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> While cosine similarity is invariant under such rotations R, one of the key insights in this paper is that the first (but not the second) objective is also invariant to rescalings of the columns of A and B

Ha interesting I wrote a blog post where I pointed this out a few years ago [1], and how we got around it for item-item similarity at an old job (essentially an implicit re-projection to original space as noted in section 3).

https://swarbrickjones.wordpress.com/2016/11/24/note-on-an-i...



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