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K-means Clustering Algorithm Testing Cases
The k-means clustering algorithm groups objects into k clusters based on their attributes. It involves selecting initial centroids, calculating distances between objects and centroids, and iteratively adjusting the clusters until no more objects change groups. The document provides a detailed example of this process using medical data with attributes weight index and pH to form two clusters.
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K-means Clustering Algorithm Testing Cases
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- 2. Outline: • What isK-means Clustering Algorithm? • How K-means Clustering Algorithm Works? • Example.
- 3. What is K-meansClustering Algorithm? It’s a concept formation (clustering) algorithm that groups objects based on some attributes/features into K clusters.
- 4. How K-means ClusteringAlgorithm Works? Having a set of unlabeled data, the aim is to group this data into different number of clusters, the algorithm starts by iterating through the following steps: FIRST ITERATION 1. Choose the number of clusters K 2. Select the centroid of each cluster K (first iteration) , for example if we have 3 clusters then we need to choose three centroids randomly (there are other ways to select centroids). 3. For each cluster, calculate the distance between objects and its centroid 4. Group based on the minimum distance. For example if we have point A(centroid), B and C(centroid), the distance between A and B is 0.5, the distance between B and C is 1.5, then B will be in the A group because the distance is less 5. Check if any object moved from one group to another: • if yes then go for another iteration (calculate new centroids then go to step 3) • Else the algorithm stops and return the formed clusters
- 5. Remark for SECOND,THIRD, FOURTH, … ITERATIONS Starting from the second iteration, the algorithm updates the centroids , since by now we have for example n groups, and each group has some objects, the centroid will be calculated as = the sum of objects in the group/the number of objects
- 6. EXAMPLE: STEP 1: Choosenumber of clusters K Each medicine represents a point in the graph, in this example our goal is to group objects into two clusters (K=2) based on the two attributes weight index and pH. Object (X): weight index (Y):pH Medicine A 1 1 Medicine B 2 1 Medicine C 4 3 Medicine D 5 4
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- 8. STEP3:Calculatedistancebetweeneachobjectandcentroid(EuclideanDistance) D1 = A BC D STEP 4: Choose the minimum distance G1 = A B C D In this 1st iteration: cluster 1 has only A, cluster 2 has B,C, and D. Euclidean Distance Formula: D =
- 9. 2nd iteration Now we needto compute the new centroid of each cluster, since cluster 1 has only A then the centroid remains c1 = (1,1). However, cluster 2 now has three members B,C, and D, so we calculate the centroid by taking the average of the three members. C2 = () = (3.67 , 2.67)
- 10. Calculatethedistancesfor2nd iteration D2 = A BC D Choose the minimum distance G2 = A B C D In this 2nd iteration: cluster 1 has A,B and cluster 2 has C,D
- 11. 3rd Iteration We repeat thesame steps, first we compute the new centroid for each cluster by taking the average. C1 = () = (1.5 , 1) C2 = () = (4.5 , 3.5)
- 12. Calculatethedistancesfor3rd iteration D3 = A BC D Choose the minimum distance G3 = A B C D In this 3rd iteration: cluster 1 has A,B and cluster 2 has C,D
- 13. • We foundout that G3=G2, this means that no object moved to another group so we stop the algorithm. Now we have divided our data into two clusters. • Cluster 1: A,B • Cluster 2: C,D