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6. Consider a binary classification problem using lnearest neighbors with the Euclidean dis- tance metric. We have N 1-dimensional training points xª), x², ...) and corresponding labels y", ya,...) with x) ER and y) e (0, 1 Assume the points x), xa, .. L are in ascend- ing order by value. Ifthere are ties during the 1-NN algorithm, we break ties by choosing the label corresponding to the x") with lower value. (a) Is it possible to build a decision tree that behaves exactly the same as the 1-nearest neighbor classifier? Assume that the decision at each node takes the form of“ X st or x> ," where t ER. O Yes O No If your answer is yes, please explain how you will construct the decision tree. If your answer is no, explain why it's not possīble.

6. Consider a binary classification problem using lnearest neighbors with the Euclidean dis- tance metric. We have N 1-dimensional training points xª), x², ...) and corresponding labels y", ya,...) with x) ER and y) e (0, 1 Assume the points x), xa, .. L are in ascend- ing order by value. Ifthere are ties during the 1-NN algorithm, we break ties by choosing the label corresponding to the x") with lower value. (a) Is it possible to build a decision tree that behaves exactly the same as the 1-nearest neighbor classifier? Assume that the decision at each node takes the form of“ X st or x> ," where t ER. O Yes O No If your answer is yes, please explain how you will construct the decision tree. If your answer is no, explain why it's not possīble.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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 6. Consider a binary classification problem using 1-nearest neighbors with the Euclidean distance metric. We have N 1-dimensional training points x(1), x(2), . . . x(N ) and corresponding labels
y(1), y(2), . . . y(N ) with x(i ) ∈ R and y(i ) ∈ {0, 1}. Assume the points x(1), x(2), . . . x(N ) are in ascending order by value. If there are ties during the 1-NN algorithm, we break ties by choosing the label
corresponding to the x(i ) with lower value. 

 

6. Consider a binary classification problem using lnearest neighbors with the Euclidean dis- tance metric. We have N 1-dimensional training points x2), x2),... ) and corresponding labels ya, y?,... ) with x6) ER and y) e 0, 1 Assume the points x", x², ... are in ascend- ing order by value. If there are ties during the 1-NN algorithm, we break ties by choosing the label corresponding to the x") with lower value. (a) Is it possible to build a decision tree that behaves exactly the same as the 1-nearest neighbor classifier? Assume that the decision at each node takes the form of“ x st or x > t," where t eR. O Yes O No If your answer is yes, please explain how you will construct the decision tree. If your answer is no, explain why it's not possible. Your answer: 4 Decision Trees, k-NN, Regression (b) where x = k, x) eR? and the decision at each node takes the form of “ X¡ st or X¡ > t," where t eR and j E (1, 2. Give an example with at most 3 training points for which it isn't possible to build a decision tree that behaves exactly the same as a 1-nearest neighbor classifier. Let's add a dimension! Now assume the training points are 2-dimensional Your answer:
Transcribed Image Text:6. Consider a binary classification problem using lnearest neighbors with the Euclidean dis- tance metric. We have N 1-dimensional training points x2), x2),... ) and corresponding labels ya, y?,... ) with x6) ER and y) e 0, 1 Assume the points x", x², ... are in ascend- ing order by value. If there are ties during the 1-NN algorithm, we break ties by choosing the label corresponding to the x") with lower value. (a) Is it possible to build a decision tree that behaves exactly the same as the 1-nearest neighbor classifier? Assume that the decision at each node takes the form of“ x st or x > t," where t eR. O Yes O No If your answer is yes, please explain how you will construct the decision tree. If your answer is no, explain why it's not possible. Your answer: 4 Decision Trees, k-NN, Regression (b) where x = k, x) eR? and the decision at each node takes the form of “ X¡ st or X¡ > t," where t eR and j E (1, 2. Give an example with at most 3 training points for which it isn't possible to build a decision tree that behaves exactly the same as a 1-nearest neighbor classifier. Let's add a dimension! Now assume the training points are 2-dimensional Your answer:
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