1. 1 CLARACLARA

2. 2 data 104 29 69 549 81 54 08 80 41 62 82 96 732 Algorithm CLARA 1. For i= 1 to 5, repeat the following steps: k = 2 mincost = 9999 bestset = {} i = 1

3. 3 Algorithm CLARA 2. Draw a sample of 40 + 2k objects randomly from the entire data set, and call Algorithm PAM to find k medoids of the sample. Sample data 6 objects sample of data 104 54 81 41 62 73 Kcost { (10,4), (5,4) }11.24 { (10,4), (8,1) }12.715 { (10,4), (4,1) }12.166 { (10,4), (6,2) }8.1224 { (10,4), (7,3) }9.4919 { (8,1), (5,4) }11.24 { (4,1), (5,4) }13.472 { (6,2), (5,4) }10.358 { (7,3), (5,4) }9.9748 min cost

4. 4 Algorithm CLARA 3. For each object Oj in the entire data set, determine which of the k medoids is the most similar to Oj. 4. Calculate the average dissimilarity of the cluster- ing obtained in the previous step. If this value is less than the current minimum, use this value as the current minimum, and retain the k medoids found in Step (2) as the best set of medoids ob- tained so far. medoids = { (10,4), (6,2) } cost(medoids) = 49.473 cost(medoids) < mincost mincost = cost(medoids) = 49.473 bestset = medoids = { (10,4), (6,2) } Datacostk# 10401 298.06232 696.40311 542.23612 995.0991 812.23612 542.23612 088.48532 802.82842 412.23612 6202 8222 962.23611 731.41422 2242

5. 5 Algorithm CLARA 5. Return to Step (1) to start the next iteration. 1. next iteration. 2. Draw a sample of 40 + 2k objects randomly from the entire data set, and call Algorithm PAM to find k medoids of the sample. mincost 49.473 bestset { (10,4), (6,2) } Step 1. i = i+1, i = 2 Step 2. Sample data 6 objects sample of data 29 54 81 08 62 96 Kcost { (2,9), (9,6) }16.807 { (2,9), (5,4) }13.187 { (2,9), (8,1) }13.814 { (2,9), (0,8) }31.509 { (2,9), (6,2) }11.708 { (5,4), (9,6) }18.713 { (8,1), (9,6) }23.314 { (0,8), (9,6) }16.807 { (6,2), (9,6) }20.573 min cost

6. 6 Algorithm CLARA 3. For each object Oj in the entire data set, determine which of the k medoids is the most similar to Oj. 4. Calculate the average dissimilarity of the cluster- ing obtained in the previous step. If this value is less than the current minimum, use this value as the current minimum, and retain the k medoids found in Step (2) as the best set of medoids ob- tained so far. medoids = { (2,9), (6,2) } cost(medoids) = 41.895 cost(medoids) < mincost mincost = cost(medoids) = 41.895 bestset = medoids = { (2,9), (6,2) } Datacostk# 1044.47212 2901 6941 542.23612 9971 812.23612 542.23612 082.23611 802.82842 412.23612 6202 8222 9652 731.41422 2242

7. 7 Algorithm CLARA 5. Return to Step (1) to start the next iteration. 1. next iteration. 2. Draw a sample of 40 + 2k objects randomly from the entire data set, and call Algorithm PAM to find k medoids of the sample. mincost 41.895 bestset { (2,9), (6,2) } Step 1. i = i+1, i = 3 Step 2. Sample data 6 objects sample of data 104 299 54 62 73 Kcost { (5,4), (7,3) }16.732 { (5,4), (10,4) }15.402 { (5,4), (2,9) }15.875 { (5,4), (9,9) }15.303 { (5,4), (6,2) }18.12 { (10,4), (7,3) }16.56 { (2,9), (7,3) }13.137 { (9,9), (7,3) }13.813 { (6,2), (7,3) }19.533 min cost

8. 8 Algorithm CLARA 3. For each object Oj in the entire data set, determine which of the k medoids is the most similar to Oj. 4. Calculate the average dissimilarity of the cluster- ing obtained in the previous step. If this value is less than the current minimum, use this value as the current minimum, and retain the k medoids found in Step (2) as the best set of medoids ob- tained so far. medoids = { (2,9), (7,3) } cost(medoids) = 40.732 cost(medoids) < mincost mincost = cost(medoids) = 40.732 bestset = medoids = { (2,9), (7,3) } Datacostk# 1043.16232 2901 6941 542.23612 996.32462 812.23612 542.23612 082.23611 803.16232 413.60562 621.41422 821.41422 963.60562 7302 225.0992

9. 9 Algorithm CLARA 5. Return to Step (1) to start the next iteration. 1. next iteration. 2. Draw a sample of 40 + 2k objects randomly from the entire data set, and call Algorithm PAM to find k medoids of the sample. mincost 40.732 bestset { (2,9), (7,3) } Step 1. i = i+1, i = 4 Step 2. Sample data 6 objects sample of data 104 549 62 82 73 Kcost { (9,9), (8,2) }9.8482 { (9,9), (10,4) }15.463 { (9,9), (5,4) }13.078 { (9,9), (6,2) }10.122 { (9,9), (7,3) }8.2268 { (10,4), (8,2) }12.119 { (5,4), (8,2) }12.646 { (6,2), (8,2) }13.55 { (7,3), (8,2) }12.803 min cost

10. 10 Algorithm CLARA 3. For each object Oj in the entire data set, determine which of the k medoids is the most similar to Oj. 4. Calculate the average dissimilarity of the cluster- ing obtained in the previous step. If this value is less than the current minimum, use this value as the current minimum, and retain the k medoids found in Step (2) as the best set of medoids ob- tained so far. medoids = { (9,9), (7,3) } cost(medoids) = 49.168 cost(medoids) < mincost ?= false Datacostk# 1043.16232 2971 6931 542.23612 9901 812.23612 542.23612 088.60232 803.16232 413.60562 621.41422 821.41422 9631 7302 225.0992

11. 11 Algorithm CLARA 5. Return to Step (1) to start the next iteration. 1. next iteration. 2. Draw a sample of 40 + 2k objects randomly from the entire data set, and call Algorithm PAM to find k medoids of the sample. mincost 40.732 bestset { (2,9), (7,3) } Step 1. i = i+1, i = 5 Step 2. Sample data 6 objects sample of data 29 699 62 82 96 Kcost { (6,9), (6,2) }13.243 { (6,9), (2,9) }21.523 { (6,9), (9,9) }21.071 { (6,9), (8,2) }13.123 { (6,9), (9,6) }16.123 { (2,9), (6,2) }18 { (9,9), (6,2) }15 { (8,2), (6,2) }26.256 { (9,6), (6,2) }16.858 min cost

12. 12 Algorithm CLARA 3. For each object Oj in the entire data set, determine which of the k medoids is the most similar to Oj. 4. Calculate the average dissimilarity of the cluster- ing obtained in the previous step. If this value is less than the current minimum, use this value as the current minimum, and retain the k medoids found in Step (2) as the best set of medoids ob- tained so far. medoids = { (6,9), (8,2) } cost(medoids) = 43.783 cost(medoids) < mincost ?= false Datacostk# 1042.82842 2941 6901 543.60562 9931 8112 543.60562 086.08281 8022 414.12312 6222 8202 964.12312 731.41422 2262

13. 13 Algorithm CLARA 5. Return to Step (1) to start the next iteration. mincost 40.732 bestset { (2,9), (7,3) } Stop.