Hierarchical clustering is sometimes used to generate K clusters, K > 1 by taking the clusters at the Kth level of the dendrogram. (Root is at level 1.) By looking at the clusters produced in this way, we can evaluate the behavior of hierarchical clustering on different types of data and clusters, and also compare hierarchical approaches to K-means. The following is a set of one-dimensional points: {6, 12, 18, 24, 30, 42, 48}. a) For each of the following sets of initial centroids, create two clusters by assigning each point to the nearest centroid, and then calculate the total squared error for each set of two clusters. Show both the clusters and the total squared error for each set of centroids. 1) { 3, 7.5} 2) {15, 25}
b) Do both sets of centroids represent stable solutions, i. e., if the K-means algorithm was run on this set of points using the given centroids as the starting centroids, would there be any change in the clusters generated?
c) What are the two clusters produced by MIN? (MIN is singlelink clustering, also called minimum method)
d) Which technique, K-means or MIN, seems to produce the "most natural" clustering in this situation?
e) What well-known characteristic of the K-means algorithm explains the previous behavior? Please show detailed calculation of why a point belongs to a specific cluster?