Related papers: Generalized $\beta$-skeletons
Many physical systems can be best understood as sets of discrete data with associated relationships. Where previously these sets of data have been formulated as series or image data to match the available machine learning architectures,…
We characterize uniform $k$-rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call $\iota$-numbers. The characterization follows from an abstract statement…
Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the…
Gait recognition, a long-distance biometric technology, has aroused intense interest recently. Currently, the two dominant gait recognition works are appearance-based and model-based, which extract features from silhouettes and skeletons,…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
Graph classification aims to extract accurate information from graph-structured data for classification and is becoming more and more important in graph learning community. Although Graph Neural Networks (GNNs) have been successfully…
Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…
Graph Neural Networks (GNNs) are playing an increasingly important role in the efficient operation and security of computing systems, with applications in workload scheduling, anomaly detection, and resource management. However, their…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Let $P$ be a set of $n$ points in the plane. A geometric graph $G$ on $P$ is said to be {\it locally Gabriel} if for every edge $(u,v)$ in $G$, the disk with $u$ and $v$ as diameter does not contain any points of $P$ that are neighbors of…
A spanner is a sparse subgraph of a given graph $G$ which preserves distances, measured w.r.t.\ some distance metric, up to a multiplicative stretch factor. This paper addresses the problem of constructing graph spanners w.r.t.\ the group…
We study the distance on the Bruhat-Tits building of the group $\mathrm{SL}_d(\mathbb{Q}_p)$ (and its other combinatorial properties). Coding its vertices by certain matrix representatives, we introduce a way how to build formulas with…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We give a survey of joint work with Mircea Musta\c{t}\u{a} and Chenyang Xu on the connections between the geometry of Berkovich spaces over the field of Laurent series and the birational geometry of one-parameter degenerations of smooth…
Path geometries provide a geometric encoding of systems of second order ODE, which serves as a model for the geometric theory of more general systems of ODE and for cone structures. They are an instance of the family of parabolic…
Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…
3D skeleton-based action recognition and motion prediction are two essential problems of human activity understanding. In many previous works: 1) they studied two tasks separately, neglecting internal correlations; 2) they did not capture…