supervised learning. teacher response: emulation. error: y1 – y2, where y1 is teacher response (...

Supervised Learning

Teacher response: Emulation.

Error: y1 – y2, where y1 is teacher response ( desired response, y2 is actual response ).Aim: To reduce the error.

It’s Closed Feedback System.

Suppose the error, Error, is on the surface, due to teacher response, we have to bring it down, which is called minimising error, Point is called Local Minimum, or Global Minimum.

Reinforcement Learning.

There is no teacher.

Converts Primary reinforcement to heuristic reinforcement.

There can be delay for primary reinforcement, as the inputs have to be analysed, which is called credit assignement problem.

Example Character Recognition.

Unsupervised Learning

Error Correction Learning.

Desired Output – Actual Output

Consider Multi Layer Network.

Multi Layer Network, showing output.

Cost Function or Index of Performance.

Widrow Hoff Rule ( Delta Rule )

New Weights

New Weights ( after Unit Delay )

z (power ) – 1, is called unit delay operator.n is disrete time.

Memory Based Learning

Past experinces are stores, to find the relatiion between Input and desired output.

Consider,

Consider

K Nearest Neighbour

Hebb’s Associative Rules.

Hebb’s Synapse

Four Characteristics of Hebbian Synapse.

Hebb’s Model

Hebb’s Hypothesis:

Covariance Hypothesis

Increase in inputs, presynapsis, increases outputs ( postsynapsis), leads to saturation.( Activity Product Rule)

Here thresholds are used on inputs and outputs.

Output Function.

Summation of Weights.

Change in Weights.

Xj is input and xk is output

T is pseudotempearature.

There are two types of neurons, visible and hiddeen

This is applicable in Error Correction Learning.

1)Pattern association problemPattern Recognition tasks by Feed Forward Networks

1) Here every input ( training data ) is associated with an output.

2) So if an input ( test data ) , is close to any training data, like,

Then , Is associated with

3)But if the test data, is very far away from , training data, then Test data, will be associated with an output,

Note: Is very small

And not

4) System displays Accretive Behaviour.

5) Follows Feed Forward Network.

Ai=al + i1, i1 is small number.

2)Pattern classification problem

1)In Pattern Association problem, if a set of inputs map to an output, the size of output data set is smaller than input data set. Classes of inputs get a label.2)If a test data, which is close to any inputs ( training data ), in a class, it gets classified , to that class, for which there is a label.3) Here, test data is not associated , with output, but the class has a label, and test data is part of it.4) It creates Accretive behaviour.5) Follows Feed Forward Network.

3)Pattern mapping

1) Here output is a map of input.

2) So if any input ( test data ) , is close to any one training data, the output of test data, will be interpolation of output of training data, means they are in one range.3) Pattern Association and Pattern Classification are derived from Pattern Mapping. Show it by Interpolation.4) Pattern Mapping performs Generalization.5) Follows Feed Forward Network.

Auto Association Problem

Pattern Storage Problem

Pattern Environment Storage Problem

Pattern Recognition tasks by Feed Backward Networks

1)Auto Association Networks

1) Inputs and Outputs are identical.2) Implementation has to be done by feed backward networks.3)Follows Feed Back Network.

2)Pattern Storage problem.

The input and output are once again identical.

Three separate neurons are used to realize, the output.So output points and input points are different.Follows Feed Back Network.

3)Pattern Environment Storage problem

If set of patterns, have certain probability, it is called as pattern environment Storage problem. Follows Feed Back Network.There is feedback, as to getOutput, we have to look at flip of states.

Pattern Recognition tasks by Competitive Learning.

If input patterns are replaced by new patterns, so that, the patterns get the output, over other patterns, it is called as temporary storageProblem. Follows CL. Some Input patterns want to reach output,

1)Temporary Storage problem

2)Pattern Clustering problem

The test data is classified to the output, based on being near to first class. It creates Accretive Behaviour.Follows CL. Somehow test data, wants to enter testing data. A student, wants to enterer cluster of engg students.

Output is interpolative.Follows CL.Test Data, wants to somehow reach output.

3)Feature Mapping problem

To cluster we need features by competitive Learning.Ex BP Algorithm.

Back Propagation Algorithm

Error at output neuron j.

Total Error Energy

1

2

Average of all energies ( at different discrete time intervals )

Activation Values.

3

4

Activation Function.

5

Consider

6

7

8

9

10

Substituing 7 ,8 ,9 ,10 in 6 we get

11

Using Error Correction Rule

And LMS rule, we get

12

13

Using 11 in 13, we get

14

Where , the error gradient is given by,

15

The above , is to show another way of getting error gradient, to be used in 2nd part.

Using the expression in 15,

16

17

Total error at output layer18

19

20

21

22

23

24

From 19

25

26

Substituting 20 in 16, we get

Using 14.

BP Algorithm Summary

Virtues

Limitations ( where brain is better)