  The objective of this work is to learn a compact embedding of a set of
descriptors that is suitable for efficient retrieval and ranking, whilst
maintaining discriminability of the individual descriptors. We focus on a
specific example of this general problem -- that of retrieving images
containing multiple faces from a large scale dataset of images. Here the set
consists of the face descriptors in each image, and given a query for multiple
identities, the goal is then to retrieve, in order, images which contain all
the identities, all but one, \etc
  To this end, we make the following contributions: first, we propose a CNN
architecture -- {\em SetNet} -- to achieve the objective: it learns face
descriptors and their aggregation over a set to produce a compact fixed length
descriptor designed for set retrieval, and the score of an image is a count of
the number of identities that match the query; second, we show that this
compact descriptor has minimal loss of discriminability up to two faces per
image, and degrades slowly after that -- far exceeding a number of baselines;
third, we explore the speed vs.\ retrieval quality trade-off for set retrieval
using this compact descriptor; and, finally, we collect and annotate a large
dataset of images containing various number of celebrities, which we use for
evaluation and is publicly released.
