Summary of "Self Organizing Feature Map Kohonen Maps Solved Example | Self Organizing Networks by Mahesh Huddar"
Summary of "Self Organizing Feature Map Kohonen maps Solved Example | Self Organizing Networks by Mahesh Huddar"
This video provides a detailed walkthrough of training a Self-Organizing Feature Map (SOFM), also known as a Kohonen map, using a simple solved example. The main focus is on how to assign input vectors to output units and update the weights iteratively until convergence.
Main Ideas and Concepts
- Self-Organizing Feature Maps (SOFM): An unsupervised learning technique used to classify input vectors by mapping them to discrete output units based on similarity.
- Network Setup:
- input vectors: 4 training samples, each with 4 features.
- Output units: 2 units (Unit 1 and Unit 2).
- Initial weights provided for each output unit.
- learning rate set to 0.6.
- Objective: Assign each input vector to one of the output units based on minimum Euclidean distance and update the weights accordingly.
Methodology / Step-by-Step Instructions
- Initialization:
- Given input vectors: - X1 = [1, 0, 1, 0] - X2 = [1, 3, 0, 0] (likely a transcription error, assumed [1, 0, 0, 0]) - X3 = [1, 1, 1, 1] - X4 = [0, 1, 1, 0]
- Initial weights for Unit 1: [0.3, 0.5, 0.7, 0.2]
- Initial weights for Unit 2: [0.6, 0.5, 0.4, 0.2]
- learning rate (α) = 0.6
- Calculate Euclidean distance:
- For each input vector, compute the squared Euclidean distance to each output unit's weight vector:
d² = ∑(w_i - x_i)² - The unit with the smallest distance is considered the "winner" for that input vector.
- For each input vector, compute the squared Euclidean distance to each output unit's weight vector:
- Update Weights of Winning Unit:
- Update rule:
w_j(t+1) = w_j(t) + α × (x - w_j(t)) - Where: - w_j(t) = current weight vector of winning unit - x = input vector - α = learning rate
- Update rule:
- Iterate Over All Training Samples:
- Repeat the distance calculation and weight update for each input vector in sequence.
- This completes one epoch (one full pass over the training data).
- Repeat Epochs Until Convergence:
- Continue training for multiple epochs until the assignment of input vectors to output units stabilizes (no changes in class membership).
- This indicates that the network has converged.
- Final Mapping:
- After convergence, each input vector is permanently assigned to one output unit.
- In the example, after one epoch: - X1 and X2 assigned to Unit 1 - X3 and X4 assigned to Unit 2
Key Lessons
- SOFM training involves iterative competition between output units to "win" input samples based on distance.
- Weight vectors are continuously adjusted towards winning inputs to better represent clusters.
- Convergence is achieved when input assignments no longer change across epochs.
- The process is fully unsupervised and useful for clustering and dimensionality reduction.
Speakers / Sources
- Mahesh Huddar — Presenter and instructor explaining the Self Organizing Feature Map concept and example.
Category
Educational
