where the superscript in the argmax function indicates the number k ? N of neighbors to be returned, and sim is any well defined similarity measure, such as, for example, the usual cosine similarity measure, i. e., sim(xu,xv) := ?xu,xv? ?xu??xv?
Multi-mode Recommendations Having the neighborhood computed, we can extract the set T? (u, r) of n recommended tags for a given user u, a given resource r, and some n ? N, as follows: