Related papers: A Wasserstein Graph Distance Based on Distribution…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
Given a determinate (multivariate) probability measure $\mu$, we characterize Gaussian mixtures $\nu\_\phi$ which minimize the Wasserstein distance $W\_2(\mu,\nu\_\phi)$ to $\mu$ when the mixing probability measure $\phi$ on the parameters…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
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…
Computing efficiently a robust measure of similarity or dissimilarity between graphs is a major challenge in Pattern Recognition. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in…
Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
In this paper we deal with the analysis of the solutions of traffic flow models at multiple scales, both in the case of a single road and of road networks. We are especially interested in measuring the distance between traffic states (as…
In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph…
Graphs are often used to organize data because of their simple topological structure, and therefore play a key role in machine learning. And it turns out that the low-dimensional embedded representation obtained by graph representation…
Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
Disentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight…
An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…