Neural Networks Chapter 9 Joost N. Kok Universiteit Leiden

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

Unsupervised Competitive Learning 321

output input (n-dimensional) winner

Simple Competitive Learning Winner: Lateral inhibition

Simple Competitive Learning Update weights for winning neuron

Simple Competitive Learning Update rule for all neurons:

Graph Bipartioning Patterns: edges = dipole stimuli Two output units

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

Vector Quantization Classes are represented by prototype vectors Voronoi tessellation

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

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

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

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

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

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

Self Organizing Map

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

Self Organizing Map

Feature Mapping Retinotopic Map Somatosensory Map Tonotopic Map

Feature Mapping

Kohonen’s Algorithm

Travelling Salesman Problem

Hybrid Learning Schemes unsupervised supervised

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

Radial Basis Functions First layer with normalized Gaussian activation functions