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Other Applications of Energy Minimzation

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

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Other Applications of Energy Minimzation

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

  2. 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... Self-Organizing Maps (Kohonen 1984)

  3. 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 Learning Algorithm

  4. 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 SOM as Energy Minimization Get Matlab code: http://www.cs.wlu.edu/~levy/software/som

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

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