Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
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48 results for “graph spectral learning”
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
problem Predicting signals on graph nodes with various structures.
method Spectral kernel learning approach that incorporates a polynomial function in the graph spectral domain.
result The model accurately recovers ground truth spectral filters and outperforms in real-world graph data.
Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time, we present a highly-scalable spectral approach (GRASPEL) for learning large…
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.
problem Understanding when graph convolutional networks fail compared to spectral embedding.
method Presented a simple generative model to illustrate failure.
result Graph convolutional networks fail to use eigenvectors beyond the first in certain graphs.
SpGAT learns graph representations using spectral attention for efficiency.
problem Efficiently capturing global graph patterns with minimal parameters.
method Introduces Spectral Graph Attention Network (SpGAT) using spectral domain attention mechanisms and a fast Chebychev approximation.
result SpGAT achieves better global pattern recognition with fewer parameters compared to GAT.
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
IGT learns graph representations without supervision.
problem Building deep unsupervised graph representations.
method Generic complex-valued spectral graph architecture from Fourier transform generalization, greedy concave objective for discriminative and invariant features.
result IGT learns both discriminative and invariant features from graph topology.
New equivariant filters improve graph classification.
problem Designing deep learning models for graph symmetries.
method Nonlinear spectral filters (NLSFs) that are equivariant to graph functional shifts.
result NLSFs outperform existing spectral GNNs in graph classification.
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
This study bridges the gap between spatial and spectral GNNs.
problem Lack of direct comparison and cross-reference of existing GNNs.
method Systematically categorizes and examines GNNs into spatial and spectral domains.
result Establishes a strong relationship between spatial and spectral GNNs.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
problem Learning invariant graph representations from eigenvectors.
method SignNet and BasisNet neural architectures that are invariant to sign flips and basis symmetries.
result Proven to be universal, approximating any continuous function of eigenvectors with desired invariances.
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a -dimensional compact submanifold in , we establish the spectral convergence rate…
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
problem Lack of suitable Laplacian for directed graphs in spectral graph theory.
method Inspired by Haar-like transformation, introduces a Hermitian matrix preserving direction and weight.
result HaarNet outperforms in weight prediction and denoising on directed graphs.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.
Multi-centrality Graph Spectral Decompositions and their Application to Cyber Intrusion Detectioncs.SI
Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address thi…
Spectro-Riemannian Graph Neural Networks integrate spectral and curvature signals for better graph representation learning.
problem Enhance graph representation learning by leveraging spectral and curvature signals.
method Proposes Spectro-Riemannian Graph Neural Networks (CUSP) that combines spectral and curvature insights.
result Empirical evaluation shows CUSP outperforms state-of-the-art models by up to 5.3%.
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density.…
Spectral sparsification improves Laplacian-constrained graph learning.
problem Improving accuracy of Laplacian-constrained graph learning.
method Spectral graph sparsification as a post-estimation operation.
result Improved accuracy of Laplacian-constrained graph learning.
New model learns graph spectra accurately, outperforming existing methods.
problem Graph diffusion models struggle to distinguish certain graph families and their spectra.
method Leveraged random matrix theory to analytically extract spectral properties, introducing Dyson Diffusion Model.
result Dyson Diffusion Model learns graph spectra accurately and outperforms existing models.
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for graph sparsification. This choice is motivated by the observation…
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
Enhances graph neural networks with spectral and topological information.
problem Improving graph neural networks' expressivity beyond Weisfeiler-Leman hierarchy.
method Integrates spectral information into Persistent Homology diagrams.
result SpectRe is strictly more expressive than PH and spectral information alone.
Graph Laplacians and machine learning predict properties of finite graphs.
problem Understanding properties of finite graphs using spectral and topological methods.
method Combining graph Laplacians, spectral inequalities, machine learning, and topological data analysis.
result Neural networks can accurately predict graph properties like Ricci-flatness and spectral gaps.
The paper bridges spectral and spatial graph convolutions, improving model capacity and transferability.
problem Improving graph neural networks by bridging spectral and spatial design.
method Theoretical demonstration and general framework for spectral analysis, new spectral convolutions, and depthwise separable convolutions.
result General framework allows spectral analysis of ConvGNNs, showing their performance and limits, and proposing new spectral convolutions.
Developed a framework for designing filters in spectral GCNNs with improved performance.
problem Designing effective filters for spectral GCNNs with regularization properties.
method Exploring regularization properties of graph Laplacian and proposing a generalized framework for filter design.
result New filters derived from the framework outperform state-of-the-art techniques in semi-supervised node classification.
SPARC tackles cold-start nodes in graphs by using spectral embeddings.
problem Cold-start nodes in graphs lacking initial connections.
method Introduces SPARC, a framework utilizing spectral embeddings to predict on cold-start nodes.
result SPARC outperforms existing models on cold-start nodes across tasks.
FoSR adds edges to graphs to prevent oversquashing and oversmoothing in GNNs.
problem Oversquashing and oversmoothing in graph neural networks (GNNs).
method First-order spectral rewiring to add edges based on spectral expansion, combined with a relational architecture.
result Our algorithm outperforms existing graph rewiring methods in graph classification tasks.
PatchGT uses non-trainable graph patches to improve graph representation learning.
problem Learning high-level information in graph tasks with direct Transformer models.
method PatchGT segments graphs into non-trainable patches, uses GNN for patch-level learning, and Transformer for graph-level learning.
result PatchGT achieves higher expressiveness and competitive performance on benchmark datasets.
A panoply of multi-view clustering algorithms has been developed to deal with prevalent multi-view data. Among them, spectral clustering-based methods have drawn much attention and demonstrated promising results recently. Despite progress, there are still two fundamental questions that stay unanswered to date. First, h…
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
Galerkin method outperforms graph-based methods in spectral decompositions.
problem Improving spectral decomposition methods in machine learning.
method Restricting study to a small set of test functions using the Galerkin method.
result Statistical and computational superiority of Galerkin method over graph-based approaches.
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for …
LASE learns graph embeddings by unrolling GD iterations into a neural network.
problem Learning graph embeddings from graph inputs.
method Truncating and interpreting GD iterations as layers in a GNN.
result LASE outperforms eigendecomposition routines and GNNs in link prediction and node classification.
Paper introduces a new metric to select optimal Graph Shift Operator for GNNs.
problem Empirical selection of Graph Shift Operator remains challenging.
method Introduces a novel alignment gain metric connecting geometric distortion to generalization bounds via spectral proxy.
result Provides a principled, computation-efficient criterion to rank and select optimal GSO.
A novel graph spectral method for mixed categorical and numerical data.
problem Feature learning for mixed data types (numerical and categorical).
method Graph spectral decomposition of the graph Laplacian to model probabilistic dependence structure.
result Increased separability and clusterability of observations in the transformed feature space.
Paper proposes JDR to denoise graph features and rewire graphs for better node classification.
problem Jointly denoise noisy graph features and rewire graphs for improved node classification.
method Align leading spectral spaces of graph and feature matrices to solve non-convex optimization problem.
result JDR consistently outperforms existing methods on various node classification tasks.
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…
Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, -graphs and -NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…
COPT optimizes graph distances via simultaneous optimal transport.
problem Learning graph representations unsupervisedly.
method Simultaneous optimization of dual transport plans between vertices and graph signals.
result COPT preserves spectral information and outperforms state-of-the-art methods.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
This paper refines understanding of decentralized learning by considering graph topology.
problem Current theory fails to predict performance in decentralized learning settings.
method Quantifies how graph topology influences convergence in decentralized learning.
result Graph topology significantly impacts convergence in decentralized learning, contrary to spectral gap theory.
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
problem Challenges in clustering large attributed graphs due to high computational and memory costs.
method SASE combines node features smoothing, scalable spectral clustering, and adaptive order selection.
result SASE achieves a 6.9% improvement in ACC and a 5.87x speedup on the ArXiv dataset.
This paper explains GNNs using graph signal denoising.
problem Understanding how GNNs work for node representation learning.
method Spectral graph convolutional networks and graph attention networks are analyzed from the perspective of graph signal denoising.
result GNNs implicitly solve graph signal denoising problems.
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-bas…