How to add ellipse/polygon and legend in the scatterplot 3D in r?

Question

I did kmeans clustering 3D using scatterplot3d where I computed optimal number of cluster 4. Now I did below code to make 3d kmeans diagram. but i don't know how add legend (Cluster 1, Cluster 2, ...) and polygon or ellipse in the diagram.

library(scatterplot3d)
df = read.csv(file.choose(), header = T)
str(df)
set.seed(137)
km = kmeans(df, 4, nstart=25)
df$cluster = factor(kmeans(df, 4)$cluster)
shapes = c(15, 17, 18, 19)
shapes = shapes[as.numeric(km$cluster)]
zz <- scatterplot3d(df[,-1], pch = shapes, grid = F, color = rainbow(4)[km$cluster])
zz.coords <- zz$xyz.convert(df[,-1]) 
text(zz.coords$x, 
     zz.coords$y,             
     labels = df[,1],               
     cex = .5, 
     pos = 4)

data I have used

df = structure(list(Station = c(91L, 92L, 94L, 95L, 96L, 97L, 98L, 
99L, 103L, 105L, 106L, 107L, 112L, 113L, 114L, 115L, 116L, 117L, 
119L, 122L, 123L), PC1 = c(-1.12015813, -0.162603353, -0.691170969, 
1.290790838, -1.544758302, -0.027602401, -0.614168423, -0.495333696, 
1.279949324, -0.63809094, -0.122668147, 0.744142235, -0.778789917, 
-2.633418969, 0.758488847, -1.066042887, -0.721002477, 1.079359567, 
-0.175695907, 5.318351482, 0.320422224), PC2 = c(0.415530088, 
0.666545002, 0.695404632, -0.554688073, 0.222592134, 0.697855329, 
1.242555625, 0.64505761, 0.702722431, 0.86363373, 0.827648227, 
1.204083925, -4.232859175, -1.636251717, -0.685291914, 1.16637059, 
-0.122979187, -1.485372609, 0.079916797, -0.402557579, -0.309915867
), PC3 = c(0.698238358, -0.071855245, -0.563762392, -0.382756976, 
0.224635711, -0.786947583, -1.983627389, -0.032803567, -0.465769148, 
-0.076804882, -1.775067301, -0.203906481, -0.419354014, -0.121035409, 
-1.171532233, 3.578306494, 0.91365978, 0.951076125, 0.516367241, 
0.770666924, 0.402271986), cluster = structure(c(2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 
1L, 1L), .Label = c("1", "2", "3", "4"), class = "factor")), row.names = c(NA, 
-21L), class = "data.frame")

Answer 1

You could use the legend() function with scatterplot3d(), but I don't think there's a way to draw the ellipses. To do that you could switch to using the rgl package. After running your code, this will do the plot:

shapes <- c(15, 17, 18, 19)
shapes1 <- shapes[as.numeric(km$cluster)]

library(rgl)

plot3d(df[,-1], type = "n")
pch3d(df[,-1], pch = shapes1, col = rainbow(4)[km$cluster], cex = 0.5)
text3d(df[,-1], text = df[,1], pos=4)

for (i in 1:4) {
  cl <- subset(df, cluster == i)
  if (nrow(cl) > 3) {
    sigma <- cov(cl[,2:4])
    mu <- apply(cl[,2:4], 2, mean)
    shade3d(ellipse3d(sigma, centre = mu), alpha = 0.2, col = rainbow(4)[i])
  }
}

legend3d("right", pch = shapes, col = rainbow(4), 
         legend = paste("Cluster", 1:4), cex=2)

After some fiddling with the size of the window and rotating the plot, this produces

It doesn't draw an ellipsoid for cluster 1, because you only have 3 points there: you need at least 4 points not all in a plane to get a non-degenerate ellipsoid.