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Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation

ADVANCES IN COMPUTATIONAL MATHEMATICS 2025年第2期51卷 1-27页

作者： Albrecht, Kristof Entzian, Juliane Iske, Armin Univ Hamburg Dept Math Hamburg Germany

This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a low-dimensional Euclidean space. Due to Aronszajn (Trans. Am. Math. Soc. 68, 337-404 1950), the product of positive semi-definite kernel functions is again positive semi-definite, where, moreover, the corresponding native space is a particular instance of a tensor product, referred to as Hilbert tensor product. We first analyze the general problem of multivariate interpolation by product kernels. Then, we further investigate the tensor product structure, in particular for grid-like samples. We use this case to show that the product of positive definite kernel functions is again positive definite. Moreover, we develop an efficient computation scheme for the well-known Newton basis. Supporting numerical examples show the good performance of product kernels, especially for their flexibility.

关键词： Kernel-based approximation Product kernels greedy algorithms

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An Iterated Carousel greedy Algorithm for Finding Minimum Positive Influence Dominating Sets in Social Networks

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IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS 2022年第3期9卷 830-838页

作者： Shan, Yunfan Kang, Qinma Xiao, Ran Chen, Yiran Kang, Yunfan Shandong Univ Sch Mech Elect & Informat Engn Weihai 264209 Peoples R China Univ Calif Riverside Dept Comp Sci & Engn Riverside CA 92521 USA

The online social network has become an integral part of modern society and serves as an excellent platform for information diffusion, marketing, and so on. The minimum positive influence dominating set (MPIDS) problem aims to find a set of at least half neighbors of every individual with minimum cardinality and has lots of applications in the social network. Even though numerous algorithms have been proposed for this hard combinatorial problem, challenges such as poor quality and scalability have motivated the researchers for better solutions. In this article, we focus on designing a simple and effective method and propose an iterated carousel greedy (ICG) algorithm for the MPIDS problem. The destruction, carousel, and reconstruction (DCR) procedures are well-designed based on the problem-specific knowledge to improve the algorithm performance, while maintaining the simplicity of the ICG algorithm. The ICG algorithm uses a fast greedy algorithm to generate an initial solution with a certain quality. It then obtains a sequence of better solutions by iterating over DCR phases. A carefully designed experiment is carried out to determine the best parameter configuration. The experimental results on real-world networks indicate that the proposed ICG algorithm significantly outperforms the current state-of-the-art algorithms.

关键词： Social networking (online) Heuristic algorithms greedy algorithms Approximation algorithms Search problems Memetics Mathematical model Carousel greedy iterated greedy metaheuristic minimum positive influence dominating set (MPIDS) social networks

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Let's Make Block Coordinate Descent Converge Faster: Faster greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-74页

作者： Nutini, Julie Laradji, Issam Schmidt, Mark Univ British Columbia Dept Comp Sci ICICS CS Bldg 201-2366 Main Mall Vancouver BC V6T 1Z4 Canada

Block coordinate descent (BCD) methods are widely used for large-scale numerical opti-mization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block se-lection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guaran-tee more progress per iteration than the Gauss-Southwell rule;(ii) explore practical issues like how to implement the new rules when using "variable" blocks;(iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for prob-lems with sparse dependencies between variables;and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numer-ical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

关键词： Convex optimization convergence rates block coordinate descent greedy algorithms large-scale

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Pointwise-Sparse Actuator Scheduling for Linear Systems With Controllability Guarantee

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 2361-2366页

作者： Ballotta, Luca Joseph, Geethu Thete, Irawati Rahul Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands Delft Univ Technol Signal Proc Syst Grp NL-2628 CD Delft Netherlands Texas Instruments Inc APP IPP MPP Bengaluru 560093 India

This letter considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization.

关键词： Schedules Actuators Controllability greedy algorithms Sparse matrices Costs Measurement Indexes Control design Signal processing algorithms Actuator scheduling control design energy-aware control greedy algorithm sparse control

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Iterative greedy LMI for Sparse Control

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 986-991页

作者： Nagahara, Masaaki Ogura, Masaki Yamamoto, Yutaka Univ Kitakyushu Inst Environm Sci & Technol Fukuoka 8080139 Japan Osaka Univ Grad Sch Informat Sci & Technol Suita Osaka 5650871 Japan Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan

In this letter, we propose a novel method to find matrices that satisfy sparsity and LMI (linear matrix inequality) constraints at the same time. This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter design, to name a few. We propose an efficient algorithm for the solution based on Dykstra's projection algorithm. We then prove a convergence theorem of the proposed algorithm, and show some control examples to illustrate merits and demerits of the proposed method.

关键词： Optimization Sparse matrices Projection algorithms Linear matrix inequalities Finite impulse response filters Eigenvalues and eigenfunctions Power system dynamics greedy algorithms linear matrix inequalities sparse control network theory

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Base station siting optimization based on greedy and simulated annealing algorithms

Base station siting optimization based on greedy and simulat...

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Signal Processing, Communications and Engineering Management Conference (ISPCEM), International

作者： Linfeng Du Yu Xiang Nuo Xu College of Computer Science Sichuan University Sichuan Chengdu China

In this paper, we establish an optimization model based on the greedy algorithm and simulated annealing algorithm to provide a reference for network operators and base station planners to select sites for 5G network base stations, and establish a transitive clustering model based on chunking idea and concurrent set for larger data volume. In this paper, under the constraint that the distance between new base stations and between old and new base stations is greater than 10, the service coverage is taken as the first optimization objective and the base station construction cost is taken as the second optimization objective, and the construction cost is taken as the first optimization objective after the service coverage reaches 90%. Based on the idea of the greedy algorithm, we calculate the “cost performance” of the optional base station coordinates under the establishment of two types of base stations, macro, and micro. On this basis, the formula for determining whether a weak coverage point is covered by a BTS is adjusted, and the angle constraints of three sectors are newly added, and the simulated annealing algorithm is used to randomly adjust the angle of three sectors of some BTSs at each iteration. The model-derived BTS siting scheme can cover 90% of the total service volume of the weak coverage point.

关键词： greedy algorithms Base stations Solid modeling Costs Engineering management Signal processing algorithms Simulated annealing

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greedy Minimum-Energy Scheduling 1

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21st International Workshop on Approximation and Online algorithms (WAOA) part of ALGO Conference

作者： Bidlingmaier, Gunther Tech Univ Munich Dept Comp Sci Munich Germany

ISBN: (数字)9783031498152

ISBN: (纸本)9783031498145;9783031498152

We consider the problem of energy-efficient scheduling across multiple processors with a power-down mechanism. In this setting a set of n jobs with individual release times, deadlines, and processing volumes must be scheduled across m parallel processors while minimizing the consumed energy. When idle, each processor can be turned off to save energy, while turning it on requires a fixed amount of energy. For the special case of a single processor, the greedy Left-to-Right algorithm [7] guarantees an approximation factor of 2. We generalize this simple greedy policy to the case of m >= 1 processors running in parallel and show that the energy costs are still bounded by 2OPT+P, whereOPT is the energy consumed by an optimal solution and P < OPT is the total processing volume. Our algorithm has a running time of O(nf log d), where d is the difference between the last deadline and the earliest release time, and f is the running time of a maximum flow calculation in a network of O( n) nodes.

关键词： Scheduling greedy algorithms Approximation algorithms

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Unsupervised Deep Learning for Distributed Service Function Chain Embedding

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IEEE ACCESS 2023年 11卷 91660-91672页

作者： Rodis, Panteleimon Papadimitriou, Panagiotis Univ Macedonia Dept Appl Informat Thessaloniki 54636 Greece

Network Function Virtualization (NFV) has paved the way for the migration of Virtual Network Functions (VNFs) into multi-tenant datacenters, lowering the barrier for the introduction of new processing functionality into the network. Recent trends for resource orchestration across the entire compute continuum raise the need for decision making at low timescales, a requirement which can be hardly met by centralized resource optimizers that rely either on Linear Programming or Machine Learning (ML). In this respect, we present a distributed approach tailored to a crucial resource orchestration aspect, i.e., the embedding of Service Function Chains (SFCs) onto large-scale virtualized network infrastructures. In order to confront the computational hardness of the SFC embedding problem, we utilize a clustering method for the partitioning of the solution space, empowering the search for efficient solutions in parallel across all clusters. Another salient feature of our approach is the use of unsupervised deep learning for the computation of embeddings within each cluster. Our distributed SFC embedding framework is benchmarked against a state-of-the-art heuristic and a distributed greedy algorithm. Our evaluation results uncover notable gains in terms of resource efficiency, combined with solver runtimes in the order of milliseconds with thousands of substrate nodes.

关键词： Substrates greedy algorithms Deep learning Computational modeling Bandwidth Service function chaining Search problems Network function virtualization Distributed computing resource orchestration deep learning distributed computation

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A Novel greedy Algorithm for Optimazition of Multibeam Survey Line 6

A Novel Greedy Algorithm for Optimazition of Multibeam Surve...

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6th IEEE International Conference on Automation, Electronics and Electrical Engineering, AUTEEE 2023

作者： Liu, Wenjie Zheng, Boyou Ge, Yunxiang Xie, Bing National University of Defense Technology Changsha China

ISBN: (纸本)9798350305623

This paper focuses on an Optimal Problem of Multibeam Survey Line (OPMSL) under complex and variable terrain of seabed. Firstly, we analyze overlap rate and coverage width of the lines in different course directions during multibeam line surveying, based on which we establish an Isobath path planning model. Then, we analyze the angle relationship between the slope line and the survey line, and projected the OPPM from 3D surface to the two-dimensional space. Throughout the dimension reduction processing, it actually reduces the problem search space. Thirdly, considering irregular and continuous slope characteristics of seabed topography, we propose to use greedy algorithms to solve the OPPM. Finally, we design a series of simulation experiment to check our algorithm performance. The result shows that, isobath path planning according to the greedy algorithm is optimal. © 2023 IEEE.

关键词： Coverage widths greedy algorithms Isobath paths Multibeam survey line Optimization problems Slope lines

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A Submodular Optimization Framework for Imbalanced Text Classification With Data Augmentation

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IEEE ACCESS 2023年 11卷 41680-41696页

作者： Alemayehu, Eyor Fang, Yi Santa Clara Univ Dept Comp Sci & Engn Santa Clara CA 95053 USA

In the domain of text classification, imbalanced datasets are a common occurrence. The skewed distribution of the labels of these datasets poses a great challenge to the performance of text classifiers. One popular way to mitigate this challenge is to augment underwhelmingly represented labels with synthesized items. The synthesized items are generated by data augmentation methods that can typically generate an unbounded number of items. To select the synthesized items that maximize the performance of text classifiers, we introduce a novel method that selects items that jointly maximize the likelihood of the items belonging to their respective labels and the diversity of the selected items. Our proposed method formulates the joint maximization as a monotone submodular objective function, whose solution can be approximated by a tractable and efficient greedy algorithm. We evaluated our method on multiple real-world datasets with different data augmentation techniques and text classifiers and compared results with several baselines. The experimental results demonstrate the effectiveness and efficiency of the proposed method.

关键词： Data augmentation Data models Optimization Predictive models Perturbation methods Task analysis greedy algorithms text classification imbalanced datasets submodular optimization

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