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…
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “smooth graph signal”
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.
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.
Estimates smooth graph signals from partial measurements.
problem Estimating latent signals on a graph from limited measurements.
method Smoothness penalized least squares estimator.
result Weak consistency for joint recovery of signals under stringent sampling.
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 …
Paper learns hypergraph structures from signals with smoothness priors.
problem Learning hypergraph structures from signals with high-order relationships.
method Proposes HGSL framework with dual smoothness prior to map signals to hypergraph structure.
result HGSL efficiently infers meaningful hypergraph topologies from 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…
Develops method for learning signed graphs from smooth signals.
problem Learning signed graphs from observed data, especially in contexts with both positive and negative interactions.
method Uses net Laplacian as graph shift operator and minimizes total variation of observed signals with ADMM.
result Theoretical proofs of convergence and estimation error bound provided.
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…
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.
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…
A new method boosts graph neural networks by preventing over-smoothing and over-squashing.
problem Graph Neural Networks struggle with long-range signals and over-smoothing/over-squashing.
method Proposes PowerEmbed, a layer-wise normalization technique inspired by spectral graph embedding.
result PowerEmbed prevents over-smoothing and avoids over-squashing, improving performance on heterophilous graphs.
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery s…
Unified view of GNNs as graph signal denoising.
problem Understanding and improving GNNs for graph data.
method Established GNNs as graph denoising problems with smoothness assumptions.
result Unified framework UGNN for adaptive smoothness graphs.
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.
It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this recovery condition, we propose a sampling strategy for smooth graph signals based on …
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibi…
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…
New analysis improves denoising of modulo signals on graphs.
problem Robustly unwrapping noisy modulo samples of smooth functions.
method Analyzing sphere-relaxation and unconstrained relaxation of a QCQP on a graph.
result Proves denoising of modulo observations w.r.t the norm in Gaussian noise.
We propose a framework that learns the graph structure underlying a set of smooth signals. Given whose rows reside on the vertices of an unknown graph, we learn the edge weights under the smoothness assumption that is small. We show that …
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…
Smoothed fitness landscape improves protein optimization.
problem Infeasibility of combinatorially large protein sequence space.
method Formulate protein fitness as a graph signal, smooth using Tikunov regularization, and optimize with Gibbs sampling.
result 2.5 fold fitness improvement over training set.
Proposes GFMMD for comparing signals on graphs.
problem Computing distances between distributions on graphs.
method Graph Fourier MMD (GFMMD) using optimal witness functions.
result Analytical solution and embedding of distributions.
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an explicit expression of the Wasserstein distance between graph s…
We propose a novel framework for graph mean computation.
problem Defining a mean for graph data is difficult.
method Embeddings in the space of smooth graph signal distributions, using the Wasserstein metric.
result Existence and uniqueness of the graph mean established, and an iterative algorithm provided.
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.
This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph signal, defined over some graph (network) structure intrinsic to the dataset. Follo…
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 analyzes the trade-off between smoothness and sparsity in GCN using lp-regularized learning.
problem Quantifying the trade-off between smoothness and sparsity in GCN.
method Proposes a novel SGD proximal algorithm for GCNs with an inexact operator to analyze the stability of the -regularized stochastic learning.
result Establishes an explicit theoretical understanding of GCN with -regularized stochastic learning.
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.
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel…
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.
SAIL improves graph node representation learning by distilling knowledge between graphs.
problem Improving graph node representation learning with GNNs in unsupervised scenarios.
method SAIL framework with intra- and inter-graph knowledge distillation.
result SAIL consistently outperforms state-of-the-art baselines on various benchmark datasets.
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.
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.
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.
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.
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…
Estimates multiple linear systems on a graph with smoothness constraints.
problem Joint estimation of multiple linear systems under graph smoothness constraints.
method Proposes estimators for joint estimation of system matrices with error bounds.
result MSE converges to zero as increases, typically polynomially fast w.r.t .
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.
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 …
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.
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred f…
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.
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
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.