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Question Although we have only a rudimentary understanding of biological neural networks, is it possible to construct a small set of simple artificial “neurons” and perhaps train them to serve a useful function? The answer is “yes.” Architecture ? Learning Rule ? Architecture Architecture Architecture Architecture Learning Rule, Biological Inspiration Learning is viewed as the establishment of new connections between neurons or the modification of existing connections. Neural structures continue to change throughout life. These later changes tend to consist mainly of strengthening or weakening of synaptic junctions. For instance, it is believed that new memories are formed by modification of these synaptic strengths. Thus, the process of learning a new friend’s face consists of altering various synapses. Learning Rule, ANN Learning is viewed as the establishment of new connections between neurons or the modification of existing connections. learning rule is defined as a procedure for modifying the weights and biases of a network. This procedure may also be referred to as a training algorithm Learning Rules Categories In supervised learning, the learning rule is provided with a set of examples (the training set) of proper network behavior Where pq is an input to the network, and tq is the corresponding correct (target) output. In unsupervised learning, the weights and biases are modified in response to network inputs only. There are no target outputs available. Most of these algorithms perform clustering operations. They categorize the input patterns into a finite number of classes. Perceptrons The perceptron was created by Rosenblatt. Single-layer network whose weights and biases could be trained to produce a correct target vector when presented with the corresponding input vector. Perceptron Architecture ? Perceptron Learning Rule ? Perceptron Neuron 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. Perceptron Architecture Perceptron Architecture 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, and e = 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. 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 1. If e = 0, then make a change Δw equal to 0. CASE 2. If the neuron output is 0 and should have been 1 (a = 0 and t = 1, and e = t – a = 1), the input vector p is added to the weight vector w. CASE 2. If e = 1, then make a change Δw equal to pT. 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 3. If e = –1, then make a change Δw equal to –pT. Perceptron Learning Rule (learnp) 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 Perceptron Learning Rule (learnp) The Perceptron Learning Rule can be summarized as follows Wnew = Wold + epT bnew = bold +e where e =t–a 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) An Illustrative Example A produce dealer has a warehouse that stores a variety of fruits and vegetables. When fruit is brought to the warehouse, various types of fruit may be mixed together. The dealer wants a machine that will sort the fruit according to type. There is a conveyer belt on which the fruit is loaded. This conveyer passes through a set of sensors, which measure three properties of the fruit: shape, texture and weight . The shape sensor will output a 1 if the fruit is approximately round and a 0 if it is more elliptical. The texture sensor will output a 1 if the surface of the fruit is smooth and a 0 if it is rough. The weight sensor will output a 1 if the fruit is more than one pound and a 0 if it is less than one pound. Pineapple Banana Perceptron Learning Rule (learnp)