Intro to Statistical Learning (2nd Ed), Solution to Problem 9.3c | Maximal Margin Classifier

9.3C: 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 associated class label. Obs. X1 X2 Y 1 3 4 Red 2 2 2 Red 3 4 4 Red 4 1 4 Red 5 2 1 Blue 6 4 3 Blue 7 4 1 Blue Sketch the observations. (b) Sketch the optimal separating hyperplane, and provide the equation for this hyperplane (of the form (9.1)) (c) Describe the classification rule for the maximal margin classifier. It should be something along the lines of “Classify to Red if β0+β1X1+β2X2 gt gt 0 , and classify to Blue otherwise.” Provide the values for β0 , β1 , and β2 . (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 margin hyperplane. (g) Sketch a hyperplane that is not the optimal separating hyperplane, and provide the equation for this hyperplane. (h) Draw an additional observation on the plot so that the two classes are no longer separable by a hyperplane. Download Book: https://www.statlearning.com/ Authors' Lectures (R): https://youtube.com/playlist?list=PLoROMvodv4rOzrYsAxzQyHb8n_RWNuS1e&si=NP0wJ6RjP8XkxU7y Authors' Lectures (Python): https://youtube.com/playlist?list=PLoROMvodv4rPP6braWoRt5UCXYZ71GZIQ&si=0Z8tx4xlPLEyjZ70 https://colab.research.google.com/drive/1nC6mQqSwo8kjmvias_0JlQeVp2aZyKJD?usp=sharing