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
Consider,
Past experinces are stores, to find the relatiion between
Input and desired output.
Consider
K Nearest Neighbour
Hebb’s Associative Rules.
Hebb’s Synapse
Four Characteristics of Hebbian Synapse.
Hebb’s Model
Hebb’s Hypothesis:
Increase in inputs, presynapsis, increases outputs ( postsynapsis),
leads to saturation.( Activity Product Rule)
Covariance Hypothesis
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.
Pattern Recognition tasks by Feed Forward Networks
1)Pattern association problem
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 ,
Note:
Is associated with
Is very small
3)But if the test data, is very far away from , training data, then
Test data, will be associated with an output,
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.
Pattern Recognition tasks by Feed Backward Networks
Auto Association Problem
Pattern Storage Problem
Pattern Environment Storage Problem
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 get
Output, we have to look at flip of states.
Pattern Recognition tasks by Competitive Learning.
1)Temporary Storage problem
If input patterns are replaced by new patterns, so that, the patterns
get the output, over other patterns, it is called as temporary storage
Problem. Follows CL. Some Input patterns want to reach output,
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.
1
Total Error Energy
2
Average of all energies ( at different discrete time intervals )
3
Activation Values.
4
Activation Function.
5
Consider
6
7
8
9
10
Substituing 7 ,8 ,9 ,10 in 6 we get
11
Using
Error Correction Rule
12
And LMS rule, we get
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 layer
18
19
20
21
22
23
24
From 19
25
Substituting 20 in 16, we get
26
Using 14.
BP Algorithm Summary
Virtues
Limitations ( where brain is better)