On Projection Based Operators in Lp space for Exact Similarity Search

TL;DR

This paper explores projection-based operators in Lp spaces to improve exact similarity search, introducing orthogonal and adaptive projections that satisfy the 1-Lipschitz property for high-dimensional data.

Contribution

It introduces a new orthogonal projection satisfying the 1-Lipschitz property and an adaptive projection based on the first principal component for Lp norms.

Findings

Orthogonal projection satisfying 1-Lipschitz property described

Adaptive projection based on first principal component introduced

Potential improvements in high-dimensional similarity search accuracy

Abstract

We investigate exact indexing for high dimensional Lp norms based on the 1-Lipschitz property and projection operators. The orthogonal projection that satisfies the 1-Lipschitz property for the Lp norm is described. The adaptive projection defined by the first principal component is introduced.