Please provide an explanation for all parts of the question a,b,c.

The perceptron will only converge if the data is linearly separable. For linearly separable data withmargin, if||x|| R for all data points, then it will converge in at mostR22iterations (In class we assumed that||x||1). It is possible to force your data to be linearly separable as follows. If you have N data points in D dimensions, map data point xn to the (D + N)-dimensional point (xn,en), where en is a N-dimensional vector of zeros, except for the nth position, which is 1. (Eg.,e4= (0,0,0,1,0,...).)

(a) Show that if you apply this mapping the data becomes linearly separable (you may wish to do so by providing a weight vector w in (D + N)-dimensional space that successfully separates the data).

(b) How long will it take the perceptron algorithm to converge on this augmented data?

(c) How does this mapping affect generalization (i.e., test performance)?