$(20$pts$)$ Unsupervised Learning.

$($a$)(5$pts$)$ Suppose we want to cluster $n$ samples into $c$ clusters,

$($i$)$ what is the definition of the "Sum$-$of$-$Squared$-$Error" clustering

criterion?

$($ii$)$ what is the interpretation of this criterion?

$($b$)(10$pts$)$ Consider the application of the $k-$means clustering algorithm to

the fol$-$ lowing $2-$dimensional data for $c=2$ clusters $($using Euclidean

distance measure$).$

Start with the two cluster means: $m_1(0)=(0,0)$ and $m_2(0)=(3,3).$

$($i$)$ what are the means and the cluster membership at the next

iteration?

$($ii$)$ what are the final cluster means and the cluster membership after

convergence of the algorithm?