Overview of Self-Organizing Maps

Self-Organizing Maps (SOMs), introduced by Teuvo Kohonen, are a type of unsupervised neural network used for clustering and visualizing high-dimensional data. This blog provides a detailed explanation of SOMs, including their mathematical foundations and a practical Python implementation.

Introduction to Self-Organizing Maps

SOMs organize data points into a grid of neurons (nodes) based on their similarities. This process helps in clustering and visualizing data by mapping it from a high-dimensional space to a lower-dimensional grid, usually two dimensions.

Mechanism of SOMs

1. Initialization: Neurons in the grid are initialized with random weight vectors.
2. Competition: For each input data point, the neuron with the closest weight vector to the input (known as the Best Matching Unit, BMU) is identified.
3. Cooperation: The weights of the BMU and its neighboring neurons are adjusted to become more similar to the input data point.
4. Adaptation: The influence of the BMU and its neighbors decreases over time, typically controlled by a decaying learning rate and neighborhood radius.

1. Distance Calculation

To identify the BMU, we calculate the Euclidean distance between the input vector x and the weight vector wj of each neuron j:

where:

• x is the input vector.