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