1. K-Means Clustering Problem
Ahmad Sabiq
Febri Maspiyanti
Indah Kuntum Khairina
Wiwin Farhania
Yonatan

2. What is k-means?
• To partition n objects into k clusters, based on
attributes.
– Objects of the same cluster are close their
attributes are related to each other.
– Objects of different clusters are far apart their
attributes are very dissimilar.

3. Algorithm
• Input: n objects, k (integer k ≤ n)
• Output: k clusters
• Steps:
1. Select k initial centroids.
2. Calculate the distance between each object and
each centroid.
3. Assign each object to the cluster with the nearest
centroid.
4. Recalculate each centroid.
5. If the centroids don’t change, stop (convergence).
Otherwise, back to step 2.
• Complexity: O(k.n.d.total_iteration)

4. Initialization
• Why is it important? What does it affect?
– Clustering result local optimum!
– Total iteration / complexity

5. Good Initialization
3 clusters with 2 iterations…

6. Bad Initialization
3 clusters with 4 iterations…

7. Initialization Methods
1. Random
2. Forgy
3. Macqueen
4. Kaufman

8. Random
• Algorithm:
1. Assigns each object to a random cluster.
2. Computes the initial centroid of each cluster.

9. Random

10. Random

11. Random
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20 25 30 35

12. Forgy
• Algorithm:
1. Chooses k objects at random and uses them as the initial
centroids.

13. Forgy
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20 25 30 35

14. MacQueen
• Algorithm:
1. Chooses k objects at random and uses them as the initial
centroids.
2. Assign each object to the cluster with the nearest
centroid.
3. After each assignment, recalculate the centroid.

15. MacQueen
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20 25 30 35

16. MacQueen

17. MacQueen

18. MacQueen

19. MacQueen

20. MacQueen

21. MacQueen

22. MacQueen

23. MacQueen

24. MacQueen

25. Kaufman

26. Kaufman

27. Kaufman

28. Kaufman

29. Kaufman

30. Kaufman

31. Kaufman

32. Kaufman

33. Kaufman
C=0
d = 24,33
D = 15,52

34. Kaufman
C=0
C=0 C=0
C=0
C=0

35. Kaufman
C=0
C=0 C=0
C=0
∑C1 = 2,74
C=0

36. Kaufman
∑C5 = 52,55
∑C6 = 55,88 ∑C9 = 42,69
∑C7 = 53,77
∑C1 = 2,74 ∑C8 = 51,16
∑C2 = 12,,21
∑C3 = 12,36
∑C3 = 8,38

37. Kaufman
∑C5 = 52,55
∑C6 = 55,88 ∑C9 = 42,69
∑C7 = 53,77
∑C1 = 2,74 ∑C8 = 51,16
∑C2 = 12,,21
∑C3 = 12,36
∑C3 = 8,38

38. Reference
1. J.M. Peña, J.A. Lozano, and P. Larrañaga. An Empirical
Comparison of Four Initialization Methods for the K-
Means Algorithm. Pattern Recognition Letters, vol. 20,
pp. 1027–1040. 1999.
2. J.R. Cano, O. Cordón, F. Herrera, and L. Sánchez. A
Greedy Randomized Adaptive Search Procedure
Applied to the Clustering Problem as an Initialization
Process Using K-Means as a Local Search Procedure.
Journal of Intelligent and Fuzzy Systems, vol. 12, pp.
235 – 242. 2002.
3. L. Kaufman and P.J. Rousseeuw. Finding Groups in
Data: An Introduction to Cluster Analysis. Wiley. 1990.

39. Questions
1. Kenapa inisialisasi penting pada k-means?
2. Metode inisialisasi apa yang memiliki greedy
choice property?
3. Jelaskan kompleksitas O(nkd) pada metode
Random.