Self-Organizing Maps (SOM)

• Invented by Tuevo Kohonen
  • Often called “Kohonen map” or “Kohonen network”
  • Online learning variant described below devised by Claude Touzet
• Two dimensional grid
  • Each grid entry is an ideal input.
• Input/Output
  • SOM input: A data item of the same type as map entries.
  • SOM output: Coordinates of closest matching entry.
• Finding the closest matching entry
  • Calculate the distance between the SOM input and every entry.
  • Whichever has the closest distance is the output.

Training the SOM Online

• Training set
  • Contains inputs only
  • No labels needed
• Training parameters
  • Size of the SOM (n x n square)
• For each input:
  • Determine the winning output node
  • Modify the winning node and its four cardinal neighbors
    • For each feature j:
      • node_j = (1 - learningRate * node_j) + learningRate * input_j
• Determining the learning rate
  • 0.9 for the winning node
  • 0.4 for the neighbor nodes
• This is an online learning algorithm
  • It updates itself when it receives each training input
• When to terminate training? Some options:
  • When it has been trained once on every input.
  • When every input has a “good” match to a map node.
  • When every node in the map has been the winner, and hence changed.
  • It need not ever terminate!
    • It can continue updating itself as part of a system control loop.