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Neural Networks Chapter 9 Joost N. Kok Universiteit Leiden

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Unsupervised Competitive Learning Competitive learning Winner-take-all units Cluster/Categorize input data Feature mapping

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Unsupervised Competitive Learning 321

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output input (n-dimensional) winner

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Simple Competitive Learning Winner: Lateral inhibition

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Simple Competitive Learning Update weights for winning neuron

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Simple Competitive Learning Update rule for all neurons:

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Graph Bipartioning Patterns: edges = dipole stimuli Two output units

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Simple Competitive Learning Dead Unit Problem Solutions –Initialize weights tot samples from the input –Leaky learning: also update the weights of the losers (but with a smaller ) –Arrange neurons in a geometrical way: update also neighbors –Turn on input patterns gradually –Conscience mechanism –Add noise to input patterns

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Vector Quantization Classes are represented by prototype vectors Voronoi tessellation

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Learning Vector Quantization Labelled sample data Update rule depends on current classification

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Adaptive Resonance Theory Stability-Plasticity Dilemma Supply of neurons, only use them if needed Notion of “sufficiently similar”

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Adaptive Resonance Theory Start with all weights = 1 Enable all output units Find winner among enabled units Test match Update weights

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Feature Mapping Geometrical arrangement of output units Nearby outputs correspond to nearby input patterns Feature Map Topology preserving map

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Self Organizing Map Determine the winner (the neuron of which the weight vector has the smallest distance to the input vector) Move the weight vector w of the winning neuron towards the input i Before learning i w After learning i w

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Self Organizing Map Impose a topological order onto the competitive neurons (e.g., rectangular map) Let neighbors of the winner share the “prize” (The “postcode lottery” principle) After learning, neurons with similar weights tend to cluster on the map

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Self Organizing Map

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Input: uniformly randomly distributed points Output: Map of 20 2 neurons Training –Starting with a large learning rate and neighborhood size, both are gradually decreased to facilitate convergence

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Self Organizing Map

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Feature Mapping Retinotopic Map Somatosensory Map Tonotopic Map

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Feature Mapping

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Kohonen’s Algorithm

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Travelling Salesman Problem

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Hybrid Learning Schemes unsupervised supervised

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Counterpropagation First layer uses standard competitive learning Second (output) layer is trained using delta rule

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Radial Basis Functions First layer with normalized Gaussian activation functions

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