1. Perform two iterations of the k-means algorithm in order to obtain two clusters for the input instances given in table 1. Assume that the first centers are the instances 2 and 4. Explain if more iterations are needed in order to get the final clusters.

2. What is the usual shape of clusters generated by k-means? Give an example of cases where k-means has the limitation in detecting the patterns formed by the data points.

3. Describe a pre-processing strategy that can help detect non-spherical clusters using K-means. You can come up with a strategy that works only for the above image.

Instance X Y 2 4 12.0 15.0 12.033.0 18.0 15.0 18.0 27.0 24.021.0 36.042.0 Table 1: Dataset