CS4347: Homework # 1. (50 pt) The k-means algorithm is pretty straight forward. Here is the pseudo-code for it. Please implement k-means on 2-dimensional numerical data by C++, which should be fairly easy to derive from this. Let k be the number of clusters vou want Let S be the set of data samples (S is the size of the set) Let A be the set of associate clusters for each data sample Let sim(x.y) be the similarity function Let c[k] be the vectors for cluster centers Init Let S. = S /choose k random vectors to start our clusters for i-1 to k rand(S S-S- e[n]) //remove that vector from S' so we can't choose it again end Wassign initial clusters for i= l to SI A[i] = arginin(j = 1 to k) { sim(S[i], c(j]); end Run: Let change-true /recalculate cluster locations if a change occurred if change for i = l to k mean, count 0 for j-1 to S if Ali]-. mean = mean + S[j] count = count + 1 end end c[i] mean/count end end while change = false /assume there is no change change- /reassign feature vectors to clusters for i = l to S a = argmin(j = l to k) { sim(s[i], cli) } if a!-A[i) A[i] = a