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In this paper, we consider the simplest class of stratified spaces -- linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled…

World modeling is a crucial task for enabling intelligent agents to effectively interact with humans and operate in dynamic environments. In this work, we propose MineWorld, a real-time interactive world model on Minecraft, an open-ended…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

Computing shortest paths is a fundamental operation in processing graph data. In many real-world applications, discovering shortest paths between two vertices empowers us to make full use of the underlying structure to understand how…

Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…

This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding…

Graph machine learning has been extensively studied in both academia and industry. However, in the literature, most existing graph machine learning models are designed to conduct training with data samples in a random order, which may…

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…

Existing graph layout algorithms are usually not able to optimize all the aesthetic properties desired in a graph layout. To evaluate how well the desired visual features are reflected in a graph layout, many readability metrics have been…

Kinematics is a core topic in early physics courses, yet students often struggle to interpret motion and its graphical representations. To tackle these difficulties, we developed MissionMotion, a physical-computational videogame where…

Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…

Many modern deep-learning techniques do not work without enormous datasets. At the same time, several fields demand methods working in scarcity of data. This problem is even more complex when the samples have varying structures, as in the…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…

Graph learning has emerged as a promising technique for multi-view clustering with its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency…

We propose a robust and efficient framework to generate global trajectories for ground robots in complex 3D environments. The proposed method takes point cloud as input and efficiently constructs a multi-level map using triangular patches…

Data association across frames is at the core of Multiple Object Tracking (MOT) task. This problem is usually solved by a traditional graph-based optimization or directly learned via deep learning. Despite their popularity, we find some…

Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…

Recent work on Graph Neural Networks has demonstrated that self-supervised pretraining can further enhance performance on downstream graph, link, and node classification tasks. However, the efficacy of pretraining tasks has not been fully…