1. Perceptron Learning Rule

2. Learning Rules
Learning Rules : A procedure for modifying the weights and biases of a net work.
Learning Rules :
Supervised Learning
Reinforcement Learning
Unsupervised Learning

3. Learning Rules Network is provided with a set of examples
• Supervised Learning
Network is provided with a set of examples
of proper network behavior (inputs/targets)
{p1, t1}, {p2, t2}, ……{pn, tn}
• Reinforcement Learning
Network is only provided with a grade, or score,
which indicates network performance
• Unsupervised Learning
Only network inputs are available to the learning
algorithm. Network learns to categorize (cluster)
the inputs.

4. Perceptron ArchitectureW w T 1 2 S = w i 1 , 2 R =

5. Single-Neuron Perceptron

6. Decision Boundary

7. Example - OR

8. OR Solution
Weight vector should be orthogonal to the decision boundary.
Pick a point on the decision boundary to find the bias.

9. Multiple-Neuron Perceptron
Each neuron will have its own decision boundary.
iwTp+bi =0
A single neuron can classify input vectors into two categories.
A S-neuron perceptron can classify input vectors into 2S categories.

10. Learning Rule Test Problem

11. Starting Point Random initial weight: Present p1 to the network:
Incorrect Classification.

12. Tentative Learning Rule

13. Second Input Vector
(Incorrect Classification)
Modification to Rule:

14. Patterns are now correctly classified.
Third Input Vector
(Incorrect Classification)
Patterns are now correctly classified.

15. Unified Learning Rule
A bias is a
weight with
an input of 1.

16. Multiple-Neuron Perceptrons
To update the i-th row of the weight matrix:
Matrix form:

17. Apple/Orange Example
Training Set
Initial Weights

18. Apple/Orange Example
First Iteration e t 1 a – -1 =

19. Second Iteration
Second Iteration

20. Third Iteration
Third Iteration e t 1 a – -1 =

21. Check
a = hardlim(-3.5) = 0 = t1
a = hardlim(0.5) = 1 = t2

22. Perceptron Rule Capability
The perceptron rule will always converge to weights which accomplish the desired classification, assuming that such weights exist.

23. Perceptron Limitations
Linear Decision Boundary
Linearly Inseparable Problems

24. Example

25. Example

26. Example

27. Example

28. Example

29. Example

30. Example

31. Example