arXiv Machine Learning By Antonio Pariente, Ignacio Hounie, Santiago Segarra, Alejandro Ribeiro

Infinity Search: Approximate Vector Search with Projections on q-Metric Spaces

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The paper introduces a method for approximate vector search in ultrametric (infinity-metric) spaces by using a projection operator that transforms arbitrary dissimilarity functions into ultrametric ones while preserving nearest neighbors. It extends this approach to q-metric spaces, where triangle inequalities involve q-th powers, and learns an efficient approximation of the projected distances. Experiments show that higher q values speed up search at the cost of recall, yet the proposed methods remain competitive with existing search techniques.

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