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Which of the following distance/similarity measure is invariant to scaling and translation?a.Correlationb.Cosinec.Euclideand.Manhattan

Question

Which of the following distance/similarity measure is invariant to scaling and translation?a.Correlationb.Cosinec.Euclideand.Manhattan

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Solution

The distance/similarity measure that is invariant to scaling and translation is Cosine.

Here's why:

a. Correlation: It is not invariant to scaling and translation. It measures the linear relationship between two variables, but if we scale or translate the variables, the correlation will change.

b. Cosine: It is invariant to scaling and translation. Cosine similarity measures the cosine of the angle between two vectors, and this measure will not change if we scale or translate the vectors.

c. Euclidean: It is not invariant to scaling and translation. Euclidean distance measures the straight line distance between two points. If we scale or translate the points, the Euclidean distance will change.

d. Manhattan: It is not invariant to scaling and translation. Manhattan distance measures the sum of the absolute differences of their coordinates. If we scale or translate the coordinates, the Manhattan distance will change.

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