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Efficient Signed graph sampling via Balancing & Gershgorin Disc Perfect Alignment

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2025年第4期47卷 2330-2348页

作者： Dinesh, Chinthaka Cheung, Gene Bagheri, Saghar Bajic, Ivan V. Northeastern Univ Coll Engn Vancouver BC V6B 1Z3 Canada York Univ Dept Elect Engn & Comp Sci Toronto ON M3J 1P3 Canada Simon Fraser Univ Sch Engn Sci Burnaby BC V5A 1S6 Canada

A basic premise in graph signal processing (GSP) is that a graph encoding pairwise (anti-)correlations of the targeted signal as edge weights is leveraged for graph filtering. Existing fast graph sampling schemes are designed and tested only for positive graphs describing positive correlations. However, there are many real-world datasets exhibiting strong anti-correlations, and thus a suitable model is a signed graph, containing both positive and negative edge weights. In this paper, we propose the first linear-time method for sampling signed graphs, centered on the concept of balanced signed graphs. Specifically, given an empirical covariance data matrix (C) over bar, we first learn a sparse inverse matrix L, interpreted as a graph Laplacian corresponding to a signed graph G. We approximate G with a balanced signed graph G(b) via fast edge weight augmentation in linear time, where the eigenpairs of Laplacian L-b for G(b) are graph frequencies. Next, we select a node subset for sampling to minimize the error of the signal interpolated from samples in two steps. We first align all Gershgorin disc left-ends of LaplacianL(b) at the smallest eigenvalue lambda(min) (L-b) via similarity transform L-s = SLb S-1, leveraging a recent linear algebra theorem called Gershgorin disc perfect alignment (GDPA). We then perform sampling on L-s using a previous fast Gershgorin disc alignment sampling (GDAS) scheme. Experiments show that our signed graph sampling method outperformed fast sampling schemes designed for positive graphs on various datasets with anti-correlations.

关键词： Laplace equations Covariance matrices sampling methods Symmetric matrices Kernel Eigenvalues and eigenfunctions Sparse matrices Interpolation Electronic mail Correlation graph signal processing graph spectrum graph sampling Gershgorin circle theorem

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CAGS: Context-Aware Document Ranking With Contrastive graph sampling

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2025年第1期37卷 89-101页

作者： Huang, Zhaoheng Zhu, Yutao Dou, Zhicheng Wen, Ji-Rong Renmin Univ China Gaoling Sch Artificial Intelligence Beijing 100872 Peoples R China Renmin Univ China Engn Res Ctr Next Generat Intelligent Search & Rec MOE Beijing 100872 Peoples R China

In search sessions, a series of interactions in the context has been proven to be advantageous in capturing users' search intents. Existing studies show that designing pre-training tasks and data augmentation strategies for session search improves the robustness and generalizability of the model. However, such data augmentation strategies only focus on changing the original session structure to learn a better representation. Ignoring information from outside the session, users' diverse and complex intents cannot be learned well by simply reordering and deleting historical behaviors, proving that such strategies are limited and inadequate. In order to solve the problem of insufficient modeling under complex user intents, we propose exploiting information outside the original session. More specifically, in this paper, we sample queries and documents from the global click-on and follow-up session graph, alter an original session with these samples, and construct a new session that shares a similar user intent with the original one. Specifically, we design four data augmentation strategies based on session graphs in view of both one-hop and multi-hop structures to sample intent-associated query/document nodes. Experiments conducted on three large-scale public datasets demonstrate that our model outperforms the existing ad-hoc and context-aware document ranking models.

关键词： Data augmentation Context modeling Data models Search engines Training Search problems Encoding Bidirectional control Predictive models Context-aware document ranking contrastive learning graph sampling graph sampling

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graph sampling with applications to estimating the number of pattern embeddings and the parameters of a statistical relational model

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DATA MINING AND KNOWLEDGE DISCOVERY 2018年第4期32卷 913-948页

作者： Ravkic, Irma Znidarsic, Martin Ramon, Jan Davis, Jesse Katholieke Univ Leuven Dept Comp Sci B-3001 Heverlee Leuven Belgium Jozef Stefan Inst Jamova Cesta 39 Ljubljana 1000 Slovenia

Counting the number of times a pattern occurs in a database is a fundamental data mining problem. It is a subroutine in a diverse set of tasks ranging from pattern mining to supervised learning and probabilistic model learning. While a pattern and a database can take many forms, this paper focuses on the case where both the pattern and the database are graphs (networks). Unfortunately, in general, the problem of counting graph occurrences is #P-complete. In contrast to earlier work, which focused on exact counting for simple (i.e., very short) patterns, we present a sampling approach for estimating the statistics of larger graph pattern occurrences. We perform an empirical evaluation on synthetic and real-world data that validates the proposed algorithm, illustrates its practical behavior and provides insight into the trade-off between its accuracy of estimation and computational efficiency.

关键词： graph sampling graph pattern matching Parameter estimation Statistical relational learning

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graph sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 2814-2829页

作者： Wang, Fen Wang, Yongchao Cheung, Gene Yang, Cheng Xidian Univ State Key Lab ISN Xian 710071 Shaanxi Peoples R China York Univ Dept EECS Toronto ON M3J 1P3 Canada

Matrix completion algorithms fill missing entries in a large matrix given a subset of observed samples. The problem of how to pre-select a subset of entries for sampling to maximize the reconstructed matrix fidelity is largely unaddressed. In this paper, we propose two sampling algorithms to tackle this problem: (i) a fast base sampling algorithm on general single graphs, and (ii) an extended sampling algorithm from the base algorithm for active matrix completion. Assuming the double graph smoothness prior where rows / columns of the matrix signal are smooth with respect to row / column factor graphs, we first show that a matrix signal can be recovered from partial observations by solving a system of linear equations, where the sought matrix is vectorized as and interpreted as a signal residing on a single graph. On this single graph, to promote small reconstruction error and stability of the linear system, we maximize the smallest eigenvalue of by greedily selecting samples corresponding to the largest magnitude entries in the first eigenvectors of , based on a corollary of the Gershgorin circle theorem. Extending to the active matrix completion case, we alternately choose entries in the rows and columns corresponding to the largest magnitude entries in the first eigenvectors of the row / column coefficient matrices and . Our algorithm benefits computationally from warm start as the first eigenvectors are computed recurrently for more samples. Extensive experiments on both synthetic and real-world datasets show that our extended graph sampling algorithm outperforms existing sampling schemes for matrix completion, when combined with a range of modern matrix completion algorithms.

关键词： Signal processing algorithms sampling methods Laplace equations Motion pictures Eigenvalues and eigenfunctions Complexity theory Linear systems graph sampling matrix completion graph Laplacian regularization Gershgorin circle theorem

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graph sampling for Internet topologies using normalized Laplacian spectral features

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INFORMATION SCIENCES 2019年 481卷 574-603页

作者： Jiao, Bo Shi, Jianmai Zhang, Wensheng Xing, Lining Foshan Univ Sch Math & Big Data Foshan 528000 Peoples R China Natl Univ Def Technol Coll Syst Engn Changsha 410073 Hunan Peoples R China

A crucial task in the process of constructing Internet testbeds is to substantially reduce the number of nodes in the interdomain Internet topology, while maintaining its essential properties. In this paper, we first decompose the Internet topology into seven bipartite graphs, a matching graph and a core graph using two normalized Laplacian spectral features, namely, the weighted spectral distribution and the multiplicity of the eigenvalue 1. Then, we accomplish a marked reduction in size of the topology by sampling and merging these graphs. The proposed approach was tested on realistic Internet graphs that were explored from 2000 to 2016 and a large-scale simulated graph. The experimental results confirm that our approach can effectively reduce the number of nodes in these graphs by more than 96%, while maintaining their essential properties. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Weighted spectral distribution graph sampling Interdomain Internet topology Bipartite graph Normalized Laplacian spectrum

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graph sampling for Map Comparison

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ACM TRANSACTIONS ON SPATIAL ALGORITHMS AND SYSTEMS 2024年第3期10卷 1-24页

作者： Aguilar, Jordi Buchin, Kevin Buchin, Maike Sereshgi, Erfan Hosseini Silveira, Rodrigo I. Wenk, Carola Univ Politecn Cataluna Dept Matemat Aplicada 2 Barcelona Spain TU Dortmund Dept Comp Sci Dortmund Nordrhein Westf Germany Ruhr Univ Bochum Dept Comp Sci Bochum Germany Tulane Univ Dept Comp Sci New Orleans LA USA

Comparing two road maps is a basic operation that arises in a variety of situations. A map comparison method that is commonly used, mainly in the context of comparing reconstructed maps to ground-truth maps, is based on graph sampling . The essential idea is to first compute a set of point samples on each map and then to match pairs of samples-one from each map-in a one-to-one fashion. For deciding whether two samples can be matched, different criteria, e.g., based on distance or orientation, can be used. The total number of matched pairs gives a measure of how similar the maps are. Since the work of Biagioni and Eriksson [ 11 , 12 ], graph sampling methods have become widely used. However, there are different ways to implement each of the steps, which can lead to significant differences in the results. This means that conclusions drawn from different studies that seemingly use the same comparison method cannot necessarily be compared. In this work we present a unified approach to graph sampling for map comparison. We present the method in full generality, discussing the main decisions involved in its implementation. In particular, we point out the importance of the sampling method (GEO vs. TOPO) and that of the matching definition, discussing the main options used, and proposing alternatives for both key steps. We experimentally evaluate the different sampling and matching options considered on map datasets and reconstructed maps. Furthermore, we provide a code base and an interactive visualization tool to set a standard for future evaluations in the field of map construction and map comparison.

关键词： Map comparison map construction graph sampling

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graph sampling Methods for Big Complex Networks integrating Centrality, K-core, and Spectral Sparsification 20

Graph Sampling Methods for Big Complex Networks integrating ...

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35th Annual ACM Symposium on Applied Computing (SAC)

作者： Hong, Seok-Hee Lu, Shan Univ Sydney Sydney NSW Australia

ISBN: (纸本)9781450368667

graph sampling methods have been used to reduce the size of big complex graphs, however existing methods to compute graph samples based on random sampling techniques often fails to retain the important structure in the original graph. This paper introduces two new graph sampling techniques for big complex networks. The first method is based on the k-core analysis, a well-known cohesive subgroup analysis in social network analysis. The second method integrates various centrality values (Degree, Closeness, Betweenness, and vector Centrality), k-core analysis as well as spectral sparsification. Extensive experimental results with real world big complex graphs using sampling quality metrics and visual comparison show that both methods outperform existing random vertex sampling method, in particular for the benchmark (real-world) graphs.

关键词： graph sampling Centrality k-core analysis Spectral sparsification

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graph sampling WITH AND WITHOUT INPUT PRIORS

GRAPH SAMPLING WITH AND WITHOUT INPUT PRIORS

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

作者： Chepuri, Sundeep Prabhakar Eldar, Yonina C. Leus, Geert Delft Univ Technol TU Delft Delft Netherlands Technion Israel Inst Technol Haifa Israel

ISBN: (纸本)9781538646588

In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior knowledge on the original signal when available such as smoothness or subspace priors related to the underlying graph. For reconstructing arbitrary signals, we constrain the reconstruction to the graph, and provide a consistent reconstruction method, in which both the reconstructed signal and the input yield exactly the same measurements. Given a set of graph frequency domain samples, the sampling and interpolation operations may be efficiently implemented using linear shift-invariant graph filters.

关键词： graph sampling graph signal processing consistent reconstruction subspace prior frequency domain sampling

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graph sampling with Fast Random Walker on HBM-enabled FPGA Accelerators 31

Graph Sampling with Fast Random Walker on HBM-enabled FPGA A...

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31st International Conference on Field-Programmable Logic and Applications (FPL)

作者： Su, Chunyou Liang, Hao Zhang, Wei Zhao, Kun Ai, Baole Shen, Wenting Wang, Zeke Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Peoples R China Alibaba Grp Hangzhou Peoples R China Zhejiang Univ Collaborat Innovat Ctr Artificial Intelligence Hangzhou Peoples R China

ISBN: (纸本)9781665437592

graph neural networks (GNNs) have gained increasing popularity among researchers recently and have been employed in many applications. Training GNNs introduce a crucial stage called graph sampling. One of the most important sampling algorithms is Random Walk. However, Random Walk and many of its variants share and suffer from the same performance problem caused by random and fragmented memory access patterns, leading to significant system performance degradation. In this work, we present an efficient graph sampling engine on modern FPGAs integrated with in-package high bandwidth memory (HBM), which brings data closer and faster to the core logic. The hardware walker design is modular and easily scalable for massive parallelism, to fully utilize the available HBM channels. Our design also provides the flexibility to support Random Walk and two of its variants on both homogeneous and heterogeneous graphs. On real-world graph datasets, we achieve a 1.39 x-3.74 x speedup with a 2.42 x-6.69 x higher energy efficiency over highly optimized parallel baselines on a Xeon CPU. We also implement these algorithms on a NVIDIA Tesla V100 GPU and achieve comparable dynamic energy consumption.

关键词： graph sampling random walk HBM FPGA

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graph sampling: ESTIMATION OF DEGREE DISTRIBUTIONS

GRAPH SAMPLING: ESTIMATION OF DEGREE DISTRIBUTIONS

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

作者： Deri, Joya A. Moura, Jose M. F. Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA

ISBN: (纸本)9781479903566

Online social networks and the World Wide Web lead to large underlying graphs that might not be completely known because of their size. To compute reliable statistics, we have to resort to sampling the network. In this paper, we investigate four network sampling methods to estimate the network degree distribution and the so-called biased degree distribution of a 3.7 million wireless subscriber network. We measure the quality of our estimates of the degree distributions by using the Kolmogorov-Smirnov statistic. Among all four sampling methods, node sampling yields Pareto optimal sample sizes in terms of the Kolomogorov-Smirnov statistic for the degree distribution, while node-by-edge sampling yields optimal sample sizes for the biased distribution. We also find that random walk sampling performs better than the Metropolis-Hastings random walk.

关键词： graph sampling Markov Chain Monte Carlo (MCMC) sampling Pareto optimality large-scale networks

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