Generalized Relational Similarity

This R function implements Kovacs’s (2010) generalized relational similarity measure for two-mode networks, which computes similarities by iterating through the row and column spaces of an affiliation matrix.

Reference

• Kovacs, B. (2010). Generalized relational similarity. Social Networks, 32(3), 197-210.

You can find the raw function on GitHub: gen.sim.corr.abs.R.

Source Code

gen.sim.corr.abs <- function(x, sigma = 1e-05) {
  library(expm) 
  r <- nrow(x) 
  c <- ncol(x) 
  r.c <- diag(r) 
  c.c <- diag(c) 
  r.m <- rowMeans(x) 
  c.m <- colMeans(x) 
  d.r.c <- 1 
  d.c.c <- 1 
  k <- 1 
  while (d.r.c > sigma | d.c.c > sigma) { 
    p.r.c <- r.c
    p.c.c <- c.c
    for (i in 1: r) { 
      for (j in 1:r) {
        if (i != j) {
          r.x <- x[i, ] - r.m[i]
          r.y <- x[j, ] - r.m[j]
          r.xy <- r.x %*% c.c %*% t(r.y)
          r.xx <- r.x %*% c.c %*% t(r.x)
          r.yy <- r.y %*% c.c %*% t(r.y)
          r.c[i, j] <- r.xy / sqrt(r.xx * r.yy)
        }
      }
    }
    for (i in 1:c) {
      for (j in 1:c) {
        if (i != j) {
          c.x <- x[, i] - c.m[i]
          c.y <- x[, j] - c.m[j]
          c.xy <- t(c.x) %*% r.c %*% c.y
          c.xx <- t(c.x) %*% r.c %*% c.x
          c.yy <- t(c.y) %*% r.c %*% c.y
          c.c[i, j] <- c.xy / sqrt(c.xx * c.yy)
        }
      }
    }
    d.r.c <- sum(abs(r.c - p.r.c))
    d.c.c <- sum(abs(c.c - p.c.c))
    k <- k + 1
  }
  return(list(r.sim = r.c, c.sim = c.c, iterations = k))
}