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作者： Oleksii Abramenko Aalto University

学位级别：硕士

graph signal sampling is one the major problems in graph signal processing and arises in a variety of practical applications, such as data compression, image denoising and social network analysis. In this thesis we formulate graph signal sampling as a reinforcement learning (RL) problem, which unleashes powerful methods developed recently within RL. Within our approach the signal sampling is carried out by an agent which crawls over the empirical graph and selects the most relevant graph nodes to sample, i. e., determines the corresponding graph signal values. Overall, the goal of the agent is to select signal samples which allow for the smallest graph signal recovery error. The behavior of the sampling agent is described using a policy which determines whether or not a particular node should be sampled. The policy is continuously adjusted which implies an inherent robustness to changes in the data structure. We propose two RL-based sampling algorithms and evaluate their performance by means of illustrative numerical experiments. After this we conduct elaborative discussion on strengths and weaknesses of the proposed solutions and explain phenomenons observed during simulations. Based on the simulation results, we identify some major challenges related to application of RL to graph signal sampling and propose possible solutions leading to prospects for the future work.

关键词： machine learning reinforcement learning graph signal sampling convex optimization multi-armed bandit policy gradient complex networks

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DESIGN OF graph signal sampling MATRICES FOR ARBITRARY signal SUBSPACES

DESIGN OF GRAPH SIGNAL SAMPLING MATRICES FOR ARBITRARY SIGNA...

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IEEE International Conference on Acoustics, Speech and signal Processing (ICASSP)

作者： Hara, Junya Yamada, Koki Ono, Shunsuke Tanaka, Yuichi Tokyo Univ Agr & Technol Tokyo Japan Tokyo Inst Technol Tokyo Japan Japan Sci & Technol Agcy PRESTO Saitama Japan

ISBN: (纸本)9781728176055

We propose a design method of sampling matrices for graph signals that guarantees perfect recovery for arbitrary graph signal subspaces. When the signal subspace is known, perfect reconstruction is always possible from the samples with an appropriately designed sampling matrix. However, most graph signal sampling methods so far design sampling matrices based on the bandlimited assumption and sometimes violates the perfect reconstruction condition for the other signal models. In this paper, we formulate an optimization problem for the design of the sampling matrix that guarantees perfect recovery, thanks to a generalized sampling framework for standard signals. In experiments with various signal models, our sampling matrix presents better reconstruction accuracy both for noiseless and noisy situations.

关键词： graph signal sampling generalized sampling correction filter ADMM

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Topology-Aware graph signal sampling for Pooling in graph Neural Networks 26

Topology-Aware Graph Signal Sampling for Pooling in Graph Ne...

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26th International Computer Conference of the Computer-Society-of-Iran

作者： Nouranizadeh, Amirhossein Matinkia, Mohammadjavad Rahmati, Mohammad Amirkabir Univ Technol Dept Comp Engn Tehran Iran

ISBN: (纸本)9781665412414

As a generalization of convolutional neural networks to graph-structured data, graph convolutional networks learn feature embeddings based on the information of each nodes local neighborhood. However, due to the inherent irregularity of such data, extracting hierarchical representations of a graph becomes a challenging task. Several pooling approaches have been introduced to address this issue. In this paper, we propose a novel topology-aware graph signal sampling method to specify the nodes that represent the communities of a graph. Our method selects the sampling set based on the local variation of the signal of each node while considering vertex-domain distances of the nodes in the sampling set. In addition to the interpretability of the sampled nodes provided by our method, the experimental results both on stochastic block models and real-world dataset benchmarks show that our method achieves competitive results compared to the state-of-the-art in the graph classification task.

关键词： graph neural networks pooling layer graph signal sampling graph classification

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ROBUST graph signal sampling 44

ROBUST GRAPH SIGNAL SAMPLING

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44th IEEE International Conference on Acoustics, Speech and signal Processing (ICASSP)

作者： Guler, Basak Jayawant, Ajinkya Avestimehr, A. Salman Ortega, Antonio Univ Southern Calif Ming Hsieh Dept Elect & Comp Engn Los Angeles CA 90007 USA

ISBN: (纸本)9781479981311

This paper considers the graph signal sampling problem when some of the selected samples are lost or unavailable due to sensor failures or adversarial erasures. We formulate a robust graph signal sampling problem where only a subset of selected samples are received, and the goal is to maximize the worst-case performance. We propose a novel greedy robust sample selection algorithm and study its performance guarantees. Our numerical results demonstrate the performance improvement of the proposed algorithm over the existing schemes.

关键词： graph signal sampling robust optimization approximate submodular function maximization

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Near-Optimal graph signal sampling by Pareto Optimization

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SENSORS 2021年第4期21卷 1415-1415页

作者： Luo, Dongqi Si, Binqiang Zhang, Saite Yu, Fan Zhu, Jihong Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China Beijing Informat Sci & Technol Univ Sch Instrumentat Sci & Optoelect Engn Beijing 100192 Peoples R China Tsinghua Univ Dept Precis Instrument Beijing 100084 Peoples R China

In this paper, we focus on the bandlimited graph signal sampling problem. To sample graph signals, we need to find small-sized subset of nodes with the minimal optimal reconstruction error. We formulate this problem as a subset selection problem, and propose an efficient Pareto Optimization for graph signal sampling (POGSS) algorithm. Since the evaluation of the objective function is very time-consuming, a novel acceleration algorithm is proposed in this paper as well, which accelerates the evaluation of any solution. Theoretical analysis shows that POGSS finds the desired solution in quadratic time while guaranteeing nearly the best known approximation bound. Empirical studies on both Erdos-Renyi graphs and Gaussian graphs demonstrate that our method outperforms the state-of-the-art greedy algorithms.

关键词： graph signal processing graph signal sampling supermodularity ratio evolutionary algorithms pareto optimization

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Leveraging multi-level correlations for imputing monitoring data in water supply systems using graph signal sampling theory

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WATER RESEARCH X 2024年 25卷 100274页

作者： Zhou, Xiao Man, Yacan Liu, Shuming Zhang, Juan Yuan, Rui Wang, Wei Su, Kuizu Hefei Univ Technol Coll Civil Engn Hefei Peoples R China Tsinghua Univ Sch Environm Beijing Peoples R China Hebei Construction & Investment Grp Water Investme Shijiazhuang Peoples R China

Data missing and anomalies in monitoring equipment have become critical barriers to developing intelligent Water Supply Systems (WSS). The valid data preceding and after the missing segments can be utilized to impute missing values. However, traditional imputation methods, such as linear interpolation and prediction-based methods, have limited capacity to use data relationships or can only utilize information before the missing values. Therefore, existing methods still need to work on efficiently and conveniently achieving high-accuracy imputation. According to the continuity and periodicity of WSS data, missing values often exhibit multi-level correlations with valid data. This paper innovatively employs graph structures to analyze the multi-level correlations at different timestamps and applies graph signal sampling algorithms to extract low-frequency features for imputation. A novel graph-based Data Imputation (GDI) method has been developed, which leverages multilevel correlations to propagate information and completes imputation tasks without requiring complex feature engineering and pre-training processes. Results indicate that GDI outperforms Holt-Winters, Support Vector Regression, and Gated Recurrent Unit in the task of imputing continuous missing data. It can still achieve R- 2 > 0.8 even when the proportion of missing values reaches 80 %. These results demonstrate that GDI ensures a more streamlined and efficient imputation with high robustness and accuracy.

关键词： Monitoring data imputation Water supply systems graph signal sampling graph Theory Machine Learning

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Parallel graph signal Processing: sampling and Reconstruction

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IEEE TRANSACTIONS ON signal AND INFORMATION PROCESSING OVER NETWORKS 2023年 9卷 190-206页

作者： Dapena, Daniela Lau, Daniel L. L. Arce, Gonzalo R. R. Univ Delaware Financial Serv Analyt Newark DE 19713 USA Univ Kentucky Elect & Comp Engn Lexington KY 40506 USA Univ Delaware Elect Engn Newark DE 19716 USA

graph signal processing (GSP) extends classical signal processing methods to analyzing signals supported over irregular grids represented by graphs. Within the scope of GSP, sampling and reconstruction represent fundamental tools that have received considerable attention. For very large graphs, however, many of the current methods struggle with the computational and memory requirements. Vertex domain and randomized sampling strategies somewhat ameliorate the computational requirements, but these algorithms perform poorly at preserving signal fidelity for graphs with hundreds of thousands of vertices. To address these shortcomings, this article introduces a new and scalable approach that can be easily parallelized. This new approach uses existing graph partitioning algorithms in concert with vertex-domain blue-noise sampling and reconstruction, performed independently across partitions. In the reconstruction, some degree of overlapping is added to the partitions to induce trans-partition smoothness in the recovered signal. We also propose two sampling schemes based on the spatial characteristic of the graph that minimizes the recovery error. The first combines graph partitioning with the Void-and-Cluster algorithm, while the second approach uses Error Diffusion. We conclude this article with experiments on synthetic and real data that show the effectiveness of these new approaches on very large graphs.

关键词： Partitioning algorithms Approximation algorithms signal processing algorithms signal processing Laplace equations Information processing Parallel processing graph signal reconstruction blue-noise graph signal sampling graph signal processing

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Joint sampling and Reconstruction of Time-Varying signals Over Directed graphs

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IEEE TRANSACTIONS ON signal PROCESSING 2023年 71卷 2204-2219页

作者： Xiao, Zhenlong Fang, He Tomasin, Stefano Mateos, Gonzalo Wang, Xianbin Xiamen Univ Sch Informat Dept Informat & Commun Engn Xiamen 361005 Peoples R China Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China Univ Padua Dept Informat Engn I-35122 Padua Italy Univ Rochester Dept Elect & Comp Engn Rochester NY 14627 USA Western Univ Dept Elect & Comp Engn London ON N6A 5B9 Canada

Vertex-domain and temporal-domain smoothness of time-varying graph signals are cardinal properties that can be exploited for effective graph signal reconstruction from limited samples. However, existing approaches are not directly applicable when the signal's frequency occupancy changes with time. Moreover, while e.g., sensor network applications can benefit from directed graph models, the non-orthogonality of the graph eigenvectors can challenge spectral-based signal reconstruction algorithms. In this context, here we consider K-sparse time-varying signals with unknown frequency supports. By exploiting the smoothness of the varying graph frequency supports and employing shift operations over directed graphs, we study joint sampling of multiple varying signals based on Schur decomposition to reconstruct each signal by orthogonal frequency components. Firstly, joint frequency support of the multiple signals is identified by proposing a two-stage Individual-Joint sampling scheme. Based on the estimated frequency support, the GFT coefficients of each signal can be recovered using data collected in individual sampling stage. Greedy algorithms are proposed for vertex set selection and graph shift order selection, which enable a robust signal reconstruction against additive noise. Considering the signals in applications may be approximately K-sparse, we further exploit the samples in both individual and joint sampling stages and investigate the optimal signal reconstruction as a convex optimization problem with adaptive frequency support selection. The proposed optimal sampling and reconstruction algorithms outperform several existing schemes in random network and sensor network data gathering.

关键词： Directed graph frequency domain graph signal sampling signal reconstruction time-varying signals

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sampling graph signals with Sparse Dictionary Representation 29

Sampling Graph Signals with Sparse Dictionary Representation

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29th European signal Processing Conference (EUSIPCO)

作者： Zhang, Kaiwen Coutino, Mario Isufi, Elvin Delft Univ Technol Fac Elect Engn Math & Comp Sci Delft Netherlands

ISBN: (纸本)9789082797060

graph sampling strategies require the signal to be relatively sparse in an alternative domain, e.g. bandlimitedness for reconstructing the signal. When such a condition is violated or its approximation demands a large bandwidth, the reconstruction often comes with unsatisfactory results even with large samples. In this paper, we propose an alternative sampling strategy based on a type of overcomplete graph-based dictionary. The dictionary is built from graph filters and has demonstrated excellent sparse representations for graph signals. We recognize the proposed sampling problem as a coupling between support recovery of sparse signals and node selection. Thus, to approach the problem we propose a sampling procedure that alternates between these two. The former estimates the sparse support via orthogonal matching pursuit (OMP), which in turn enables the latter to build the sampling set selection through greedy algorithms. Numerical results corroborate the role of key parameters and the effectiveness of the proposed method.

关键词： Compressive sensing graph signal sampling graph signal processing signal reconstruction sparse sensing

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sampling of Power System graph signals 11

Sampling of Power System Graph Signals

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11th IEEE-PES Innovative Smart Grid Technologies Europe (IEEE-PES ISGT Europe)

作者： Abul Hasnat, Md Rahnamay-Naeini, Mahshid Univ S Florida Dept Elect Engn Tampa FL 33620 USA

ISBN: (纸本)9781665448758

While sampling in classical signal processing is well-developed and studied, sampling in the graph signal Processing framework and its application domains are fairly new. In this paper, sampling of power grids' graph signals are discussed and analyzed in the context of two applications including the recovery of missing measurements during cyber stresses and the optimal PMU placement problem. The effects of various topological and power-dynamical factors in the system are evaluated for the selection of the sampling-set for power grid graph signals and graph signal reconstruction performance. Moreover, a novel sampling-set selection criterion based on the error introduced in the process of band-limiting the graph signal has been proposed.

关键词： graph signal processing graph signal sampling graph-frequency smart Grid PMU placement

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