Self-Organizing Maps

• Two-layer directed, weighted graph
  • First layer: input nodes
  • Second layer: output nodes
  • Every input node is connected to every output node
  • Output nodes are arranged in a rectangular (or hexagonal) Cartesian grid
• Computing an output
  • For each output
    • Calculate the sum-of-squared-differences (SSD) between the input node values and the edge weights for the output
    • This is the distance.
      • Technically, we take the square root of the SSD to get the distance, but for comparison purposes there is no need to do so
  • The output with the shortest distance to the input is the winner. It is the only output neuron that fires.