In this homework, you'll have the chance to implement the perceptron algorithm to separate the following data (given in the file homework3_data.csv).

Recall that the perceptron step works as follows. For a point with coordinates (p,q), label y, and prediction given by the equation y^=step(w1x1+w2x2+b):

If the point is correctly classified, do nothing.

If the point is classified positive, but it has a negative label, update w_1, w_2,w1,w2, and b respectively.

If the point is classified negative, but it has a positive label, update w_1, w_2,w1,w2, and b respectively.

ZOOM

import numpy as np # Setting the random seed, feel free to change it and see different solutions. np.random.seed(42) def stepFunction(t): if t >= 0: return 1 return 0 def prediction(X, W, b): return stepFunction((np.matmul(X,W)+b)[0]) # TODO: Fill in the code below to implement the perceptron trick. # The function should receive as inputs the data X, the labels y, # the weights W (as an array), and the bias b, # update the weights and bias W, b, according to the perceptron algorithm, # and return W and b. def perceptronStep(X, y, W, b, learn_rate = 0.01): # Fill in code return W, b # This function runs the perceptron algorithm repeatedly on the dataset, # and returns a few of the boundary lines obtained in the iterations, # for plotting purposes. # Feel free to play with the learning rate and the num_epochs, # and see your results plotted below. def trainPerceptronAlgorithm(X, y, learn_rate = 0.01, num_epochs = 25): x_min, x_max = min(X.T[0]), max(X.T[0]) y_min, y_max = min(X.T[1]), max(X.T[1]) W = np.array(np.random.rand(2,1)) b = np.random.rand(1)[0] + x_max # These are the solution lines that get plotted below. boundary_lines = [] for i in range(num_epochs): # In each epoch, we apply the perceptron step. W, b = perceptronStep(X, y, W, b, learn_rate) boundary_lines.append((-W[0]/W[1], -b/W[1])) return boundary_lines

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