Locality Sensitive Hashing (LSH) is an effective method to index a set of\npoints such that we can efficiently find the nearest neighbors of a query\npoint. We extend this method to our novel Set-query LSH (SLSH), such that it\ncan find the nearest neighbors of a set of points, given as a query.\n Let $ s(x,y) $ be the similarity between two points $ x $ and $ y $. We\ndefine a similarity between a set $ Q$ and a point $ x $ by aggregating the\nsimilarities $ s(p,x) $ for all $ p\\in Q $. For example, we can take $ s(p,x) $\nto be the angular similarity between $ p $ and $ x $ (i.e., $1-{\\angle\n(x,p)}/{\\pi}$), and aggregate by arithmetic or geometric averaging, or taking\nthe lowest similarity.\n We develop locality sensitive hash families and data structures for a large\nset of such arithmetic and geometric averaging similarities, and analyze their\ncollision probabilities. We also establish an analogous framework and hash\nfamilies for distance functions. Specifically, we give a structure for the\neuclidean distance aggregated by either averaging or taking the maximum.\n We leverage SLSH to solve a geometric extension of the approximate near\nneighbors problem. In this version, we consider a metric for which the unit\nball is an ellipsoid and its orientation is specified with the query.\n An important application that motivates our work is group recommendation\nsystems. Such a system embeds movies and users in the same feature space, and\nthe task of recommending a movie for a group to watch together, translates to a\nset-query $ Q $ using an appropriate similarity.\n