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Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
At present, there are a large number of quantum neural network models to deal with Euclidean spatial data, while little research have been conducted on non-Euclidean spatial data. In this paper, we propose a novel quantum graph…
Identifying an appropriate underlying graph kernel that reflects pairwise similarities is critical in many recent graph spectral signal restoration schemes, including image denoising, dequantization, and contrast enhancement. Existing graph…
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…
We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to…
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…
This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant…
We propose a novel pool-based Active Learning framework constructed on a sequential Graph Convolution Network (GCN). Each image's feature from a pool of data represents a node in the graph and the edges encode their similarities. With a…
Existing graph contrastive learning methods rely on augmentation techniques based on random perturbations (e.g., randomly adding or dropping edges and nodes). Nevertheless, altering certain edges or nodes can unexpectedly change the graph…
Generative modeling of 3D shapes has become an important problem due to its relevance to many applications across Computer Vision, Graphics, and VR. In this paper we build upon recently introduced 3D mesh-convolutional Variational…
Contrastive learning has recently attracted plenty of attention in deep graph clustering for its promising performance. However, complicated data augmentations and time-consuming graph convolutional operation undermine the efficiency of…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…