Other Applications of Energy Minimzation

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Presentation transcript:

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

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...

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

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: http://www.cs.wlu.edu/~levy/software/som

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

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