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Community detection by a riemannian projected proximal gradient method

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arXiv 2020年

作者： Wei, Meng Huang, Wen Gallivan, Kyle A. van Dooren, Paul Department of Mathematics Florida State University 208 Love Building 1017 Academic Way TallahasseeFL32306-4510 United States School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian361005 China Department of Mathematics Florida State University 208 Love Building 1017 Academic Way TallahasseeFL32306-4510 United States Department of Mathematical Engineering Université catholique de Louvain Louvain-La-Neuve Belgium

Community detection plays an important role in understanding and exploiting the structure of complex systems. Many algorithms have been developed for community detection using modularity maximization or other techniques. In this paper, we formulate the community detection problem as a constrained nonsmooth optimization problem on the compact Stiefel manifold. A Riemannian projected proximal gradient method is proposed and used to solve the problem. To the best of our knowledge, this is the first attempt to use Riemannian optimization for community detection problem. Numerical experimental results on synthetic benchmarks and real-world networks show that our algorithm is effective and outperforms several state-of-art algorithms. Copyright © 2020, The Authors. All rights reserved.

关键词： Population dynamics

Toward a MapReduce-Based K-Means Method for Multi-dimensional Time Serial Data Clustering 17th

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Toward a MapReduce-Based K-Means Method for Multi-dimensiona...

17th International Conference on Intelligent Systems Design and Applications, ISDA 2017

作者： Lin, Yongzheng Ma, Kun Sun, Runyuan Abraham, Ajith School of Information Science and Engineering University of Jinan Jinan250022 China Shandong Provincial Key Laboratory of Network Based Intelligent Computing University of Jinan Jinan250022 China Scientific Network for Innovation and Research Excellence AuburnWA98071 United States

ISBN: (纸本)9783319763477

Time series data is a sequence of real numbers that represent the measurements of a real variable at equal time intervals. There are some bottlenecks to process large scale data. In this paper, we firstly propose a K-means method for multi-dimensional time serial data clustering. As an improvement, MapReduce framework is used to implement this method in parallel. Different versions of k-means for several distance measures are compared, and the experiments show that MapReduce-based K-means has better speedup when the scale of data is larger. © 2018, Springer International Publishing AG, part of Springer Nature.

关键词： MapReduce

Unique continuation properties for one dimensional higher order Schrödinger equations

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arXiv 2019年

作者： Huang, Tianxiao Huang, Shanlin Zheng, Quan Sun Yat-sen University Guangdong Zhuhai519082 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China

We study two types of unique continuation properties for the higher order Schrödinger equation with potential i∂tu = (−∆x)mu + V(t, x)u, (t, x) ∈ 1+n, 2 ≤ m ∈ N+. The first one says if u has certain exponential decay at two times, then u ≡ 0, and this result is sharp by constructing critical non-trivial solutions. The second one says if u ≡ 0 in an arbitrary half-space of 1+n, then u ≡ 0 identically. The uniqueness theorems are given when n = 1, but we also prove partial results when n ∈ N+ for their own interests. Possibility or obstacles to proving these unique continuation properties in higher spatial dimensions are also discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Geometry

Nonlocal TV-Gaussian (NLTG) prior for Bayesian inverse problems with applications to Limited CT Reconstruction

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arXiv 2019年

作者： Lv, Didi Zhou, Qingping Choi, Jae Kyu Li, Jinglai Zhang, Xiaoqun School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Tongji University Shanghai200082 China Department of Mathematical Sciences University of Liverpool LiverpoolL69 6ZL United Kingdom MOE Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

Bayesian inference methods have been widely applied in inverse problems, largely due to their ability to characterize the uncertainty associated with the estimation results. In the Bayesian framework the prior distribution of the unknown plays an essential role in the Bayesian inference, and a good prior distribution can significantly improve the inference results. In this paper, we extend the total variation-Gaussian (TG) prior in [41], and propose a hybrid prior distribution which combines the nonlocal total variation regularization and the Gaussian (NLTG) distribution. The advantage of the new prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the NLTG prior. The proposed prior is applied to limited-angle tomography reconstruction problem with difficulties of severe data missing. We compute both MAP and CM estimates through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

Sparse representation of gaussian molecular surface

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arXiv 2019年

作者： Gui, Sheng Chen, Minxin Lu, Benzhuo STATE KEY LABORATORY of SCIENTIFIC and ENGINEERING COMPUTING NATIONAL CENTER for MATHEMATICS and INTERDISCIPLINARY SCIENCES ACADEMY of MATHEMATICS and SYSTEMS SCIENCE CHINESE ACADEMY of SCIENCES BEIJING100190 China SCHOOL of MATHEMATICAL SCIENCES UNIVERSITY of CHINESE ACADEMY of SCIENCES BEIJING100049 China DEPARTMENT of MATHEMATICS SOOCHOW UNIVERSITY SUZHOU215006 China

In this paper, we propose a model and algorithm for sparse representing Gaussian molecular surface. The original Gaussian molecular surface is approximated by a relatively small number of radial basis functions (RBFs) with rotational ellipsoid feature. The sparsity of the RBF representation is achieved by solving a nonlinear L1optimization problem. Experimental results demonstrate that the original Gaussian molecular surface is able to be represented with good accuracy by much fewer RBFs using our L1model and algorithm. The sparse representation of Gaussian molecular surface is useful in various applications, such as molecular structure alignment, calculating molecular areas and volumes, and the method in principle can be applied to sparse representation of general shapes and coarse-grained molecular modeling. Copyright © 2019, The Authors. All rights reserved.

关键词： Radial basis function networks

Collisionless periodic orbits in the free-fall three-body problem

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arXiv 2018年

作者： Li, Xiaoming Liao, Shijun Centre of Advanced Computing School of Naval Architecture Ocean and Civil Engineering Shanghai Jiaotong University China Ministry-of-Education Key Laboratory in Scientific and Engineering Computing Shanghai200240 China

Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we report 234 collisionless periodic orbits of the free-fall three-body system with some mass ratios, including three known collisionless periodic orbits. Thus, 231 collisionless free-fall periodic orbits among them are entirely new. In theory, we can gain periodic orbits of the free-fall three-body system in arbitrary ratio of mass. Besides, it is found that, for a given ratio of masses of two bodies, there exists a generalized Kepler's third law for the periodic three-body system. All of these would enrich our knowledge and deepen our understanding about the famous three-body problem as a whole. Copyright © 2018, The Authors. All rights reserved.

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An initial attempt of converged machine-learning assisted turbulence modeling in RANS simulations with eddy-viscosity hypothesis

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arXiv 2019年

作者： Liu, Weishuo Fang, Jian Rolfo, Stefano Lu, Lipeng National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics School of Energy and Power Engineering Beihang University 37 Xueyuan Road Haidian District Beijing100191 China Scientific Computing Department Science and Technology Facilities Council Daresbury Laboratory Keckwick Lane Daresbury WarringtonWA4 4AD United Kingdom

This work presents a converged framework of Machine-Learning Assisted Turbulence Modeling (MLATM). Our objective is to develop a turbulence model directly learning from high fidelity data (DNS/LES) with eddy-viscosity hypothesis induced. First, the target machine-learning quantity is discussed in order to avoid the ill-conditioning problem of RANS equations. Then, the novel framework to build the turbulence model using the prior estimation of traditional models is demonstrated. A close-loop computational chain is designed to ensure the convergence of result. Besides, reasonable non-dimensional variables are selected to predict the target learning variables and make the solver re-converge to DNS mean flow field. The MLATM is tested in incompressible turbulent channel flows, and it proved that the result converges well to DNS training data for both mean velocity and turbulence viscosity profiles. Copyright © 2019, The Authors. All rights reserved.

关键词： Turbulence models

General propagation lattice Boltzmann model for nonlinear advection-diffusion equations

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Physical Review E 2018年第4期97卷 043310-043310页

作者： Xiuya Guo Baochang Shi Zhenhua Chai School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, a general propagation lattice Boltzmann model is proposed for nonlinear advection-diffusion equations (NADEs), and the Chapman-Enskog analysis shows that the NADEs with variable coefficients can be recovered correctly from the present model. We also perform some simulations of the linear advection-diffusion equation, nonlinear heat conduction equation, NADEs with anisotropic diffusion, and variable coefficients to test the present model, and find that the numerical results agree well with the corresponding analytical solutions. Moreover, it is also shown that by properly adjusting the two free parameters introduced into the propagation step, the present model could be more stable and more accurate than the standard lattice Bhatnagar-Gross-Krook model.

关键词： Lattice-Boltzmann methods

SVM-based deep stacking networks

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arXiv 2019年

作者： Wang, Jingyuan Feng, Kai Wu, Junjie MOE Engineering Research Center of Advanced Computer Application Technology School of Computer Science Engineering Beihang University Beijing100191 China Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations School of Economics and Management Beihang University Beijing100191 China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China

The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network approaches to build diverse deep structures, and the Deep Stacking Network (DSN) model is one of such approaches that uses stacked easy-to-learn blocks to build a parameter-training-parallelizable deep network. In this paper, we propose a novel SVM-based Deep Stacking Network (SVM-DSN), which uses the DSN architecture to organize linear SVM classifiers for deep learning. A BP-like layer tuning scheme is also proposed to ensure holistic and local optimizations of stacked SVMs simultaneously. Some good math properties of SVM, such as the convex optimization, is introduced into the DSN framework by our model. From a global view, SVM-DSN can iteratively extract data representations layer by layer as a deep neural network but with parallelizability, and from a local view, each stacked SVM can converge to its optimal solution and obtain the support vectors, which compared with neural networks could lead to interesting improvements in anti-saturation and interpretability. Experimental results on both image and text data sets demonstrate the excellent performances of SVM-DSN compared with some competitive benchmark models. Copyright © 2019, The Authors. All rights reserved.

关键词： Convex optimization