Please answer (a), (b) and (c). Thank you.

1. (8%) A robot has collected data with its sensor. We want to use the data to build a classifier using support vector machine. Currently, the feature space is a one dimensional space XR. The desired classification output is Y={+,}, as shown in the figure below. The training set contains three positive examples, x1=0,x3=3,x4=4, and one negative example x2=1. a) Currently, the data points are not linearly separable. We want to define a transformation that maps the data into a projected 2D space in R2. If we consider the feature mapping function as (X)=(X,(X1)2), draw the data points after the transformation to the 2D space, and draw the line of decision boundary. (4%) b) In the above situation, indicate which examples out of x1,x2,x3,x4 are support vectors? c) If the robot got one more negative data point x5=1.5, would it affect the margin? Please justify the reason. (2%)