In this thread ( partial derivative of cosine similarity ) is discussed the derivation of the partial derivative of cosine similarity between two vectors.
Let's say we want the cosine similarity between a whole matrix of vectors. So cossim(X), where X is a matrix of vectors. The main diagonal is all 1's. The rest of the values are symmetrical, and represent the similarity between vector "a" and vector "b"
This derivation then provides the update value for each specific point. Given any two vectors, a and b, from matrix X, each value of a's derivative (a1 in this example), is calculated with the solved for equation.
As such, the entire derivative for the cossim of a matrix can be solved point-by-point, row-by-row, using this formula, correct?
