In this case, two items are thought of as two vectors in the
*m* dimensional user-space. The similarity between them is measured by
computing the cosine of the angle between these two
vectors. Formally, in the
ratings matrix in
Figure 2, similarity between items *i* and *j*, denoted by *sim*(*i*,*j*) is given by

where ``'' denotes the dot-product of the two vectors.