相关论文: The Multiscale Laplacian Graph Kernel

This work proposes a framework LGKDE that learns kernel density estimation for graphs. The key challenge in graph density estimation lies in effectively capturing both structural patterns and semantic variations while maintaining…

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…

We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…

Large Language Models (LLMs) often suffer from hallucinations, which Retrieval-Augmented Generation (RAG) and GraphRAG mitigate by incorporating external knowledge and knowledge graphs (KGs). However, GraphRAG remains text-centric due to…

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any…

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.

We propose a hierarchical normalizing flow model for generating molecular graphs. The model produces new molecular structures from a single-node graph by recursively splitting every node into two. All operations are invertible and can be…

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…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

Graph representation learning has now become the de facto standard when handling graph-structured data, with the framework of message-passing graph neural networks (MPNN) being the most prevailing algorithmic tool. Despite its popularity,…

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of…

We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…

Recently, graph convolutional network (GCN) has been widely used for semi-supervised classification and deep feature representation on graph-structured data. However, existing GCN generally fails to consider the local invariance constraint…

Graph signal processing (GSP) has become an important tool in image processing because of its ability to reveal underlying data structures. Many real-life multimedia datasets, however, exhibit heterogeneous structures across frames.…

We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Recent work on graph generative models has made remarkable progress towards generating increasingly realistic graphs, as measured by global graph features such as degree distribution, density, and clustering coefficients. Deep generative…

Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…

Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good…