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A spectral METHOD FOR COMMUNITY DETECTION IN MODERATELY SPARSE DEGREE-CORRECTED STOCHASTIC BLOCK MODELS

ADVANCES IN APPLIED PROBABILITY 2017年第3期49卷 686-721页

作者： Gulikers, Lennart Lelarge, Marc Massoulie, Laurent Microsoft Res INRIA Joint Ctr Campus Ecole PolytechBatiment Alan Turing F-91120 Palaiseau France Ecole Normale Super Palaiseau France INRIA Paris France Inria Paris CS 42112 2 Rue Simone Iff F-91120 Palaiseau 12 France

We consider community detection in degree-corrected stochastic block models. We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the block membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log (n) or higher. Recovery succeeds even for very heterogeneous degree distributions. The algorithm does not rely on parameters as input. In particular, it does not need to know the number of communities.

关键词： Social and information network random graph degree-corrected stochastic block model spectral algorithm machine learning

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Maximizing the Number of Spanning Trees in a Connected Graph

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第2期66卷 1248-1260页

作者： Li, Huan Patterson, Stacy Yi, Yuhao Zhang, Zhongzhi Fudan Univ Sch Comp Sci Shanghai Key Lab Intelligent Informat Proc Shanghai 200433 Peoples R China Shanghai Engn Res Inst Blockchain Fudan Zhongan Joint Lab Blockchain & Informat Sec Shanghai 200433 Peoples R China Rensselaer Polytech Inst Dept Comp Sci Troy NY 12180 USA

We study the problem of maximizing the number of spanning trees in a connected graph with n vertices and m edges, by adding at most k edges from a given set of q candidate edges, a problem that has applications in many domains. We give both algorithmic and hardness results for this problem: 1) We give a greedy algorithm that obtains an approximation ratio of (1 - 1/e - epsilon) in the exponent of the number of spanning trees for any epsilon > 0 in time O(m epsilon(-1) + (n + q)epsilon(-3)), where (O) over tilde(center dot) hides poly log(n) factors. Our running time is optimal with respect to the input size, up to logarithmic factors, and improves on the O(n(3)) running time of the previous proposed greedy algorithm with an approximation ratio (1 - 1/e) in the exponent. Notably, the independence of our running time of k is novel, compared to conventional top-k selections on graphs that usually run in Omega (mk) time. 2) We show the exponential inapproximability of this problem by proving that there exists a constant c > 0 such that it is NP-hard to approximate the optimum number of spanning trees in the exponent within (1 - c).

关键词： Approximation algorithms Reliability Simultaneous localization and mapping Resistance Communication networks Heuristic algorithms Greedy algorithms Number of spanning trees network entropy optimization spectral algorithm complexity

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Fast Mesh Refinement in Pseudospectral Optimal Control

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2019年第4期42卷 711-722页

作者： Koeppen, N. Ross, I. M. Wilcox, L. C. Proulx, R. J. Naval Postgrad Sch USMC Control & Optimizat Labs Dept Mech & Aerosp Engn Monterey CA 93943 USA Naval Postgrad Sch Control & Optimizat Dept Mech & Aerosp Engn Monterey CA 93943 USA Naval Postgrad Sch Dept Appl Math Monterey CA 93943 USA Naval Postgrad Sch Control & Optimizat Labs Space Syst Acad Grp Monterey CA 93943 USA

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy: simply increase the order N of the Lagrange interpolating polynomial, and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as N increases, the condition number of the resulting linear algebra increases as N-2;hence, spectral efficiency and accuracy are lost in practice. In this paper, Birkhoff interpolation concepts are advanced over an arbitrary grid to generate well-conditioned PS optimal control discretizations. It is shown that the condition number increases only as root N in general, but it is independent of N for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as N increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using polynomials of over one-thousandth order to solve a low-thrust long-duration orbit transfer problem.

关键词： Pseudospectral Optimal Control spectral algorithm Chebyshev Pseudospectral Method Low Thrust Maneuvers Runge Kutta Methods Canonical Units MATLAB Dirichlet Boundary Condition State Space Representation Boundary Value Problems

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spectral co-clustering ensemble

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KNOWLEDGE-BASED SYSTEMS 2015年 84卷 46-55页

作者： Huang, Shudong Wang, Hongjun Li, Dingcheng Yang, Yan Li, Tianrui Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu 610031 Peoples R China Mayo Clin Dept Biomed Stat & Informat Hlth Sci Res Rochester MN 55905 USA

The goal of co-clustering is to simultaneously cluster the rows and columns of an input data matrix. It overcomes several limitations associated with traditional clustering methods by allowing automatic discovery of similarity based on a subset of attributes. However, different co-clustering models usually produce very distinct results since each algorithm has its own bias due to the optimization of different criteria. The idea of combining different co-clustering results emerged as an alternative approach for improving the performance of co-clustering algorithms. Similar to clustering ensembles, co-clustering ensembles provide a framework for combining multiple base co-clusterings of a dataset to generate a stable and robust consensus co-clustering result. In this paper, a novel co-clustering ensemble algorithm named spectral co-clustering ensemble (SCCE) is presented. SCCE performs ensemble tasks on base row clusters and column clusters of a dataset simultaneously, and obtains an optimization co-clustering result. Meanwhile, SCCE is a matrix decomposition based approach which can be formulated as a bipartite graph partition problem and solve it efficiently with the selected eigenvectors. To the best of our knowledge, this is the first work on using spectral algorithm for co-clustering ensemble. Extensive experiments on benchmark datasets demonstrate the effectiveness of the proposed method. Our study also shows that SCCE has some favorable merits compared with many state of the art methods. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Co-clustering Ensemble learning spectral co-clustering ensemble spectral algorithm Mutual information

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A spectral RMIL plus Conjugate Gradient Method for Unconstrained Optimization With Applications in Portfolio Selection and Motion Control

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IEEE ACCESS 2021年 9卷 75398-75414页

作者： Awwal, Aliyu Muhammed Sulaiman, Ibrahim Mohammed Malik, Maulana Mamat, Mustafa Kumam, Poom Sitthithakerngkiet, Kanokwan King Mongkuts Univ Technol Thonburi KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE Fac Sci Bangkok 10140 Thailand Gombe State Univ Dept Math Fac Sci Gombe 760214 Nigeria Univ Sultan Zainal Abidin UniSZA Fac Informat & Comp Kuala Terengganu 22200 Malaysia Univ Indonesia UI Fac Math & Nat Sci Dept Math Depok 16424 Indonesia Univ Malaysia Perlis Inst Engn Math Arau 02600 Malaysia China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan King Mongkuts Univ Technol North Bangkok KMUTNB Fac Appl Sci Dept Math Intelligent & Nonlinear Dynam Innovat Res Ctr Bangkok 10800 Thailand

The spectral conjugate gradient (SCG) methods are among the efficient variants of CG algorithms which are obtained by combining the spectral gradient parameter and CG parameter. The success of SCG methods relies on effective choices of the step-size alpha(k) and the search direction d(k). This paper presents an SCG method for unconstrained optimization models. The search directions generated by the new method possess sufficient descent property without the restart condition and independent of the line search procedure used. The global convergence of the new method is proved under the weak Wolfe line search. Preliminary numerical results are presented which show that the method is efficient and promising, particularly for large-scale problems. Also, the method was applied to solve the robotic motion control problem and portfolio selection problem.

关键词： spectral algorithm conjugate gradient algorithms unconstrained optimization models motion control line search procedure portfolio selection

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Expert algorithm for Substance Identification Using Mass Spectrometry: Application to the Identification of Cocaine on Different Instruments Using Binary Classification Models

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JOURNAL OF THE AMERICAN SOCIETY FOR MASS SPECTROMETRY 2023年第7期34卷 1235-1247页

作者： Mehnert, Samantha A. Davidson, J. Tyler Adeoye, Alexandra Lowe, Brandon D. Ruiz, Emily A. King, Jacob R. Jackson, Glen P. West Virginia Univ Dept Forens & Invest Sci Morgantown WV 26506 USA West Virginia Univ C Eugene Bennett Dept Chem Morgantown WV 26506 USA Purdue Univ Dept Chem W Lafayette IN 47907 USA Sam Houston State Univ Dept Forens Sci Huntsville TX 77340 USA

Thisis the second of two manuscripts describing how general linearmodeling (GLM) of a selection of the most abundant normalized fragmention abundances of replicate mass spectra from one laboratory can beused in conjunction with binary classifiers to enable specific andselective identifications with reportable error rates of spectra fromother laboratories. Here, the proof-of-concept uses a training setof 128 replicate cocaine spectra from one crime laboratory as thebasis of GLM modeling. GLM models for the 20 most abundant fragmentsof cocaine were then applied to 175 additional test/validation cocainespectra collected in more than a dozen crime laboratories and 716known negative spectra, which included 10 spectra of three diastereomersof cocaine. spectral similarity and dissimilarity between the measuredand predicted abundances were assessed using a variety of conventionalmeasures, including the mean absolute residual and NIST's spectralsimilarity score. For each spectral measure, GLM predictions werecompared to the traditional exemplar approach, which used the averageof the cocaine training set as the consensus spectrum for *** unsupervised models, EASI provided better than a 95% true positiverate for cocaine with a 0% false positive rate. A supervised binarylogistic regression model provided 100% accuracy and no errors usingEASI-predicted abundances of only four peaks at m/z 152, 198, 272, and 303. Regardless of the measureof spectral similarity, error rates for identifications using EASIwere superior to the traditional exemplar/consensus approach. As asupervised binary classifier, EASI was more reliable than using Mahalanobisdistances.

关键词： spectral comparisons spectral algorithm searchalgorithm forensic science binary classification drug identification

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Impurity bands and quasi-Bloch waves for a one-dimensional model of modulated crystal

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2008年第3期9卷 927-948页

作者： Gosse, Laurent IAC CNR Mauro Picone Sez Bari I-70126 Bari Italy

This paper investigates a simple one-dimensional model of incommensurate "harmonic crystal" in terms of the spectrum of the corresponding Schrodinger equation. Two angles of attack are studied: the first exploits techniques borrowed from the theory of quasi-periodic functions while the second relies on periodicity properties in a higher-dimensional space. It is shown that both approaches lead to essentially the same results;that is, the lower spectrum is split between "Cantor-like zones" and "impurity bands" to which correspond critical and extended eigenstates, respectively. These "new bands" seem to emerge inside the band gaps of the unperturbed problem when certain conditions are met and display a parabolic nature. Numerical tests are extensively performed on both steady and time-dependent problems. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： quasi-periodic potential impurity band quasi-Bloch wave quantum chaos spectral algorithm deformed crystal Charge-Density Wave (CDW)

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Simple Approximation algorithms for Balanced MAX 2SAT

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algorithmICA 2018年第3期80卷 995-1012页

作者： Paul, Alice Poloczek, Matthias Williamson, David P. Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14850 USA

We study simple algorithms for the balanced MAX 2SAT problem, where we are given weighted clauses of length one and two with the property that for each variable x the total weight of clauses that x appears in equals the total weight of clauses for . We show that such instances have a simple structural property in that any optimal solution can satisfy at most the total weight of the clauses minus half the total weight of the unit clauses. Using this property and a novel analysis of the computation tree, we are able to show that a large class of greedy algorithms, including Johnson's algorithm, gives a -approximation algorithm for balanced MAX 2SAT;a similar statement is false for general MAX 2SAT instances. We further give a spectral 0.81-approximation algorithm for balanced MAX E2SAT instances (in which each clause has exactly 2 literals) by a reduction to a spectral algorithm of Trevisan for the maximum colored cut problem. We provide experimental results showing that this spectral algorithm performs well and is slightly better than Johnson's algorithm and the Goemans-Williamson semidefinite programming algorithm on balanced MAX E2SAT instances.

关键词： Maximum satisfiability Approximation algorithm Greedy algorithm spectral algorithm Balanced instances Priority algorithm

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Flight Implementation of Shortest-Time Maneuvers for Imaging Satellites

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2014年第4期37卷 1069-1079页

作者： Karpenko, Mark Bhatt, Sagar Bedrossian, Nazareth Ross, I. Michael Naval Postgrad Sch Dept Mech & Aerosp Engn Monterey CA 93943 USA Charles Stark Draper Lab Inc Vehicle Dynam & Control Grp Houston TX 77058 USA

Shortest-time maneuvers are constrained time-optimal slews that enable spacecraft to be maneuvered more quickly than conventional rotations. Shortest-time maneuvers can increase a spacecraft's imaging capability without any changes to the hardware. Previous studies have shown that, depending upon the spacecraft design, the increased capability can be over 50%. Motivated by such high increases in efficiencies, the first flight demonstration of a shortest-time maneuver was performed on 10 August 2010 onboard NASA's TRACE Space Telescope. To transition this new technology from flight demonstration to standard operational procedures, several qualification thresholds need to be met. This paper demonstrates two of these qualification thresholds: 1) the ability to consistently and reliably generate flight-implementable shortest-time maneuvers on demand, and 2) flight demonstrations over multiple operational scenarios involving minimum-time slewing, attitude hold for point data collection, and transition maneuvers for scanning operations. The key technology for meeting both thresholds is flight-implementable pseudospectral controls. Flight and operational considerations quickly narrow down the plethora of pseudospectral options to the Legendre and Chebyshev techniques. All flight implementations were performed using the spectral algorithm of the Legendre pseudospectral method.

关键词： Satellites Transition Region and Coronal Explorer spectral algorithm Spacecraft Structures Space Telescopes Legendre Pseudospectral Method Spacecraft Attitude Flight Testing Pseudospectral Optimal Control Attitude Control System

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Expert algorithm for Substance Identification Using Mass Spectrometry: Statistical Foundations in Unimolecular Reaction Rate Theory

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JOURNAL OF THE AMERICAN SOCIETY FOR MASS SPECTROMETRY 2023年第7期34卷 1248-1262页

作者： Jackson, Glen P. P. Mehnert, Samantha A. A. Davidson, J. Tyler Lowe, Brandon D. D. Ruiz, Emily A. A. King, Jacob R. R. West Virginia Univ Dept Forens & Invest Sci Morgantown WV 26506 USA West Virginia Univ C Eugene Bennett Dept Chem Morgantown WV 26506 USA Purdue Univ Dept Chem W Lafayette IN 47907 USA Sam Houston State Univ Dept Forens Sci Huntsville TX 77340 USA

Thisstudy aims to resolve one of the longest-standing problemsin mass spectrometry, which is how to accurately identify an organicsubstance from its mass spectrum when a spectrum of the suspectedsubstance has not been analyzed contemporaneously on the same *** one of this two-part report describes how Rice-Ramsperger-Kassel-Marcus(RRKM) theory predicts that many branching ratios in replicate electron-ionizationmass spectra will provide approximately linear correlations when analysisconditions change within or between instruments. Here, proof-of-conceptgeneral linear modeling is based on the 20 most abundant fragmentsin a database of 128 training spectra of cocaine collected over 6months in an operational crime laboratory. The statistical validityof the approach is confirmed through both analysis of variance (ANOVA)of the regression models and assessment of the distributions of theresiduals of the models. General linear modeling models typicallyexplain more than 90% of the variance in normalized abundances. Whenthe linear models from the training set are applied to 175 additionalknown positive cocaine spectra from more than 20 different laboratories,the linear models enabled ion abundances to be predicted with an accuracyof <2% relative to the base peak, even though the measured abundancesvary by more than 30%. The same models were also applied to 716 knownnegative spectra, including the diastereomers of cocaine: allococaine,pseudococaine, and pseudoallococaine, and the residual errors werelarger for the known negatives than for known positives. The secondpart of the manuscript describes how general linear regression modelingcan serve as the basis for binary classification and reliable identificationof cocaine from its diastereomers and all other known negatives.

关键词： spectral comparisons spectral algorithm searchalgorithm forensic science compound identification binary classification drug identification

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