Distance and KNN Checkpoint

Reconstruct a new trace and diagnose implementation mistakes. Select one answer per multiple-choice question.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. Which pair has cosine similarity 1 but nonzero Euclidean distance?

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[1,0] and [0,1] [1,0] and [-1,0] [1,0] and [3,0] [0,0] and [0,0]

2. A numeric feature changes units from meters to centimeters. What is guaranteed about cosine similarity?

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It is unchanged for all pairs It may change because only one coordinate was rescaled It becomes Euclidean distance It is multiplied by 100

3. What does the distance exercise return for cosine similarity when one input is the zero vector?

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It raises in every case It returns 1 because the zero vector is normalized It returns -1 It returns 0 as a declared fallback, although mathematical cosine is undefined

4. Sorted neighbors have labels [2,1,1,2,1]. With k=3, which integer label wins?

5. The two selected neighbors are [(0.1,2),(0.9,1)]. Under the exercise vote-tie rule, what happens?

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Label 2 wins because it appears first in the sorted neighbors Label 1 always wins because its numeric value is smaller Distance values are averaged to create a new label Both labels must be returned

6. A learner normalizes every feature without considering its meaning. Which evaluation is most useful?

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Only check that every vector has equal width Assume normalization always improves the classifier Fit candidate transforms on training data and compare held-out neighbor decisions Select the transform giving the smallest training distances

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