Self-Organizing Map (SOM)

Self-organizing maps (SOMs) are a class of unsupervised learning methods that arrange data samples in a low-dimensional, non-linear manifold in a topology-preserving fashion, i.e. neighbored samples will be mapped to neighbored regions in the manifold. Thus they are well-suited for non-linear dimensionality reduction and visualization. Usually SOMs use discretized maps on a regular grid. Each node on the grid has an associated prototype vector , and learning works in a very similar fashion to vector quantization: pulling the prototype closest to a particular data sample even closer to : Key to toplogy-preservation is the additional neighborhood function , that ensures that not only the winner node is adapted, but also its neighbors in the map - weighted exponentially by their distance in the map: