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

arXiv: https://arxiv.org/abs/2602.10530 · HTML: https://mlsanity.com/paper/2602.10530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 60 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Nonparametric Canonical Correlation Analysis](https://mlsanity.com/paper/1511.04839/) (2015)
- [Spectral Convergence of the connection Laplacian from random samples](https://mlsanity.com/paper/1306.1587/) (2013)
- [Latent common manifold learning with alternating diffusion: analysis and applications](https://mlsanity.com/paper/1602.00078/) (2016)
- [Graph Structural Attack by Perturbing Spectral Distance](https://mlsanity.com/paper/2111.00684/) (2021)
- [Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud](https://mlsanity.com/paper/2011.10725/) (2020)
- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [Multi-view Data Visualisation via Manifold Learning](https://mlsanity.com/paper/2101.06763/) (2021)
- [MultiView Diffusion Maps](https://mlsanity.com/paper/1508.05550/) (2015)
- [How do kernel-based sensor fusion algorithms behave under high dimensional noise?](https://mlsanity.com/paper/2111.10940/) (2021)
- [Multi-View Kernels for Low-Dimensional Modeling of Seismic Events](https://mlsanity.com/paper/1706.01750/) (2017)

## Abstract (arXiv)

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.