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Efficient and Adaptive CUR Matrix Decomposition for Flexible Compression of Network Monitoring Data

IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2025年第3期12卷 2231-2242页

作者： Wen, Jigang Wang, Shiqin Xie, Kun Tian, Jiazheng Wang, Yixuan Hunan Univ Sci & Technol Sch Comp Sci & Engn Xiangtan 411201 Peoples R China Hunan Univ Coll Comp Sci & Elect Engn Changsha 410012 Peoples R China Hunan Univ Key Lab Convergence Comp Supercomp & Artificial In Minist Educ Changsha 410002 Peoples R China

Network-wide monitoring is indispensable for a variety of network applications. However, as network sizes increase and the demand for fine-grained, continuous measurements grows, the challenges associated with storing and transmitting such data intensify. Recent studies have shown that network-wide monitoring data exhibits a low-rank structure, which can be exploited using matrix decomposition techniques for compression. This paper presents a compression algorithm for low-rank matrices based on CUR decomposition, which offers enhanced interpretability compared to SVD-based compression. Existing CUR solutions, however, lack the capability for fast and flexible compression that can dynamically adjust to matrix size requirements while preserving maximal approximation accuracy. We address the challenges associated with CUR row and column selection by formulating it as a deterministic CUR matrix decomposition problem, involving a selection matrix $\mathbf{W}$. To achieve rapid compression, we propose an algorithm that effectively accelerates the process of solving for the parameter matrix $\mathbf{W}$. Our approach reveals that the vectors in $\mathbf{W}$ indicate the importance of each row and column in forming the respective row and column subspaces. Leveraging this insight, we develop a flexible compression algorithm based on the sorted vectors in the selection matrix $\mathbf{W}$. This method not only ensures the required compression ratio but also maintains maximal approximation accuracy. Extensive experiments on both synthesized and real data demonstrate that our algorithm can deliver fast and precise matrix compression, aligning with the desired compression ratio.

关键词： Matrix decomposition Monitoring Vectors approximation algorithms Accuracy Sparse matrices Frequency measurement Compression algorithms Electronic mail Computational complexity Matrix compression matrix decomposition CUR decomposition

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Set-Membership State Estimation for 2-D Roesser Systems Based on Zonotope Radius and Its Application

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2024年第1期71卷 465-469页

作者： Zhao, Chenyang Zhang, Xiangkui Xu, Changyi Fei, Zhongyang Dalian Univ Technol Key Lab Intelligent Control & Optimizat Ind Equipm Minist Educ Dalian 116024 Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian 116024 Peoples R China Dalian Univ Technol Sch Artificial Intelligence Dalian 116024 Peoples R China

This brief is concerned with the problem of zonotopic set-membership state estimation for 2-D Roesser systems subjected to unknown-but-bounded disturbance. First ,a general guaranteed state estimation algorithm is designed to obtain a set of zonotopes containing the system states that are consistent with the model parameters and the measurement out-puts. Then, based on the constructed P-radius functions, an optimal correction matrix design criterion with L-infinity performance is provided for the obtained zonotope. Furthermore, an offline optimization problem is constructed to obtain the optimal correction matrix. Finally, a numerical example is provided to certify the effectiveness of the proposed approach.

关键词： State estimation Estimation Symmetric matrices Optimization Integrated circuit modeling approximation algorithms Upper bound 2-D systems set-membership estimation zonotope Roesser model

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Accelerating the k-Means plus plus Algorithm by Using Geometric Information

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IEEE ACCESS 2025年 13卷 67693-67717页

作者： Corominas, Guillem Rodriguez Blesa, Maria J. Blum, Christian Univ Politecn Catalunya UPC Dept Comp Sci Barcelona 08034 Spain Artificial Intelligence Res Inst IIIA CSIC Bellaterra 08193 Spain

Clustering is a fundamental task in data analysis with applications across a wide range of fields, such as computer vision, pattern recognition, and data mining. Real-world use cases include social network analysis, medical imaging, market segmentation, and anomaly detection, to name a few. In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate that the accelerated version outperforms the standard k-means++ version in terms of the number of visited points and distance calculations, achieving greater speedup as the number of clusters increases. The version utilizing the Triangle Inequality is particularly effective for low-dimensional data, while the additional norm-based filter enhances performance in high-dimensional instances with greater norm variance among points. Additional experiments show the behavior of our algorithms when executed concurrently across multiple jobs and examine how memory performance impacts practical speedup.

关键词： Clustering algorithms approximation algorithms Standards Measurement Machine learning algorithms Vectors Filters Computational efficiency Scalability Prediction algorithms Clustering D-2 sampling k-means plus plus norm triangle inequality

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Autonomous clustering by fast find of mass and distance peaks

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IEEE Transactions on Pattern Analysis and Machine Intelligence 2025年第7期47卷 5336-5349页

作者： Yang, Jie Lin, Chin-Teng Australian AI Institute FEIT University of Technology Sydney Computational Intelligence and Brain Computer Interface Lab Australia

Clustering is an essential analytical tool across a wide range of scientific fields, including biology, chemistry, astronomy, and pattern recognition. This paper introduces a novel clustering algorithm as a competitive alternative to existing methods, based on the intuitive principle that a cluster should merge with its nearest neighbor with a higher mass, unless both clusters have relatively large masses and the distance between them is also substantial. By identifying peaks in mass and distance, the algorithm effectively detects and removes incorrect mergers. The proposed method is entirely parameter-free, enabling it to autonomously recognize various cluster types, determine the optimal number of clusters, and identify noise. Extensive experiments on synthetic and real-world data sets demonstrate the algorithm's versatility and consistently strong performance compared to other state-of-the-art methods. © 1979-2012 IEEE.

关键词： Clustering algorithms Partitioning algorithms Noise Nearest Neighbor Methods Merging Torque Biology approximation algorithms Accuracy High Dimensional Data Clustering Parameter Free Data Analysis Unsupervised Learning Clustering Algorithm Real World Data Large Mass Real World Datasets Hierarchical Clustering Distance Matrix Image Dataset Density Estimation Cutoff Distance Agglomerative Clustering Challenging Dataset Average Rank Hierarchical Algorithm High Dimensional Datasets Abnormal Connectivity Hierarchical Tree Hierarchical Clustering Algorithm Recent algorithms Square Of The Distance Agglomerative Method Automatic Determination Cluster Mass Automatic Clustering Global Mean Value Optical Character Recognition Hierarchical Clustering Method Cell Tracking Partitional Clustering Comprehensive Evaluation Image Recognition

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Oversampled Low Ambiguity Zone Sequences for Channel Estimation Over Doubly Selective Channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第4期73卷 2616-2630页

作者： Gu, Zhi Zhou, Zhengchun Fan, Pingzhi Adhikary, Avik Ranjan Liu, Zilong Southwest Jiaotong Univ Chengdu 611756 Peoples R China Southwest Jiaotong Univ Inst Mobile Commun Chengdu 611756 Peoples R China Univ Essex Sch Comp Sci & Elect Engn Colchester CO4 3SQ England

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called "oversampled low ambiguity zone (O-LAZ) sequences". Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

关键词： Channel estimation OFDM Correlation Complexity theory Optimization Iterative algorithms Doppler shift approximation algorithms Heuristic algorithms Frequency estimation Ambiguity function channel estimation doubly selective channel ITROX algorithm orthogonal frequency division multiplexing (OFDM) oversampled ambiguity zone (O-AZ) sequences

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An Improved approximation Guarantee for Prize-Collecting TSP 2023

An Improved Approximation Guarantee for Prize-Collecting TSP

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55th Annual ACM Symposium on Theory of Computing (STOC) part of the ACM Federated Computing Research Conference (FCRC)

作者： Blauth, Jannis Naegele, Martin Univ Bonn Res Inst Discrete Math & Hausdorff Ctr Math Bonn Germany

ISBN: (纸本)9781450399135

We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may choose to not include a vertex of the input graph in the returned tour at the cost of a given vertex-dependent penalty, and the objective is to balance the length of the tour and the incurred penalties for omitted vertices by minimizing the sum of the two. We present an algorithm that achieves an approximation guarantee of 1.774 with respect to the natural linear programming relaxation of the problem. This significantly reduces the gap between the approximability of classical TSP and PCTSP, beating the previously best known approximation factor of 1.915. As a key ingredient of our improvement, we present a refined decomposition technique for solutions of the LP relaxation, and show how to leverage components of that decomposition as building blocks for our tours.

关键词： approximation algorithms traveling salesperson problem linear programming splitting off randomized rounding

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A Scalable Algorithm for Fair Influence Maximization with Unbiased Estimator

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IEEE Transactions on Knowledge and Data Engineering 2025年第7期37卷 3881-3895页

作者： Rui, Xiaobin Wang, Zhixiao Peng, Hao Chen, Wei Yu, Philip S. China University of Mining and Technology School of Computer Science Jiangsu Xuzhou221116 China Mine Digitization Engineering Research Center of the Ministry of Education Jiangsu Xuzhou221116 China Beihang University School of Cyber Science and Technology Beijing100191 China Theory Center of Microsoft Research Asia Beijing100080 China University of Illinois at Chicago Department of Computer Science ChicagoIL60607 United States

This paper studies the fair influence maximization problem with efficient algorithms. In particular, given a graph G, a community structure C consisting of disjoint communities, and a budget k, the problem asks to select a seed set S (||S|| = k) that maximizes the influence spread while narrowing the influence gap between different communities. This problem derives from some significant social scenarios, such as health interventions (e.g. suicide/HIV prevention) where individuals from racial minorities or LGBTQ communities may be disproportionately excluded from the benefits of the intervention. To depict the concept of fairness in the context of influence maximization, researchers have proposed various notions of fairness, where the welfare fairness notion that better balances fairness level and influence spread has shown promising effectiveness. However, the lack of efficient algorithms for optimizing the objective function under welfare fairness restricts its application to networks of only a few hundred nodes. In this paper, we modify the objective function of welfare fairness to maximize the exponentially weighted sum and the logarithmically weighted sum over all communities' influenced fractions (utility). To achieve efficient algorithms with theoretical guarantees, we first introduce two unbiased estimators: one for the fractional power of the arithmetic mean and the other for the logarithm of the arithmetic mean. Then, by adapting the Reverse Influence Sampling (RIS) approach, we convert the optimization problem to a weighted maximum coverage problem. We also analyze the number of reverse reachable sets needed to approximate the fair influence at a high probability. Finally, we present an efficient algorithm that guarantees 1 - 1/e - ϵ (positive objective function) or 1 + 1/e + ϵ (negative objective function) approximation for any small ϵ > 0. Experiments demonstrate that our proposed algorithm could efficiently handle large-scale networks with good performa

关键词： approximation algorithms

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Online Influence Maximization With Semi-Bandit Feedback Under Corruptions

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2025年第3期12卷 2308-2321页

作者： Cheng, Xiaotong Nourani-Koliji, Behzad Maghsudi, Setareh Ruhr Univ Bochum Dept Elect Engn & Informat Technol D-44801 Bochum Germany Univ Tubingen Dept Comp Sci D-72074 Tubingen Germany Fraunhofer Heinrich Hertz Inst D-10587 Berlin Germany

In this article, we investigate the online influence maximization in social networks. Most prior research studies on online influence maximization assume that the nodes are fully cooperative and act according to their stochastically generated influence probabilities on others. In contrast, we study the online influence maximization problem in the presence of some corrupted nodes whose damaging effects diffuse throughout the network. We propose a novel bandit algorithm, CW-IMLinUCB, which robustly learns and finds the optimal seed set in the presence of corrupted users. Theoretical analyses establish that the regret performance of our proposed algorithm is better than the state-of-the-art online influence maximization algorithms. Extensive empirical evaluations on synthetic and real-world datasets also show the superior performance of our proposed algorithm.

关键词： Integrated circuit modeling Social networking (online) Diffusion models approximation algorithms Stochastic processes Reviews Vectors Training Optimization Network topology Contextual bandit influence maximization sequential decision-making

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A Nearly Time-Optimal Distributed approximation of Minimum Cost k-Edge-Connected Spanning Subgraph 34

A Nearly Time-Optimal Distributed Approximation of Minimum C...

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34th ACM-SIAM Annual Symposium on Discrete algorithms (SODA)

作者： Dory, Michal Ghaffari, Mohsen Univ Haifa Haifa Israel MIT Cambridge MA USA

ISBN: (纸本)9781611977554

The minimum-cost k-edge-connected spanning subgraph (k-ECSS) problem is a generalization and strengthening of the well-studied minimum-cost spanning tree (MST) problem. While the round complexity of distributedly computing the latter has been well-understood, the former remains mostly open, especially as soon as k >= 3. In this paper, we present the first distributed algorithm that computes an approximation of k -ECSS in sublinear time for general k. Concretely, we describe a randomized distributed algorithm that, in (O) over tilde (k(D + k root n)) rounds, computes a k-edge-connected spanning subgraph whose cost is within an O (log n log k) factor of optimal. Here, n and D denote the number of vertices and diameter of the graph, respectively. This time complexity is nearly optimal for any k = poly(log n), almost matching an Omega(D+root n/k) lower bound. Our algorithm is the first to achieve a sublinear round complexity for k >= 3. We note that this case is considerably more challenging than the well-studied and well-understood k = 1 case|better known as MST|and the closely related k = 2 case. Our algorithm is based on reducing the k-ECSS problem to k set cover instances, in which we gradually augment the connectivity of the spanning subgraph. To solve each set cover instance, we combine new structural observations on minimum cuts with graph sketching ideas. One key ingredient in our algorithm is a novel structural lemma that allows us to compress the information about all minimum cuts in a graph into a succinct representation, which is computed in a decentralized fashion. We hope that this succinct representation may find applications in other computational settings or for other problems.

关键词： approximation algorithms

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Exact Solutions to Minmax Optimal Control Problems for Constrained Noisy Linear Systems

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 2063-2068页

作者： Ganguly, Siddhartha Chatterjee, Debasish Indian Inst Technol Syst & Control Engn Mumbai 400076 India

We present a numerically tractable technique for exact solutions to a class of robust minmax optimal control problems (OCPs) under constraints. The underlying dynamical system is assumed to be linear and subjected to bounded disturbances, and the objective function is a sum of quadratic stage and quadratic terminal costs. We impose convex constraints on the states and the control;the control minimizes and the disturbance maximizes the objective. The resulting constrained minmax OCP admits a reformulation in the language of convex semi-infinite programs (CSIPs), and we employ recently developed numerical tools in CSIP to solve the ensuing optimization problem. A simple benchmark numerical example is provided to illustrate our results.

关键词： Optimization Optimal control Vectors Uncertainty approximation algorithms Symmetric matrices Noise measurement Robust optimal control control under uncertainty constrained control linear systems

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