Learning Graphs From Data: A Signal Representation Perspective

@article{Dong2019LearningGF,
  title={Learning Graphs From Data: A Signal Representation Perspective},
  author={Xiaowen Dong and Dorina Thanou and M. Rabbat and P. Frossard},
  journal={IEEE Signal Processing Magazine},
  year={2019},
  volume={36},
  pages={44-63}
}
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis, and visualization of structured data. [...] Key Result We conclude with several open issues and challenges that are keys to the design of future signal processing and machine-learning algorithms for learning graphs from data.Expand
A survey of signal processing based graph learning techniques
TLDR
In this survey, signal processing based graph learning approaches that have been proposed in the literature and proposed new research directions are explored. Expand
Learning graphs from observed graph signals
    Description: ​Graph Signal Processing (GSP) is a new and emerging field at the intersection of Signal Processing, Graph Theory, and Machine Learning. GSP manifestates the generalization of standardExpand
    Graph Signal Processing - Part III: Machine Learning on Graphs, from Graph Topology to Applications
    TLDR
    An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems, as many graph neural networks and convolutional graph networks are emerging. Expand
    Kernel-Based Graph Learning From Smooth Signals: A Functional Viewpoint
    TLDR
    A novel graph learning framework that incorporates prior information along node and observation side, and in particular the covariates that help to explain the dependency structures in graph signals, and develops a novel graph-based regularisation method which enables the model to capture both the dependency explained by the graph and the dependency due to graph signals observed under different but related circumstances. Expand
    A Low-Dimensionality Method for Data-Driven Graph Learning
    TLDR
    This paper proposes a numerically efficient method for estimating of the normalized Laplacian through its eigenvalues estimation and by promoting its sparsity. Expand
    Learning Causal Networks Topology From Streaming Graph Signals
    TLDR
    This paper shows how, by introducing a simple yet powerful data model, it can infer a graph structure from streaming data with a distributed online learning algorithm and is tested experimentally to illustrate its usefulness, and successfully compared to a centralized offline solution of the literature. Expand
    Bayesian Topology Learning and noise removal from network data
    TLDR
    A graph topology inference approach is proposed to learn the underlying graph structure from a given set of noisy multi-variate observations, which are modeled as graph signals generated from a Gaussian Markov Random Field (GMRF) process. Expand
    Mask Combination of Multi-Layer Graphs for Global Structure Inference
    TLDR
    This paper presents a novel method for combining the multiple graphs into a global graph using mask matrices, which are estimated through an optimization problem that accommodates the multi-layer graph information and a signal representation model. Expand
    Graph Laplacian Mixture Model
    TLDR
    This work proposes a novel generative model that represents a collection of distinct data which naturally live on different graphs that demonstrates promising performance in data clustering and multiple graph inference, and shows desirable properties in terms of interpretability and coping with high dimensionality on weather and traffic data. Expand
    Graph Learning Under Spectral Sparsity Constraints
    TLDR
    Numerical results on synthetic data show the proposed inference algorithm can effectively capture the meaningful graph topology from observed data under the wideband assumption. Expand
    ...
    1
    2
    3
    4
    5
    ...

    References

    SHOWING 1-10 OF 112 REFERENCES
    Graph topology inference based on transform learning
    TLDR
    The aim of this paper is to propose an efficient strategy for learning the graph topology from signals defined over the vertices of a graph, under a signal band-limited assumption, which corresponds to signals having clustering properties. Expand
    Graph Learning from Data under Structural and Laplacian Constraints
    TLDR
    This paper proposes a novel framework for learning/estimating graphs from data and demonstrates that the proposed algorithms outperform the current state-of-the-art methods in terms of graph learning performance. Expand
    Learning Laplacian Matrix in Smooth Graph Signal Representations
    TLDR
    This paper addresses the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology and proposes an algorithm for learning graphs that enforces such property and is based on minimizing the variations of the signals on the learned graph. Expand
    Learning time varying graphs
    TLDR
    A primal-dual optimization algorithm that scales linearly with the number of allowed edges and can be easily parallelized is proposed that is shown to outperform standard graph learning and other baseline methods both on a synthetic and a real dataset. Expand
    Network Topology Inference from Spectral Templates
    TLDR
    The novel idea is to find a graph shift that, while being consistent with the provided spectral information, endows the network with certain desired properties such as sparsity, and develops efficient inference algorithms stemming from provably tight convex relaxations of natural nonconvex criteria. Expand
    Graph learning under sparsity priors
    TLDR
    This paper forms a graph learning problem, whose solution provides an ideal fit between the signal observations and the sparse graph signal model, and proposes to solve it by alternating between a signal sparse coding and a graph update step. Expand
    The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
    TLDR
    This tutorial overview outlines the main challenges of the emerging field of signal processing on graphs, discusses different ways to define graph spectral domains, which are the analogs to the classical frequency domain, and highlights the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. Expand
    ONLINE GRAPH LEARNING FROM SEQUENTIAL DATA
    TLDR
    An online algorithm is developed that is able to learn the underlying graph structure from observations of the signal evolution and is adaptive in nature and able to respond to changes in the graph structure and the perturbation statistics. Expand
    Learning Heat Diffusion Graphs
    TLDR
    This paper focuses on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown, and casts a new graph learning problem and solves it with an efficient nonconvex optimization algorithm. Expand
    Characterization and Inference of Graph Diffusion Processes From Observations of Stationary Signals
    TLDR
    This paper proposes a characterization of the space of valid graphs, in the sense that they can explain stationary signals, and illustrates how this characterization can be used for graph recovery. Expand
    ...
    1
    2
    3
    4
    5
    ...