#------------------------------------------------------------------------------
# kmeans fails badly when the clusters are of different sizes
#------------------------------------------------------------------------------

require(stats) # for rnorm

#generate points using two normal distributions
# large gaussian center = (clx,cly),  sd = lsd 
# small gaussian center = (csx,csy),  sd = ssd

clx = 10
cly = 8
lsd = 2

csx = 4
csy = 2
ssd = 1

lx = rnorm(1000, mean = clx, sd = lsd)
ly = rnorm(1000, mean = cly, sd = lsd)

#create a 1000 by 2 matrix by "binding" these vectors - this is the large cluster
L<-cbind(lx,ly)



sx = rnorm(20, mean = csx, sd = ssd)
sy = rnorm(20, mean = csy, sd = ssd)
#create another matrix for the smaller clister
S<- cbind(sx,sy)



#Plot on the same graph, with two different colors



plot(0:12, 0:12, type = "n")
points(sx,sy,col="red")
points(lx,ly,col="blue") 

#pause here and see the plot


#combine the two clusters
T<- rbind(S,L)

#cluster using kmeans with k=2

twomeans = kmeans(T,2)

plot(T,col=twomeans$cluster)
#add centers
points(twomeans$centers, col = "green", pch = 8)

#------------------------------------------------------------------------------
# kmeans fails badly when the clusters are non-spherical
#------------------------------------------------------------------------------

require(stats) # for rnorm

# create cluster 1
clx = 10
cly = 8


lx = rnorm(1000, mean = clx, sd = 0.5)
ly = rnorm(1000, mean = cly, sd =2.5)

L<-cbind(lx,ly)

#create cluster 2

csx = 6
csy = 8


sx = rnorm(1000, mean = csx, sd = 0.5)
sy = rnorm(1000, mean = csy, sd = 2.5)

S<- cbind(sx,sy)


#Plotting on the same graph with two colors

plot(0:12, 0:12, type = "n")
points(sx,sy,col="red")
points(lx,ly,col="blue") 

#combine data sets
T<- rbind(S,L)

#run kmeans

twomeans = kmeans(T,2)

plot(T,col=twomeans$cluster)
#add centers
points(twomeans$centers, col = "green", pch = 8)