Cosine distance is another classic measuring factor. If you look closely, the cosine of the angle between the standardized vectors is Pearson's correlation, the same formula. This distance uses cosine properties: if the two vectors are co-directed (that is, the angle between them is 0), then the cosine of the angle between them is 1. Conversely, the cosine of the angle between perpendicular vectors is 0. An example is shown here:

We discussed methods for user preferences' similarity estimation. The next important issue we will discuss is data preparation for use in recommender system algorithms.