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- 1. 2013 KSE Seminar 2013/10/11 Jung hoon Kim
- 2. TOPIC
- 3. Selection of K in K-means clustering
- 4. Why I choose this paper • There is always an assumption in k-means algorithm, but I really want to execute without human’s intuition or insight. • This paper is first review existing automatical method for selecting the number of clusters for k-means algorithm
- 5. Paper Format 1) 2) 3) 4) 5) Introduction review the main known method for selecting K analyses the factors influencing the selection of K describes the proposed evaluation measure presents the results of applying the proposed measure to select K for different data sets 6) concludes the paper
- 6. Small introduction
- 7. K-means Algorithm • k-means algorithm is a method of clustering algorithm originally from signal processing, that is popular for machine learning and data mining. • k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean until move distance is smaller than threshold
- 8. K-means Algorithm 1) Pick a number (k) of point randomly 2) Assign every node to its nearest cluster center 3) Move each cluster center to the mean of its assigned nodes 4) Repeat 2-3 until convergence
- 9. Clustering: Example 2, Step 1 Algorithm: k-means, Distance Metric: Euclidean Distance expression in condition 2 5 4 k1 3 k2 2 1 k3 0 0 1 2 3 4 expression in condition 1 5
- 10. Clustering: Example 2, Step 2 Algorithm: k-means, Distance Metric: Euclidean Distance expression in condition 2 5 4 k1 3 k2 2 1 k3 0 0 1 2 3 4 expression in condition 1 5
- 11. Clustering: Example 2, Step 3 Algorithm: k-means, Distance Metric: Euclidean Distance expression in condition 2 5 4 k1 3 2 k3 k2 1 0 0 1 2 3 4 expression in condition 1 5
- 12. Clustering: Example 2, Step 4 Algorithm: k-means, Distance Metric: Euclidean Distance expression in condition 2 5 4 k1 3 2 k3 k2 1 0 0 1 2 3 4 expression in condition 1 5
- 13. Clustering: Example 2, Step 5 Algorithm: k-means, Distance Metric: Euclidean Distance expression in condition 2 5 4 k1 3 2 k2 k3 1 0 0 1 2 3 4 expression in condition 1 5
- 14. Comments on the K-Means Metho d • Strength • Relatively efficient: O(tkn), where n is # instances, c is # clusters , and t is # iterations. Normally, k, t << n. • Often terminates at a local optimum. The global optimum may be found using techniques such as: simulated annealing or ge netic algorithms • Weakness • Need to specify c, the number of clusters, in advance • Initialization Problem • Not suitable to discover clusters with non-convex shapes
- 15. What’s the problem?
- 16. What’s the problem? • Initialization problem • it's a problem which is caused when much point is assigned to the part of high density and less point is assigned to the part of low density
- 17. What’s the problem? • hard to find cluster in non-convex shape
- 18. What’s the problem? • Selection of K
- 19. Existing Method • Values of K determined through human’s viewpoint • Using probabilistic theory • Akeike’s information criterion • if data sets are constructed by a set of Gaussian dist • Hardy method • if data sets are constructed by a set of Possion dist • Monte Carlo techniques(associated null hypothesis)
- 20. Paper proposed
- 21. Formula
- 22. Research Method • The method has been validated on 15 artificial and 12 benchmark data sets. • Also there are 12 benchmark data sets from the UCI Repository Machine Learning Databases • These fifteen artificial data sets show effective sample of lots of distribution which can be usually generated.
- 23. Sample
- 24. Sample
- 25. Sample
- 26. Sample
- 27. Recommendation Example f(X) < 0.85, K = X else K=1
- 28. Conclusion • The new method is closely related to the approach of K-means clustering because it takes into account information reflecting the performance of the algorithm • The proposed method can suggest multiple values of K to users for cases when different clustering results could be obtained with various required levels of detail • this method is computationally expensive if used with large data sets
- 29. improvement • This paper did not mentioned how can we calculate threshold(e.g, f(x) < 0.85), if we have lots of data sets, we can apply learning algorithm to determine threshold • Experiment data sets are almost biased. This means, having set of data is too ideal. It doesn't consider the complexity in reality at all. It can be a way to evaluate data randomly. • It is an important issue that we know the range, or maximum value of K.
- 30. Do you have any question?
- 31. thank you

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