University of California Support Vector Machines Questions

Question Description

Here we explore the maximal margin classifier on a toy data set.

(a) We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associatedclass label.Obs. X1 X2 Y1 3 4 Red2 2 2 Red3 4 4 Red4 1 4 Red5 2 1 Blue6 4 3 Blue7 4 1 BlueSketch the observations.(b) Sketch the optimal separating hyperplane, and provide the equation for this hyperplane such as inexercise #1.(c) Describe the classification rule for the maximal margin classifier. It should be something along thelines of Classify to Red if ?0 + ?1X1 + ?2X2 > 0, and classify to Blue otherwise. Provide thevalues for ?0, ?1, and ?2.(d) On your sketch, indicate the margin for the maximal margin hyperplane.(e) Indicate the support vectors for the maximal margin classifier.(f) Argue that a slight movement of the seventh observation would not affect the maximal marginhyperplane.(g) Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation forthis hyperplane.(h) Draw an additional observation on the plot so that the two classes are no longer separable by ahyperplane.

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