pwcca: Projection-Weighted Canonical Correlation Analysis

Description

Compute pairwise projection-weighted CCA (PWCCA) similarities between multiple representations. PWCCA reweights canonical directions by the magnitude of each representation’s projection onto those directions, emphasizing components that are most used by the representation.

Usage

pwcca(mats)

Value

An \(M \times M\) symmetric matrix of PWCCA similarities.

Arguments

mats: A list of length \(M\) containing data matrices of size \((n_\mathrm{samples},\, p_k)\). All matrices must share the same number of rows for matching samples.

References

morcos_2018_InsightsRepresentationalSimilarityrepsim

Examples

Run this code

# \donttest{
# --------------------------------------------------
# Use "iris" and "USArrests" datasets
#   1. apply scaling to reduce the effect of scales
#   2. add white noise to create multiple representations
#   3. generate 10 perturbations per each dataset
# --------------------------------------------------
# prepare the prototype
set.seed(1)
X = as.matrix(scale(as.matrix(iris[sample(1:150, 50, replace=FALSE),1:4])))
Y = as.matrix(scale(as.matrix(USArrests)))
n = nrow(X)
p_X = ncol(X)
p_Y = ncol(Y)

# generate 10 of each by perturbation
mats = vector("list", length=20L)
for (i in 1:10){
  mats[[i]] = X + matrix(rnorm(n*p_X, sd=1), nrow=n)
}
for (j in 11:20){
  mats[[j]] = Y + matrix(rnorm(n*p_Y, sd=1), nrow=n)
}

# compute the similarity
sim_pwcca = pwcca(mats)

# visualize
opar <- par(no.readonly=TRUE)
labs <- paste0("rep ",1:20)
par(pty="s")

image(sim_pwcca[,20:1], axes=FALSE, main="PWCCA")
axis(1, seq(0, 1, length.out=20), labels = labs, las = 2)
axis(2, at = seq(0, 1, length.out=20), labels = labs[20:1], las = 2)

par(opar)
# }