Related papers: IGUG: A MATLAB package for $3$D inversion of gravi…

A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…

Motion retargeting for specific robot from existing motion datasets is one critical step in transferring motion patterns from human behaviors to and across various robots. However, inconsistencies in topological structure, geometrical…

Many machine learning algorithms for tabular data produce black-box models, which prevent users from understanding the rationale behind the model predictions. In their unconstrained form, graph neural networks fall into this category, and…

Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

Subsurface ore detection is of paramount importance given the gradual depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods.…

The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust…

3D point cloud (PC) -- a collection of discrete geometric samples of a physical object's surface -- is typically large in size, which entails expensive subsequent operations like viewpoint image rendering and object recognition. Leveraging…

Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…

Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…

Data imputation addresses the challenge of imputing missing values in database instances, ensuring consistency with the overall semantics of the dataset. Although several heuristics which rely on statistical methods, and ad-hoc rules have…

We consider the exact continuous relaxation model of matrix rank minimization problem proposed by Yu and Zhang (Comput.Optim.Appl. 1-20, 2022). Motivated by the inertial techinique, we propose a general inertial smoothing proximal gradient…

Incomplete data are common in real-world applications. Sensors fail, records are inconsistent, and datasets collected from different sources often differ in scale, sampling rate, and quality. These differences create missing values that…

The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined…

3D Gaussian Splatting (3DGS) has emerged as a key rendering pipeline for digital asset creation due to its balance between efficiency and visual quality. To address the issues of unstable pose estimation and scene representation distortion…

Many scientific and engineering processes produce spatially unstructured data. However, most data-driven models require a feature matrix that enforces both a set number and order of features for each sample. They thus cannot be easily…

In this paper, we propose a graph neural network to detect objects from a LiDAR point cloud. Towards this end, we encode the point cloud efficiently in a fixed radius near-neighbors graph. We design a graph neural network, named Point-GNN,…

Gravity inversion is the problem of estimating subsurface density distributions from observed gravitational field data. We consider the two-dimensional (2D) case, in which recovering density models from one-dimensional (1D) measurements…

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee…

This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…