Optimal spherical codes for locality-sensitive hashing

Rana Alkhoury Maroun, Henry Gouk, Yihe Lu, Barbara Webb

Keywords: Optimal spherical codes, locality sensitive hashing, similarity search, sparse coding

TL;DR: A new LSH method that leverages optimal spherical codes for optimal performance on cosine similarity search.

Abstract: In the realm of Locality-Sensitive Hashing (LSH), striking the right balance between computational efficiency and accuracy has been a persistent challenge. Most existing unsupervised methods rely on dense representations, which can lead to inefficiencies. To tackle this, we advocate for the adoption of sparse representations and introduce the use of quasi-Optimal Spherical Codes (OSCs) to minimise space distortion. OSCs strive to maximise the minimum angle between any pair of points on the hypersphere, ensuring that the relative angular information between data points is preserved in the representation, which is particularly valuable in tasks involving cosine similarity. We employ Adam-based optimisation to obtain these codes and use them to partition the space into a $k^\text{th}$-order Voronoi diagram. This approach consistently outperforms existing methods across four datasets on $K$-nearest neighbors search with cosine similarity, while capping the query time for a given embedding size.

Primary Area: metric learning, kernel learning, and sparse coding

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Submission Number: 9173