  The method of random projections has become a standard tool for machine
learning, data mining, and search with massive data at Web scale. The effective
use of random projections requires efficient coding schemes for quantizing
(real-valued) projected data into integers. In this paper, we focus on a simple
2-bit coding scheme. In particular, we develop accurate nonlinear estimators of
data similarity based on the 2-bit strategy. This work will have important
practical applications. For example, in the task of near neighbor search, a
crucial step (often called re-ranking) is to compute or estimate data
similarities once a set of candidate data points have been identified by hash
table techniques. This re-ranking step can take advantage of the proposed
coding scheme and estimator.
  As a related task, in this paper, we also study a simple uniform quantization
scheme for the purpose of building hash tables with projected data. Our
analysis shows that typically only a small number of bits are needed. For
example, when the target similarity level is high, 2 or 3 bits might be
sufficient. When the target similarity level is not so high, it is preferable
to use only 1 or 2 bits. Therefore, a 2-bit scheme appears to be overall a good
choice for the task of sublinear time approximate near neighbor search via hash
tables.
  Combining these results, we conclude that 2-bit random projections should be
recommended for approximate near neighbor search and similarity estimation.
Extensive experimental results are provided.
