Generalized Laplacian precision matrix estimation for graph signal processing

Pavéz, Eduardo; Ortega, Antonio

doi:10.1109/icassp.2016.7472899

Cited by 97 publications

(82 citation statements)

References 20 publications

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“…Under this model, the sampled covariance matrix of {y } L =1 is low rank with at most rank R. As mentioned, under such setting it is difficult to reconstruct L from {y } L =1 using the existing methods [15][16][17][18][19][20]. Before discussing the proposed methods for inferring communities from {y } L =1 in Section 4 and 5, let us justify the model (11), (12) with three motivating examples.…”

Section: Graph Signal Modelmentioning

confidence: 99%

“…where α ∈ (0, 1) is the speed of the diffusion process. As (I − αL) T is a polynomial of the graph's Laplacian, we observe that y is an output of a graph filter (11). On the other hand, the excitation signal x may model the changes in temperature in the region due to a weather condition.…”

Section: Example 1: Diffusion Dynamicsmentioning

confidence: 99%

“…Naturally, graph or network inference is relevant to network and data science, and has been studied extensively. Classical methods are based on partial correlations [10], Gaussian graphical models [11], and structural equation models [12], among others. Recently, GSP-based methods for graph inference have emerged, which tackle the problem as a system identification task.…”

Section: Introductionmentioning

confidence: 99%

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Blind Community Detection From Low-Rank Excitations of a Graph Filter

Wai

Segarra

Ozdaglar

et al. 2020

IEEE Trans. Signal Process.

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This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on a 'low-pass' property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical experiments demonstrate that our approach is effective.

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Section: Graph Signal Modelmentioning

confidence: 99%

Section: Example 1: Diffusion Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Blind Community Detection From Low-Rank Excitations of a Graph Filter

Wai

Segarra

Ozdaglar

et al. 2020

IEEE Trans. Signal Process.

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“…of identifying the graph underlying the observed data values according to given criteria, such as graph smoothness or graph sparsity [1], [2]. In fact, except for specific SoG applications where the data are univocally associated to an underlying graph structure -e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Model-based graph learning has been recently analyzed in [1], where the authors resort to a parametric smooth signal model and develop a procedure for learning the graph Laplacian matrix via an alternating minimization algorithm jointly enforcing the SoG smoothness and the Laplacian properties of sparsity and semidefinite positiveness. In [2], the authors propose an iterative Laplacian matrix learning algorithm that, stemming on the knowledge of which edges are active, updates one row/column of the precision matrix at a time by solving a non-negative quadratic program and superimposing prior constraints on the Laplacian matrix structure.…”

Section: Introductionmentioning

confidence: 99%

Graph adjacency matrix learning for irregularly sampled Markovian natural images

Colonnese

Biagi

Cusani

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-The boost of signal processing on graph has recently solicited research on the problem of identifying (learning) the graph underlying the observed signal values according to given criteria, such as graph smoothness or graph sparsity. This paper proposes a procedure for learning the adjacency matrix of a graph providing support to a set of irregularly sampled image values. Our approach to the graph adjacency matrix learning takes into account both the image luminance and the spatial samples' distances, and leads to a flexible and computationally light parametric procedure. We show that, under mild conditions, the proposed procedure identifies a near optimal graph for Markovian fields; specifically, the links identified by the learning procedure minimize the potential energy of the Markov random field for the signal samples under concern. We also show, by numerical simulations, that the learned adjacency matrix leads to a higly compact spectral wavelet graph transform of the so obtained signal on graph and favourably compares to stateof-the-art graph learning procedures, definetly matching the intrinsic signal structure.

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Graph Spectral Image Processing

Cheung

Magli

Tanaka

et al. 2021

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Generalized Laplacian precision matrix estimation for graph signal processing

Cited by 97 publications

References 20 publications

Blind Community Detection From Low-Rank Excitations of a Graph Filter

Blind Community Detection From Low-Rank Excitations of a Graph Filter

Graph adjacency matrix learning for irregularly sampled Markovian natural images

Graph Spectral Image Processing

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