  Many emerging use cases of data mining and machine learning operate on large
datasets with data from heterogeneous sources, specifically with both sparse
and dense components. For example, dense deep neural network embedding vectors
are often used in conjunction with sparse textual features to provide high
dimensional hybrid representation of documents. Efficient search in such hybrid
spaces is very challenging as the techniques that perform well for sparse
vectors have little overlap with those that work well for dense vectors.
Popular techniques like Locality Sensitive Hashing (LSH) and its data-dependent
variants also do not give good accuracy in high dimensional hybrid spaces. Even
though hybrid scenarios are becoming more prevalent, currently there exist no
efficient techniques in literature that are both fast and accurate. In this
paper, we propose a technique that approximates the inner product computation
in hybrid vectors, leading to substantial speedup in search while maintaining
high accuracy. We also propose efficient data structures that exploit modern
computer architectures, resulting in orders of magnitude faster search than the
existing baselines. The performance of the proposed method is demonstrated on
several datasets including a very large scale industrial dataset containing one
billion vectors in a billion dimensional space, achieving over 10x speedup and
higher accuracy against competitive baselines.
