Related papers: Optimal Transport for structured data with applica…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
Given a graph pair $(G^1, G^2)$, graph edit distance (GED) is defined as the minimum number of edit operations converting $G^1$ to $G^2$. GED is a fundamental operation widely used in many applications, but its exact computation is NP-hard,…
Recently, the Gromov-Wasserstein Optimal Transport (GWOT) problem has attracted the special attention of the ML community. In this problem, given two distributions supported on two (possibly different) spaces, one has to find the most…
We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…
Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels,…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
Semantic correspondence is essential for handling diverse in-the-wild images lacking explicit correspondence annotations. While recent 2D foundation models offer powerful features, adapting them for unsupervised learning via…
A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity constraint, it is inherently sensitive to rotations. Conversely,…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
The challenge of describing model drift is an open question in unsupervised learning. It can be difficult to evaluate at what point an unsupervised model has deviated beyond what would be expected from a different sample from the same…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
When a large collection of objects (e.g., robots, sensors, etc.) has to be deployed in a given environment, it is often required to plan a coordinated motion of the objects from their initial position to a final configuration enjoying some…
An algorithm for approximating the p-Wasserstein distance between histograms defined on unstructured discrete grids is presented. It is based on the computation of a barycenter constrained to be supported on a low dimensional subspace,…