R Code for canonical correlation analysis

Jun 29th, 2015
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Texas Woman's University
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R11 <- cor(sepal.meas) R22 <- cor(petal.meas) R12 <- c(cor(sepal.meas[,1], petal.meas[,1]), cor(sepal.meas[,1], etal.meas[,2]), cor(sepal.meas[,2], petal.meas[,1]), cor(sepal.meas[,2].

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############################################### R Code for canonical correlation analysis ################################################ We will use the built-in iris data set.# We will consider the entire data set (all three species)attach(iris)# We will standardize the variables first# by dividing by each column's standard deviation:# (we will remove column 5, the species labels)iris.std <- sweep(iris[,-5], 2, sqrt(apply(iris[,-5],2,var)), FUN="/")sepal.meas <- iris.std[,1:2]petal.meas <- iris.std[,3:4]### Doing the CCA the long way:# Finding blocks of the correlation matrix:R11 <- cor(sepal.meas)R22 <- cor(petal.meas)R12 <- c(cor(sepal.meas[,1], petal.meas[,1]), cor(sepal.meas[,1], petal.meas[,2]), cor(sepal.meas[,2], petal.meas[,1]), cor(sepal.meas[,2], petal.meas[,2]))R12 <- matrix(R12, ncol=ncol(R22), byrow=T) # R12 has q2 columns, same as number of petal measurementsR21 <- t(R12) # R21=transpose of R12# Finding the E1 and E2 matrices:E1 <- solve(R11) %*% R12 %*% solve(R22) %*% R21E2 <- solve(R22) %*% R21 %*% solve(R11) %*% R12# print(E1)# print(E2)eigen(E1)eigen(E2)# The canonical correlations are:canon.corr <- sqrt(eigen(E1)$values)canon.corr# The canonical variates are based on the eigenvectors of E1 and E2:# a1 = (0.922, -0.388)# b1 = (0.943, -0.333)# a2 = (0.457, 0.890)# b2 = (-0.679, 0.734)# Only the first canonical correlation is really substantial:# u1 = 0.92*Sepal.Length - 0.39*Sepal.Width# v1 =

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