Related papers: COPT: Coordinated Optimal Transport for Graph Sket…
Multi-object tracking (MOT) and trajectory prediction are two critical components in modern 3D perception systems that require accurate modeling of multi-agent interaction. We hypothesize that it is beneficial to unify both tasks under one…
This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and…
Comprehensive understanding of dynamic scenes is a critical prerequisite for intelligent robots to autonomously operate in their environment. Research in this domain, which encompasses diverse perception problems, has primarily been focused…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…
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…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
In this paper, we introduce a new model for sublinear algorithms called \emph{dynamic sketching}. In this model, the underlying data is partitioned into a large \emph{static} part and a small \emph{dynamic} part and the goal is to compute a…
We propose and study a method called FLOT that estimates scene flow on point clouds. We start the design of FLOT by noticing that scene flow estimation on point clouds reduces to estimating a permutation matrix in a perfect world. Inspired…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
Many graph problems can be solved using ordered parallel graph algorithms that achieve significant speedup over their unordered counterparts by reducing redundant work. This paper introduces a new priority-based extension to GraphIt, a…
Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a…