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This contribution features an accelerated computation of the Sinkhorn'salgorithm, which approximates the Wasserstein transportation distance, byemploying nonequispaced fast Fourier transforms (NFFT). The algorithm proposedallows approximations of the Wasserstein distance by involving not more than$\mathcal O(n\log n)$ operations for probability measures supported by~$n$points. Furthermore, the proposed method avoids expensive allocations of thecharacterizing matrices. With this numerical acceleration, the transportationdistance is accessible to probability measures out of reach so far. Numericalexperiments using synthetic and real data affirm the computational advantageand superiority.

Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm