New Metrics Between Rational Spectra and their Connection to Optimal Transport
Machine Learning
2020-04-21 v1 Machine Learning
Systems and Control
Signal Processing
Systems and Control
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2004.09152,
title = {New Metrics Between Rational Spectra and their Connection to Optimal Transport},
author = {Fredrik Bagge Carlson and Mandar Chitre},
journal= {arXiv preprint arXiv:2004.09152},
year = {2020}
}
Comments
17 pages, 12 figures