相关论文: Convergence of Graph Laplacian with kNN Self-tuned…

In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions…

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…

The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…

Given i.i.d.\ samples $X_n =\{ x_1, \dots, x_n \}$ from a distribution supported on a low dimensional manifold ${M}$ embedded in Eucliden space, we consider the graph Laplacian operator $\Delta_n$ associated to an $\varepsilon$-proximity…

Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test. We adapt Manifold-Constrained Hyper-Connections (\mhc)~\citep{xie2025mhc}, recently proposed for…

We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or $\delta$-type), which show how various types of changes of a local or…

Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised…

We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced…

Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of…

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…

Tracking of moving objects is crucial to security systems and networks. Given a graph $G$, terminal vertices $s$ and $t$, and an integer $k$, the \textsc{Tracking Paths} problem asks whether there exists at most $k$ vertices, which if…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

In graph motivated learning, label propagation largely depends on data affinity represented as edges between connected data points. The affinity assignment implicitly assumes even distribution of data on the manifold. This assumption may…

Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with…

We consider the reconstruction of the vertex weight in the discrete Gel'fand's inverse boundary spectral problem for the graph Laplacian. Given the boundary vertex weight and the edge weight of the graph, we develop reconstruction…

In this paper, we propose a new homological method to study weighted directed networks. Our model of such networks is a directed graph $Q$ equipped with a weight function $w$ on the set $Q_{1}$ of arrows in $Q$. We require that the range…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…

While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…

Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…