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Other Applications of Energy Minimzation

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Presentation on theme: "Other Applications of Energy Minimzation"— Presentation transcript:

1 Other Applications of Energy Minimzation
Simon D. Levy BIOL 274 30 November 2010

2 Self-Organizing Maps (Kohonen 1984)
Input data consisting of N-dimensional vectors Nodes (units) in a 2D grid Each node has a synaptic weight vector of N dimensions Simple, “unsupervised” learning algorithm...

3 SOM Learning Algorithm
Pick an input vector at random “Winning” node is one whose weight vector is closest to the input vector in vector space. Update weights of winner and its grid neighbors to move them closer to the input

4 SOM as Energy Minimization
Think of the difference between the winning node’s weights and the input as a degree of disorder or “excitement” Solving the problem corresponds to “relaxing” to a minimally-disordered state Get Matlab code:

5 Other Applications Hopfield Networks for pattern completion
Replicator Equations for graph isomorphism

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