Given the following 6 data points, simulate K-means clustering manually with K = 2. Each example consists of two features and initially assigned to the cluster k.

Compute the centroid of each cluster. Continue with above question. Assign each data point to its closest centroid, reporting the new cluster label k. (in format of a list in order of i, eg. [1,2,1,1,1,2]. Repeat above two steps until convergence. Once the centroids and the cluster labels stop changing, report the cluster label k for each data point and final centroids.

\begin{tabular}{c|cc|c} \hlinei & x1(i) & x2(i) & k \\ \hline 1 & 1 & 4 & 1 \\ 2 & 1 & 3 & 2 \\ 3 & 0 & 4 & 1 \\ 4 & 5 & 1 & 1 \\ 5 & 6 & 2 & 1 \\ 6 & 4 & 0 & 2 \\ \hline \end{tabular}