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Oh, thanks for the correction. If all the vectors are on the unit ball, then cosine = dot product. But then the dot product is a linear transformation away fro
by VHRanger 3y ago
Oh, thanks for the correction.
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-distance-and-dot-product 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.
- gbjw 3y agoTo 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.