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Automatic Robotic Assembly Sequence Planning (RASP) can significantly improve productivity and resilience in modern manufacturing along with the growing need for greater product customization. One of the main challenges in realizing such…
Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately,…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Generating scene graph to describe all the relations inside an image gains increasing interests these years. However, most of the previous methods use complicated structures with slow inference speed or rely on the external data, which…
Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…
Given the input graph and its label/property, several key problems of graph learning, such as finding interpretable subgraphs, graph denoising and graph compression, can be attributed to the fundamental problem of recognizing a subgraph of…
In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph…
Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically…
This paper is concerned with long-time interest of us, especially, the author, in realizing graphs as Reeb graphs of real algebraic functions of certain nice classes. The Reeb graph of a differentiable function is the set consisting of all…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…
Accurate High-Definition (HD) map construction is critical for autonomous driving, yet existing methods face a fundamental trade-off: vectorization-based approaches preserve topology but struggle with geometric fidelity, while…
The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…
Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has…
Recently there has been a significant effort to automate UV mapping, the process of mapping 3D-dimensional surfaces to the UV space while minimizing distortion and seam length. Although state-of-the-art methods, Autocuts and OptCuts,…
Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…