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# Problem 1: (9 points) K-Nearest Neighbor Classication Consider the following set of training data, consisting of two-dimensional real-valued features...

Problem 1: (9 points) K-Nearest Neighbor Classification

Consider the following set of training data, consisting of two-dimensional real-valued features and a binary class value, for a k-nearest-neighbors classifier. Positive data are shown as circles, negative as squares.

(1) Sketch the decision boundary for k = 1. Show your work and justify your answer in a few sentences (2-3).

(2) Sketch the decision boundary for k = 5, in the relevant part of the feature space (i.e., near the training data). Again, show your work and justify your answer in a few sen- tences.

(3) Sketch the basic shape you would expect to see for the error rate on training data, and on test data, as a function of increasing k = 1, . . . , 7. For the training error rate, indicate the values (error rates) of the endpoints (k = 1 and k = 7).

Problem 1: (9 points) K-Nearest Neighbor Classiﬁcation Consider the following set of training data, consisting of two-dimensional real-valued features and a
binary class value, for a k-nearest-neighbors classiﬁer. Positive data are shown as circles, negative
as squares. (1) Sketch the decision boundary for k = 1.
few sentences (2-3). 3 :r (2) Sketch the decision boundary for k = 5, in the relevant part of the feature space (i.e., near the training data). Again, show your 5 work and justify your answer in a few sen-
tences (3) Sketch the basic shape you would expect
to see for the error rate on training data, and
on test data, as a function of increasing k =
1, . . . ,7. For the training error rate, indicate
the values (error rates) of the endpoints (k =
l and k = 7). Error rate

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