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

The answer is b. Cosine.

Cosine similarity is a measure of similarity between two non-zero vectors of an inner product space that measures the cosine of the angle between them. This measure is invariant to scaling and translation as it only considers the angle between the vectors, not their magnitude or position.

Here's a step-by-step explanation:

1. Scaling: When we scale a vector, we're essentially changing its magnitude (length). However, the direction of the vector (which is what cosine similarity considers) remains the same. Therefore, scaling a vector does not affect the cosine similarity.

2. Translation: Translation involves shifting a vector from one place to another. This doesn't change the direction of the vector either, so the cosine similarity remains the same.

On the other hand, correlation, Euclidean, and Manhattan distances are not invariant to scaling and translation. They consider the magnitude and position of the