# New Metrics Between Rational Spectra and their Connection to Optimal Transport

arXiv: https://arxiv.org/abs/2004.09152 · HTML: https://mlsanity.com/paper/2004.09152/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)

## Abstract (arXiv)

We propose a series of metrics between pairs of signals, linear systems or rational spectra, based on optimal transport and linear-systems theory. The metrics operate on the locations of the poles of rational functions and admit very efficient computation of distances, barycenters, displacement interpolation and projections. We establish the connection to the Wasserstein distance between rational spectra, and demonstrate the use of the metrics in tasks such as signal classification, clustering, detection and approximation.