Related papers: Computing Wasserstein Distance for Persistence Dia…

The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…

In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence $d_{sym}$, the divergence induced by all…

Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest code vectors within a learnable codebook. Two critical issues…

We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional projections of spatially distributed signal patterns with a broad spectrum of…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such…

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…

We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original…

Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware…

We describe and demonstrate a method for the computation of quantum dynamics on small, noisy universal quantum computers. This method relies on the idea of `restarting' the dynamics; at least one approximate time step is taken on the…

This paper focuses on the Monge-Kantorovich formulation of the optimal transport problem and the associated $L^2$ Wasserstein distance. We use the $L^2$ Wasserstein distance in the Nearest Neighbour (NN) machine learning architecture to…

We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…

Computing the quadratic transportation metric (also called the $2$-Wasserstein distance or root mean square distance) between two point clouds, or, more generally, two discrete distributions, is a fundamental problem in machine learning,…

Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale…

We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other. We show how Wasserstein distortion reduces to a pure…

We suggest that the tools of contraction analysis for deterministic systems can be applied towards studying the convergence behavior of stochastic dynamical systems in the Wasserstein metric. In particular, we consider the case of Ito…

We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as a data term with a regularization given by the length of…