1 Figure 31 showed how a circle at the origin can be linearly separated by mapping from...

1 Figure 31 showed how a circle at the origin can be linearly separated by mapping

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from the features (21, 22) to the two dimensions (2, 3). But what if the circle is not located at the origin? What if it is an ellipse, not a circle? The general equation for a circle (and hence the decision boundary) is (1 - a)2 + (2-6) - r2=0, and the general equation for an ellipse is c(x1a)2+d(x2 - b)2-1=0. a. Expand out the equation for the circle and show what the weights we would be for the decision boundary in the four-dimensional feature space (21, 22, 22, 2). Explain why this means that any circle is linearly separable in this space. b. Do the same for ellipses in the five-dimensional feature space (x1, x2, x, x, x1 x2).