Читать книгу Machine Learning for Tomographic Imaging - Professor Ge Wang - Страница 57

The cosine proximity function calculates the angular distance between the predicted and real vectors in terms of their inner product. It is well known that the inner product of the two unit vectors gives the cosine value of the angle between them. The formula is as follows:

L=−y·yˆ∥y∥2·∥yˆ∥2=−∑i=1ny(i)·yˆ(i)∑i=1ny(i)2·∑i=1nyˆ(i)2.(3.24)

It is also called cosine similarity. In this context, the vectors are maximally ‘similar’ if they are parallel and maximally ‘dissimilar’ if they are orthogonal.