2. In this problem you will code a multiclass classifier to use the OvR method. For each 2-class problem, use a nearest-means classifier. You will apply this multiclass classifier separately to

each of datasets 4, 5, 6 from Homework 1, as directed below. p. 1 of 3 For the plots below, you may find it useful to use plotDecBoundaries code that was given with Homework 1. You may need to modify it somewhat for this problem. For the decision rule that combines the results of the 2-class classifiers ("combining rule"), you will use 3 different methods, as follows. (a) Use the default decision rule we gave in Lecture 3 for OvR method, leaving points in indeterminate regions as unclassified. Plot the training points, decision regions and boundaries, for each 2-class (binary) classifier (3 plots for each dataset). Plot the final decision boundary and regions for the 3-class problem (1 plot for each dataset). Report the training classification accuracy, error rate, and unclassified rate, on the training set and separately on the test set (18 numbers total): report them in a table: columns labeled "accuracy", "error", "unclassified"; and rows labeled "dataset_4 train", "dataset_4 test", "dataset_5 train", "dataset_5 test", "dataset_6 train", "dataset_6 test". (b) Use the default decision rule we gave in Lecture 3 for OvR method, but also classify points in indeterminate regions using the rule: x € Txiff k = argmax (gm (x)} in which the discriminant g(x) for each m is the discriminant function value for the Si vs. S 2-class (nearest-means) classifier. Repeat the plots and numerical-results table of part (a), except using this decision rule. (c) Use an alternate decision rule instead of the default decision rule: classify all points in feature space according to: x € I'xiff k = argmaxm{gm (x)} in which the discriminant gm (x) for each m is the discriminant function value for the Sm vs. S 2-class (nearest-means) classifier. Repeat the plots and accuracy reports of part (a), except using this decision rule. (d) Compare the 3 different combining rules: comment on, and explain if you can, any observed similarities and differences.