Exercise 2

Use k-means clustering algorithm to partition the students into two clusters. Use students 1 and 4 as the starting points in the two clusters.

Show all the underlying steps clearly and easy to read and understand.

A<-c(1.0,1.5,3,5,3.5,4.5,3.5)
B<-c(1,2,4,7,5,5,4.5)
z<-c(A,B)

Perform K-Means with 2 clusters set.seed(4)

dat<-matrix(z,nrow = 7,ncol = 2)
dat

     [,1] [,2]
[1,]  1.0  1.0
[2,]  1.5  2.0
[3,]  3.0  4.0
[4,]  5.0  7.0
[5,]  3.5  5.0
[6,]  4.5  5.0
[7,]  3.5  4.5

km1 = kmeans(dat, 2, nstart=2,iter.max = 2,algorithm = c( "MacQueen"), trace=False)

Let’s plot the results

plot(dat, col =(km1$cluster +1) , main="K-Means result with 2 clusters", pch=20, cex=2)

km1$centers

  [,1] [,2]
1 3.90  5.1
2 1.25  1.5