Answer Happy

Suppose that you have the following collection T of data points in two dimensions: x 4 1 12 3 3 2 4 y 1 2 B B R R B The picture below illustrates these points, together with the classifier if r+y-3> 0 then BLUE else RED, corresponding to the weight vector (1,1,3). 4. DO B 3 2 1 Classified red 1 2 3 4 A. Compute the value of the error function for this classifier: ET(w) = Σ PET p misclassified E Classified blue W₁Pr + W₂Py - Ws|
B. Compute the gradient of the error function with respect to the weight vector w. The gradient is a vector VE = (91,92,93) computed as follows: For a given weight vector and data point p = T let 1 8(P) if p is labelled RED in 7 but is classified BLUE by -1 if p is labelled BLUE in T but is classified RED by p is correctly classified by 0 if Then VE = S(p) (Pz. Py, -1) PET C. Compute the new weight vector after one step of gradient descent: w' = -8 VE where 8 = 0.1. D. How does the new weight vector w' classify the points? E. What is the value of the error function at the new weight vector w'?