Eigendecomposition-Free Sampling Set Selection for Graph Signals

Sakiyama, Akie; Tanaka, Yuichi; Tanaka, Toshihisa; Ortega, Antonio

doi:10.1109/tsp.2019.2908129

Cited by 87 publications

(88 citation statements)

References 32 publications

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“…To compare our method with classical graph sampling strategies, we conduct experiments on small-size datasets, where the matrix is completed by dual smoothness based method (2). Two relatively low-complexity classical methods called graph weight coherence (GWC) [30] and localized operator coverage (LOC) [33] are implemented, which select samples on matrix L p = I n ⊗L r +L c ⊗I m directly. Authors in [26] proposed a structured sampling method to collect data assuming the matrix signal is (η 1 , η 2 )-bandlimited on the product graph.…”

Section: • Intelligent Sampling Improves Matrix Completion Performancementioning

confidence: 99%

“…We then propose an iterative sampling strategy that efficiently collects a variable number of samples block-wise on the two smaller factor graphs alternately. Extensive experiments on synthetic and real-world datasets show that our proposed graph sampling methods achieve smaller RMSE than competing sampling schemes for matrix completion [26,30,33], when combined with different state-of-the-art matrix completion methods [7,24,31].…”

Section: Introductionmentioning

confidence: 99%

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Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift

Fen

Wang

Cheung

et al. 2020

IEEE Trans. Signal Process.

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While matrix completion algorithms fill missing entries in a matrix given a subset of samples, how to best pre-select matrix entries to collect informative observations given a sampling budget is largely unaddressed. In this paper, we propose a fast graph sampling algorithm to select entries for matrix completion. Specifically, we first regularize the matrix reconstruction objective using a dual graph signal smoothness prior, resulting in a system of linear equations for solution. We then seek to maximize the smallest eigenvalue λ min of the coefficient matrix by choosing appropriate samples, thus maximizing the stability of the linear system. To efficiently optimize this combinatorial problem, we derive a greedy sampling strategy, leveraging on Gershgorin circle theorem, that iteratively selects one sample at a time corresponding to the largest magnitude entry in the first eigenvector of a shifted graph Laplacian matrix. Our algorithm benefits computationally from warm start as the first eigenvectors of progressively shifted Laplacian matrices are computed recurrently for more samples. Towards computation-scalable sampling on large matrices, we further rewrite the coefficient matrix as a sum of two separate components, each of which exhibits attractive block-diagonal structure that we exploit for alternating block-wise sampling. Extensive experiments on both synthetic and real-world datasets show that our graph sampling algorithms substantially outperform existing sampling schemes for matrix completion, when combined with a range of modern matrix completion algorithms.Preprint. Under review.

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Section: • Intelligent Sampling Improves Matrix Completion Performancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift

Fen

Wang

Cheung

et al. 2020

IEEE Trans. Signal Process.

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“…where p(·) denotes probability density function. The Bayesian solution is provided by the design that maximizes (5). Select the utility function that describes the information gain inf K after sampling, then the expected utility can be given as…”

Section: Frameworkmentioning

confidence: 99%

Bayesian Design of Sampling Set for Bandlimited Graph Signals

Xie

Feng

et al. 2019

2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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The design of sampling set (DoS) for bandlimited graph signals (GS) has been extensively studied in recent years, but few of them exploit the benefits of the stochastic prior of GS. In this work, we introduce the optimization framework for Bayesian DoS of bandlimited GS. We also illustrate how the choice of different sampling sets affects the estimation error and how the prior knowledge influences the result of DoS compared with the non-Bayesian DoS by the aid of analyzing Gershgorin discs of error metric matrix. Finally, based on our analysis, we propose a heuristic algorithm for DoS to avoid solving the optimization problem directly.

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“…One of the topics of interest in GSP is graph sampling theory [1]- [10] which is aimed at recovering a graph signal Y. Tanaka is with the Graduate School of BASE, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan. Y. Tanaka is also with PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan (email: ytnk@cc.tuat.ac.jp).…”

Section: Introductionmentioning

confidence: 99%

Generalized Sampling on Graphs With Subspace and Smoothness Priors

Tanaka

Eldar

2020

IEEE Trans. Signal Process.

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We consider a framework for generalized sampling of graph signals that parallels sampling in shift-invariant (SI) subspaces. This framework allows for arbitrary input signals, which are not constrained to be bandlimited. Furthermore, the sampling and reconstruction filters can be different. We present design methods of the correction filter that compensates for these differences and can be obtained in closed form in the graph frequency domain. This paper considers two priors on graph signals: The first is a subspace prior, where the signal is assumed to lie in a periodic graph spectrum (PGS) subspace. The PGS subspace is proposed as a counterpart of the SI subspace used in standard sampling theory. The second is a smoothness prior that imposes a smoothness requirement on the graph signal. We suggest recovery methods both for the case when the recovery filter can be optimized and in the setting in which a predefined filter must be used. Sampling is performed in the graph frequency domain, which is a counterpart of "sampling by modulation" in SI subspaces. We compare our approach with existing sampling methods in graph signal processing. The effectiveness of the proposed generalized sampling is validated numerically through several experiments.

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Eigendecomposition-Free Sampling Set Selection for Graph Signals

Cited by 87 publications

References 32 publications

Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift

Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift

Bayesian Design of Sampling Set for Bandlimited Graph Signals

Generalized Sampling on Graphs With Subspace and Smoothness Priors

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