A Quasi-isometric Embedding Algorithm
arXiv:1709.01972v33 citations
Originality Synthesis-oriented
AI Analysis
This addresses the challenge of dimensionality reduction for data on manifolds, but appears incremental as it builds on the Whitney embedding theorem.
The paper tackles the problem of embedding data lying on a manifold into a lower dimension with minimal distortion, presenting an algorithm to achieve this.
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.