Practical Data-dependent Metric Compression With Provable Guarantees | Awesome Similarity Search Papers

Practical Data-dependent Metric Compression With Provable Guarantees

We introduce a new distance-preserving compact representation of multi-dimensional point-sets. Given (n) points in a (d)-dimensional space where each coordinate is represented using (B) bits (i.e., (dB) bits per point), it produces a representation of size (O( d log(d B/\epsilon) + log n)) bits per point from which one can approximate the distances up to a factor of (1 \pm \epsilon). Our algorithm almost matches the recent bound of~\cite{indyk2017near} while being much simpler. We compare our algorithm to Product Quantization (PQ)~\cite{jegou2011product}, a state of the art heuristic metric compression method. We evaluate both algorithms on several data sets: SIFT (used in \cite{jegou2011product}), MNIST~\cite{lecun1998mnist}, New York City taxi time series~\cite{guha2016robust} and a synthetic one-dimensional data set embedded in a high-dimensional space. With appropriately tuned parameters, our algorithm produces representations that are comparable to or better than those produced by PQ, while having provable guarantees on its performance.

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