Is empty sparse vector valid in cosine similarity calculation.

Reason why this is not valid operation:

• From the calculational point of view there is a problem of normalizing similarity measure since one vector's length is zero therefore you get 0/0 which is undefined.

However, in my opinion it should be valid and return 0:

• Since from conceptual perspective cosine similarity is only normalized dot product similatiry. So if dot product can say that similarity to empty sparse vector it zero tha also cosine similarity should.