# Partitioning signal classes using transport transforms for data analysis and machine learning

arXiv: https://arxiv.org/abs/2008.03452 · HTML: https://mlsanity.com/paper/2008.03452/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2020.

## Built on by (most cited first, 15 of 15)

- [Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning](https://mlsanity.com/paper/2204.06645/) (2022)
- [Supervised learning of sheared distributions using linearized optimal transport](https://mlsanity.com/paper/2201.10590/) (2022)
- [Linearized Wasserstein dimensionality reduction with approximation guarantees](https://mlsanity.com/paper/2302.07373/) (2023)
- [The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification](https://mlsanity.com/paper/2106.02146/) (2021)
- [Linear Optimal Partial Transport Embedding](https://mlsanity.com/paper/2302.03232/) (2023)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Measure transfer via stochastic slicing and matching](https://mlsanity.com/paper/2307.05705/) (2023)
- [LCOT: Linear circular optimal transport](https://mlsanity.com/paper/2310.06002/) (2023)
- [Approximation properties of slice-matching operators](https://mlsanity.com/paper/2310.10869/) (2023)
- [Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification](https://mlsanity.com/paper/2506.08761/) (2025)
- [Resistance Distance and Linearized Optimal Transport on Graphs](https://mlsanity.com/paper/2404.15261/) (2024)
- [The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images](https://mlsanity.com/paper/2307.15339/) (2023)
- [Point Cloud Classification via Deep Set Linearized Optimal Transport](https://mlsanity.com/paper/2401.01460/) (2024)
- [Linear optimal transport subspaces for point set classification](https://mlsanity.com/paper/2403.10015/) (2024)
- [Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis](https://mlsanity.com/paper/2206.01984/) (2022)

## Abstract (arXiv)

A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many others. It is hence worthwhile to elucidate some of the mathematical properties that explain the successes of these transforms when they are used as tools in data analysis, signal processing or data classification. In particular, we give conditions under which classes of signals that are created by algebraic generative models are transformed into convex sets by the transport transforms. Such convexification of the classes simplify the classification and other data analysis and processing problems when viewed in the transform domain. More specifically, we study the extent and limitation of the convexification ability of these transforms under an algebraic generative modeling framework. We hope that this paper will serve as an introduction to these transforms and will encourage mathematicians and other researchers to further explore the theoretical underpinnings and algorithmic tools that will help understand the successes of these transforms and lay the groundwork for further successful applications.