DBSCAN OPTICS and Clustering Evaluation

Assignment #3: DBSCAN, OPTICS, and Clustering Evaluation

  1. If Epsilon is 2 and minpoint is 2 (including the centroid itself), what are the clusters that

DBScan would discover with the following 8 examples: A1=(2,10), A2=(2,5), A3=(8,4),

A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9). Use the Euclidean distance. Draw the 10 by 10 space and illustrate the discovered clusters. What if Epsilon is increased to sqrt(10)? (30 pts)

  1. Use OPTICS algorithm to output the reachability distance and the cluster ordering for the dataset provided, starting from Instance 1. Use the following parameters for discovering the cluster ordering: minPts =2 and epsilon =2. Use epsilonprime =1.2 to generate clusters from the cluster ordering and their reachability distance. Don’t forget to record the core distance of a data point if it has a dense neighborhood. You don’t need to include the core distance in your result but you may need to use them in generating clusters. (45 pts)

Dataset visualization

Below are the first few lines of the calculation. You need to complete the remaining lines and generate clusters based on the given epsilonprime value:

Instance           (X,Y)     Reachability Distance


Instance 1:        (1, 1) Undefined(or infinity)

Instance 2:        (0, 1) 1.0

Instance 3:        (1, 0) 1.0

Instance 16:      (5, 9) Undefined

Instance 13:      (9, 2) Undefined

Instance 12:      (8, 2) 1

  1. Use F-measure and the Pairwise measures (TP, FN, FP, TN) to measure the agreement between a clustering result (C1, C2, C3) and the ground truth partitions (T1, T2, T3) as shown below. Show details of your calculation. (25 pts)



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