Homework 3C

1 Homework 3 Problem 3 Consider the following dataset shown in Table 1. Samples Feature 1 Feature 2 1 0 0 2 0 1 3 1 0 4 1 1 Table 1: Simple Dataset for Problem 3 Answer the following questions: 1. Suppose that • we assign Sample 1 and 2 to the first cluster (Cluster 1) and assign Samples 3 and 4 to the second cluster (Cluster 2), i.e., C 1 = {1 , 2} , C 2 = {3 , 4}, and Suppose that: • we assign Sample 1, 2, and 3 to Cluster 1 and Sample 4 to Cluster 2, and • we use squared Euclidean distance to calculate how “dissimilar” the two points are. Using the definition of S (C) introduced in 3-clustering.pdf to compute S (C 1 ) + S (C 2 ) and show your work. • we use Euclidean distance to calculate how “dissimilar” the two points are. • Using the definition of S (C) introduced in 3-clustering.pdf to compute S (C 1 ) + S (C 2 ) and show your work.

2 Problem 4 1. If the goal is to assign all four data samples into 2 clusters, list all candidate clustering (i.e., all possible ways to assign the four samples into 2 clusters). For example, C 1 = {1 , 2} , C 2 = {3 , 4} could be one candidate clustering; C 1 = {1} , C 2 = {2 , 3 , 4} could be another, and what else? (please show your work) Options: 1. Option 1: C 1 = {1} , C 2 = {2 , 3 , 4} 2. Option 2: C 1 = {1,2} , C 2 = {3 , 4} 3. Option 3: C 1 = {1,2,3} , C 2 = {4} 4. Option 4: C 1 = {1,3} , C 2 = {2 , 4} 5. Option 5: C 1 = {1,2,4}, C 2 = {3} 6. Option 6: C 1 = {1,4}, C 2 = {2,3} 7. Option 7: C 1 = {2}, C 2 = {1,3,4} 2. Compute the total “dissimilarity” scores, i.e., S (C 1 ) + S (C 2 ), of all the candidate clusterings above (using squared Euclidean distance ). What is the best way to divide the four data points into 2 cluster? Options: 1. Option 1: C 1 = {1} , C 2 = {2 , 3 , 4} = S (C 1 ) + S (C 2 ) = 0 + 4/3 = 4/3 2. Option 2: C 1 = {1,2} , C 2 = {3 , 4} = S (C 1 ) + S (C 2 ) = 0.5 + 0.5 = 1 3. Option 3: C 1 = {1,2,3} , C 2 = {4} = S (C 1 ) + S (C 2 ) = 4/3 + 0 = 4/3 4. Option 4: C 1 = {1,3} , C 2 = {2 , 4} = S (C 1 ) + S (C 2 ) = 0.5 + 0.5 = 1 5. Option 5: C 1 = {1,2,4}, C 2 = {3} = S (C 1 ) + S (C 2 ) = 4/3 + 0 = 4/3 6. Option 6: C 1 = {1,4}, C 2 = {2,3} = S (C 1 ) + S (C 2 ) = 1 + 1 = 2 7. Option 7: C 1 = {2}, C 2 = {1,3,4} = S (C 1 ) + S (C 2 ) = 0 + 4/3 = 4/3 The best ways to divide the four data points into 2 clusters are option 2 and 4 because dissimilarity scores are closer to 0 than the other options.