Local Neighbor Propagation Embedding

TL;DR

This paper introduces Local Neighbor Propagation Embedding (LNPE), a manifold learning method inspired by GCNs, which enhances local neighborhood interactions to produce more faithful and robust embeddings with improved topological properties.

Contribution

LNPE extends LLE by incorporating neighbor propagation inspired by GCNs, increasing neighborhood interactions with linear complexity, and improving embedding quality.

Findings

LNPE achieves more faithful embeddings.

LNPE produces more robust embeddings.

LNPE improves topological and geometrical properties.

Abstract

Manifold Learning occupies a vital role in the field of nonlinear dimensionality reduction and its ideas also serve for other relevant methods. Graph-based methods such as Graph Convolutional Networks (GCN) show ideas in common with manifold learning, although they belong to different fields. Inspired by GCN, we introduce neighbor propagation into LLE and propose Local Neighbor Propagation Embedding (LNPE). With linear computational complexity increase compared with LLE, LNPE enhances the local connections and interactions between neighborhoods by extending $1$-hop neighbors into $n$-hop neighbors. The experimental results show that LNPE could obtain more faithful and robust embeddings with better topological and geometrical properties.