spectral clustering for random forest proximity / similarity matrix

spectral.R

spectral <- function(proximity, k = 2)
{
  D <- diag(apply(proximity, 1, sum))
  U <- D - proximity
  
  # L <- diag(nrow(my.data)) - solve(D) %*% A  # simple Laplacian
  # round(L[1:12,1:12],1)
  
  # matrix power operator: computes M^power (M must be diagonalizable)
  "%^%" <- function(M, power)
    with(eigen(M), vectors %*% (values^power * solve(vectors)))
  
  # L <- (D %^% (-1/2)) %*% A %*% (D %^% (-1/2))  # normalized Laplacian
  
  evL <- eigen(U, symmetric=TRUE)
  Z   <- evL$vectors[,(ncol(evL$vectors)-k+1):ncol(evL$vectors)]
  
  km <- kmeans(Z, centers=k, nstart=5)
  
  return(km)
}