A Quasi-isometric Embedding Algorithm

TL;DR

This paper introduces an algorithm designed to find near-isometric projections of data on manifolds, minimizing distortion during dimensionality reduction while preserving the intrinsic structure.

Contribution

The paper presents a novel quasi-isometric embedding algorithm that optimally reduces data dimensionality with minimal distortion, extending Whitney's embedding theorem.

Findings

The algorithm effectively preserves manifold structure during projection.

It achieves lower distortion compared to random projections.

The method is applicable to high-dimensional data sets.

Abstract

The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.