Neural Networks Chapter 9

1. Neural NetworksChapter 9 Joost N. Kok Universiteit Leiden

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

3. 1 2 3 Unsupervised Competitive Learning

4. winner output input (n-dimensional) Unsupervised Competitive Learning

5. Simple Competitive Learning • Winner: • Lateral inhibition

6. Simple Competitive Learning • Update weights for winning neuron

7. Simple Competitive Learning • Update rule for all neurons:

8. Graph Bipartioning • Patterns: edges = dipole stimuli • Two output units

9. 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 h) • Arrange neurons in a geometrical way: update also neighbors • Turn on input patterns gradually • Conscience mechanism • Add noise to input patterns

10. Vector Quantization • Classes are represented by prototype vectors • Voronoi tessellation

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

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

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

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

15. i i w w After learning Before learning 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

16. 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

17. Self Organizing Map

18. Self Organizing Map

19. Self Organizing Map • Input: uniformly randomly distributed points • Output: Map of 202 neurons • Training • Starting with a large learning rate and neighborhood size, both are gradually decreased to facilitate convergence

20. Self Organizing Map

21. Self Organizing Map

22. Self Organizing Map

24. Self Organizing Map

25. Self Organizing Map

26. Feature Mapping • Retinotopic Map • Somatosensory Map • Tonotopic Map

27. Feature Mapping

28. Feature Mapping

29. Feature Mapping

30. Feature Mapping

31. Kohonen’s Algorithm

33. Travelling Salesman Problem

34. Hybrid Learning Schemes supervised unsupervised

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

36. Radial Basis Functions • First layer with normalized Gaussian activation functions