# Latent common manifold learning with alternating diffusion: analysis and applications

arXiv: https://arxiv.org/abs/1602.00078 · HTML: https://mlsanity.com/paper/1602.00078/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2016.

## Built on by (most cited first, 16 of 16)

- [On the Parameter Combinations That Matter and on Those That do Not](https://mlsanity.com/paper/2110.06717/) (2021)
- [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024)
- [Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators](https://mlsanity.com/paper/2201.08530/) (2022)
- [How do kernel-based sensor fusion algorithms behave under high dimensional noise?](https://mlsanity.com/paper/2111.10940/) (2021)
- [Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators](https://mlsanity.com/paper/2405.12317/) (2024)
- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)
- [Augmentation Invariant Manifold Learning](https://mlsanity.com/paper/2211.00460/) (2022)
- [Landmark Alternating Diffusion](https://mlsanity.com/paper/2404.19649/) (2024)
- [On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them](https://mlsanity.com/paper/2406.06812/) (2024)
- [Joint Geometric and Topological Analysis of Hierarchical Datasets](https://mlsanity.com/paper/2104.01395/) (2021)
- [Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy](https://mlsanity.com/paper/2403.08376/) (2024)
- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)
- [Generalized Robust Adaptive-Bandwidth Multi-View Manifold Learning in High Dimensions with Noise](https://mlsanity.com/paper/2602.10530/) (2026)
- [Accelerate Vector Diffusion Maps by Landmarks](https://mlsanity.com/paper/2603.21247/) (2026)
- [Complex Interpolation of Matrices with an application to Multi-Manifold Learning](https://mlsanity.com/paper/2604.14118/) (2026)
- [From Layers to Networks: Comparing Neural Representations via Diffusion Geometry](https://mlsanity.com/paper/2605.15901/) (2026)

## Abstract (arXiv)

The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion. A method based on alternating diffusion is presented and analyzed; we provide theoretical analysis of the method under the latent common manifold model. To exemplify the power of the proposed framework, experimental results in several applications are reported.