  This paper addresses the nearest neighbor search problem under inner product
similarity and introduces a compact code-based approach. The idea is to
approximate a vector using the composition of several elements selected from a
source dictionary and to represent this vector by a short code composed of the
indices of the selected elements. The inner product between a query vector and
a database vector is efficiently estimated from the query vector and the short
code of the database vector. We show the superior performance of the proposed
group $M$-selection algorithm that selects $M$ elements from $M$ source
dictionaries for vector approximation in terms of search accuracy and
efficiency for compact codes of the same length via theoretical and empirical
analysis. Experimental results on large-scale datasets ($1M$ and $1B$ SIFT
features, $1M$ linear models and Netflix) demonstrate the superiority of the
proposed approach.
