K means clustering | K Means ++
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The document outlines k-means clustering, an unsupervised learning algorithm that groups unlabeled data into k clusters based on feature similarity. It highlights the limitations of k-means, such as sensitivity to initialization and clusters of varying sizes or densities, and provides a detailed description of the k-means algorithm, including the improved k-means++ initialization method. Additionally, it includes illustrative examples and visualizations to enhance understanding of the concepts presented.
K means clustering | K Means ++
- 2. Presentation Outline: 1. What is K-means Clustering 2. Limitation of K-means 3. K-means Algorithm 4. Example of k-means++ clustering 5. Initialization with k-means++ 6. K- means++ Visualized Page-2
- 3. What is K-means Clustering: K-means clustering is a type of unsupervised learning, which is used when you have unlabeled data (i.e., data without defined categories or groups). The goal of this algorithm is to find groups in the data, with the number of groups represented by the variable K. The algorithm works iteratively to assign each data point to one of K groups based on the features that are provided. Data points are clustered based on feature similarity. The results of the K-means clustering algorithm are: 1.The centroids of the K clusters, which can be used to label new data 2.Labels for the training data (each data point is assigned to a single cluster) Page-3
- 4. Limitations of K-means: 1. Clusters of different size 2. Clusters of different density 3. Clusters of non-globular shape 4. Sensitive to initialization Page-4
- 5. K-means Algorithm: The exact algorithm is as follows: 1. Choose one center uniformly at random from among the data points. 2. For each data point x, compute D(x), the distance between x and the nearest center that has already been chosen. 3. Choose one new data point at random as a new center, using a weighted probability distribution where a point x is chosen with probability proportional to D(x)2. 4. Repeat Steps 2 and 3 until k centers have been chosen. 5. Now that the initial centers have been chosen, proceed using standard K-means clustering. Page-5
- 6. Here, K= 3 Data Sets= A1(2,8) , A2(6,9) , A3(4,8) , A4(8,4) , A5(4,9) , A6(5,8) , A7(3,4) A1 A2 A3 A4 A5 A6 A7 C1 C2 C3 Figure: Data points Page-6
- 7. Date Sets A1(2,8) A2(6,9) A3(4,8) A4(8,4) A5(4,9) A6(5,8) A7(3,4) Let, M1 = A1(2,8) M2 = A5(4,9) M3 = A7(3,4) Calculation: |X2-X1| + |Y2-Y1| Page-7
- 8. Table: Data Points K1 M1= A1(2,8) K2 M2 = A5(4,9) K3 M3 = A7(3,4) New Cluster A1(2,8) 0 3 7 1 A2(6,9) 5 2 8 2 A3(4,8) 2 1 5 2 A4(8,4) 10 9 5 3 A5(4,9) 3 0 6 2 A6(5,8) 3 2 6 2 A7(3,4) 5 6 0 3 Page-8
- 9. Table-2: Data Points K1 M1= A1(2,8) K2 M2 = A5(4,8) K3 M3 = A7(5,4) New Cluster A1(2,8) 0 2 7 1 A2(6,9) 5 3 6 2 A3(4,8) 2 0 5 2 A4(8,4) 10 8 3 3 A5(4,9) 3 1 6 2 A6(5,8) 3 1 4 2 A7(3,4) 5 5 1 3 Page-9
- 10. Initialization with k-means++ 1. Choose first cluster center uniformly at random from data points. 2. For each obs x, compute distance d(x) to nearest cluster center 3. Choose new cluster center from amongst data points, with probability of X being chosen proportional to d(X)2 4. Repeat steps 2 and 3 until k centers have been chosen. Page-10
- 11. K- means++ Visualized Figure: Data points Page-11
- 12. Thank you for being with me up to now. Page-12
Editor's Notes
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