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KMK2233 Assignment 1 (15%) Due: 27 May 2022 Instructions: • This is an individual assignment; you have to do the coding and run on the data provided on your own. You must demonstrate one of the outputs (as required in Table 1, Table 2) in the Jupyter notebook. Share the link of the jupyter notebook in google colab. • Submit a report that consists of answers for questions 1-5 and the jupyter notebook link. Question The analysis of a fractional distillation process for petrol revealed that a given oil could be classified into two purity classes (P₁ and P:) from the measurement of three variables (x₁, x2 and xs), 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 (trainingdata.csv), using a convention where the value -1 indicates oil belonging to class Pi and value 1 indicates oil belonging to class P₂. Therefore, the neuron that implements the Perceptron has three inputs and one output, as illustrated in Fig. 1. 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 process. If necessary, update the random number generator (seed value) in each process so that the initial elements composing the vector are different on each training. The training set is given in csv file. 2. Record the results from the five training processes in Table 1. Fig. 1 Perceptron -1 (x₂) architecture for the practical work W₁ Σ y W₂ Table 1: Results from the Perceptron training Training Vector of weights Vector of weights Number of epochs (initial) (final) Wo W1 W₂ Ws Wo W1 W₂ Ws #1(TI) #2 (T2) # 3 (T3) #4 (T4) Semester 2 2021 2022 e-W₂ U g(.)
# 5 (T5) Table 2: Oil samples for validating the Perceptron network Output values produced by each of the trained models* (T1-T5) |y (11) │y (12) |y (13) Sample 1 X1 -0.3665 X3 5.9891 y (14) | y (T5) 2 -0.7842 1.1267 5.5912 3 0.3012 0.5611 5.8234 4 0.7757 1.0648 8.0677 5 0.1570 0.8028 6.3040 6 -0.7014 1.0316 3.6005 7 0.3748 0.1536 6.1537 8 -0.6920 0.9404 4.4058 9 -1.3970 0.7141 4.9263 10 -1.8842 -0.2805 1.2548 3. After training the Perceptron put the network into operation to classify the oil samples from Table 2, indicating in 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? Marking scheme Question Mark 20 10 3 10 4 5 5 Semester 2 2021 2022 5