By R. Beale

ISBN-10: 0852742622

ISBN-13: 9780852742624

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G, then Bayes’s rule assigns it to a class on the following basis. Decide z belongs to class i for P(G;IX) > P(Gj1-X) for i = 1 , 2 , . . ,n i #j Put simply, it says that we assign a pattern t o the class that has Copyright © 1990 IOP Publishing Ltd. 34 PATTERN RECOGNITION the highest conditional probability of the vector X belonging t o it. It may come as something of a surprise t o find that it can be proven that this will provide us with the best estimate that we could hope for-if we measure our performance in terms of smallest average error rate.

Perceptron Learning Algorithm 1. Initialise weights and threshold Define w;(t),(0 5 i 5 n), t o be the weight from input i at time t , and 6 t o be the threshold value in the output node. Set W O t o be -9, the bias, and 5 0 t o be always 1. Set w;(O) t o small random values, thus initialising all the weights and the threshold. 2. Present input and desired output Present input 20,q , z 2 , . ,z, and desired output d ( t ) 3. Calculate actual output .. r n 1 Li=o J 4. Adapt weights if correct if output 0, should be 1 (class A) if output 1, should be 0 (class B) w;(t w;(t w;(t + 1) + 1) + 1) = w;(t) = w;(t) -t z ; ( t ) = wi(t)- z ; ( t ) Note that weights are unchanged if the net makes the correct decision.

We can achieve this by adding the input values to the weights when we want the output to be on, and subtracting the input values from the weights when we want the output to be off. This defines our learning rule. Notice that only those inputs which are active at the time will be affected; this is sensible since the inactive ones do not contribute Copyright © 1990 IOP Publishing Ltd. LEARNING IN SIMPLE NEURONS 47 to the weighted sum, and so changing them will not affect the result for the particular input in question, but may well upset what has already been learnt.

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