# Curvature Corrected Nonnegative Manifold Data Factorization

arXiv: https://arxiv.org/abs/2502.15124 · HTML: https://mlsanity.com/paper/2502.15124/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data](https://mlsanity.com/paper/1903.08977/) (2019)
- [Structure-adaptive manifold estimation](https://mlsanity.com/paper/1906.05014/) (2019)
- [Curvature corrected tangent space-based approximation of manifold-valued data](https://mlsanity.com/paper/2306.00507/) (2023)
- [Principal Component Analysis in Space Forms](https://mlsanity.com/paper/2301.02750/) (2023)

## Built on by (most cited first, 2 of 2)

- [Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry](https://mlsanity.com/paper/2505.08087/) (2025)
- [Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions](https://mlsanity.com/paper/2605.24113/) (2026)

## Abstract (arXiv)

Data with underlying nonlinear structure are collected across numerous application domains, necessitating new data processing and analysis methods adapted to nonlinear domain structure. Riemannanian manifolds present a rich environment in which to develop such tools, as manifold-valued data arise in a variety of scientific settings, and Riemannian geometry provides a solid theoretical grounding for geometric data analysis. Low-rank approximations, such as nonnegative matrix factorization (NMF), are the foundation of many Euclidean data analysis methods, so adaptations of these factorizations for manifold-valued data are important building blocks for further development of manifold data analysis. In this work, we propose curvature corrected nonnegative manifold data factorization (CC-NMDF) as a geometry-aware method for extracting interpretable factors from manifold-valued data, analogous to nonnegative matrix factorization. We develop an efficient iterative algorithm for computing CC-NMDF and demonstrate our method on real-world diffusion tensor magnetic resonance imaging data.