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Topological Signal Processing and Learning: Recent Advances and Future Challenges

https://doi.org/10.2139/ssrn.5043391
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Sparse Bayesian vector autoregressions in huge dimensions
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Discrete Calculus: Applied Analysis on Graphs for Computational Science
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Coidentification of Group-Level Hole Structures in Brain Networks via Hodge Laplacian
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Modelling Cycles in Brain Networks with the Hodge Laplacian
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Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data
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Convolving Directed Graph Edges via Hodge Laplacian for Brain Network Analysis
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Multi-order Simplex-Based Graph Neural Network for Brain Network Analysis
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New Introduction to Multiple Time Series Analysis
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Computational Topology: An Introduction
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Optimal surface smoothing as filter design
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Statistical ranking and combinatorial Hodge theory
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Estimating the state of epidemics spreading with graph neural networks
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Topological Data Analysis
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Multiscale Hodge scattering networks for data analysis
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Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise
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A compact review of molecular property prediction with graph neural networks
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Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!
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Binarized Simplicial Convolutional Neural Networks
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Signal processing on higher-order networks: Livin’ on the edge... and beyond
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Towards transferable metamodels for water distribution systems with edge-based graph neural networks
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Hypergraphs - Combinatorics of Finite Sets
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Modelling and analysis of gene regulatory networks
inferredcites →https://doi.org/10.1038/s41467-019-10431-6openalex-snapshot
Simplicial models of social contagion
inferredcites →https://doi.org/10.1038/s41467-022-30706-9openalex-snapshot
Full reconstruction of simplicial complexes from binary contagion and Ising data
inferredcites →https://doi.org/10.1038/s41467-023-37190-9openalex-snapshot
Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
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Reconstructing higher-order interactions in coupled dynamical systems
inferredcites →https://doi.org/10.1038/s41524-021-00493-wopenalex-snapshot
Topological representations of crystalline compounds for the machine-learning prediction of materials properties
inferredcites →https://doi.org/10.1038/s41567-019-0459-yopenalex-snapshot
From networks to optimal higher-order models of complex systems
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The physics of higher-order interactions in complex systems
inferredcites →https://doi.org/10.1038/s41598-022-12877-zopenalex-snapshot
Hodge theory-based biomolecular data analysis
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Higher-order non-Markovian social contagions in simplicial complexes
inferredcites →https://doi.org/10.1088/1367-2630/acf33copenalex-snapshot
Dirac signal processing of higher-order topological signals
inferredcites →https://doi.org/10.1088/2632-072x/ad353bopenalex-snapshot
Higher-order connection Laplacians for directed simplicial complexes
inferredcites →https://doi.org/10.1088/2632-2153/adf375openalex-snapshot
Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures
inferredcites →https://doi.org/10.1090/s0273-0979-07-01191-3openalex-snapshot
Barcodes: The persistent topology of data
inferredcites →https://doi.org/10.1093/biostatistics/kxm045openalex-snapshot
Sparse inverse covariance estimation with the graphical lasso
inferredcites →https://doi.org/10.1093/oso/9780198522195.001.0001openalex-snapshot
Graphical Models
inferredcites →https://doi.org/10.1098/rsif.2022.0043openalex-snapshot
Dynamics on higher-order networks: a review
inferredcites →https://doi.org/10.1103/physreve.104.064303openalex-snapshot
Spectral detection of simplicial communities via Hodge Laplacians
inferredcites →https://doi.org/10.1103/physreve.106.034319openalex-snapshot
Weighted simplicial complexes and their representation power of higher-order network data and topology
inferredcites →https://doi.org/10.1103/revmodphys.87.925openalex-snapshot
Epidemic processes in complex networks
inferredcites →https://doi.org/10.1109/79.91217openalex-snapshot
Wavelets and signal processing
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Online Non-linear Topology Identification from Graph-connected Time Series
inferredcites →https://doi.org/10.1109/eucnc/6gsummit60053.2024.10597087openalex-snapshot
Goal-Oriented and Semantic Communication in 6G AI-Native Networks: The 6G-GOALS Approach
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On the degrees of freedom of signals on graphs
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ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing
inferredcites →https://doi.org/10.1109/icassp.2016.7472914openalex-snapshot
An introduction to hypergraph signal processing
inferredcites →https://doi.org/10.1109/icassp43922.2022.9747233openalex-snapshot
Signal Processing On Cell Complexes
inferredcites →https://doi.org/10.1109/icassp48485.2024.10445983openalex-snapshot
Sampling and Recovery of Signals Over Product Cell Structures
inferredcites →https://doi.org/10.1109/icassp48485.2024.10446051openalex-snapshot
Disentangling the Spectral Properties of the Hodge Laplacian: not all small Eigenvalues are Equal
inferredcites →https://doi.org/10.1109/icassp48485.2024.10447519openalex-snapshot
SC-MAD: Mixtures of Higher-Order Networks for Data Augmentation
inferredcites →https://doi.org/10.1109/icassp48485.2024.10448180openalex-snapshot
Evolution Backcasting of Edge Flows From Partial Observations Using Simplicial Vector Autoregressive Models
inferredcites →https://doi.org/10.1109/icassp49357.2023.10094927openalex-snapshot
Topological Signal Processing Over Weighted Simplicial Complexes
inferredcites →https://doi.org/10.1109/icassp49357.2023.10095803openalex-snapshot
Topological Slepians: Maximally Localized Representations of Signals Over Simplicial Complexes
inferredcites →https://doi.org/10.1109/icassp49357.2023.10096866openalex-snapshot
Pooling Strategies for Simplicial Convolutional Networks
inferredcites →https://doi.org/10.1109/icassp49660.2025.10890264openalex-snapshot
Higher-Order Topological Directionality and Directed Simplicial Neural Networks
inferredcites →https://doi.org/10.1109/icmla.2019.00205openalex-snapshot
Bayesian Topological Learning for Brain State Classification
inferredcites →https://doi.org/10.1109/ieeeconf53345.2021.9723256openalex-snapshot
Topological Signal Processing over Cell Complexes
inferredcites →https://doi.org/10.1109/ieeeconf56349.2022.10051892openalex-snapshot
Simplicial Trend Filtering (Invited Paper)
inferredcites →https://doi.org/10.1109/ieeeconf59524.2023.10476944openalex-snapshot
Gaussian Processes for Edge Flow Prediction with Active Learning
inferredcites →https://doi.org/10.1109/ieeeconf59524.2023.10477035openalex-snapshot
Probabilistic Topological Models over Simplicial Complexes
inferredcites →https://doi.org/10.1109/isbi56570.2024.10635590openalex-snapshot
Hodge-Decomposition of Brain Networks
inferredcites →https://doi.org/10.1109/jiot.2019.2950213openalex-snapshot
Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications
inferredcites →https://doi.org/10.1109/jstsp.2017.2730040openalex-snapshot
Graph Filters and the Z-Laplacian
inferredcites →https://doi.org/10.1109/lsp.2024.3475915openalex-snapshot
Recovery of Signals on a Simplicial Complex From Subsampled Neighborhood Aggregations
inferredcites →https://doi.org/10.1109/mcom.005.2200829openalex-snapshot
Semantic Communications Based on Adaptive Generative Models and Information Bottleneck
inferredcites →https://doi.org/10.1109/mlsp52302.2021.9596512openalex-snapshot
Random Feature Approximation for Online Nonlinear Graph Topology Identification
inferredcites →https://doi.org/10.1109/msp.2010.939537openalex-snapshot
Dictionary Learning
inferredcites →https://doi.org/10.1109/msp.2012.2233865openalex-snapshot
Machine Learning with Brain Graphs: Predictive Modeling Approaches for Functional Imaging in Systems Neuroscience
inferredcites →https://doi.org/10.1109/msp.2012.2235192openalex-snapshot
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
inferredcites →https://doi.org/10.1109/msp.2014.2329213openalex-snapshot
Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure
inferredcites →https://doi.org/10.1109/msp.2018.2890143openalex-snapshot
Connecting the Dots: Identifying Network Structure via Graph Signal Processing
inferredcites →https://doi.org/10.1109/msp.2020.3014067openalex-snapshot
Topological Signal Processing: Making Sense of Data Building on Multiway Relations
inferredcites →https://doi.org/10.1109/msp.2020.3016908openalex-snapshot
Sampling Signals on Graphs: From Theory to Applications
inferredcites →https://doi.org/10.1109/ojsp.2023.3339376openalex-snapshot
Unrolling of Simplicial ElasticNet for Edge Flow Signal Reconstruction
inferredcites →https://doi.org/10.1109/ojsp.2024.3444707openalex-snapshot
Multilinear Kernel Regression and Imputation via Manifold Learning
inferredcites →https://doi.org/10.1109/sam60225.2024.10636498openalex-snapshot
Learning the Topology of a Simplicial Complex Using Simplicial Signals: A Greedy Approach
inferredcites →https://doi.org/10.1109/sam60225.2024.10636653openalex-snapshot
Gaussian Processes for Predicting Simplicial Closure
inferredcites →https://doi.org/10.1109/tac.2021.3124979openalex-snapshot
Topology Learning of Linear Dynamical Systems With Latent Nodes Using Matrix Decomposition
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Graph Learning: A Survey
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Hodge Laplacian of Brain Networks
inferredcites →https://doi.org/10.1109/tmm.2021.3111440openalex-snapshot
Graph Signal Processing for Geometric Data and Beyond: Theory and Applications
inferredcites →https://doi.org/10.1109/tnnls.2020.2978386openalex-snapshot
A Comprehensive Survey on Graph Neural Networks
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Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis
inferredcites →https://doi.org/10.1109/tpwrs.2023.3266956openalex-snapshot
Learning Power Grid Outages With Higher-Order Topological Neural Networks
inferredcites →https://doi.org/10.1109/tsg.2024.3389948openalex-snapshot
Locational Detection of False Data Injection Attacks in the Edge Space via Hodge Graph Neural Network for Smart Grids
inferredcites →https://doi.org/10.1109/tsp.2014.2321121openalex-snapshot
Discrete Signal Processing on Graphs: Frequency Analysis
inferredcites →https://doi.org/10.1109/tsp.2016.2573748openalex-snapshot
Signals on Graphs: Uncertainty Principle and Sampling
inferredcites →https://doi.org/10.1109/tsp.2019.2929930openalex-snapshot
Forecasting Time Series With VARMA Recursions on Graphs
inferredcites →https://doi.org/10.1109/tsp.2019.2940122openalex-snapshot
Nonlinear Structural Vector Autoregressive Models With Application to Directed Brain Networks
inferredcites →https://doi.org/10.1109/tsp.2020.2981920openalex-snapshot
Topological Signal Processing Over Simplicial Complexes
inferredcites →https://doi.org/10.1109/tsp.2020.3042940openalex-snapshot
Online Topology Identification From Vector Autoregressive Time Series
inferredcites →https://doi.org/10.1109/tsp.2022.3207045openalex-snapshot
Simplicial Convolutional Filters
inferredcites →https://doi.org/10.1109/tsp.2023.3282068openalex-snapshot
Sparse Online Learning With Kernels Using Random Features for Estimating Nonlinear Dynamic Graphs
inferredcites →https://doi.org/10.1109/tsp.2023.3347069openalex-snapshot
Topological Signal Processing Over Generalized Cell Complexes
inferredcites →https://doi.org/10.1109/tsp.2024.3349788openalex-snapshot
Graph Filters for Signal Processing and Machine Learning on Graphs
inferredcites →https://doi.org/10.1109/tsp.2024.3379862openalex-snapshot
Tangent Bundle Convolutional Learning: From Manifolds to Cellular Sheaves and Back
inferredcites →https://doi.org/10.1109/tsp.2024.3503063openalex-snapshot
Simplicial Vector Autoregressive Models
inferredcites →https://doi.org/10.1111/cgf.12942openalex-snapshot
Spectral Processing of Tangential Vector Fields
inferredcites →https://doi.org/10.1111/j.1467-937x.2005.00353.xopenalex-snapshot
Time Varying Structural Vector Autoregressions and Monetary Policy
inferredcites →https://doi.org/10.1137/18m1201019openalex-snapshot
Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
inferredcites →https://doi.org/10.1137/18m1223101openalex-snapshot
Hodge Laplacians on Graphs
inferredcites →https://doi.org/10.1137/21m1414024openalex-snapshot
What Are Higher-Order Networks?
inferredcites →https://doi.org/10.1137/22m1480021openalex-snapshot
Simplicial \({\boldsymbol{q}}\) -Connectivity of Directed Graphs with Applications to Network Analysis
inferredcites →https://doi.org/10.1140/epjds/s13688-017-0109-5openalex-snapshot
A roadmap for the computation of persistent homology
inferredcites →https://doi.org/10.1145/2504435.2504442openalex-snapshot
Digital geometry processing with discrete exterior calculus
inferredcites →https://doi.org/10.1145/2818143.2818167openalex-snapshot
Vector field processing on triangle meshes
inferredcites →https://doi.org/10.1145/3292500.3330872openalex-snapshot
Graph-based Semi-Supervised & Active Learning for Edge Flows
inferredcites →https://doi.org/10.1145/3450626.3459797openalex-snapshot
HodgeNet
inferredcites →https://doi.org/10.1145/3528223.3530166openalex-snapshot
DeltaConv
inferredcites →https://doi.org/10.1145/3588432.3591544openalex-snapshot
Spectral Coarsening with Hodge Laplacians
inferredcites →https://doi.org/10.1145/3596711.3596724openalex-snapshot
A Signal Processing Approach To Fair Surface Design
inferredcites →https://doi.org/10.1145/3605776openalex-snapshot
A Survey on Hypergraph Representation Learning
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A Review of Graph Neural Networks in Epidemic Modeling
inferredcites →https://doi.org/10.1214/12-aos970openalex-snapshot
Factor modeling for high-dimensional time series: Inference for the number of factors
inferredcites →https://doi.org/10.1214/17-aos1613openalex-snapshot
Principal component analysis for second-order stationary vector time series
inferredcites →https://doi.org/10.13140/rg.2.2.26493.64480openalex-snapshot
A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material
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Social and Economic Networks
inferredcites →https://doi.org/10.1609/aaai.v33i01.33013558openalex-snapshot
Hypergraph Neural Networks
inferredcites →https://doi.org/10.1609/aaai.v36i6.20583openalex-snapshot
BScNets: Block Simplicial Complex Neural Networks
inferredcites →https://doi.org/10.1609/aaai.v38i11.29160openalex-snapshot
Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes
inferredcites →https://doi.org/10.2312/spbg/spbg07/091-100openalex-snapshot
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
inferredcites →https://doi.org/10.23919/eusipco63174.2024.10714960openalex-snapshot
Hodge-Aware Matched Subspace Detectors
inferredcites →https://doi.org/10.23919/eusipco63174.2024.10714988openalex-snapshot
Topological Adaptive Learning over Cell Complexes
inferredcites →https://doi.org/10.23919/eusipco63174.2024.10715366openalex-snapshot
Simplicial Complex Learning from Edge Flows via Sparse Clique Sampling
inferredcites →https://doi.org/10.24963/ijcai.2022/443openalex-snapshot
SGAT: Simplicial Graph Attention Network
inferredcites →https://doi.org/10.3389/frai.2021.681108openalex-snapshot
A Survey of Topological Machine Learning Methods
inferredcites →https://doi.org/10.4230/lipics.cp.2025.27openalex-snapshot
Relational inductive biases, deep learning, and graph networks
inferredcites →https://doi.org/10.4230/lipics.ecoop.2025.6openalex-snapshot
Detecting Functionality-Specific Vulnerabilities via Retrieving Individual Functionality-Equivalent APIs in Open-Source Repositories
inferredcites →https://doi.org/10.48550/arxiv.1710.09412openalex-snapshot
mixup: Beyond Empirical Risk Minimization
inferredcites →https://doi.org/10.48550/arxiv.2004.11198openalex-snapshot
SIGN: Scalable Inception Graph Neural Networks
inferredcites →https://doi.org/10.48550/arxiv.2010.03633openalex-snapshot
Paper-author bipartite graph from Semantic Scholar
inferredcites →https://doi.org/10.48550/arxiv.2103.03212openalex-snapshot
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks
inferredcites →https://doi.org/10.48550/arxiv.2104.12826openalex-snapshot
HodgeNet: Learning Spectral Geometry on Triangle Meshes
inferredcites →https://doi.org/10.48550/arxiv.2104.13478openalex-snapshot
A Realization-Theoretic Foundation for Fault Diagnosis, with Diagnosability Equivalence Predictions
inferredcites →https://doi.org/10.48550/arxiv.2203.07485openalex-snapshot
Simplicial Attention Neural Networks
inferredcites →https://doi.org/10.48550/arxiv.2204.09455openalex-snapshot
Simplicial Attention Networks
inferredcites →https://doi.org/10.48550/arxiv.2206.00606openalex-snapshot
Topological Deep Learning: Going Beyond Graph Data
inferredcites →https://doi.org/10.48550/arxiv.2301.11163openalex-snapshot
Convolutional Learning on Simplicial Complexes
inferredcites →https://doi.org/10.48550/arxiv.2305.06315openalex-snapshot
NervePool: A Simplicial Pooling Layer
inferredcites →https://doi.org/10.48550/arxiv.2305.16174openalex-snapshot
From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module
inferredcites →https://doi.org/10.48550/arxiv.2309.01632openalex-snapshot
Normal-Tangential Flow Response to Edge Truncation in Capacitated Networks
inferredcites →https://doi.org/10.48550/arxiv.2309.07453openalex-snapshot
SC-MAD: Mixtures of Higher-order Networks for Data Augmentation
inferredcites →https://doi.org/10.48550/arxiv.2310.19450openalex-snapshot
Hodge-Compositional Edge Gaussian Processes
inferredcites →https://doi.org/10.48550/arxiv.2311.01198openalex-snapshot
Gaussian Processes on Cellular Complexes
inferredcites →https://doi.org/10.48550/arxiv.2312.10545openalex-snapshot
Learning graphs and simplicial complexes from data
inferredcites →https://doi.org/10.48550/arxiv.2409.05135openalex-snapshot
Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
inferredcites →https://doi.org/10.48550/arxiv.2409.05211openalex-snapshot
ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain
inferredcites →https://doi.org/10.52202/075280-0712openalex-snapshot
Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes
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