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This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Distributed training of graph neural networks (GNNs) has become a crucial technique for processing large graphs. Prevalent GNN frameworks are model-centric, necessitating the transfer of massive graph vertex features to GNN models, which…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
Several techniques for visualization of dynamic graphs are based on different spatial arrangements of a temporal sequence of node-link diagrams. Many studies in the literature have investigated the importance of maintaining the user's…
In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or…
Denoising diffusion models have been a mainstream approach for image generation, however, training these models often suffers from slow convergence. In this paper, we discovered that the slow convergence is partly due to conflicting…
Computing a graph prototype may constitute a core element for clustering or classification tasks. However, its computation is an NP-Hard problem, even for simple classes of graphs. In this paper, we propose an efficient approach based on…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…
Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing…
We introduce a force-directed algorithm, called Sync-and-Burst, which falls into the category of classical force-directed graph drawing algorithms. A distinct feature in Sync-and-Burst is the use of simplified forces of attraction and…