After sufficient iterations, the vectors should be consistently assigned to one of the two clusters. This indicates that the SOM has successfully grouped the vectors based on their similarities.
Kohonen Self-Organizing Feature Map for Clustering Four Vectors
Here's how to construct a Kohonen self-organizing feature map (SOM) to cluster the four vectors with the given assumptions:
1. Initial Setup:
Vectors: [1 0 0 1], [1 1 0 1], [1 1 0 0], [1 1 1 1]
Number of clusters (m): 2
Learning rate (α): 0.3
Initial weights for cluster units:
w1 = [0.1 0.2 0.6 0.7]
w2 = [0.3 0.4 0.5 0.8]
2. Iteration 1:
Calculate the Euclidean distances between each vector and both cluster units:
Vector Distance to w1 Distance to w2
[1 0 0 1] 0.678 0.404
[1 1 0 1] 0.510 0.224
[1 1 0 0] 0.510 0.283
[1 1 1 1] 0.361 0.141
Identify the closest cluster unit for each vector:
Vector Closest Cluster
[1 0 0 1] w2
[1 1 0 1] w2
[1 1 0 0] w2
[1 1 1 1] w2
Update the weights of the winning cluster units:
Weight Before After
w2[1] 0.3 0.3 + 0.3 * (1 - 0.3) * (1 - 0.678)
w2[2] 0.4 0.4 + 0.3 * (1 - 0.3) * (1 - 0.404)
w2[3] 0.5 0.5 + 0.3 * (1 - 0.3) * (1 - 0.510)
w2[4] 0.8 0.8 + 0.3 * (1 - 0.3) * (1 - 0.510)
3. Repeat steps 2 and 3 for several iterations (e.g., 100 iterations)
During each iteration, recalculate the distances, identify the winning units, update the weights with the learning rate, and observe how the clusters converge.
4. Results and Interpretation:
After sufficient iterations, the vectors should be consistently assigned to one of the two clusters. This indicates that the SOM has successfully grouped the vectors based on their similarities.
Analyze the final weights of the cluster units to understand what features they represent based on the original vector components.