Get representational distances

Given a list of embeddings, this function computes the procrustes distance between each pair and returns this as a distance matrix.

Usage

get.rep.dist(elist, rootflag = TRUE)

Arguments

elist

List of embeddings.

rootflag

Computer square root of distance? Defaults to TRUE

Value

A matrix of distances between each pair of embeddings.

Details

Each element of the list should contain a matrix of embedding coordinates from one participant. Each embedding should contain the same items in the same order, and should be of the same dimension.

By default the distance metric is the procrustes equivalent of Pearon's correlation, that is 1 - sqrt(1 - ss) where ss is the normalized sum of squares from the aligned embeddings. If rootflag=FALSE, the normalized sum of squares is used as the distance metric.

Examples

#Subject 1 data
s1 <- matrix(
      c(1,1,
      2,2,
      3,3,
      4,4,
      5,5), 5,2,byrow = TRUE)

#Subject 2 is noisy version of subject 1
s2 <- s1 + runif(10) / 10

#Subject 3 is different:
s3 <- matrix(
      c(1,2,
      3,4,
      4,3,
      2,1,
      5,2), 5,2,byrow = TRUE)

slist <- list(s1,s2,s3)

sdist <- get.rep.dist(slist)

head(sdist)
#>              [,1]         [,2]      [,3]
#> [1,] 0.0000000000 0.0001596312 0.3822792
#> [2,] 0.0001596312 0.0000000000 0.3806020
#> [3,] 0.3822792319 0.3806020118 0.0000000