Fuzzy c means manual work
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Fuzzy C-means is an extension of k-means clustering that allows data points to belong to multiple clusters simultaneously. It assigns a membership value between 0 and 1 to each data point for each cluster, indicating the likelihood of membership. The example demonstrates fuzzy C-means clustering on a dataset with 6 data points and 2 clusters, calculating the membership values and distances over multiple iterations until the cluster centroids stabilize.
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![Manual Work
E. N. Sathishkumar M.Sc., M.Phil., [Ph.D.,]](https://image.slidesharecdn.com/fuzzycmeansmanualwork-150219231928-conversion-gate01/85/Fuzzy-c-means-manual-work-1-320.jpg)
Fuzzy c means manual work
- 1. Manual Work E. N. Sathishkumar M.Sc., M.Phil., [Ph.D.,]
- 2. Fuzzy C-Means An extension of k-means Hierarchical, k-means generates partitions each data point can only be assigned in one cluster Fuzzy c-means allows data points to be assigned into more than one cluster each data point has a degree of membership (or probability) of belonging to each cluster
- 3. Fuzzy C Means Algorithm
- 4. Worked out Example Input: Number of Objects = 6 Number of clusters = 2 X Y C1 C2 1 6 0.8 0.2 2 5 0.9 0.1 3 8 0.7 0.3 4 4 0.3 0.7 5 7 0.5 0.5 6 9 0.2 0.8
- 9. Cluster 1 Cluster 2 Datapoint Distance Datapoint Distance (1,6) 1.40 (1,6) 3.88 (2,5) 1.17 (2,5) 3.32 (3,8) 1.99 (3,8) 2.16 (4,4) 2.64 (4,4) 2.91 (5,7) 2.75 (5,7) 0.28 (6,9) 4.62 (6,9) 2.50
- 14. Now the New Membership value is Step 5 : Now continue this process until get the same centroids. X Y C1 C2 1 6 0.7 0.3 2 5 0.6 0.4 3 8 0.5 0.5 4 4 0.5 0.5 5 7 0.1 0.9 6 9 0.3 0.7