相关论文: The Multiscale Laplacian Graph Kernel

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…

In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels…

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…

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…

We analyze the spectral clustering procedure for identifying coarse structure in a data set $x_1, \dots, x_n$, and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More…

For semi-supervised learning on graphs, we study how initial kernels in a supervised learning regime can be augmented with additional information from known priors or from unsupervised learning outputs. These augmented kernels are…

Graph Neural Networks (GNNs) have been widely employed for feature representation learning in molecular graphs. Therefore, it is crucial to enhance the expressiveness of feature representation to ensure the effectiveness of GNNs. However, a…

Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…

We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and…

We introduce random-kernel networks, a multilayer extension of random feature models where depth is created by deterministic kernel composition and randomness enters only in the outermost layer. We prove that deeper constructions can…

Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…

The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…

The surface structure of Few-Layer Graphene (FLG) epitaxially grown on the C-face of SiC has been investigated by TM-AFM in ambient air and upon interaction with diluted aqueous solutions of bio-organic molecules (dimethyl sulfoxide, DMSO,…

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…

Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion…

Graphs data is crucial for many applications, and much of it exists in the relations described in textual format. As a result, being able to accurately recall and encode a graph described in earlier text is a basic yet pivotal ability that…

Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs…

An interesting approach to analyzing neural networks that has received renewed attention is to examine the equivalent kernel of the neural network. This is based on the fact that a fully connected feedforward network with one hidden layer,…

Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…