Related papers: Mapper Comparison with Wasserstein Metrics

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…

We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…

The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…

A key challenge in off-road navigation is that even visually similar terrains or ones from the same semantic class may have substantially different traction properties. Existing work typically assumes no wheel slip or uses the expected…

We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…

This paper leverages macroscopic models and multi-source spatiotemporal data collected from automatic traffic counters and probe vehicles to accurately estimate traffic flow and travel time in links where these measurements are unavailable.…

Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem…

We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…

Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the…

Comparing images to recommend items from an image-inventory is a subject of continued interest. Added with the scalability of deep-learning architectures the once `manual' job of hand-crafting features have been largely alleviated, and…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…

The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. Many unsupervised…

Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…