For the double semicircle task in Problem, set sep = -5 and generate 2, 000 examples.
(a) What will happen if you run P LA on those examples?
(b) Run the pocket algorithm for 100, 000 iterations and plot Ein versus the iteration number t.
(c) Plot the data and the final hypothesis in part (b).
(d) Use the linear regression algorithm to obtain the weights w, and compare this result with the pocket algorithm in terms of computation time and quality of the solution.
(e) Repeat (b) - (d) with a 3rd order polynomial feature transform.
Problem
Consider the double semi-circle "toy" learning task below.
There are two semi circles of width the k with inner radius rad, separated by sep as shown (red is -1 and blue is +1). The center of the top semicircle is aligned with the middle of the edge of the bottom semicircle. This task is linearly separable when sep 2: 0, and not so for sep k = 5 and sep = 5. Then, generate 2, 000 examples uniformly, which means you will have a pproximately 1, 000 exam ples for each class.
(a) Run the PLA starting from w = 0 until it converges. P lot the data and the final hypothesis.
(b) Repeat part (a) using the linear regression (for classification) to obtain w. Explain your observations.