Unsupervised SOM visualisation

Question

There is a need to plot the result of a unsupervised rectangular SOM model. Additional requirements: 1) draw each node as a pie chart with corresponding observed classes; size of a chart should reflect the number of samples in the node. Default plot.kohonen doesn't suit such a case.

Answer 1

Here is a possible solution. The first function som.prep.df is called from the second 'som.draw', which has only two parameters SOM model and observed classes of training set.

som.prep.df <- function(som.model, obs.classes, scaled) {
  require(reshape2)
  lev <- factor(wine.classes)
  df <- data.frame(cbind(unit=som.model$unit.classif, class=as.integer(lev)))
  # create table
  df2 <- data.frame(table(df))
  df2 <- dcast(df2, unit ~ class, value.var="Freq")
  df2$unit <- as.integer(df2$unit)
  # calc sum
  df2$sum <- rowSums(df2[,-1])
  # calc fraction borders of classes in each node
  tmp <- data.frame(cbind(X0=rep(0,nrow(df2)), 
                          t(apply(df2[,-1], 1, function(x) {
                            cumsum(x[1:(length(x)-1)]) / x[length(x)]
                          }))))
  df2 <- cbind(df2, tmp)
  df2 <- melt(df2, id.vars=which(!grepl("^\\d$", colnames(df2))))
  df2 <- df2[,-ncol(df2)]
  # define border for each classs in each node
  tmp <- t(apply(df2, 1, function(x) {
    c(x[paste0("X", as.character(as.integer(x["variable"])-1))], 
      x[paste0("X", as.character(x["variable"]))])
  }))
  tmp <- data.frame(tmp, stringsAsFactors=FALSE)
  tmp <- sapply(tmp, as.numeric)
  colnames(tmp) <- c("ymin", "ymax")
  df2 <- cbind(df2, tmp)
  # scale size of pie charts
  if (is.logical(scaled)) {
    if (scaled) {
      df2$xmax <- log2(df2$sum)
    } else {
      df2$xmax <- df2$sum
    }
  }
  df2 <- df2[,c("unit", "variable", "ymin", "ymax", "xmax")]
  colnames(df2) <- c("unit", "class", "ymin", "ymax", "xmax")
  # replace classes with original levels names
  df2$class <- levels(lev)[df2$class]
  return(df2)
}

som.draw <- function(som.model, obs.classes, scaled=FALSE) {
  # scaled - make or not a logarithmic scaling of the size of each node
  require(ggplot2)
  require(grid)
  g <- som.model$grid
  df <- som.prep.df(som.model, obs.classes, scaled)
  df <- cbind(g$pts, df[,-1])
  df$class <- factor(df$class)
  g <- ggplot(df, aes(fill=class, ymax=ymax, ymin=ymin, xmax=xmax, xmin=0)) +
    geom_rect() +
    coord_polar(theta="y") +
    facet_wrap(x~y, ncol=g$xdim, nrow=g$ydim) + 
    theme(axis.ticks = element_blank(), 
          axis.text.y = element_blank(),
          axis.text.x = element_blank(),
          panel.margin = unit(0, "cm"),
          strip.background = element_blank(),
          strip.text = element_blank(),
          plot.margin = unit(c(0,0,0,0), "cm"),
          panel.background = element_blank(),
          panel.grid = element_blank())
  return(g)
}

Usage example.

require(kohonen)
data(wines)
som.wines <- som(scale(wines), grid = somgrid(5, 5, "rectangular"))

# Non-scaled map
som.draw(som.wines, wine.classes)

# Scaled map
som.draw(som.wines, wine.classes, TRUE)

This function can also be used for the visualization of supervised models as well. But it suits only for rectangular maps. Hope this will help someone.

There are several possible improvements:

1. Choose a better scaling function than logarithm. Because now nodes with single sample become invisible after scaling.
2. Add legend to the whole plot which will reflect the size of nodes.
3. Or add information about nodes population on each chart.

PS. The code isn't very elegant, so any suggestions and improvements are welcome.