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

TL;DR

The paper introduces GRAB-MDM, a kernel-based diffusion geometry method with view-dependent bandwidths that robustly fuses multiview high-dimensional noisy data, providing theoretical guarantees and improved embedding quality.

Contribution

It proposes a novel adaptive bandwidth strategy for multiview diffusion maps, with proven convergence and robustness in noisy, high-dimensional settings.

Findings

Significantly improves robustness over fixed-bandwidth methods

Achieves better embedding quality in noisy multiview data

Outperforms existing algorithms in numerical experiments

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.