We demonstrate the first possibility of a sub-linear memory sketch for solving the approximate near-neighbor search problem. In particular, we develop an online sketching algorithm that can compress $N$ vectors into a tiny sketch consisting of small arrays of counters whose size scales as $O(N^{b}\log^2{N})$, where $b < 1$ depending on the stability of the near-neighbor search. This sketch is sufficient to identify the top-$v$ near-neighbors with high probability. To the best of our knowledge, this is the first near-neighbor search algorithm that breaks the linear memory ($O(N)$) barrier. We achieve sub-linear memory by combining advances in locality sensitive hashing (LSH) based estimation, especially the recently-published ACE algorithm, with compressed sensing and heavy hitter techniques. We provide strong theoretical guarantees; in particular, our analysis sheds new light on the memory-accuracy tradeoff in the near-neighbor search setting and the role of sparsity in compressed sensing, which could be of independent interest. We rigorously evaluate our framework, which we call RACE (Repeated ACE) data structures on a friend recommendation task on the Google plus graph with more than 100,000 high-dimensional vectors. RACE provides compression that is orders of magnitude better than the random projection based alternative, which is unsurprising given the theoretical advantage. We anticipate that RACE will enable both new theoretical perspectives on near-neighbor search and new methodologies for applications like high-speed data mining, internet-of-things (IoT), and beyond.

本条研究提出了史上首个可查询到数据集中最近邻居的亚线性内存草图，并利用局部敏感哈希（LSH）估计器、在线核密度估计和压缩感知相结合来实现稳定查询的子线性内存性能，以取得内存-精度权衡的理论效果。

流数据近邻搜索的次线性内存草图