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…
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48 results for “graph filters”
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions,…
Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more …
A guide to using low-pass graph filters for network data.
problem Understanding and processing graph data with low-pass filters.
method Definition and application of low-pass graph filters to graph data.
result Low-pass filters effectively retain lower frequency graph data contents.
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
problem Handling multi-channel graph signals with limited architectures.
method BankGCN decomposes multi-channel signals into subspaces and uses adapted filters for each subspace.
result BankGCN achieves excellent performance in graph classification on benchmark datasets.
Graph Kalman Filterscs.LG
Graph Kalman filters adapt classical filters to graph data.
problem Adapting classical Kalman filters to graph data.
method Generalizes Kalman filters to attributed graphs, learning state-transition and readout functions end-to-end.
result Adapted Kalman filters can predict graph outputs.
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.
Graph neural networks leverage graph filters to learn from network data.
problem Learning from network data with graph structure.
method Characterize graph neural networks using graph signal processing and graph convolutional filters.
result Graph neural networks have permutation equivariance and stability to topology changes.
Trend Filtering on Graphsstat.ML
We introduce a family of adaptive estimators on graphs, based on penalizing the norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filteri…
Method finds multiple noisy graph templates in large graphs.
problem Finding multiple graph templates in noisy large graphs.
method Iteratively penalizes node-pair similarity matrix in matched filter algorithm.
result Method can sequentially discover multiple templates under mild model conditions.
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter…
Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional…
Identifies directed graphs from node measurements using polynomial filters.
problem Inferring directed network topology from nodal measurements.
method System identification of graph convolutional filter followed by topology inference.
result Effective recovery of directed graphs from measurements.
Proposes a GNN for multivariate time-series prediction with filtering.
problem Low signal-to-noise ratio in complex systems data.
method Integrates a spatial-temporal GNN with a matrix filtering module to generate filtered graphs.
result Proposed model outperforms baseline approaches in multivariate time-series prediction.
Graph-based methods have been demonstrated as one of the most effective approaches for semi-supervised learning, as they can exploit the connectivity patterns between labeled and unlabeled data samples to improve learning performance. However, existing graph-based methods either are limited in their ability to jointly …
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signals…
Filtered conformal ellipsoids for graph-native time series
problem Joint prediction sets for multivariate time series
method Filtered conformal ellipsoids
result Sharper at-target ellipsoids than static-covariance and non-filter baselines
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
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.
In this paper, we consider recommender systems with side information in the form of graphs. Existing collaborative filtering algorithms mainly utilize only immediate neighborhood information and have a hard time taking advantage of deeper neighborhoods beyond 1-2 hops. The main caveat of exploiting deeper graph informa…
AGE improves graph embedding by smoothing features and iteratively enhancing node embeddings.
problem Challenges in attributed graph embedding, especially in preserving optimal low-pass characteristics and robustness.
method AGE, a novel framework combining Laplacian smoothing and adaptive encoding, addresses these issues.
result AGE consistently outperforms state-of-the-art methods on node clustering and link prediction tasks.
GWCA analyzes cross-graph correlations for movie retrieval.
problem Cross heterogeneous graph comparison in movie retrieval.
method Spectral graph filtering, Wasserstein metric learning, generalized eigenvalue decomposition.
result Surprise consistency in learning processes and closed-form solution.
Graph filtering reduces intra-class noise for improved classification accuracy.
problem Noise in training data affects classifier performance.
method Graph filtering to connect similar samples within a class.
result Asymptotic reduction of intra-class variance while maintaining mean.
The paper bounds the complexity of GCNs using Rademacher complexity.
problem Understanding the sample complexity of GCNs.
method Derived tight upper and lower bounds of Rademacher complexity for GCN models.
result The derived bounds depend on the largest eigenvalue of the graph filter and the degree distribution.
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.
Generative model controls heterophily in graph signals.
problem Controlling heterophily in graph signals for better model effectiveness.
method Combines graphon-based generator with spectral filtering of Gaussian node features.
result Establishes theoretical guarantees for heterophily control and convergence.
A new hybrid GNN framework tackles oversmoothing in graph data.
problem Oversmoothing in graph convolutional networks limits their expressive power and generalization.
method Combines traditional GCN filters with band-pass filters defined via geometric scattering and introduces an attention framework.
result Improves expressive power and generalization of graph convolutional networks.
Proposes a new graph trend filtering model for inhomogeneous graph signals.
problem Estimating piecewise smooth signals over a graph with varying smoothness levels.
method Introduces a l2,0 norm penalized Graph Trend Filtering (GTF) model and two solution methods: spectral decomposition and simulated annealing.
result The GTF model performs better than existing approaches in denoising, support recovery, and semi-supervised classification.
New framework models graph signals as distribution-valued signals in Wasserstein space.
problem Limitations of classical vector-based GSP, including synchronous observations and uncertainty.
method Introduces graph distribution-valued signals (GDSs) in the Wasserstein space.
result GDSs naturally encode uncertainty and stochasticity, generalizing traditional graph signals.
We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called feedback-looped filters, to provide better localization on vertices, while still attaining…
RGCF improves collaborative filtering by refining graph convolution embeddings.
problem GCN-based recommendation models introduce noise and redundancy, limiting high-order connectivity capture.
method Developed RGCF, a new GCN-based Collaborative Filtering model with redesigned embeddings.
result RGCF significantly outperforms state-of-the-art models on public datasets.
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%.
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.
New graph convolution captures local features on non-Euclidean grids.
problem Capturing local features on irregular, coarse non-Euclidean grids.
method Low-rank learnable local filters in graph convolutions.
result Proves more expressive than previous spectral graph convolution methods.
RP-GFRFT unifies fractional order and rotation control for graph signals.
problem Lack of rotation-based spectral control in GFRFT and zero-angle degeneracy in AGFT.
method Rotation-parameterized graph fractional Fourier transform (RP-GFRFT) with degeneracy preserving rotation matrix.
result RP-GFRFT improves spectral filtering performance over existing methods.
GNNs improve graph signal discrimination by adding nonlinearities.
problem Improving graph signal discrimination in physical networks.
method Analyzing the discriminability of GNNs and their relation to graph filter banks.
result GNNs are at least as discriminative as linear graph filter banks.
MFCNs use sparse graphs to approximate manifold convergence.
problem Understanding manifold neural networks (MNNs).
method Sparse graph approximation for manifold convergence.
result Method converges to continuum limit as data points increase.
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.
GNNs generalize CNNs for graph data, showing equivariance and stability.
problem Processing signals on graphs.
method Graph convolutional filters, nonlinearities, stacked layers.
result GNNs converge to graphon neural networks under graph convergence.
GCN improved for large graphs with LCF to reduce complexity and noise.
problem Efficiency and effectiveness of graph convolution in large graphs.
method Proposed Low-pass Collaborative Filter (LCF) to simplify graph convolution.
result Significant improvement in effectiveness and efficiency of GCN.
New method constructs graphs from data efficiently, suitable for large datasets.
problem Memory and runtime limitations of traditional TMFG for large datasets.
method Uses k-Nearest Neighbors Graphs and memory management for scalable graph construction.
result Provides a parsimonious way to construct graphs for learning tasks.
Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.
problem Generating graphs with arbitrary sizes and arbitrary structures.
method Induces graphons from observed graphs, uses Chebyshev filters for latent representation, and learns encoder and decoder to minimize Wasserstein distance.
result Graphon autoencoder provides a new paradigm for graph generation with good generalizability and transferability.
Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-s…
This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal and graph Fourier transform (JFT) and demonstrate its attractive properties. We b…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the graph Laplacian matrix to extract its leading eigenvectors, where is the desired number of clusters among objects. This is pro…
This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this m…
Augments GNNs with diversification to preserve node identity.
problem Current GNNs filter node information, potentially losing node identity.
method Integrates diversification operators with aggregation to enrich node representations.
result Significant performance boost on 9 node classification tasks.