

robbery 0.397 0.044 0.496 -0.558 -0.519 0.120 0.005

assault 0.399 -0.353 -0.063 0.629 -0.502 -0.166 -0.191

burglary 0.440 0.204 -0.211 -0.057 0.095 -0.540 0.645

larceny 0.358 0.401 -0.541 -0.231 0.023 -0.037 -0.602

autotheft 0.295 0.504 0.567 0.418 0.372 0.054 -0.148

m4 <- empca(dat)

Show that the Principal Components are orthogonal

round(crossprod(m4$loadings),3)

PC1 PC2 PC3 PC4 PC5 PC6 PC7

PC1 1 0 0 0 0 0 0

PC2 0 1 0 0 0 0 0

PC3 0 0 1 0 0 0 0

PC4 0 0 0 1 0 0 0

PC5 0 0 0 0 1 0 0

PC6 0 0 0 0 0 1 0

PC7 0 0 0 0 0 0 1

round(m4$loadings,3)

PC1 PC2 PC3 PC4 PC5 PC6 PC7

murder 0.301 -0.642 0.168 -0.433 0.447 0.062 0.278

rape 0.431 -0.146 -0.266 0.106 -0.018 -0.799 -0.269

robbery 0.399 0.023 0.488 -0.306 -0.712 0.028 -0.012

assault 0.396 -0.336 -0.099 0.734 -0.161 0.349 0.181

burglary 0.441 0.197 -0.191 -0.179 0.229 0.459 -0.659

larceny 0.353 0.430 -0.515 -0.245 -0.044 0.050 0.601

autotheft 0.295 0.478 0.593 0.275 0.461 -0.150 0.150

See also

A python version of this package can be found at https://pypi.org/project/nipals/.