2. (30 points) Build a (Multilayer) Perceptron to recognize a certain area of the plane. That is, the Perceptron should output a "1" if the input vector lies in the shaded region. (a) Determine the vector of coefficients w = [wo, w1, w2] for a single layer perceptron of the form in Figure 1 to recognize the area in Figure 2 and again for Figure 3 shaded blue. Use a step-function as the non-linear activation function at desig nated nodes: (1, if a > 0 s(a) = 0, otherwise T (b) Determine coefficients W= W10 W11 W12 , V = [vo, v1, v2]" in the 2-layer Per- W20 W21 W22 ceptron of the form in Figure 4 to recognize the shaded region in Figure 5. Hint: The shaded region in Figure 5 equals to the intersection of the regions of Figures 2 & 3.Figure 1: Single-layer perception. The non-linearity is a step function yielding a discrete value 1/0. Figure 2: Accept shaded region. Figure 3: Accept shaded region. Figure 4: Multi-layer perception. Figure 5: Accept shaded region (internet- tion of Figures 2 & 3) 2