Manifold-aligned Neighbor Embedding

TL;DR

This paper presents a neighbor embedding framework for aligning manifolds, demonstrating its effectiveness through a manifold-aligned version of UMAP that produces visually competitive embeddings.

Contribution

Introduces a novel neighbor embedding framework for manifold alignment, extending UMAP to produce aligned manifolds for improved visualization.

Findings

Aligned manifolds are visually comparable to full dataset embeddings

The framework effectively aligns data manifolds across different datasets

The method enhances interpretability of manifold structures

Abstract

In this paper, we introduce a neighbor embedding framework for manifold alignment. We demonstrate the efficacy of the framework using a manifold-aligned version of the uniform manifold approximation and projection algorithm. We show that our algorithm can learn an aligned manifold that is visually competitive to embedding of the whole dataset.