# Recovering Hidden Components in Multimodal Data with Composite Diffusion Operators

arXiv: https://arxiv.org/abs/1808.07312 · HTML: https://mlsanity.com/paper/1808.07312/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2018.

## Built on by (most cited first, 10 of 10)

- [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)
- [Multi-modal Differentiable Unsupervised Feature Selection](https://mlsanity.com/paper/2303.09381/) (2023)
- [DiSC: Differential Spectral Clustering of Features](https://mlsanity.com/paper/2211.05314/) (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)
- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)
- [Complex Interpolation of Matrices with an application to Multi-Manifold Learning](https://mlsanity.com/paper/2604.14118/) (2026)
- [TraceGuard: Adaptive Multimodal Poison Filtering through Cross-Feature Rank Agreement](https://mlsanity.com/paper/2609.29099/) (2026)

## Abstract (arXiv)

Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning, where the data from each modality is assumed to lie on some manifold. In this context, the goal is to characterize the relations between the different modalities by studying their underlying manifolds. We propose two new diffusion operators that allow to isolate, enhance and attenuate the hidden components of multi-modal data in a data-driven manner. Based on these new operators, efficient low-dimensional representations can be constructed for such data, which characterize the common structures and the differences between the manifolds underlying the different modalities. The capabilities of the proposed operators are demonstrated on 3D shapes and on a fetal heart rate monitoring application.