论文标题
理性光谱与它们与最佳运输的联系之间的新指标
New Metrics Between Rational Spectra and their Connection to Optimal Transport
论文作者
论文摘要
我们根据最佳传输和线性系统理论提出了一对信号，线性系统或理性光谱对之间的一系列指标。指标在有理函数的极点的位置运行，并接受了距离，重中心，位移插值和投影的有效计算。我们建立了与理性光谱之间的瓦斯汀距离的联系，并证明了在信号分类，聚类，检测和近似等任务中使用指标。
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.
