Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection

Mollaebrahim, Siavash; Beferull-Lozano, Baltasar

doi:10.1109/tsp.2021.3066787

Cited by 10 publications

(14 citation statements)

References 42 publications

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“…Although the proposed method produces better results than those achieved using conventional graph-filter-based classifiers, it requires dealing with a non-convex optimization problem whose solution involves a relatively high computational cost. In [27], motivated by the typical scenario of asymmetric communications in wireless sensor networks, the authors study the optimal design of graph shift operators to perform decentralized subspace projection for asymmetric topologies. Obtaining the referred operators can be performed either by solving an optimization problem or by employing a decentralized algorithm based on an Alternating Direction Method of Multipliers (ADMM).…”

Section: Introductionmentioning

confidence: 99%

On the Fractionalization of the Shift Operator on Graphs

2022

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The theory of graph signal processing has been established with the purpose of generalizing tools from classical digital signal processing to the cases where the signal domain can be modeled by an arbitrary graph. In this context, the present paper introduces the notion of fractional shift of signals on graphs, which is related to considering a non-integer power of the graph adjacency matrix. Among the results we derive throughout this work, we prove that the referred fractional operator can be implemented as a linear and shift-invariant graph filter for any graph and verify its convergence to the classical fractional delay when a directed ring graph is considered. By means of a real-world example, we show that, using the proposed operator, we can obtain graph filters that approximate an ideal filter better than those designed using the ordinary adjacency matrix. An additional example dealing with noise removal from graph signals illustrates the gain provided by the mentioned filter design strategy.

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Section: Introductionmentioning

confidence: 99%

On the Fractionalization of the Shift Operator on Graphs

2022

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“…The amount of data generated from interconnected networks such as sensor networks, financial time-series, brainnetworks, etc., are increasing rapidly. Extraction of meaningful information from such interconnected data, represented in the form of a graph can have many practical applications such as, signal denoising [1], change point detection [2], time series prediction [3], etc. Many of the functional relationships in such networks are causal and identification of this causal graph structure is termed topology identification.…”

Section: Introductionmentioning

confidence: 99%

Random Feature Approximation for Online Nonlinear Graph Topology Identification

Money¹,

Krishnan²,

Beferull-Lozano³

2021

Preprint

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Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments conducted on real and synthetic data show that the proposed method outperforms its competitors.

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“…This correspondence comments on [1], where the goal is to design shift matrices for graph filters whose output is the result of projecting their input onto a given subspace. The paper relies on a Schur decomposition S = W (D + Q)W ⊤ of the sought shift matrix S. The goal is therefore the same as in the earlier paper [2] with the exception that S is required to be symmetric in [2].…”

Section: Introductionmentioning

confidence: 99%

“…The reason for such a requirement in [2] was to render the problem tractable. The work in [1] claims to solve the problem when that assumption is lifted. However, the present correspondence shows that this is not the case.…”

Section: Introductionmentioning

confidence: 99%

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Comments on "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection"

Romero

2021

Preprint

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This correspondence disproves the main results in the paper "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection" by S. Mollaebrahim and B. Beferull-Lozano. Counterexamples and counterproofs are provided when applicable. When those problems can be amended, a correction is suggested. However, in most cases, no correction may be possible since the problem addressed by the aforementioned paper is for the most part intractable.

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Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection

Cited by 10 publications

References 42 publications

On the Fractionalization of the Shift Operator on Graphs

On the Fractionalization of the Shift Operator on Graphs

Random Feature Approximation for Online Nonlinear Graph Topology Identification

Comments on "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection"

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