perceptron

1. Perceptrons
The perceptron is the simplest form of a neural network used for the classification of patterns said to be linearly separable . basically , it consists of a single neuron with adjustable synaptic weights and bais.
The summing node of the neuronal model computes a linear combination of the inputs applied to its synapses, and also incorporates an externally applied bais. The resulting sum, that is applied to a hard limiter. Accordingly, the neuron produced an output equal to +1 if the hard limiter input is positive, and -1 if it is negative.
In the signal flow graph model of fig. 1 , the synaptic weights of the perceptron are denoted by w1,w2,….,wm . correspondingly, the inputs applied to the perceptron are denoted by x1,x2,…,xm. The externally applied bais is denoted by b. from the model ,the hard limiter input is



Perceptron Algorithm
The perceptron learning algorithm (Delta rule) can be summarized as follows:
Step 1: Initialize the weights W1, W2…Wn and threshold ? to small random values.
Step 2: Present new input X1, X2,..Xn and desired output dk .
Step 3: Calculate the actual output based on the following formula:
Yk=ƒ(?(xi*wi)-?)
Step4: Adapt the weights according to the following equation:
Wi(new)=Wi(old)+?(dk-yk).xi 0? i ?N