基于超节点LDL分解的大规模结构计算

采用列压缩稀疏(Compressed Sparse Column,CSC)矩阵存储策略对矩阵LDL分解前进行填充元优化排序;基于消去树进行LDL符号分解,使之独立于数值分解,避免多余的内存消耗,减少不必要的数值运算.利用矩阵非零元的分布特性分析并实现超节点LDL分解算法,将稀疏矩阵的分解运算变为一系列稠密矩阵运算,并使用优化的BLAS函数库加速分解.测试表明:算法在成倍地提高计算速度的同时进一步降低内存消耗,适用于大规模的结构计算.     

一种基于XML的One to One营销优化建模方法

针对一种One to One营销优化过程,提出一种基于XML的OnetoOne营销优化自定义建模方法,利用DOMAPI技术设计实现了XML文件接口。通过该接口可提取记录模型信息的XML文档用于建模,也可将模型信息自动生成XML文档,并给出了具体建模流程和方法。     

一种快速分解大整数的小因子的优化分解树OFT算法

分解大整数的小因子是解决IFP，DLP问题的诸多攻击方法中的重要运算模块．本文在目前分解大整数小因子算法的基础上，提出的优化分解树(Optimized Factorization Tree)算法，利用树型数据结构和相应的构造算法与回溯算法，配合以作者提出的分解表截支方法和优化分组策略，可以将分解大整数小因子的速度提高50％以上．该算法还可以为大整数素性判别做高效过滤，快速识别大部分合数．     

灰度图像质心快速算法

对矩因子x^py^q。做差分变换为函数Fl()，将图像函数f(x，y)做累进求和变换为函数F2()．用Fl()和F2()相乘求取质心．由于0阶和1阶矩因子中的P，q不大于1，经差分后的F1()除右端点外，其值都为1，乘1的运算当然可以不做，从而消去了乘法运算．对任意大小和任意级别的灰度图像，乘除法运算次数仅为3次，而加法运算次数也有降低．文中算法计算结果精确，其运算效率高于已有其他算法．     

基于Slope One算法的图书推荐系统优化

Slope One算法是一种易实现,运算效率高,可扩展性好的协同过滤推荐算法,但该算法依赖大量用户对待预测项目的评分,在数据稀疏的情况下用户评分的可靠性对推荐结果的影响很大。该文首先利用Lens Kit工具下的Slope One算法和某在线图书网站的数据进行了图书推荐实验,分析了三个导致图书推荐效果不好的原因,然后提出了稀疏数据下的基于预测评分可靠性加权的Slope One算法优化,最后对优化后的推荐算法进行对比实验,证明改进后的图书推荐系统在内存使用率和推荐质量上均有明显提高。     

基于图嵌入的用户加权Slope One算法

针对传统Slope One推荐算法在稀疏数据集上预测准确率较低的问题,提出一种基于图嵌入的加权Slope One算法。本文算法首先以融合时间信息的用户相似度为边权建立用户关联图,对该图进行图嵌入得到用户特征向量,然后基于Canopy聚类对用户进行类内加权Slope One推荐。另外,为优化算法性能,本文算法基于Spark计算框架实现。实验结果表明,对比传统的加权Slope One,本文算法在稀疏数据集和显式、隐式评分数据集上的推荐效果和评分预测准确率都更优。     

矩阵的Doolittle递归分解算法及符号程序设计

将矩阵An×n的Doolittle分解推广到Am×n上，并在常规的迭代算法上加以创新，给出了递归的分解算法．在实现算法的过程中，对数据进行了巧妙处理，使中间数据及最终计算结果都具有分数形式，提高了结果的精确度，而且更符合人们阅读的习惯．经过运行测试，算法设计合理，程序运行高效准确．程序是对MathSoft公司的交互式的数学文字软件Mathcad的矩阵分解的数值计算扩充到符号运算．     

一种辨识多变量系统结构和参数地递推算法*

本文基于Guidorzi方法,提出一种辨识多变量系统结构和参数的递推算法。本算法通过对矩阵进行分解,根据分解过程中某参数的变化情况,判断矩阵的奇异性,从而辨识出系统的结构和参数,使得原来对矩阵求逆及求行列式的运算变为简单的代数运算,大大减少了辨识过程中的计算量,数值实例表明了这种算法的有效性。     

基于聚类和Spark框架的加权Slope One算法

针对传统Slope One算法在相似性计算时未考虑项目属性信息和时间因素对项目相似性计算的影响,以及推荐在当前大数据背景下面临的计算复杂度高、处理速度慢的问题,提出了一种基于聚类和Spark框架的加权Slope One算法。首先,将时间权重加入到传统的项目评分相似性计算中,并引入项目属性相似性生成项目综合相似度;然后,结合Canopy-K-means聚类算法生成最近邻居集;最后,利用Spark计算框架对数据进行分区迭代计算,实现该算法的并行化。实验结果表明,基于Spark框架的改进算法与传统Slope One算法、基于用户相似性的加权Slope One算法相比,评分预测准确性更高,较Hadoop平台下的运行效率平均可提高3.5~5倍,更适合应用于大规模数据集的推荐。     

一种基于局部近邻Slope One协同过滤推荐算法

经典的Slope One算法采用线性回归模型对目标项目进行预测评分,但在项目评分偏差表构建过程中产生了部分噪声数据,影响了算法的推荐性能。为了解决该问题,建立了一种基于局部近邻Slope One协同过滤推荐算法。算法计算了当前活跃用户针对不同推荐商品的近邻用户集,其邻居用户集根据目标项目的不同而动态变化;根据活跃用户关于不同目标项目的邻居用户数据来进一步优化项目之间的平均偏差,进而产生推荐。对比实验说明,该算法在MovieLens数据集上具有较高推荐精度。     

A Fast LDL-factorization Approach for Large Sparse Positive Definite System and Its Application to One-to-one Marketing Optimization Computation

LDL-factorization is an efficient way of solving Ax=b for a large symmetric positive definite sparse matrix A.This paper presents a new method that further improves the efficiency of LDL-factorization.It is based on the theory of elimination trees for the factorization factor.It breaks the computations involved in LDL-factorization down into two stages:1) the pattern of nonzero entries of the factor is predicted,and 2) the numerical values of the nonzero entries of the factor are computed.The factor is stored using the form of an elimination tree so as to reduce memory usage and avoid unnecessary numerical operations.The calculation results for some typical numerical examples demonstrate that this method provides a significantly higher calculation efficiency for the one-to-one marketing optimization algorithm.     

一类One to One营销优化模型及其解决方案

针对OnetoOne营销问题进行简单的案例分析,得出了在一般情况下的优化模型。通过把OnetoOne营销优化问题转换成线性规划问题,应用改进的单纯形法、基于Bartels-GolubLU分解的单纯形法和原始-对偶内点法等三种典型的线性规划算法,在MATLAB环境下进行仿真和分析。     

Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem

This paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Gröbner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial spectral factorization in the presence of real parameters. It is discussed that parametric polynomial spectral factorization enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs two quantifier elimination techniques. This proposed approach is demonstrated in a numerical example of a particular control problem.     

One to One营销优化算法的BenchMark验证方法

该文针对OnetoOne营销优化问题,提出了一种BenchMark验证方法。基于这一BenchMark验证方法,对原始Simplex法、DFS法和LIPSOL法进行了基于理论的BenchMark验证和基于MATLAB的BenchMark验证,给出了仿真结论,证明了提出的BenchMark验证方法的有效性。     

Efficient sparse LU factorization with partial pivoting ondistributed memory architectures

A sparse LU factorization based on Gaussian elimination with partial pivoting (GEPP) is important to many scientific applications, but it is still an open problem to develop a high performance GEPP code on distributed memory machines. The main difficulty is that partial pivoting operations dynamically change computation and nonzero fill-in structures during the elimination process. This paper presents an approach called S* for parallelizing this problem on distributed memory machines. The S* approach adopts static symbolic factorization to avoid run-time control overhead, incorporates 2D L/U supemode partitioning and amalgamation strategies to improve caching performance, and exploits irregular task parallelism embedded in sparse LU using asynchronous computation scheduling. The paper discusses and compares the algorithms using 1D and 2D data mapping schemes, and presents experimental studies on Cray-T3D and T3E. The performance results for a set of nonsymmetric benchmark matrices are very encouraging, and S* has achieved up to 6.878 GFLOPS on 128 T3E nodes. To the best of our knowledge, this is the highest performance ever achieved for this challenging problem and the previous record was 2.583 GFLOPS on shared memory machines     

Factorization in large-scale many-body calculations

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.     

Decomposition-Fusion for Label Distribution Learning

Label Distribution Learning (LDL) is a general learning framework that assigns an instance to a distribution over a set of labels rather than to a single label or multiple labels. Current LDL methods have proven their effectiveness in many real-life machine learning applications. However, LDL is a generalization of the classification task and as such it is exposed to the same problems as standard classification algorithms, including class-imbalanced, noise, overlapping or irregularities. The purpose of this paper is to mitigate these effects by using decomposition strategies. The technique devised, called Decomposition-Fusion for LDL (DF-LDL), is based on one of the most renowned strategy in decomposition: the One-vs-One scheme, which we adapt to be able to deal with LDL datasets. In addition, we propose a competent fusion method that allows us to discard non-competent classifiers when their output is probably not of interest. The effectiveness of the proposed DF-LDL method is verified on several real-world LDL datasets on which we have carried out two types of experiments. First, comparing our proposal with the base learners and, second, comparing our proposal with the state-of-the-art LDL algorithms. DF-LDL shows significant improvements in both experiments.     

决策树在基于消费者外表的服装营销中的应用

服装销售人员常常根据消费者的外表特征来进行快速营销活动,以提高购买率。从数据挖掘技术的角度来探讨基于消费者外表印象的快速营销技术,以帮助营销人员快速寻找外表印象营销规则。介绍了决策树算法原理;其次,讨论了消费者外表印象评价指标体系,并根据该体系由销售人员在服装店铺里进行了消费者的外表及其行为数据采集;应用了计算实例来说明服装消费者的外表营销决策树分类模型;利用工具Clementine中的决策树方法来进行营销规则的挖掘。研究表明了该应用是切实可行的。     

Condition Numbers of Approximate Schur Complements in Two- and Three-Dimensional Discretizations on Hierarchically Ordered Grids

We investigate multilevel incomplete factorizations of M-matrices arising from finite difference discretizations. The nonzero patterns are based on special orderings of the grid points. Hence, the Schur complements that result from block elimination of unknowns refer to a sequence of hierarchical grids. Having reached the coarsest grid, Gaussian elimination yields a complete decomposition of the last Schur complement. The main focus of this paper is a generalization of the recursive five-point/nine-point factorization method (which can be applied in two-dimensional problems) to matrices that stem from discretizations on three-dimensional cartesian grids. Moreover, we present a local analysis that considers fundamental grid cells. Our analysis allows to derive sharp bounds for the condition number associated with one factorization level (two-grid estimates). A comparison in case of the Laplace operator with Dirichlet boundary conditions shows: Estimating the relative condition number of the multilevel preconditioner by multiplying corresponding two-grid values gives the asymptotic bound O(h ^−0.347) for the two- respectively O(h ^−4/5) for the three-dimensional model problem. Received October 19, 1998; revised September 27, 1999