EECS 445, Fall 2020 Homework 1 , Due: Tuesday, September 22nd at 11:59pm 5 6 Perceptron Algorithm with Offset (10 pts) Consider a sequence of 2dimensional data points, 5:\") , aim , . . . ,5:(\") and their corresponding labels, y\"), 31(2), . . . , gm). Recall the perceptron algorithm updates the parameters whenever y\") 7 Mar\"); (5, b) where Mi\"); 3, b) = sign( ~ 5:\") + b). Assume that the points are linearly separable, and that both d and b are initialized to zero. Let m,- denote the number of times is\") is misclassied during training. (a) (5 pts) Derive the nal decision boundary for the perceptron in terms of mg, :sz and y\"). (b) (3 pt) Table 2 shows a dataset and the number of times each point is misclassied when one applies the perceptron algorithm (with offset). 0 Table 2: Dataset and misclassication counts for 6(b) Assuming d and b are initialized to zero, what are the values for d and b post training? (0) (2 pt) Given a set of linearly separable points, does the order in which the points are presented to the algorithms affect whether or not the algorithm will converge? In general, if the algorithm converges, could the order affect the uniqueness of the solution that the algorithm converges to