3 Perceptron: Linear Separability and Weight Scaling (a) (2 pts) Suppose we have the following data representing the XOR function: Table 1: XOR function data Evidently, the data is not linearly separable. Therefore the perceptron algorithm will not be able to learn a classifier for XOR, based on this data. However, we can add a 3rd dimension/feature to each input such that the data becomes linearly separable. If we add (1,0,0,1) to the 3rd dimension (x3) of the four data points in order, will the new data be linearly separable? Assume 0 is the threshold for classification. Justify your answer. Does the ability to add a 3rd dimension indicate that the perceptron algorithm is capable of learning the XOR function? Why or why not? (b) (2 pts) Suppose we have a trained Perceptron with parameters (W,b). If we scale W by a positive constant factor c, will the new set of weights produce the exact same prediction for all the test data? Assume the threshold for classification is 0 . Justify your answer. (c) (2 pts) With the same setting as 2, this time we translate W by a positive constant factor c (add c to each element of W ), will the new set of weights produce the exact same prediction for all the test data? Justify your