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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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.1: Early Definitions And Postulates
Problem 36E: Consider noncoplanar points A, B, C, and D. Using three points at a time such as A, B, and C, how...
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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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