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Sub-linear Memory Sketches for Near Neighbor Search on Streaming Data
Benjamin Coleman · Richard Baraniuk · Anshumali Shrivastava

Wed Jul 15 05:00 AM -- 05:45 AM & Wed Jul 15 04:00 PM -- 04:45 PM (PDT) @ None #None
We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.

Author Information

Benjamin Coleman (Rice University)
Richard Baraniuk (OpenStax / Rice University)
Anshumali Shrivastava (Rice University)

Anshumali Shrivastava is an associate professor in the computer science department at Rice University. His broad research interests include randomized algorithms for large-scale machine learning. In 2018, Science news named him one of the Top-10 scientists under 40 to watch. He is a recipient of National Science Foundation CAREER Award, a Young Investigator Award from Air Force Office of Scientific Research, and machine learning research award from Amazon. His research on hashing inner products has won Best Paper Award at NIPS 2014 while his work on representing graphs got the Best Paper Award at IEEE/ACM ASONAM 2014. Anshumali finished his Ph.D. in 2015 from Cornell University.

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