5 Layer 1 (Correlation) We want the network to recognize the following prototype vectors: W 1 w T 1 w T 2 w T S p 1 T p 2 T p Q T == b 1 R R R = The first layer weight matrix and bias vector are given by: The response of the first layer is: The prototype closest to the input vector produces the largest response. a 1 W 1 pb 1 + p 1 T p R+ p 2 T p R+ p Q T p R+ ==
6 Layer 2 (Competition) The neuron with the largest initial condition will win the competiton. The second layer is initialized with the output of the first layer.
7 Competitive Layer nWp w 1 T w 2 T w S T p w 1 T p w 2 T p w S T p L 2 1 cos L 2 2 L 2 S ====
8 Competitive Learning For the competitive network, the winning neuron has an ouput of 1, and the other neurons have an output of 0. Instar Rule Kohonen Rule
12 Typical Convergence (Clustering) Before TrainingAfter Training Weights Input Vectors
13 Dead Units One problem with competitive learning is that neurons with initial weights far from any input vector may never win. Dead Unit Solution: Add a negative bias to each neuron, and increase the magnitude of the bias as the neuron wins. This will make it harder to win if a neuron has won often. This is called a “conscience.”