Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic [PDF]
Entropy, 2020 Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map.
Hong Zhang +4 more
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Geometric Characteristics of the Wasserstein Metric on SPD(n) and Its Applications on Data Processing [PDF]
Entropy, 2021 The Wasserstein distance, especially among symmetric positive-definite matrices, has broad and deep influences on the development of artificial intelligence (AI) and other branches of computer science.
Yihao Luo +3 more
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Distributionally robust learning-to-rank under the Wasserstein metric [PDF]
PLoS ONE, 2023 Despite their satisfactory performance, most existing listwise Learning-To-Rank (LTR) models do not consider the crucial issue of robustness. A data set can be contaminated in various ways, including human error in labeling or annotation, distributional ...
Shahabeddin Sotudian +2 more
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Nonnegative matrix factorization with Wasserstein metric-based regularization for enhanced text embedding. [PDF]
PLoS ONEText embedding plays a crucial role in natural language processing (NLP). Among various approaches, nonnegative matrix factorization (NMF) is an effective method for this purpose.
Mingming Li +3 more
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The Wasserstein Metric and Robustness in Risk Management
Risks, 2016 In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial ...
Rüdiger Kiesel +3 more
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The Wasserstein Metric between a Discrete Probability Measure and a Continuous One
MathematicsThis paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches ...
Weihua Yang, Xu Zhang, Xia Wang
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Ensemble Riemannian data assimilation over the Wasserstein space [PDF]
Nonlinear Processes in Geophysics, 2021 In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the ...
S. K. Tamang +6 more
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Wasserstein model reduction approach for parametrized flow problems in porous media [PDF]
ESAIM: Proceedings and Surveys, 2023 The aim of this work is to build a reduced order model for parametrized porous media equations. The main challenge of this type of problems is that the Kolmogorov width of the solution manifold typically decays quite slowly and thus makes usual linear ...
Battisti Beatrice +5 more
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Free complete Wasserstein algebras [PDF]
Logical Methods in Computer Science, 2018 We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages.
Radu Mardare +2 more
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Fused Gromov-Wasserstein Distance for Structured Objects
Algorithms, 2020 Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions.
Titouan Vayer +4 more
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