# A Transportation Lp Distance for Signal Analysis

arXiv: https://arxiv.org/abs/1609.08669 · HTML: https://mlsanity.com/paper/1609.08669/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2016.

## Built on by (most cited first, 11 of 11)

- [Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2210.06671/) (2022)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification](https://mlsanity.com/paper/2106.02146/) (2021)
- [Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments](https://mlsanity.com/paper/2203.05813/) (2022)
- [Multiview Sensing With Unknown Permutations: An Optimal Transport Approach](https://mlsanity.com/paper/2103.07458/) (2021)
- [Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning](https://mlsanity.com/paper/2207.01093/) (2022)
- [Immiscible Color Flows in Optimal Transport Networks for Image Classification](https://mlsanity.com/paper/2205.02938/) (2022)
- [Convolve and Conquer: Data Comparison with Wiener Filters](https://mlsanity.com/paper/2311.06558/) (2023)
- [Metric Similarity and Manifold Learning of Circular Dichroism Spectra of Proteins](https://mlsanity.com/paper/2504.19355/) (2025)
- [Quantifying the noise sensitivity of the Wasserstein metric for images](https://mlsanity.com/paper/2510.01015/) (2025)

## Abstract (arXiv)

Transport based distances, such as the Wasserstein distance and earth mover's distance, have been shown to be an effective tool in signal and image analysis. The success of transport based distances is in part due to their Lagrangian nature which allows it to capture the important variations in many signal classes. However these distances require the signal to be nonnegative and normalized. Furthermore, the signals are considered as measures and compared by redistributing (transporting) them, which does not directly take into account the signal intensity. Here we study a transport-based distance, called the TLp distance, that combines Lagrangian and intensity modelling and is directly applicable to general, non-positive and multi-channelled signals. The framework allows the application of existing numerical methods. We give an overview of the basic properties of this distance and applications to classification, with multi-channelled, non-positive one and two-dimensional signals, and color transfer.