针对高维噪声数据，提出自适应带宽多视图流形学习方法。
Generalized Robust Adaptive-Bandwidth Multi-View Manifold Learning in High Dimensions with Noise
- 各视角独立选择带宽，动态匹配数据几何与噪声水平。
- 在不同噪声和维度下仍能准确恢复共享结构，理论保证收敛性。
- 适合传感器融合等高维噪声场景，兼具理论与实用性。
多视图数据在科学与工程中普遍存在，但现有融合方法缺乏理论保障，尤其在异质高维噪声下表现有限。本文提出广义鲁棒自适应带宽多视图扩散映射（GRAB-MDM），一种基于核函数的扩散几何框架，用于整合多个含噪数据源。核心创新在于视图相关的带宽选择策略，可自适应于各视图的几何结构与噪声水平，实现稳定且有理论依据的多视图扩散算子构建。在公共流形模型下，我们建立了渐近收敛性结果，证明自适应带宽可确保在视图间噪声水平与传感器维度不同时，仍能严格恢复共享内在结构。数值实验表明，相比固定带宽与等带宽基线，GRAB-MDM显著提升鲁棒性与嵌入质量，通常优于现有算法。该框架为高维噪声环境下的多视图传感器融合提供了实用且理论扎实的解决方案。
原文摘要 · Abstract (English)
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.
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