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Influence of the normalization constraint on the integral simplex using decomposition

DISCRETE APPLIED MATHEMATICS 2017年第Part1期217卷 53-70页

作者： Rosat, Samuel Elhallaoui, Issmail Soumis, Francois Chakour, Driss Polytech Montreal CP 6079Succ Ctr Ville Montreal PQ H3C 3A7 Canada Ecole Polytech Route Saclay F-91128 Palaiseau France Gerad 3000 Ch Cote St Catherine Montreal PQ H3T 2A7 Canada

Since its introduction in 1969, the set partitioning problem has received much attention, and the structure of its feasible domain has been studied in detail. In particular, there exists a decreasing sequence of integer feasible points that leads to the optimum, such that each solution is a vertex of the polytope of the linear relaxation and adjacent to the previous one. Several algorithms are based on this observation and aim to determine that sequence;one example is the integral simplex using decomposition (ISUD) of Zaghrouti et al. (2014). In ISUD, the next solution is often obtained by solving a linear program without using any branching strategy. We study the influence of the normalization-weight vector of this linear program on the integrality of the next solution. We extend and strengthen the decomposition theory in ISUD, prove theoretical properties of the generic and specific normalization constraints, and propose new normalization constraints that encourage integral solutions. Numerical tests on scheduling instances (with up to 500,000 variables) demonstrate the potential of our approach. (C) 2016 Elsevier B.V. All rights reserved.

关键词： 0-1 programming Set partitioning problem Primal algorithms normalization constraint Augmenting algorithms

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Semi-Supervised Multi-view clustering based on orthonormality-constrained nonnegative matrix factorization

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INFORMATION SCIENCES 2020年 536卷 171-184页

作者： Cai, Hao Liu, Bo Xiao, Yanshan Lin, Luyue Guangdong Univ Technol Dept Automat Guangzhou 510006 Peoples R China Guangdong Univ Technol Dept Comp Sci Guangzhou 510006 Peoples R China

Multi-view clustering aims at integrating the complementary information between different views so as to obtain an accurate clustering result. In addition, the traditional clustering is a kind of unsupervised learning method, which does not take the label information into learning. In this paper, we propose a novel model, called semi-supervised multi-view clustering based on orthonormality-constrained nonnegative matrix factorization (MVOCNMF), to cluster the multi-view data into a number of categories. In the proposed model, based on the label information, we first learn the low-dimensional representations of data by the constrained NMF technique, and simultaneously cluster the samples with the same label into the clustering prototypes for each view. After that, we put forward a novel orthonormality constraint term to obtain the desirable representations for each view, and use the co-regularization to integrate the complementary information from different views. We further develop an alternating minimization algorithm to solve the proposed model, and present the convergence analysis and computational complexity of the proposed method. Extensive experimental results on several multi-view datasets have shown that the proposed MVOCNMF method outperforms the existing multi-view clustering methods. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Multi-view clustering NMF Orthogonal constraint normalization constraint

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normalization and Fermi-Coulomb and Coulomb hole sum rules for approximate wave functions

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2007年第4期107卷 816-823页

作者： Pan, Xiao-Yin Sahni, Viraht Massa, Lou CUNY Grad Sch New York NY 10016 USA

For approximate wave functions, we prove the theorem that there is a one-to-one correspondence between the constraints of normalization and of the Fermi-Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi-Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate "exchange-correlation" and "correlation" energy functionals of density functional theory is also discussed. (c) 2006 Wiley Periodicals, Inc.

关键词： normalization constraint Fermi-Coulomb hole sum rule density functional theory

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The nucleonic matter LOCV calculations in a periodic box versus the FHNC method

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NUCLEAR PHYSICS A 2013年 916卷 126-148页

作者： Modarres, M. Tafrihi, A. Univ Tehran Dept Phys Tehran *** Iran

The lowest order constrained variational (LOCV) method is reformulated for a fixed number of nucleons in a period box (PBLOCV) with the inter-nucleon interactions such as the Bethe homework potential, v(g), and the scalar (v(4)) part of the Argonne interaction (Av'(8))(c)(4). The two-body cluster approximation is used in the (PB)LOCV formalism to obtain the energy per particle subjected to the normalization constraint for an infinite (a finite) number of nucleons. It is shown that our (PB)LOCV results are reasonably consistent with those of Fantoni and Schmidt (Periodic-Box) Fermi Hyper Netted Chain ((PB)FHNC) calculations. In addition, unlike the thermodynamic limit, it is found that the normalization constraint in the periodic box is not exactly satisfied. However, it is realized that, by increasing the number of particles, the value of normalization constraint in the periodic box improves. Therefore, the two-body cluster approximation in the PBLOCV method becomes more reliable in the larger periodic boxes than the smaller ones. On the other hand, the PBLOCV energy per particle approaches the corresponding LOCV prediction for the large number of particles. The anisotropic behavior of the PB two-body distribution function, which is one of the main point of this report, is discussed. Finally, it is found that the PBLOCV results, i.e. the total (two-body cluster) energy and the normalization constraint, similar to the PBFHNC calculations depend on the number of particles in the periodic box and this dependence principally becomes negligible for the large number of particles. (C) 2013 Elsevier B.V. All rights reserved.

关键词： LOCV PBLOCV FHNC PBFHNC Cluster expansion normalization constraint

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The LOCV nucleonic matter correlation and distribution functions versus the FHNC/SOC and the Monte Carlo calculations

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NUCLEAR PHYSICS A 2015年 941卷 212-240页

作者： Modarres, M. Tafrihi, A. Univ Tehran Dept Phys Tehran *** Iran

The nucleonic matter operator-dependent two-body correlation and distribution functions, for different two-body potentials, e.g. the Av(18) and the Av(8)' interactions, are calculated, using the lowest order constrained variational (LOCV) approach. It is shown that the LOCV results are reasonably consistent with the corresponding predictions of the more sophisticated methods, i.e. the Fermi hypernetted chain approach in the single-operator approximation (FHNC/SOC) and the Monte Carlo (MC) technique. The main reason for this consistence is the LOCV normalization constraint of the two-body radial distribution function, which is optimally satisfied at the two-body cluster approximation. In this way, the many-body effects, which are considered in the FHNC/SOC and the MC calculations, become negligible. Furthermore, in the LOCV formalism, the spin-orbit correlation function is employed, instead of the tensor correlation function, in the P-3(2)-F-3(2) channel. It is demonstrated that using the Av(18) interaction, the nuclear (neutron) matter equation of state, for the former case, fairly differs from that of the latter case, especially at high densities. However, applying the Reid potential, the former and the latter equations of state lie close together. Finally, it should be mentioned that the spin-orbit dependent distribution functions, which have not been reported by the FHNC/SOC method, can be evaluated in the LOCV framework, for the Av(18) and the Av(8)' potentials. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Nucleonic matter Operator-dependent correlation (distribution) functions LOCV FHNC/SOC Monte Carlo Cluster expansion normalization constraint

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Optimization algorithm for measurement matrix based on fractional order Duffing system 36

Optimization algorithm for measurement matrix based on fract...

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36th Chinese Control and Decision Conference (CCDC)

作者： Yu, Jimin Ran, Jia Chongqing Univ Posts & Telecommun Automat Sch Chongqing Peoples R China

ISBN: (纸本)9798350387780;9798350387797

In order to improve the reconstruction accuracy of images in compressed sensing, a quantitative matrix optimization algorithm based on fractional order Duffing system is proposed. Firstly, the measurement matrix is constructed by using the pseudo-random sequence generated by fractional Duffing system. Then, the Gram matrix of the sensor matrix is generated by taking the identity matrix as the sparse basis and the measurement matrix, and the normalization constraint of all elements of the Gram matrix is introduced into the metric, which is accomplished by gradient descent. Finally, in view of the occurrence of local low points in the optimization process of two-dimensional compressed sensing measurement matrix, an algorithm is proposed to find the relatively optimal measurement matrix to assist the previous measurement matrix optimization algorithm. The experimental simulation results show that the proposed algorithm can improve the accuracy of image reconstruction in different degrees.

关键词： fractional order Duffing system normalization constraint gradient descent two-dimensional compressed sensing measurement matrix

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Relaxed Fuzzy c-Means Clustering Algorithm and its application

Relaxed Fuzzy c-Means Clustering Algorithm and its applicati...

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2019计算智能、工程与信息技术世界大会

作者： Chuan-jun Wen Li-fan Chen Qi Zhang School of Mathematical Sciences Changzhou Institute of Technology School of Arts and Sciences Shanghai University of Medicine and Health Sciences

The FCM algorithm was sensitive to noise data due to the normalized constraint of fuzzy membership.A novel clustering algorithm is proposed and named as relaxed fuzzy C-means clustering（RFCM） in this paper,the objective function of PCM is utilized as the objective function of RFCM,and RFCM loosens the normalized constraint and only requests the whole summation of n samples' fuzzy memberships equal to n and 0≤u≤1,particle swarm optimization algorithms（PSO） are optimally used to select the fuzzy memberships of RFCM,and the value scope of fuzzy index m is extended to m>0,the iterative formula of clustering centers are derived by gradient method for *** anti-noise performance of RFCM is analyzed theoretically,and the rationality of new value scope of m>0 is explained for RFCM,and the convergence of RFCM is discussed *** effectiveness and anti-noise performance of RFCM are proved through simulation experiments on two-dimensional Gaussian data-set for anti-noise and clustering accuracy tests.

关键词： fuzzy clustering normalization constraint fuzzy index particle swarm algorithm noise data

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