If all the vectors are on the unit ball, then cosine = dot product. But then the dot product is a linear transformation away from the euclidean distance:
If you're using it in a machine learning model, things that are one linear transform away are more or less the same (might need more parameters/layers/etc.)
If you're using it for classical statistics uses (analytics), right, they're not equivalent and it would be good to remember this distinction.
To be very explicit, if |x| = |y| = 1, we have |x - y|^2 = |x|^2 - 2xy + |y|^2 = 2 - 2xy = 2 - 2* cos(th). So they are not identical but minimizing the Euclidian distance of two unit vectors is the same as maximizing the cosine similarity.
If all the vectors are on the unit ball, then cosine = dot product. But then the dot product is a linear transformation away from the euclidean distance:
https://math.stackexchange.com/questions/1236465/euclidean-d...
If you're using it in a machine learning model, things that are one linear transform away are more or less the same (might need more parameters/layers/etc.)
If you're using it for classical statistics uses (analytics), right, they're not equivalent and it would be good to remember this distinction.