New Metrics Between Rational Spectra and their Connection to Optimal Transport

• URL: http://arxiv.org/abs/2004.09152v1
• Date: Mon, 20 Apr 2020 09:29:03 GMT
• Title: New Metrics Between Rational Spectra and their Connection to Optimal Transport
• Authors: Fredrik Bagge Carlson, Mandar Chitre
• Abstract summary: 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 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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