Instruction: In all the .txt files in this exercise, the following convention applies:
ith row contains the data points xi; yi.
Each xi 2 R2 has two coordinates xi(1) (the first entry in each row) and xi(2) (the second entry in each row).
Each yi 2 f 1; 1g is given in the third row.
The train files contain 800 points and the test files contain 200 points.
All the models have to be learnt using the train data and the performance of the models need to be evaluated on test data.
(Q1) [30 Marks] Build a k-nearest neighbour (KNN) classifier with the data given in knn-train.txt. For a given k value, write a function knn-acc(k) that measures the ac-curacy of the KNN on the test data in knn-test.txt in terms of % of correct predictions. Vary
• = 1; 2; 3; : : : and plot k versus knn-acc(k).
(Q2) [30 Marks] Learn a perceptron classifier with the data given in perceptron-train.txt. Write a function prcpt-acc(k) that measures the accuracy of the learnt perceptron on the test data in perceptron-test.txt in terms of % of correct predictions. For this exercise, please
1: Plot the data points, with class +1 in ‘green’, class 1 in ‘blue’ and the learnt perceptron direction
• in ‘red’ and the line w>x = 0 in ‘black’.
2: Print R and .
3: Print the number of iterations taken for perceptron to converge.
(Q3) [40 Marks] Repeat (Q2) for training data given in perceptron-biased-train.txt and test data in perceptron-biased-test.txt. Use the padding by 1 technique, i.e., each xi will be appended by (xi; 1), and w = (w(1); w(2); w(3)). Also while plotting, use the unpadded data for the scatter plot, and for the separating line, plot w(1)x(1) + w(2)x(2) + w(3) = 0 (colour coding is same as previous question).
