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.
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.
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 consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
The paper infers graph structure from sparse signal observations.
problem Inferring graph structure from sparse signal observations.
method Formulates a non-convex graph learning problem and solves it via alternating signal sparse coding and graph update steps.
result The method generally outperforms other network inference algorithms in graph recovery.
Improved extreme learning machines for graph signal regression.
problem Regression tasks with graph signals and limited/noisy data.
method Graph signal processing regularization for smoothness.
result Regularization improves prediction accuracy with limited data.
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…
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 new dictionary learning method for high-dimensional graph signals.
problem Challenges of traditional sparse representation methods in high-dimensional graph signals.
method Integrates graph topology implicitly through sparse combinations of graph-wavelet functions and explicitly through graph constraints.
result Demonstrates effectiveness in high-dimensional graph signal processing.
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.
Random walk sampling recovers smooth graph signals from few samples.
problem Efficiently sampling graph signals from large networks.
method Random walk sampling strategy based on network nullspace property.
result Graph signals can be accurately recovered from few samples.
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.
Unified deep learning for graph signals, simplifying existing models.
problem Efficiency of Convolutional Neural Networks on graph signals.
method Unified formalism for existing deep learning models on graph signals.
result Unified formalism simplifies and compares existing models.
Paper develops a method to identify graphs and filters from filtered signals.
problem Learning graphs and filters from filtered signals.
method Developed an algorithm to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations.
result The proposed algorithm outperforms current state-of-the-art methods.
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
Develops multi-kernel regression for graph signal processing.
problem Smoothness of graph signals over a graph.
method Estimates linear weights to learn effective kernel function using graph smoothness.
result Optimization problem is convex and accelerated projected gradient descent solution proposed.
Paper analyzes bias-variance tradeoff in graph Laplacian regularization.
problem Understanding the optimal regularization parameter for graph Laplacian.
method Spectral graph properties and signal-to-noise ratio parameter used to determine optimal regularization.
result Selecting mediocre regularization is often suboptimal, suggesting near-optimal performance.
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 graph Fourier transform distinguishes directions in multi-dimensional signals.
problem Existing graph Fourier transform fails to distinguish directions in multi-dimensional signals.
method Algebraic properties of Cartesian products rearrange 1-D spectra into multi-dimensional frequency domain.
result Solves multi-valuedness of spectra and enables directional frequency analysis.
Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …
A new graph generation model uses Mallat's scattering transform.
problem Unclear mathematical properties and difficulty in training good generative models for graphs.
method Proposes a graph generation model using a Gaussianized graph scattering transform.
result Demonstrates state-of-the-art performance in link prediction and graph/signal generation.
Learn graph structure from data using signal processing methods.
problem Constructing meaningful graph topologies from data.
method Survey of classical and GSP-based graph inference methods.
result Advantages of GSP-based methods in various scenarios.
Recursive prediction of graph signals with new nodes added.
problem Predicting graph signals with new nodes added over time.
method Recursive prediction of graph signals using incoming nodes.
result Recursive method results in good prediction performance close to full graph knowledge.
Detects graph topology changes from noisy signals using prior spectral information.
problem Detecting changes in graph topology from graph signals.
method Leverages graph filtering and subspace detection to distill problem into a CUSUM-based algorithm.
result Demonstrates the effectiveness of incorporating prior spectral signatures for change-point detection.
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,…
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.
Graph signal sampling improved using reinforcement learning.
problem Efficiently sampling and recovering graph signals with clustering.
method Formulated as a multi-armed bandit problem, optimized using gradient ascent.
result Sampling strategies based on gradient MAB outperform existing methods.
Gaussian processes over graphs enforce specific signal profiles and outperform conventional GPs.
problem Signal processing over graphs with specific profiles.
method Graph Laplacian regularization to enforce desired signal profiles, proving predictive variance advantage.
result Gaussian processes over graphs have strictly smaller predictive variance than conventional GPs.
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.
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.
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.
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 …
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 …
The paper proposes a distributed method for adaptive learning of graph signals.
problem Learning signals defined over graphs with limited observations.
method Bandlimited assumption, distributed reconstruction, mean-square error guarantee, tracking from sampled vertices.
result Guaranteed performance in mean-square error with optimal sampling strategy.
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.
Unified framework infers time-varying graphs from incomplete signals.
problem Jointly inferring time-varying network topologies and imputing missing data from partial observations.
method Unified non-convex optimization framework with Proximal Alternating Direction Method of Multipliers (PADMM) algorithm.
result Superior robustness in high missing-data regimes, demonstrated through extensive numerical experiments.
This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on gra…
We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured b…
This work improves sampling of graph signals with universal bounds and greedy methods.
problem Sampling graph signals is hard due to irregularity and noise.
method Derives universal performance bounds and near-optimal guarantees for greedy sampling.
result Explicit bounds on approximate supermodularity show greedy search can be optimized with worst-case guarantees.
The paper introduces a sampling theory for graphons with a Poincaré inequality and proves consistency.
problem Sampling on large graphs is challenging due to their non-Euclidean nature.
method The paper introduces a signal sampling theory for graphons, proving a Poincaré inequality and showing consistency.
result Unique sampling sets for graphon signals are consistent across graph sequences.
The paper infers multiple graphs from stationary signals on them.
problem Inferring multiple graphs from signals observed on their nodes.
method Convex optimization method leveraging matrix polynomial commutation.
result High-probability bounds on recovery error provided.
Two graph neural network architectures improve CNN performance for graph signals.
problem Improving CNN performance for graph signals.
method Introducing two graph neural network architectures: selection GNN and aggregation GNN.
result Multinode aggregation GNNs consistently perform best in source localization and authorship attribution tasks.
Network Lasso improves graph signal learning from few samples.
problem Ensuring network Lasso accuracy for graph signal learning.
method Compressed sensing concepts applied to network Lasso.
result Precise conditions for network Lasso accuracy quantified.
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 sampling method for graph signals using DPPs for perfect recovery on small graphs, and sub-optimal but faster approach for large graphs.
problem Sampling k-bandlimited signals on graphs efficiently.
method Determinantal Point Processes (DPP) for both small and large graphs.
result Preliminary experiments show efficient sampling especially for graphs with strong community structure.
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.
New method for efficient graph signal sampling and reconstruction.
problem Minimizing MSE in graph signal reconstruction with noisy data.
method Formulated as binary constraint minimization, approximated via SDP relaxation and greedy algorithm.
result Randomized greedy algorithm provides near-optimal subset with significant speedup.
Generative model separates mixed signals on multiple graphs.
problem Inference methods often assume all data fits a single graph.
method Heat diffusion process on multiple graphs, EM algorithm.
result Successfully separates signals into corresponding groups.