Related papers: Gromov-Wasserstein at Scale, Beyond Squared Norms
Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions,…
Graph data augmentation has shown superiority in enhancing generalizability and robustness of GNNs in graph-level classifications. However, existing methods primarily focus on the augmentation in the graph signal space and the graph…
Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to…
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a…
Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing…
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
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…
Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the…
Learning disentangled representations from unlabelled data is a fundamental challenge in machine learning. Solving it may unlock other problems, such as generalization, interpretability, or fairness. Although remarkably challenging to solve…
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
In this paper, we newly formulate and solve the optimal density control problem with Gromov-Wasserstein (GW) terminal cost in discrete-time linear Gaussian systems. Differently from the Wasserstein or Kullback-Leibler distances employed in…
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…
The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…
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…
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…
We present a versatile adaptation of existing dimensionality reduction (DR) objectives, enabling the simultaneous reduction of both sample and feature sizes. Correspondances between input and embedding samples are computed through a…
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…
This paper considers the problem of estimating a matrix that encodes pairwise distances in a finite metric space (or, more generally, the edge weight matrix of a network) under the barycentric coding model (BCM) with respect to the…