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Found 32 papers, 5 papers with code
Learning graphs and simplicial complexes from data
Graphs are widely used to represent complex information and signal domains with irregular support.
On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks
Analyzing the stability of graph neural networks (GNNs) under topological perturbations is key to understanding their transferability and the role of each architecture component.
Uncertainty in Graph Contrastive Learning with Bayesian Neural Networks
Graph contrastive learning has shown great promise when labeled data is scarce, but large unlabeled datasets are available.
Hodge-Compositional Edge Gaussian Processes
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces.
Hodge-Aware Contrastive Learning
We leverage this decomposition to develop a contrastive self-supervised learning approach for processing simplicial data and generating embeddings that encapsulate specific spectral information. Specifically, we encode the pertinent data invariances through simplicial neural networks and devise augmentations that yield positive contrastive examples with suitable spectral properties for downstream tasks.
Convolutional Learning on Simplicial Complexes
We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes.
Online Filtering over Expanding Graphs
We propose an online update of the filter, based on the principles of online machine learning.
Deep Statistical Solver for Distribution System State Estimation
While data-driven alternatives based on Machine Learning models could be a choice, they suffer in DSSE because of the lack of labeled data.
Graph Filters for Signal Processing and Machine Learning on Graphs
For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks.
Learning Stable Graph Neural Networks via Spectral Regularization
Stability of graph neural networks (GNNs) characterizes how GNNs react to graph perturbations and provides guarantees for architecture performance in noisy scenarios.
Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis
The proposed approach can work with any type of product graph and we also introduce a parametric product graph to learn also the spatiotemporal coupling.
Learning Expanding Graphs for Signal Interpolation
Specifically, we propose a stochastic attachment model for incoming nodes parameterized by the attachment probabilities and edge weights.
Graph filtering over expanding graphs
We propose a filter learning scheme for data over expanding graphs by relying only on such a model.
Learning Stochastic Graph Neural Networks with Constrained Variance
To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the stochastic deviation.
Convolutional Filtering in Simplicial Complexes
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC).
Simplicial Convolutional Filters
We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces etc.
Learning Time-Varying Graphs from Online Data
This work proposes an algorithmic framework to learn time-varying graphs from online data.
Simplicial Convolutional Neural Networks
Graphs can model networked data by representing them as nodes and their pairwise relationships as edges.
Stability of Graph Convolutional Neural Networks to Stochastic Perturbations
In particular, it proves the expected output difference between the GCNN over random perturbed graphs and the GCNN over the nominal graph is upper bounded by a factor that is linear in the link loss probability.
Finite Impulse Response Filters for Simplicial Complexes
In this paper, we study linear filters to process signals defined on simplicial complexes, i. e., signals defined on nodes, edges, triangles, etc.
Graph-Time Convolutional Neural Networks
We develop a graph-time convolutional filter by following the shift-and-sum principles of the convolutional operator to learn higher-level features over the product graph.
Nonlinear State-Space Generalizations of Graph Convolutional Neural Networks
In this work, we approach GCNNs from a state-space perspective revealing that the graph convolutional module is a minimalistic linear state-space model, in which the state update matrix is the graph shift operator.
Online Time-Varying Topology Identification via Prediction-Correction Algorithms
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology.
Graph-Adaptive Activation Functions for Graph Neural Networks
Activation functions are crucial in graph neural networks (GNNs) as they allow defining a nonlinear family of functions to capture the relationship between the input graph data and their representations.
Stochastic Graph Neural Networks
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others.
Forecasting Multi-Dimensional Processes over Graphs
The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework.
Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks
We also introduce GNN extensions using edge-varying and autoregressive moving average graph filters and discuss their properties.
EdgeNets:Edge Varying Graph Neural Networks
This is a general linear and local operation that a node can perform and encompasses under one formulation all existing graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs).
Generalizing Graph Convolutional Neural Networks with Edge-Variant Recursions on Graphs
This paper reviews graph convolutional neural networks (GCNNs) through the lens of edge-variant graph filters.
On the Transferability of Spectral Graph Filters
For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable.
Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies
Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.
Autoregressive Moving Average Graph Filtering
We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation.
