Fast Similarity Search For Learned Metrics

Jain P., Kulis, Grauman. Arxiv 2024

[Paper]    
ARXIV Independent

We propose a method to efficiently index into a large database of examples according to a learned metric. Given a collection of examples, we learn a Mahalanobis distance using an information-theoretic metric learning technique that adapts prior knowledge about pairwise distances to incorporate similarity and dissimilarity constraints. To enable sub-linear time similarity search under the learned metric, we show how to encode a learned Mahalanobis parameterization into randomized locality-sensitive hash functions. We further formulate an indirect solution that enables metric learning and hashing for sparse input vector spaces whose high dimensionality make it infeasible to learn an explicit weighting over the feature dimensions. We demonstrate the approach applied to systems and image datasets, and show that our learned metrics improve accuracy relative to commonly-used metric baselines, while our hashing construction permits effi- cient indexing with a learned distance and very large databases.

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