A self-organizing map (SOM), also called a Kohonen map or self-organizing feature map, is an unsupervised artificial neural network that converts high-dimensional training samples into a low-dimensional, discretized map. Unlike backpropagation-based error-correction learning, it uses competitive learning: neurons compete to respond, and the closest neuron becomes the best matching unit (BMU). section 11.4 section 11.10
A training step follows this pattern:
- Select an input vector and calculate Euclidean distances between it and the map’s neurons. section 11.4
- Choose the neuron with the smallest distance as the winning neuron. section 11.4
- Move the winner and its neighbors toward the input using a learning rate and neighborhood function. section 11.4
The neighborhood function makes nearby units learn together, grouping similar inputs while preserving relationships from the input space. Its bandwidth, sigma, controls the influence radius: larger values affect more neighbors, while very small values approach winner-only updates. section 11.4
Approximating a traveling-salesperson route
For the Qatar TSP instance qa194.tsp, city coordinates are normalized to [0, 1], then represented by a SOM whose neurons are updated as cities are sampled. One implementation reaches route length 9,816 against an optimal length of 9,352. A MiniSom implementation reaches 11,844.47, demonstrating that neuron count, sigma, learning rate, and iteration count require tuning. section 11.8
