Question

Please show that answer step by step and explain clearly, thx!!!!

5. Does the accuracy of a kNN classifier using the Euclidean distance change if you (a) translate the data

(b) scale the data (i.e., multiply the all the points by a constant), or (c) rotate the data? Explain.

Answer the same for a kNN classifier using Manhattan distance.

Answer 1

Euclidean distance is the ordinary distance between two point in Euclidean Space.

Euclidean Distance can be written between two points- point P(X₁,Y₁) and point Q(X₂,Y₂).

PQ=

a) If you translate the data there will be change in distance, and the kNN classifier's accuracy is the function of distance.There will be Change the accuracy.

b) If we scale the data means multiply by a constant it will not change the accuracy.

c) If we rotate the data the coordinates will get transformed thus changing the accuracy.

Manhatten Distance can be written between two points- point P(X₁,Y₁) and point Q(X₂,Y₂).

PQ=

a) If you translate the data there will be change in distance, and the kNN classifier's accuracy is the function of distance.There will be Change the accuracy.

b) If we scale the data means multiply by a constant it will not change the accuracy.

c) If we rotate the data the coordinates will get transformed thus changing the accuracy.