相关论文: Graph Induced Complex on Point Data

Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…

Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

Computation of the simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The study considers sampling critical points of a Morse function associated to a point cloud,…

Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…

In this document, we propose a bridge between the graphs and the geometric realizations of their Vietoris Rips complexes, i.e. Graphs, with their canonical \v{C}ech closure structure, have the same homotopy type that the realization of…

As an efficient and scalable graph neural network, GraphSAGE has enabled an inductive capability for inferring unseen nodes or graphs by aggregating subsampled local neighborhoods and by learning in a mini-batch gradient descent fashion.…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…

Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

Graph-based representations of point-cloud data are widely used in data science and machine learning, including epsilon-graphs that contain edges between pairs of data points that are nearer than epsilon and kNN-graphs that connect each…

There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…

The immediate snapshot complexes were introduced as combinatorial models for the protocol complexes in the context of theoretical distributed computing. In the previous work we have developed a formal language of witness structures in order…

For studying intrusion detection data we consider data points referring to individual IP addresses and their connections: We build networks associated with those data points, such that vertices in a graph are associated via the respective…

Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…

We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips complexes. We also…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

Inspired by the generation power of generative adversarial networks (GANs) in image domains, we introduce a novel hierarchical architecture for learning characteristic topological features from a single arbitrary input graph via GANs. The…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…