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Evaluation of the Sample Clustering Process on graphs

IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2020年第7期32卷 1333-1347页

作者： Zhang, Jianpeng Pei, Yulong Fletcher, George Pechenizkiy, Mykola Natl Digital Switching Syst Engn & Technol R&D Ct Zhengzhou Peoples R China Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

An increasing number of networks are becoming large-scale and continuously growing in nature, such that clustering on them in their entirety could be intractable. A feasible way to overcome this problem is to sample a representative subgraph and exploit its clustering structure (namely, sample clustering process). However, there are two issues that we should address in current studies. One underlying question is how to evaluate the clustering quality of the entire sample clustering process. Another non-trivial issue is that multiple ground-truths exist in networks, thus evaluating the clustering results in such scenario is also a challenging task. In this paper, first we utilize the set-matching methodology to quantitatively evaluate how differently the clusters of the sampled counterpart correspond to the ground-truth(s) in the original graph, and propose several new quality metrics to capture the differences of clustering structure in various aspects. Second, we put forward an evaluation framework for the general problems of evaluating the clustering quality on graph samples. Extensive experiments on various synthetic and real-world graphs demonstrate that our new quality metrics are more accurate and insightful for the sample clustering evaluation than conventional metrics (e.g., NMI). Thus the evaluation framework is effective and practical to assess the clustering quality of the sample clustering process on massive graphs.

关键词： Measurement Clustering algorithms Task analysis Memory management Social networking (online) Knowledge engineering Indexes graph clustering graph sampling multiple ground-truths evaluation framework quality metrics

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Efficient sampling of complex interdependent and multiplex networks

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JOURNAL OF COMPLEX NETWORKS 2021年第5期9卷 1-21页

作者： Subasi, Omer Chatterjee, Samrat Pacific Northwest Natl Lab Phys & Computat Sci Directorate 902 Battelle BlvdPOB 999 Richland WA 99352 USA

Efficient sampling of interdependent and multiplex infrastructure networks is critical for effectively applying failure and recovery algorithms in real-world settings, as well as to generate property-preserving reduced-order graph-based ensembles that address topological uncertainties. In this article, we first explore the performance, that is, the success in preserving graph properties, of graph sampling algorithms for interdependent and multiplex networks with synthetic and real-world graphs. We simulate sampling algorithms under different parameter settings. These settings include probabilistic graph generators, coupling patterns and various performance metrics. Our results show that while Random Node and Random Walk sampling algorithms perform best for interdependent networks, Random Edge and Forest Fire sampling algorithms perform best for multiplex networks. Second, we propose and implement a novel similarity-based sampling algorithm for multiplex networks that samples only log(N) number of layers of an N-layer multiplex network while yielding computational savings with performance guarantees. Experimental results show that similarity-based sampling outperforms complete sampling of all layers while decreasing performance costs from a linear scale to a logarithmic one. Our results also indicate that similarity-based sampling outperforms complete sampling and random selection in nearly all scenarios when tested with real-world data.

关键词： graph sampling interdependent networks multiplex networks graph generators coupling patterns

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Asymptotically Optimal sampling Policy for Quickest Change Detection With Observation-Switching Cost

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 1332-1346页

作者： Lau, Tze Siong Tay, Wee Peng Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

We consider the problem of quickest change detection (QCD) in a signal where its observations are obtained using a set of actions, and switching from one action to another comes with a cost. The objective is to design a stopping rule consisting of a sampling policy to determine the sequence of actions used to observe the signal and a stopping time to quickly detect for the change, subject to a constraint on the average observation-switching cost. We propose an open-loop sampling policy of finite window size and a generalized likelihood ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show that the GLR CuSum stopping time is asymptotically optimal with a properly designed sampling policy and formulate the design of this sampling policy as a quadratic programming problem. We prove that it is sufficient to consider policies of window size not more than one when designing policies of finite window size and propose several algorithms that solve this optimization problem with theoretical guarantees. Finally, we apply our approach to the problem of QCD of a partially observed graph signal and empirically demonstrate the performance of our proposed stopping times.

关键词： Switches Probability density function Quadratic programming Observers Random variables Quantization (signal) Bandwidth Quickest change detection GLR CuSum sampling policy graph sampling

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sampling large Internet topologies for simulation purposes

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COMPUTER NETWORKS 2007年第15期51卷 4284-4302页

作者： Krishnamurthy, Vaishnavi Faloutsos, Michalis Chrobak, Marek Cui, Jun-Hong Lao, Li Percus, Allon G. Univ Calif Riverside Dept Comp Sci & Engn Riverside CA 92521 USA Univ Connecticut Storrs CT USA Univ Calif Los Angeles Los Angeles CA 90024 USA Los Alamos Natl Labs Los Alamos NM 87545 USA

In this paper, we develop methods to "sample" a small realistic graph from a large Internet topology. Despite recent activity, modeling and generation of realistic graphs resembling the Internet is still not a resolved issue. All previous work has attempted to grow such graphs from scratch. We address the complementary problem of shrinking an existing topology. In more detail, this work has three parts. First, we propose a number of reduction methods that can be categorized into three classes: (a) deletion methods, (b) contraction methods, and (c) exploration methods. We prove that some of them maintain key properties of the initial graph. We implement our methods and show that we can effectively reduce the nodes of an Internet graph by as much as 70% while maintaining its important properties. Second, we show that our reduced graphs compare favorably against construction-based generators. Finally, we successfully validate the effectiveness of our best methods in an actual performance evaluation study of multicast routing. Apart from its practical applications, the problem of graph sampling is of independent interest. (c) 2007 Elsevier B.V. All rights reserved.

关键词： graph modeling graph sampling graph properties

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Efficient frequent subgraph mining on large streaming graphs

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INTELLIGENT DATA ANALYSIS 2019年第1期23卷 103-132页

作者： Ray, Abhik Holder, Lawrence B. Bifet, Albert Washington State Univ Sch EECS Pullman WA 99164 USA Telecom ParisTech LTCI F-75013 Paris France

We propose an efficient, approximate algorithm to solve the problem of finding frequent subgraphs in large streaming graphs. The graph stream is treated as batches of labeled nodes and edges. Our proposed algorithm finds the set of frequent subgraphs as the graph evolves after each batch. The computational complexity is bounded to linear limits by looking only at the changes made by the most recent batch, and the historical set of frequent subgraphs. As a part of our approach, we also propose a novel sampling algorithm that samples regions of the graph that have been changed by the most recent update to the graph. The performance of the proposed approach is evaluated using five large graph datasets, and our approach is shown to be faster than the state of the art large graph miners while maintaining their accuracy. We also compare our sampling algorithm against a well known sampling algorithm for network motif mining, and show that our sampling algorithm is faster, and capable of discovering more types of patterns. We provide theoretical guarantees of our algorithm's accuracy using the well known Chernoff bounds, as well as an analysis of the computational complexity of our approach.

关键词： Streaming graphs frequent subgraph mining chernoff bounds graph sampling

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Hierarchical sampling for the Visualization of Large Scale-Free graphs

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER graphICS 2023年第12期29卷 5111-5123页

作者： Jiao, Bo Lu, Xin Xia, Jingbo Gupta, Brij Bhooshan Bao, Lei Zhou, Qingshan Xiamen Univ Sch Informat Sci &Technol Tan Kah Kee Coll Zhangzhou 361005 Fujian Peoples R China Foshan Univ Sch Math & BigData Foshan 528011 Guangdong Peoples R China Asia Univ Dept Comp Sci & Informat Engn Taichung 413 Taiwan Lebanese Amer Univ Beirut 1102 Lebanon King Abdulaziz Univ Jeddah 21589 Saudi Arabia

graph sampling frequently compresses a large graph into a limited screen space. This paper proposes a hierarchical structure model that partitions scale-free graphs into three blocks: the core, which captures the underlying community structure, the vertical graph, which represents minority structures that are important in visual analysis, and the periphery, which describes the connection structure between low-degree nodes. A new algorithm named hierarchical structure sampling (HSS) was then designed to preserve the characteristics of the three blocks, including complete replication of the connection relationship between high-degree nodes in the core, joint node/degree distribution between high- and low-degree nodes in the vertical graph, and proportional replication of the connection relationship between low-degree nodes in the periphery. Finally, the importance of some global statistical properties in visualization was analyzed. Both the global statistical properties and local visual features were used to evaluate the proposed algorithm, which verify that the algorithm can be applied to sample scale-free graphs with hundreds to one million nodes from a visualization perspective.

关键词： graph sampling large scale-free graph graph visualization

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APPROXIMATE sampling AND COUNTING OF graphS WITH NEAR-REGULAR DEGREE INTERVALS

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2024年第4期38卷 2812-2840页

作者： Amanatidis, Georgios Kleer, Pieter Univ Essex Sch Math Stat & Actuarial Sci Colchester England Archimedes Athena RC Athens Greece Tilburg Univ Tilburg Sch Econ & Management NL-5037 AB Tilburg Netherlands

The approximate uniform sampling of graphs with a given degree sequence is a wellknown, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we study a generalization of the problem, where degree intervals are specified instead of a single degree sequence. We are interested in sampling and counting graphs whose degree sequences satisfy the corresponding degree interval constraints. A natural scenario where this problem arises is in hypothesis testing on networks that are only partially observed. We provide the first fully polynomial almost uniform sampler (FPAUS) as well as the first fully polynomial randomized approximation scheme (FPRAS) for sampling and counting, respectively, graphs with near-regular degree intervals, i.e., graphs in which every node has a degree from an interval not too far away from a given r \in N. In order to design our FPAUS, we rely on various state-of-the-art tools from Markov chain theory and combinatorics. In particular, by carefully using Markov chain decomposition and comparison arguments, we reduce part of our problem to the recent breakthrough of Anari et al. [Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 2019, pp. 1--12] on sampling a base of a matroid under a strongly log-concave probability distribution, and we provide the first nontrivial algorithmic application of a breakthrough asymptotic enumeration formula of Liebenau and Wormald [J. Eur. Math. Soc., 26 (2023), pp. 1-40]. As a more direct approach, we also study a natural Markov chain recently introduced by Rechner, Strowick and Mu"\ller-Hannemann [J. Complex Netw., 6 (2018), pp. 833--858], based on three local operations---switches, hinge flips, and additions/deletions of an edge. We obtain the first theoretical results for this Markov chain, showing it is rapidly mixing for the case of near-regular degree intervals of size at most one.

关键词： graph sampling switch Markov chain degree intervals

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SAKE: Estimating Katz Centrality Based on sampling for Large-Scale Social Networks

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ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA 2021年第4期15卷 1–21页

作者： Lin, Mingkai Li, Wenzhong Song, Lynda J. Nguyen, Cam-Tu Wang, Xiaoliang Lu, Sanglu Nanjing Univ State Key Lab Novel Software Technol Xianlin Rd 163 Nanjing 210023 Jiangsu Peoples R China Nanjing Univ Sino German Inst Social Comp Xianlin Rd 163 Nanjing 210023 Jiangsu Peoples R China Univ Leeds Leeds LS2 9JT W Yorkshire England

Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz-Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE, a sampling-based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.

关键词： Social network Katz centrality graph sampling

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"What Do Your Friends Think?": Efficient Polling Methods for Networks Using Friendship Paradox

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2021年第3期33卷 1291-1305页

作者： Nettasinghe, Buddhika Krishnamurthy, Vikram Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA

This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose two NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph, and (ii) the social network graph is unknown but, uniformly sampled nodes from the network are available. For both cases, algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.

关键词： Social networking (online) Voting Forecasting sampling methods Color Simulation Indexes Opinion polling election forecasting expectation polling friendship paradox variance reduction stochastic ordering degree distribution graph sampling social networks social sampling

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Obtaining Provably Legitimate Internet Topologies

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IEEE-ACM TRANSACTIONS ON NETWORKING 2012年第1期20卷 271-284页

作者： He, Yihua Faloutsos, Michalis Krishnamurthy, Srikanth V. Chrobak, Marek Univ Calif Riverside Dept Comp Sci & Engn Riverside CA 92521 USA

What topologies should be used to evaluate protocols for interdomain routing? Using the most current Internet topology is not practical since its size is prohibitive for detailed, packet-level interdomain simulations. Besides being of moderate size, the topology should be policy-aware, that is, it needs to represent business relationships between adjacent nodes (that represent autonomous systems). In this paper, we address this issue by providing a framework to generate small, realistic, and policy-aware topologies. We propose HBR, a novel sampling method, which exploits the inherent hierarchy of the policy-aware Internet topology. We formally prove that our approach generates connected and legitimate topologies, which are compatible with the policy-based routing conventions and rules. Using simulations, we show that HBR generates topologies that: 1) maintain the graph properties of the real topology;2) provide reasonably realistic interdomain simulation results while reducing the computational complexity by several orders of magnitude as compared to the initial topology. Our approach provides a permanent solution to the problem of interdomain routing evaluations: Given a more accurate and complete topology, HBR can generate better small topologies in the future.

关键词： graph sampling interdomain routing Internet topology simulation

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