非平衡数据集的支持向量域分类预测模型研究

基于非平衡数据集的支持向量域分类模型,提出了一种银行客户个人信用预测方法.首先分析了信用预测的主要方法及其不足,然后研究了支持向量域分类模型及其参数的非负二次规划乘性更新算法,进而提出基于支持向量域分类模型的银行客户个人信用预测方法,最后使用人工数据和实际数据对提出方法与支持向量机预测方法进行对比实验.实验结果表明对于银行客户个人信用预测的非平衡数据分析问题,基于支持向量域模型的分类预测方法更有效.     

加权总体最小二乘问题的分析

总体最小二乘问题由Golub和Van Loan首先进行数学的分析,随后人们对于总体最小二乘问题的算法、解的各种形式、总体最小二乘解和最小二乘解的关系、总体最小二乘解的扰动理论以及数值试验作了大量的研究工作。近来,[10]中给出了总体最小二乘问题(TLS)较一般地讨论。另一方面,Golub和Van Loan研究了总体最小二乘问题的特殊均加权形式。本文试图在[10,11]的基础上讨论最一般的总体最小二     

Toeplitz方程组极小范数最小二乘解的快速算法

给出了求以m×n阶Toeplitz矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法.     

矩阵方程AXB=C最小二乘D反对称解

首先将对称矩阵推广到D反对称矩阵,然后研究了方程AXB=C的D反对称最小二乘解,利用矩阵对的广义奇异分解、标准相关分解及子空间上的投影定理,得到了最小二乘解的通式．     

含非线性源项障碍问题的乘性非重叠区域分解算法

本文提出了求解含非线性源项障碍问题一种乘性非重叠区域分解算法,其中子区域间的界面条件为Robin条件;得到了算法的收敛性.并通过数值算例说明,适当的Robin参数的选取可以大大提高算法的收敛速度.     

矩阵最小二乘问题的迭代求解及其在机器翻译中的应用

研究一类线性矩阵方程最小二乘问题的迭代法求解,利用目标函数与矩阵迹之间的关系构造了矩阵形式的"梯度"下降法迭代格式,推广了向量形式的经典"梯度"下降法,并引入了两个矩阵之间的弱正交性来刻画迭代修正量的特点.作为本文算法的应用,给出了机器翻译优化问题的一种迭代求解格式.     

(p,n-p)共轭奇异边值问题双重非负解的存在性

本文研究如下形式的(p,n-p)共轭奇异边值问题其中n≥2,1≤p≤n-1,(?)可允许在t=0和t=1时有奇性,f可在y=0时有奇性．本文作者在R．P．Agarwal等人工作的基础上,在适当假设下证明了此问题双重非负解的存在性．     

一类线性约束矩阵不等式及其最小二乘问题

本文主要考虑一类线性矩阵不等式及其最小二乘问题,它等价于相应的矩阵不等式最小非负偏差问题.之前相关文献提出了求解该类最小非负偏差问题的迭代方法,但该方法在每步迭代过程中需要精确求解一个约束最小二乘子问题,因此对规模较大的问题,整个迭代过程需要耗费巨大的计算量.为了提高计算效率,本文在现有算法的基础上,提出了一类修正迭代方法.该方法在每步迭代过程中利用有限步的矩阵型LSQR方法求解一个低维矩阵Krylov子空间上的约束最小二乘子问题,降低了整个迭代所需的计算量.进一步运用投影定理以及相关的矩阵分析方法证明了该修正算法的收敛性,最后通过数值例子验证了本文的理论结果以及算法的有效性.     

基于偏最小二乘回归的美式期权仿真定价方法

本文应用最优停止理论给出了美式期权定价的一般理论框架，进而给出了美式期权普通多项式偏最小二乘仿真定价算法．解决丁当前普通最小二乘方法的理论缺陷．最后以数字实验演示了无红利美式股票卖权的价值计算，实验结果表明该方法是可行的．     

等式约束不定最小二乘问题的双曲MGS消去算法

众所周知,加权法是解等式约束不定最小二乘问题的方法之一.通过探讨极限意义下,双曲MGS算法解对应加权问题的本质,得到一类消去算法.实验表明,该算法以和文献中现有的GHQR算法达到一样的精度,但实际计算量只需要GHQR算法的一半.     

A multilevel approach for nonnegative matrix factorization

Nonnegative matrix factorization (NMF), the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices, has been shown to be useful in many applications, such as text mining, image processing, and computational biology. In this paper, we explain how algorithms for NMF can be embedded into the framework of multilevel methods in order to accelerate their initial convergence. This technique can be applied in situations where data admit a good approximate representation in a lower dimensional space through linear transformations preserving nonnegativity. Several simple multilevel strategies are described and are experimentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative least squares, multiplicative updates and hierarchical alternating least squares) on several standard image datasets.     

A very fast algorithm for matrix factorization

We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an ever-increasing demand for methods of dimension reduction in order to undertake the statistical analysis of interest. Our algorithm uses a gradient-based approach which can be used with an arbitrary loss function provided the latter is differentiable. The speed and effectiveness of our algorithm for dimension reduction is demonstrated in the context of supervised classification of some real high-dimensional data sets from the bioinformatics literature.     

An alternating projected gradient algorithm for nonnegative matrix factorization

Due to the extensive applications of nonnegative matrix factorizations (NMFs) of nonnegative matrices, such as in image processing, text mining, spectral data analysis, speech processing, etc., algorithms for NMF have been studied for years. In this paper, we propose a new algorithm for NMF, which is based on an alternating projected gradient (APG) approach. In particular, no zero entries appear in denominators in our algorithm which implies no breakdown occurs, and even if some zero entries appear in numerators new updates can always be improved in our algorithm. It is shown that the effect of our algorithm is better than that of Lee and Seung’s algorithm when we do numerical experiments on two known facial databases and one iris database.     

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

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Alternative gradient algorithms with applications to nonnegative matrix factorizations

Three nonnegative matrix factorization (NMF) algorithms are discussed and employed to three real-world applications. Based on the alternative gradient algorithm with the iteration steps being determined columnwisely without projection, and columnwisely and elementwisely with projections, three algorithms are developed respectively. Also, the computational costs and the convergence properties of the new algorithms are given. The numerical examples show the advantage of our algorithms over the multiplicative update algorithm proposed by Lee and Seung [11].     

非负矩阵的一些算法

本文利用有限图论和齐次有限马尔可夫链理论的有关命题和算法得到了不同于[1]、[3]的算法:(1)有限阶非负矩阵可约性的判别、有限阶可约矩阵化为主对角线上都为不可约子块的分块三角阵的算法;(2)有限阶不可约矩阵的Frobenius表示的算法.对上述二算法本文还分别给出了直观简便的图示法.     

Arithmetical characterization of class groups of the form ℤ/<Emphasis Type="Italic">n</Emphasis>ℤ<Emphasis Type="Italic">⊕</Emphasis>ℤ/<Emphasis Type="Italic">n</Emphasis>ℤ via the system of sets of lengths

Let H be a Krull monoid with finite class group such that each class contains a prime divisor (e.g., the multiplicative monoid of the ring of algebraic integers of some number field). It is shown that it can be determined whether the class group is of the form ℤ/nℤ⊕ℤ/nℤ, for n≥3, just by considering the system of sets of lengths of H. Supported by the Austrian Science Fund FWF (Project P18779-N13).     

Subspace correction multi‐level methods for elliptic eigenvalue problems

In this work, we apply the ideas of domain decomposition and multi‐grid methods to PDE‐based eigenvalue problems represented in two equivalent variational formulations. To find the lowest eigenpair, we use a “subspace correction” framework for deriving the multiplicative algorithm for minimizing the Rayleigh quotient of the current iteration. By considering an equivalent minimization formulation proposed by Mathew and Reddy, we can use the theory of multiplicative Schwarz algorithms for non‐linear optimization developed by Tai and Espedal to analyse the convergence properties of the proposed algorithm. We discuss the application of the multiplicative algorithm to the problem of simultaneous computation of several eigenfunctions also formulated in a variational form. Numerical results are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Convergence analysis of a non-negative matrix factorization algorithm based on Gibbs random field modeling

Non-negative matrix factorization (NMF) is a new approach to deal with the multivariate nonnegative data. Although the classic multiplicative update algorithm can solve the NMF problems, it fails to find sparse and localized object parts. Then a Gibbs random field (GRF) modeling based NMF algorithm, called the GRF-NMF algorithm, try to directly model the prior object structure of the components into the NMF problem. In this paper, the convergence of the GRF-NMF algorithm and its advantages are investigated. Based on a classic model, the equilibrium points are obtained. Some invariant sets are constructed to prepare for the analysis of the convergence of the GRF-NMF algorithm. Then using stability theory of the equilibrium point, the convergence of the algorithm is proved and the convergence conditions of the algorithm are obtained. We theoretically present the advantages of the GRF-NMF algorithm in the end.     

广义Cholesky分解乘法扰动分析

0引言关于实对称矩阵的广义Cholesky分解和扰动问题是矩阵计算的重要问题,可参考文献[1-2].本文首先介绍已有的采用加法扰动的角度得到的广义Cholesky分解的一阶相对