Related papers: Global Weisfeiler-Lehman Graph Kernels
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…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
Graph neural networks are designed to learn functions on graphs. Typically, the relevant target functions are invariant with respect to actions by permutations. Therefore the design of some graph neural network architectures has been…
A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
Decomposing a graph into a hierarchical structure via $k$-core analysis is a standard operation in any modern graph-mining toolkit. $k$-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere…
Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
The Weisfeiler-Leman dimension of a graph $G$ is the least number $k$ such that the $k$-dimensional Weisfeiler-Leman algorithm distinguishes $G$ from every other non-isomorphic graph. The dimension is a standard measure of the descriptive…
Stars' chemical signatures provide invaluable insights into stellar cluster formation. This study utilized the Weisfeiler-Lehman (WL) Graph Kernel to examine a 15-dimensional elemental abundance space. Through simulating chemical…
The $k$-dimensional Weisfeiler-Leman procedure ($k$-WL), which colors $k$-tuples of vertices in rounds based on the neighborhood structure in the graph, has proven to be immensely fruitful in the algorithmic study of Graph Isomorphism. More…
In this paper, we propose a novel graph kernel, namely the Quantum-based Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we commence by computing the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk…
Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature…
Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of…
A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel). Not all directed graphs contain kernels, and computing a kernel or deciding…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
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…
Graph kernels are conventional methods for computing graph similarities. However, the existing R-convolution graph kernels cannot resolve both of the two challenges: 1) Comparing graphs at multiple different scales, and 2) Considering the…
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…