Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection

TL;DR

This paper introduces a nonlinear manifold matching algorithm that leverages shortest-path distances and joint neighborhood selection to improve matching accuracy across multiple data modalities.

Contribution

It proposes a novel approach combining shortest-path distances with joint neighborhood graphs for better manifold matching of multi-modal datasets.

Findings

Superior performance over existing methods in matching disparate datasets

Effective use of joint neighborhood graphs for multi-modal data

Improved embedding accuracy in low-dimensional space

Abstract

Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear manifold matching algorithm using shortest-path distance and joint neighborhood selection. Specifically, a joint nearest-neighbor graph is built for all modalities. Then the shortest-path distance within each modality is calculated from the joint neighborhood graph, followed by embedding into and matching in a common low-dimensional Euclidean space. Compared to existing algorithms, our approach exhibits superior performance for matching disparate datasets of multiple modalities.