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randomized algorithms for Computation of Tucker Decomposition and Higher Order SVD (HOSVD)

IEEE ACCESS 2021年 9卷 28684-28706页

作者： Ahmadi-Asl, Salman Abukhovich, Stanislav Asante-Mensah, Maame G. Cichocki, Andrzej Phan, Anh Huy Tanaka, Tohishisa Oseledets, Ivan Skolkovo Inst Sci & Technol SKOLTECH CDISE Moscow 121205 Russia Tokyo Univ Agr & Technol Inst Global Innovat & Res Tokyo 1848588 Japan

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role in such analyses and facilitates feature selection and feature extraction. randomized algorithms are efficient tools for handling big data tensors. They accelerate decomposing large-scale data tensors by reducing the computational complexity of deterministic algorithms and the communication among different levels of memory hierarchy, which is the main bottleneck in modern computing environments and architectures. In this article, we review recent advances in randomization for computation of Tucker decomposition and Higher Order SVD (HOSVD). We discuss random projection and sampling approaches, single-pass and multi-pass randomized algorithms and how to utilize them in the computation of the Tucker decomposition and the HOSVD. Simulations on synthetic and real datasets are provided to compare the performance of some of best and most promising algorithms.

关键词： Tensors Matrix decomposition Signal processing algorithms Approximation algorithms Memory management Licenses Probability distribution randomized algorithm tensor decomposition random projection sampling unfolding Tucker decomposition HOSVD

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Tracking tensor ring decompositions of streaming tensors

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COMPUTATIONAL & APPLIED MATHEMATICS 2025年第1期44卷 1-30页

作者： Yu, Yajie Li, Hanyu Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China Chongqing Univ Key Lab Nonlinear Anal & its Applicat Minist Educ Chongqing Peoples R China

Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns in higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to track TR decompositions of streaming tensors. An efficient algorithm is first proposed. Then, based on this algorithm and randomized sketching techniques, we present a randomized streaming TR decomposition. The proposed algorithms make full use of the structure of TR decomposition, and the randomized version can allow any sketching type. Theoretical results on sketch size are provided. In addition, the complexity analyses for the obtained algorithms are also given. We compare our proposals with the existing batch methods using both real and synthetic data. Numerical results show that they have better performance in computing time with maintaining similar accuracy.

关键词： Tensor ring decomposition Streaming tensor randomized algorithm Alternating least squares Kronecker sub-sampled randomized Fourier transform Uniform sampling Importance sampling Leverage score

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randomized algorithms and upper bounds for multiple domination in graphs and networks

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DISCRETE APPLIED MATHEMATICS 2013年第4-5期161卷 604-611页

作者： Gagarin, Andrei Poghosyan, Anush Zverovich, Vadim Acadia Univ Dept Math & Stat Wolfville NS B4P 2R6 Canada Univ W England Dept Math & Stat Bristol BS16 1QY Avon England

We consider four different types of multiple domination and provide new improved upper bounds for the k- and k-tuple domination numbers. They generalize two classical bounds for the domination number and are better than a number of known upper bounds for these two multiple domination parameters. Also, we explicitly present and systematize randomized algorithms for finding multiple dominating sets, whose expected orders satisfy new and recent upper bounds. The algorithms for k- and k-tuple dominating sets are of linear time in terms of the number of edges of the input graph, and they can be implemented as local distributed algorithms. Note that the corresponding multiple domination problems are known to be NP-complete. (C) 2011 Elsevier B.V. All rights reserved.

关键词： randomized algorithm k-domination k-tuple domination alpha-domination alpha-rate domination

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An Effective randomized QoS Routing algorithm on Networks with Inaccurate Parameters

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Journal of Computer Science & Technology 2002年第1期17卷 38-46页

作者：王建新陈建二陈松乔 Department of Computer Science Central South University Changsha 410083 P.R. China

This paper develops an effective randomized on-demand QoS routing algorithm on networks with inaccurate link-state information. Several new techniques are proposed in the algorithm. First, the maximum safety rate and the minimum delay for each node in the network are pre-computed, which simplify the network complexity and provide the routing process with useful information. The routing process is dynamically directed by the safety rate and delay of the partial routing path developed so far and by the maximum safety rate and the minimum delay of the next node. Randomness is used at the link level and depends dynamically on the routing configuration. This provides great flexibility for the routing process, prevents the routing process from overusing certain fixed routing paths, and adequately balances the safety rate and delay of the routing path. A network testing environment has been established and five parameters are introduced to measure the performance of QoS routing *** results demonstrate that in terms of the proposed parameters, the algorithm outperforms existing QoS algorithms appearing in the literature.

关键词： QoS network routing randomized algorithm link-state information

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randomized algorithms for Feedforward Neural Networks 35

Randomized Algorithms for Feedforward Neural Networks

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第35届中国控制会议

作者： LI Fan-jun LI Ying School of Mathematical Science University of Jinan School of Science Qilu University of Technology

ISBN: (纸本)9781509009107

randomized algorithm for feedforward neural networks have been summarized and evaluated in this paper,Firstly,a simplified model of feedforward neural networks with random weights is proposed,which consists of a randomized layer and an output ***,randomized algorithms for different network structures are summarized on the basis of the simplified ***,several feedforward neural networks with different randomized layers are evaluated on ten UCI data *** results show that random vector Functional-link neural network is more powerful than multilayer perceptron structure with random weights.

关键词： randomized algorithm feedforward neural network functional-link neural network

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randomized algorithms for robust feasibility problems with general nonconvex constraints

Randomized algorithms for robust feasibility problems with g...

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Annual Conference on the Society-of-Instrument-and-Control-Engineers

作者： Wada, Takayuki Fujisaki, Yasumasa Kobe Univ Grad Sch Sci & Technol Kobe Hyogo 6578501 Japan Kobe Univ Grad Sch Engn Kobe Hyogo 6578501 Japan

ISBN: (纸本)9784907764289

A class of robust feasibility problems is considered, which is to find a design variable satisfying a parameter-dependent constraint for all parameter values. A randomized algorithm for solving the problem with a general nonconvex constraint is proposed, where random samples of candidates of the design variable and uncertain parameters are used. The algorithm stops in a finite number of iterations. Then, it gives a design variable satisfying the constraint for almost all parameter values with a prescribed confidence or says that the problem is infeasible in a probabilistic sense.

关键词： robust control robust feasibility problem randomized algorithm probabilistic solution probabilistic infeasibility

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FAST AND ACCURATE randomized algorithmS FOR LINEAR SYSTEMS AND EIGENVALUE PROBLEMS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2024年第2期45卷 1183-1214页

作者： Nakatsukasa, Yuji Tropp, Joel A. Univ Oxford Math Inst Oxford OX2 6GG England Caltech Comp & Math Sci Pasadena CA 91125 USA

This paper develops a class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized dimension reduction (``sketching"") to accelerate standard subspace projection methods, such as GMRES and Rayleigh--Ritz. This modification makes it possible to incorporate nontraditional bases for the approximation subspace that are easier to construct. When the basis is numerically full rank, the new algorithms have accuracy similar to classic methods but run faster and may use less storage. For model problems, numerical experiments show large advantages over the optimized MATLAB routines, including a 70 \times speedup over gmres and a 10 \times speedup over eigs.

关键词： eigenvalue problem linear system numerical linear algebra Petrov-Galerkin method projection method randomized algorithm Rayleigh--Ritz sketching subspace embedding

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Battery sizing for PV power plants under regulations using randomized algorithms

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RENEWABLE ENERGY 2017年 113卷 596-607页

作者： Pflaum, Peter Alamir, M. Lamoudi, M. Y. Schneider Elect Ind 37 Quai Paul Louis Merlin F-38000 Grenoble France Univ Grenoble CNRS Gipsa Lab BP 46Domaine Univ F-38400 St Martin Dheres France

The increasing amount of PV (photo-voltaic) power plants comes along with an increased instability in the power grid due to the high uncertainty of the PV power production. As a stabilizing measure, grid operators introduce regulations on the injected power profiles comprising the obligation to declare in advance the predicted power production as well as penalties which apply in case these previously declared production profiles were not respected. In order to meet these regulations power plant owners are forced to invest into expensive storage capacities. In this work an algorithm is proposed which allows to determine the optimal battery size that maximizes the to-be-expected revenue of such an installation for a given regulative framework. Moreover the scheme explicitly takes into account the uncertainty in the PV power production and it provides guaranteed lower bounds on the to-be-expected revenue at a configurable probability. The underlying method allowing to achieve these objectives is a randomized algorithm. The principle of this method is to compute probabilistic guarantees for respecting a binary constraint, considering only a limited number of uncertainty scenarios. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： PV plant Battery sizing Regulations randomized algorithm Optimization PV forecast uncertainty

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Artificial intelligence in the service of entrepreneurial finance: knowledge structure and the foundational algorithmic paradigm

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FINANCIAL INNOVATION 2025年第1期11卷 1-43页

作者： Kudelic, Robert Smaguc, Tamara Robinson, Sherry Univ Zagreb Fac Org & Informat Zagreb Croatia Penn State Hazleton Schiavo Hall30476 Univ Dr Hazleton PA 18202 USA

The study conducts a bibliometric review of artificial intelligence applications in two areas: the entrepreneurial finance literature, and the corporate finance literature with implications for entrepreneurship. A rigorous search and screening of the web of science core collection identified 1,890 journal articles for analysis. The bibliometrics provide a detailed view of the knowledge field, indicating underdeveloped research directions. An important contribution comes from insights through artificial intelligence methods in entrepreneurship. The results demonstrate a high representation of artificial neural networks, deep neural networks, and support vector machines across almost all identified topic niches. In contrast, applications of topic modeling, fuzzy neural networks, and growing hierarchical self-organizing maps are rare. Additionally, we take a broader view by addressing the problem of applying artificial intelligence in economic science. Specifically, we present the foundational paradigm and a bespoke demonstration of the Monte Carlo randomized algorithm.

关键词： Bibliometrics Artificial intelligence Entrepreneurship Finance randomized algorithm

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A randomized MAXIMUM-FLOW algorithm

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SIAM JOURNAL ON COMPUTING 1995年第2期24卷 203-226页

作者： CHERIYAN, J HAGERUP, T MAX PLANCK INST INFORMAT D-66123 SAARBRUCKENGERMANY

A randomized algorithm for computing a maximum flow is presented. For an n-vertex m-edge network, the running time is O (nm + n(2)(log n)(2)) with probability at]east 1 - 2(-)root nm. The algorithm is always correct, and in the worst case runs in O(nm log n) time. The only use of randomization is to randomly permute the adjacency lists of the network vertices at the start of the execution. The analysis introduces the notion of premature target relabeling (PTR) events and shows that each PTR event contributes O (log n) amortized time to the overall running rime. The number of PTR events is always O (nm);however, it is shown that when the adjacency lists are randomly permuted, then this quantity is O (n(3)/(2)m(1/2) + n(2) log n) with high probability.

关键词： MAXIMUM FLOW randomized algorithm RANDOM PERMUTATIONS SCALING DYNAMIC TREE FIBONACCI HEAP

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