GRNN and PNN

From the technical prospective, people usually would choose GRNN (general regression neural network) to do the function approximation for the continuous response variable and use PNN (probabilistic neural network) for pattern recognition / classification problems with categorical outcomes. However, from the practical standpoint, it is often not necessary to draw a fine line between GRNN and PNN given the fact that most classification problems in the real world are binary. After reading paper in PNN (http://courses.cs.tamu.edu/rgutier/cpsc636_s10/specht1990pnn.pdf) and in GRNN (http://research.vuse.vanderbilt.edu/vuwal/Paul/Paper/References/grnn.pdf) both by Specht, one shouldn’t be difficult to find out the similarity between two. In particular, for a 2-class classification problem, GRNN should be able to serve the same purpose after converting the 2-class categorical outcome to the numeric response with 0-1 values. In the demonstration below, I am going to show that GRNN and PNN should generate identical predictions with the same smooth parameter.

First of all, let’s train a PNN for a 2-class outcome with cran-pnn package.

pkgs <- c('doParallel', 'foreach', 'pnn')
lapply(pkgs, require, character.only = T)
registerDoParallel(cores = 8)

data(norms)
nn1 <- smooth(learn(norms), sigma = 0.5)

pred_pnn <- function(x, nn){
  xlst <- split(x, 1:nrow(x))
  pred <- foreach(i = xlst, .combine = rbind) %dopar% {
    data.frame(prob = guess(nn, as.matrix(i))$probabilities[1], row.names = NULL)
  }
}

print(pred_pnn(norms[1:10, -1], nn1))
#         prob
# 1  0.6794262
# 2  0.5336774
# 3  0.7632387
# 4  0.8103197
# 5  0.6496806
# 6  0.7752137
# 7  0.4138325
# 8  0.7320472
# 9  0.6599813
# 10 0.8015706

Secondly, I also trained a GRNN after converting the categorical outcome above to a dummy response with 0-1 values.

pkgs <- c('pnn', 'doParallel', 'foreach', 'grnn')
lapply(pkgs, require, character.only = T)
registerDoParallel(cores = 8)

data(norms)
norm2 <- data.frame(n = ifelse(norms$c == 'A', 1, 0), x = norms$x, y = norms$y)
detach('package:pnn')

nn2 <- smooth(learn(norm2), sigma = 0.5)

pred_grnn <- function(x, nn){
  xlst <- split(x, 1:nrow(x))
  pred <- foreach(i = xlst, .combine = rbind) %dopar% {
    data.frame(pred = guess(nn, as.matrix(i)), row.names = NULL)
  }
}

print(pred_grnn(norm2[1:10, -1], nn2))
#         pred
# 1  0.6794262
# 2  0.5336774
# 3  0.7632387
# 4  0.8103197
# 5  0.6496806
# 6  0.7752137
# 7  0.4138325
# 8  0.7320472
# 9  0.6599813
# 10 0.8015706

As clearly shown in outputs, for the 2-level classification problem, both PNN and GRNN generated identical predicted values.