# How do kernel-based sensor fusion algorithms behave under high dimensional noise?

arXiv: https://arxiv.org/abs/2111.10940 · HTML: https://mlsanity.com/paper/2111.10940/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 10 of 10)

- [Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator](https://mlsanity.com/paper/1801.10108/) (2018)
- [Nonparametric Canonical Correlation Analysis](https://mlsanity.com/paper/1511.04839/) (2015)
- [Latent common manifold learning with alternating diffusion: analysis and applications](https://mlsanity.com/paper/1602.00078/) (2016)
- [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)
- [Recovering Hidden Components in Multimodal Data with Composite Diffusion Operators](https://mlsanity.com/paper/1808.07312/) (2018)
- [Multi-View Kernels for Low-Dimensional Modeling of Seismic Events](https://mlsanity.com/paper/1706.01750/) (2017)
- [Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification](https://mlsanity.com/paper/1803.01710/) (2018)
- [Kernel-based Sensor Fusion with Application to Audio-Visual Voice Activity Detection](https://mlsanity.com/paper/1604.02946/) (2016)
- [Graph connection Laplacian and random matrices with random blocks](https://mlsanity.com/paper/1310.0188/) (2013)
- [Spectral Norm of Random Kernel Matrices with Applications to Privacy](https://mlsanity.com/paper/1504.05880/) (2015)

## Built on by (most cited first, 5 of 5)

- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators](https://mlsanity.com/paper/2405.12317/) (2024)
- [Landmark Alternating Diffusion](https://mlsanity.com/paper/2404.19649/) (2024)
- [Inference for Similarity and Alignability between Noisy High-Dimensional Datasets](https://mlsanity.com/paper/2511.21074/) (2025)
- [Generalized Robust Adaptive-Bandwidth Multi-View Manifold Learning in High Dimensions with Noise](https://mlsanity.com/paper/2602.10530/) (2026)

## Abstract (arXiv)

We study the behavior of two kernel based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), under the nonnull setting that the clean datasets collected from two sensors are modeled by a common low dimensional manifold embedded in a high dimensional Euclidean space and the datasets are corrupted by high dimensional noise. We establish the asymptotic limits and convergence rates for the eigenvalues of the associated kernel matrices assuming that the sample dimension and sample size are comparably large, where NCCA and AD are conducted using the Gaussian kernel. It turns out that both the asymptotic limits and convergence rates depend on the signal-to-noise ratio (SNR) of each sensor and selected bandwidths. On one hand, we show that if NCCA and AD are directly applied to the noisy point clouds without any sanity check, it may generate artificial information that misleads scientists' interpretation. On the other hand, we prove that if the bandwidths are selected adequately, both NCCA and AD can be made robust to high dimensional noise when the SNRs are relatively large.