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Perceptrons

Perceptrons. T he perceptron was created by Rosenblatt . S ingle-layer network whose weights and biases could be trained to produce a correct target vector when presented with the corresponding input vector. Perceptrons.

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Perceptrons

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  1. Perceptrons The perceptron was created by Rosenblatt. Single-layer network whose weights and biases could be trainedto produce a correcttarget vector when presented with the corresponding input vector.

  2. Perceptrons The perceptron neuron produces a 1 if the net input into the transfer function is equal to or greater than 0; otherwise it produces a 0.

  3. Perceptron Architecture Perceptron Architecture

  4. Perceptron Learning Rule (learnp) CASE 1. If an input vector is presented and the output of the neuron is correct(a = t, and e = t – a = 0), then the weight vector w is not altered. CASE 2. If the neuron output is 0 and should have been 1 (a = 0 and t = 1, ande = t – a = 1), the input vector p is added to the weight vector w. CASE 3. If the neuron output is 1 and should have been 0 (a = 1and t = 0, and e= t – a = –1), the input vector p is subtracted from the weight vector w.

  5. Perceptron Learning Rule (learnp) CASE 1. If an input vector is presented and the output of the neuron is correct(a = t, and e = t – a = 0), then the weight vector w is not altered. CASE 2. If the neuron output is 0 and should have been 1 (a = 0 and t = 1, ande = t – a = 1), the input vector p is added to the weight vector w. CASE 3. If the neuron output is 1 and should have been 0 (a = 1and t = 0, and e= t – a = –1), the input vector p is subtracted from the weight vector w. CASE 1. If e = 0, then make a change Δw equal to 0. CASE 2. If e = 1, then make a change Δw equal to pT. CASE 3. If e = –1, then make a change Δw equal to –pT.

  6. Perceptron Learning Rule (learnp) CASE 1. If an input vector is presented and the output of the neuron is correct(a = t, and e = t – a = 0), then the weight vector w is not altered. CASE 2. If the neuron output is 0 and should have been 1 (a = 0 and t = 1, ande = t – a = 1), the input vector p is added to the weight vector w. CASE 3. If the neuron output is 1 and should have been 0 (a = 1and t = 0, and e= t – a = –1), the input vector p is subtracted from the weight vector w. CASE 1. If e = 0, then make a change Δw equal to 0. CASE 2. If e = 1, then make a change Δw equal to pT. CASE 3. If e = –1, then make a change Δw equal to –pT. All three cases can then be written with a single expression Δw = (t – a)pT = epT

  7. Perceptron Learning Rule (learnp) CASE 1. If an input vector is presented and the output of the neuron is correct(a = t, and e = t – a = 0), then the weight vector w is not altered. CASE 2. If the neuron output is 0 and should have been 1 (a = 0 and t = 1, ande = t – a = 1), the input vector p is added to the weight vector w. CASE 3. If the neuron output is 1 and should have been 0 (a = 1and t = 0, and e= t – a = –1), the input vector p is subtracted from the weight vector w. CASE 1. If e = 0, then make a change Δw equal to 0. CASE 2. If e = 1, then make a change Δw equal to pT. CASE 3. If e = –1, then make a change Δw equal to –pT. The Perceptron Learning Rule can be summarized as follows Wnew = Wold + epT bnew = bold +e wheree = t – a

  8. Perceptron Learning Rule (learnp) >> net = newp([-1 1;-2 +2],1); >> p =[1 -1 0; 2 2 -2]; >> t =[0 1 1]; >> net = train(net,p,t); >> a = sim(net,p)

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