Generalized Robust Adaptive-Bandwidth Multi-View Manifold Learning in High Dimensions with Noise

2026-02-11

AI Summary

This work addresses the challenge of robustly recovering shared intrinsic manifold structures from multi-view high-dimensional data corrupted by heterogeneous noise, for which theoretically grounded fusion methods are lacking. To this end, we propose the GRAB-MDM framework, which constructs a kernel-based diffusion geometry model equipped with a view-dependent adaptive bandwidth mechanism to stably build multi-view diffusion operators for fusing noisy data sources. Under a general manifold assumption, our method provides the first theoretical guarantee of asymptotic convergence and robust recoverability of the shared structure in the presence of high-dimensional heterogeneous noise. Experimental results demonstrate that GRAB-MDM significantly outperforms baseline approaches employing fixed or uniform bandwidths, as well as other state-of-the-art algorithms, achieving notable improvements in both embedding quality and noise robustness.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Multiview datasets are common in scientific and engineering applications, yet existing fusion methods offer limited theoretical guarantees, particularly in the presence of heterogeneous and high-dimensional noise. We propose Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM), a new kernel-based diffusion geometry framework for integrating multiple noisy data sources. The key innovation of GRAB-MDM is a {view}-dependent bandwidth selection strategy that adapts to the geometry and noise level of each view, enabling a stable and principled construction of multiview diffusion operators. Under a common-manifold model, we establish asymptotic convergence results and show that the adaptive bandwidths lead to provably robust recovery of the shared intrinsic structure, even when noise levels and sensor dimensions differ across views. Numerical experiments demonstrate that GRAB-MDM significantly improves robustness and embedding quality compared with fixed-bandwidth and equal-bandwidth baselines, and usually outperform existing algorithms. The proposed framework offers a practical and theoretically grounded solution for multiview sensor fusion in high-dimensional noisy environments.

Problem

• multiview fusion
• high-dimensional noise
• manifold learning
• heterogeneous data
• intrinsic structure recovery

Innovation

• adaptive bandwidth
• multiview diffusion maps
• manifold learning
• robust fusion
• high-dimensional noise