GeometricMorphometricsMix (version 0.6.0.1)

reversePCA: 'Reverse' PCA

Description

Obtain data in the original variables starting from PCA scores

Usage

reversePCA(Scores, Eigenvectors, Mean)

Value

The function outputs a matrix n x p of the scores 'back-transformed' into the original variables

Arguments

Scores

matrix n x s of n observation for s scores. Can be a single column (for instance, if one is interested in PC1 only)

Eigenvectors

matrix p x s of eigenvectors (as column eigenvectors); notice that s (number of column eigenvectors) must be the same as the number of columns of PC scores in Scores

Mean

vector of length p with the multivariate mean computed on the original dataset (the dataset on which the PCA was carried out)

Details

Given a set of PCA scores, a set of eigenvectors and the mean of the data on which the PCA was originally computed, this function returns a set of observations in the original data space. This simple function can have many applications (not only in morphometrics) such as

• Producing predicted shapes for extreme, unobserved, values of PC scores (e.g., the shape, or other set of variables, corresponding to 3 times the most extreme positive PC1 score), or their combinations (e.g., a value of 0.4 on PC1 and 0.3 on PC2)

• Interpret results of analyses carried out on PC scores by converting these back to shapes

Examples

library(MASS)
set.seed(123)
A=mvrnorm(10,mu=rep(1,2),Sigma=diag(2))
# Create a small dataset of 10 observations and 2 variables

Mean=colMeans(A)
PCA=prcomp(A)
# Compute mean and perform PCA

B=reversePCA(Scores=PCA$x, Eigenvectors=PCA$rotation, Mean=Mean)
# 'Revert' the PCA (in this case using all scores and all axes
# to get the same results as the starting data)

round(A,10)==round(B,10)
# Check that all the results are the same
# (rounding to the 10th decimal because of numerical precision)