Proposes LSGP for better graph signal representation.
problem Local variations in graph process characteristics.
method Locally stationary graph process (LSGP) model.
result LSGP provides accurate signal representations.
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48 results for “Graph signal processing”
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
Paper reviews multi-way graph signal processing for tensor data.
problem Maximizing use of multi-way structure in irregular tensor data.
method Generalizes GSP to multi-way data, focusing on graph signals across tensor modes.
result Synthesizes common themes in combining GSP with tensor analysis.
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
Graph signal processing improves machine learning for network data.
problem Handling structured data on graphs in machine learning.
method Graph filters and transforms for efficient data processing.
result Enhanced model interpretability and improved efficiency.
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.
New method for testing directed graphs using surrogate data.
problem No established method for statistical testing on directed graphs.
method Define directed graph wide-sense stationary signals, generate surrogates preserving covariance, construct null distributions.
result Feasibility and superiority of new approach over existing methods.
Localized signal representation on graph bundles using Fourier analysis.
problem Representing signals on graph bundles with twists.
method Partition of unity and product factorization over the base graph.
result Lifted bases for signal spaces of graph bundle components.
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.
Modern data introduces new challenges to classic signal processing approaches, leading to a growing interest in the field of graph signal processing. A powerful and well established model for real world signals in various domains is sparse representation over a dictionary, combined with the ability to train the diction…
In this article, we improve extreme learning machines for regression tasks using a graph signal processing based regularization. We assume that the target signal for prediction or regression is a graph signal. With this assumption, we use the regularization to enforce that the output of an extreme learning machine is s…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide …
Graph Signal Processing improves stock market volatility forecasting.
problem Forecasting realized volatility in a global stock market context.
method Integrating Graph Signal Processing into the HAR model.
result The proposed model outperforms HAR-type benchmarks.
Convolutional Neural Networks are very efficient at processing signals defined on a discrete Euclidean space (such as images). However, as they can not be used on signals defined on an arbitrary graph, other models have emerged, aiming to extend its properties. We propose to review some of the major deep learning model…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, tr…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …
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.
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, fo…
Paper introduces signal processing on cell complexes.
problem Processing signals on non-Euclidean domains.
method Signal processing on abstract regular cell complexes.
result Hodge Laplacians for cell complexes enable convolutional filters.
Revises GNN neighborhood aggregation for more accurate node classification.
problem Flaws in benchmark GNN models for node classification.
method Statistical signal processing approach to neighborhood aggregation.
result Novel insights for designing more efficient GNN models.
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…
A method for predicting signals on graphs using Gaussian processes and optimal transport.
problem Predicting signals on complex, graph-based inputs with uncertainty quantification.
method Combining regularized optimal transport, dimension reduction, and Gaussian processes indexed by graphs.
result Efficient prediction of signals on graphs with confidence intervals.
Graph signal processing detects hallucinations in large language models.
problem Detecting factual reasoning from hallucinations in large language models.
method Modeling transformer layers as dynamic graphs, using spectral analysis to define diagnostics.
result Spectral signatures can distinguish different types of hallucinations and achieve high accuracy.
Proposes a novel graph signal model using narrowband kernels.
problem Graph signals with multiple concentrated frequency regions.
method Jointly learns graph signal model parameters and coefficients.
result Joint learning improves signal interpolation accuracy.
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.
Researchers create benchmarks to compare graph inference methods.
problem Comparing graph inference methods is difficult due to varying downstream tasks.
method Developed benchmarks for various graph tasks.
result Contrasted prominent graph inference techniques.
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus desirable to infer or learn a graph topology from the data. In this …
Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.
problem Processing complex data structures with polyadic relationships.
method Introduction to simplicial complexes and hypergraphs, Fourier analysis, signal denoising, interpolation, embeddings, neural networks.
result Multi-relational operators like the Hodge Laplacian for simplicial complexes and tensor representations for hypergraphs.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode…
Data-driven methods link graphon limits to random walks and spectral clustering.
problem Clustering signals evolving over time with graphon limits.
method Transfer operators, Koopman and Perron-Frobenius, for estimating graphon from signal data.
result Spectral clustering can be extended to graphons, reconstructing transition densities and graphons.
Paper develops an online EM algorithm for graph signal inference from streaming data.
problem Joint inference and clustering of graph signals with non-white excitation.
method Mixture model with low-rank plus sparse prior, online EM algorithm.
result Proposed online EM algorithm converges to MAP solution.
New method for identifying graph shift operators using vertex-time autoregressive models.
problem Identifying graph shift operators from graph signals.
method Online optimization using vertex-time autoregressive model and stochastic gradient projection.
result Successful recovery of graph shift operators from graph signals.
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
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.
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,…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a sampling set non-trivial and hard to analyze. Indeed, though conditions for graph …
Proposes a novel graph learning framework for robust graph topology learning from graph signals.
problem Graph learning for revealing node relationships in data entities.
method Functional learning with smoothness-promoting graph learning, incorporating Kronecker product kernel.
result Improves robustness against missing and incomplete information in graph signals.
New method interprets ranked data on permutahedron graph.
problem Interpreting and exploiting structure in ranked data sets.
method Combining combinatorial representation theory and signal processing on graphs.
result Developed scalable transform method using Parseval frames.
The paper detects changes in graph signal means offline.
problem Segmenting and detecting changes in multivariate signals over graph nodes.
method Model selection approach exploiting sparsity in spectral domain.
result Proof of non-asymptotic oracle inequality for change-point detection.
New method denoises graph signals using wavelets, scalable for large graphs.
problem Denoising graph signals with overcomplete tight frames and correlated noise.
method Data-driven wavelet tight frame, Stein's unbiased risk estimate, Chebyshev-Jackson polynomial approximations, Monte-Carlo strategy.
result Method scales to large graphs and finds applications in differential privacy.
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, …
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.
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …
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.
Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillationeess.SP
AdaCGP learns dynamic graph topology from time series data, improving over existing methods.
problem Learning dynamic graph topology from time-varying signals, especially in real-time applications.
method AdaCGP is a sparsity-aware adaptive algorithm that recursively estimates the Graph Shift Operator (GSO) through variable splitting.
result AdaCGP outperforms state-of-the-art methods in GSO estimation, achieving improvements exceeding 83%.
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have been successful for many learning tasks, they do not consider time-evolving sig…