melonpan-like visualization of "curse of dimensionality"

melonpan_in_high_dimension.R

if( require("ggplot2") == FALSE ) install.packages("ggplot2"); library(ggplot2)

dimensions   <- 1:700 
crisp_height <- .01
crisp_area   <- rep(NA, length(dimensions))

#plot(1,1,type="n", xlim=c(min(dimensions),max(dimensions)), ylim=c(0,1))
#abline(h = 1, lty="dashed")
for( D in dimensions ){
  #points(D,    1 - (1 - crisp_height)^D, pch="." )
  crisp_area[D] <- 1 - (1 - crisp_height)^D
}

theme_set( theme_bw() )

i_dimensions <- c(3, 30, 100, 500)

setwd("~/dev/R/scribble/melon")

for( i_dim in i_dimensions ){
  melonpan_plot <-
    ggplot() +
    geom_rect(aes(xmin = 0, xmax=1, ymin=0, ymax=1-crisp_area[i_dim], fill="chewy")) +
    geom_rect(aes(xmin = 0, xmax=1, ymax=1, ymin=1-crisp_area[i_dim], fill="crisp")) +
    coord_polar() +  
    #  labs(x=paste0(""i_dim)) +
    theme( axis.text.x     = element_blank(),
           axis.text.y     = element_blank(),
           axis.ticks      = element_blank(),
           legend.position = "none") +
    scale_fill_manual(values=c("#FFF0B9","#B75500")) +
    labs(title=paste("MELONPAN  IN ",i_dim, "  DIMENSIONS\n",
                     "( represented  in  2  dimensions )")) +
    theme( title = element_text(family="Copperplate Gothic Bold"))
  
  current_point <- data.frame(x=dimensions[i_dim], y=crisp_area[i_dim])
  
  curve_plot <-
    ggplot(data.frame(x=dimensions, y=crisp_area)) +
    geom_line(aes(x=x,y=y)) +
    geom_point(data = current_point,
               size=4,
               aes(x=x,y=y)) +
    geom_text(data = current_point,
              family="HiraKakuProN-W3",
              size=4,
              aes(x=x+100,y=y-.03,label=paste0(round(y*100,1),"%がサクサク"))) +
    labs(x="Number of Dimensions", y="Ratio of Crisp Area") +
    coord_cartesian(xlim=c(1,700)) +
    theme( axis.text = element_text(family="Copperplate Gothic Bold"),
           axis.title= element_text(family="Copperplate Gothic Bold", size=14)
    )
  
  
  library(gridExtra)
  png(paste0("melonpan_in_", i_dim, ".png"), width=900, height=400)
  grid.arrange(melonpan_plot, curve_plot, ncol=2,nrow=1)  
  dev.off()
}