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Execute five training processes for the Perceptron network, initializing the weight vector

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3.6 Practical Work

The analysis of a fractional distillation process for petrol revealed that a given oil could be classified into two purity classes (P, and P) from the measurement of three variables (x1, x2 and x3), which represent some physicochemical properties of the oil. The team of engineers and scientists proposed the application of a Perceptron network to perform the automatic classification of both classes.

Thus, based on the information gathered about the process, the team composed the training set presented in Appendix A, using a convention where the value -1 indicates oil belonging to class P, and value I indicates oil belonging to class P2 Therefore, the neuron that implements the Perceptron has three inputs and one output, as illustrated in Fig. 3.8.

Using the supervised Hebb's algorithm (Hebb's rule) for pattern classification and, assuming the learning rate as 0.01, do the following tasks:

1. Execute five training processes for the Perceptron network, initializing the weight vector (w) with random values between zero and one for each training processes. If necessary, update the random number generator in each process so that the initial elements composing the vector are different on each training. The training set is found in Appendix A.

2. Record the results from the five training processes on Table 3.2.

3. After training the Perceptron put the network into operation to classify the oil samples from Table 3.3, indicating on this table the output values (classes) from the five training processes performed on item 1.

4. Explain why the number of training epochs of this application varies each time the Perceptron is trained.

5. For this given application, is it possible to affirm that the classes are linearly separable?

 

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