Consider the following set of one-dimensional points: {0.1, 0.2, 0.45, 0.55, 0.8, 0.9}. All the points are located in th

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Consider The Following Set Of One Dimensional Points 0 1 0 2 0 45 0 55 0 8 0 9 All The Points Are Located In Th 1 (650.8 KiB) Viewed 25 times

Consider the following set of one-dimensional points: {0.1, 0.2, 0.45, 0.55, 0.8, 0.9}. All the points are located in the range between [0,1]. a. Suppose we apply k-means clustering to obtain three clusters, A, B, and C. If the initial centroids are located at {0.0, 0.25, 0.6}, respectively, show the cluster assignments and locations of the centroids after the first three iterations by filling out the following table. [3 points] Cluster Assignment of Data Points Centroid Locations Iter 0.1 0.2 0.45 0.55 0.80 0.90 A B С 0 0.0 0.25 0.6 1 2 3 b. Compute the SSE of the k-means solution after the third iteration. [1 point] c. Apply bisecting k-means (with k = 3) on the data. First, apply k-means on the data with k = 2 using initial centroids located at {0.1, 0.9}. Fill the following table with your answer. Cluster Assignment of Data Points Centroid Iter 0.1 0.2 0.45 0.55 0.80 0.90 A B 0 0.1 0.9 1 Next, compute the SSE for each cluster A, and B (make sure you indicate the SSE values in your answer). Choose the cluster with larger SSE value and split it further into 2 sub-clusters. You can choose the two data points with the smallest and largest values as your initial centroids. For example, if the cluster to be split contains data points (0.20, 0.40, 0.60, and 0.80), then the centroids should be initialized to 0.20 and 0.80. Show the clustering solution produced obtained applying bisecting k-means. [4 points] d. Are the solutions obtained in (a) and (c) same? If not which one is better? [2 point]