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Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm
- Source :
- ETNA - Electronic Transactions on Numerical Analysis. 58:289-315
- Publication Year :
- 2023
- Publisher :
- Osterreichische Akademie der Wissenschaften, Verlag, 2023.
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Abstract
- This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows 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 the characterizing matrices. With this numerical acceleration, the transportation distance is accessible to probability measures out of reach so far. Numerical experiments using synthetic and real data affirm the computational advantage and superiority.<br />Comment: 32 pages, 6 figures
Details
- ISSN :
- 10689613
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- ETNA - Electronic Transactions on Numerical Analysis
- Accession number :
- edsair.doi.dedup.....fda90590b5ac0e332b9a44fdd305e95d