pca with log + eps

pca_log.R

# pca

d <- data.frame(x = runif(100))
d$y <- d$x + runif(100, -0.01, 0.01)



plot(y ~ x, data = d)

# very correlated. pc1 should be along the diagonal.

m <- prcomp(x = log(d))

# x and y components in pc1 are equal. i.e. pc1 is along diagonal.


# Now add a row with 1 zero

d <- rbind(d, c(0, 0.5))

# Make vector of small numbers to add.
eps_vec <- exp(seq(-30, 1, length.out = 20))

ratio <- rep(NA, 20)

for(i in 1:20){

  m <- prcomp(x = log(d + eps_vec[i]))

  ratio[i] <- m$rotation[1, 1] / m$rotation[2, 1]

}

# When eps is 1, pca1 is still equal parts x and y
#   When eps is small, x dominates because the log(1e-10) makes x the widest.
plot(ratio ~ eps_vec)