数学建模中的数据挖掘方法

结合我校数模培训和参赛的经验，介绍了数据挖掘中的多元回归分析，主成分分析、人工神经网络等方法在建模中的一些成功应用。     

基于奇异值分解的岭型回归(英文)

本文基于设计阵的奇异值分解(SVD),从LS估计出发,应用岭回归估计方法,构造了回归系数的一个新的有偏估计,称为基于SVD的岭型回归估计,简称RRSVD估计,讨论了其性质和偏参数的选取问题,得到了许多重要结论.计算结果表明,在设计阵呈病态时,RRS善岭回归估计.     

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.     

Modelling the process of incoming problem reports on released software products

For big software developing companies, it is important to know the amount of problems of a new software product that are expected to be reported in a period after the date of release, on a weekly basis. For each of a number of past releases, weekly data are present on the number of such reports. Based on the type of data that is present, we construct a stochastic model for the weekly number of problems to be reported. The (non‐parametric) maximum likelihood estimator for the crucial model parameter, the intensity of an inhomogeneous Poisson process, is defined. Moreover, the expectation maximization algorithm is described, which can be used to compute this estimate. The method is illustrated using simulated data. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimating structure quality trends in the Protein Data Bank by equivalent resolution

The quality of protein structures obtained by different experimental and ab-initio calculation methods varies considerably. The methods have been evolving over time by improving both experimental designs and computational techniques, and since the primary aim of these developments is the procurement of reliable and high-quality data, better techniques resulted on average in an evolution toward higher quality structures in the Protein Data Bank (PDB). Each method leaves a specific quantitative and qualitative “trace” in the PDB entry. Certain information relevant to one method (e.g. dynamics for NMR) may be lacking for another method. Furthermore, some standard measures of quality for one method cannot be calculated for other experimental methods, e.g. crystal resolution or NMR bundle RMSD. Consequently, structures are classified in the PDB by the method used. Here we introduce a method to estimate a measure of equivalent X-ray resolution (e-resolution), expressed in units of Å, to assess the quality of any type of monomeric, single-chain protein structure, irrespective of the experimental structure determination method. We showed and compared the trends in the quality of structures in the Protein Data Bank over the last two decades for five different experimental techniques, excluding theoretical structure predictions. We observed that as new methods are introduced, they undergo a rapid method development evolution: within several years the e-resolution score becomes similar for structures obtained from the five methods and they improve from initially poor performance to acceptable quality, comparable with previously established methods, the performance of which is essentially stable.     

Spatial regression analysis between air pollution and childhood leukaemia in Portugal

This study aims to investigate whether known carcinogenic chemical elements in atmospheric deposition might be associated with child mortality due to leukemia in the Portuguese population. A Bayesian hierarchical model was used to explore the association between lichen biomonitoring measurements of four elements—As, Hg, Ni, Pb—and childhood leukemia death counts taken at small administrative units. This geographical epidemiological study found a non-significant positive association between the risk of childhood leukemia and levels of arsenic, mercury and lead, and a non-significant negative association between the disease and the level of nickel. Lead seems to show a weaker association with childhood leukemia than arsenic and mercury.     

多元质量特性预报：MULTIVARIATE回归分析的应用

对现象之间客观存在的因果关系建立回归分析模型,这是实际中较为普遍的做法.在这篇文章中,我们根据MULTIVARIATE回归分析的基本原理,利用从生产现场采集的观测数据,对产品两个质量特性及其五个关键影响因素之间的关系建立了多重多元回归分析方程,为说明MULTIVARIATE回归应用的可行性,我们还结合实例给出了因变量向量估计的两种形式,以及无条件预报的置信区间。     

用LSD法再探泥石流地貌要素之隐式关系

藉助MATLAB工具,对泥石流沟的六个地貌要素之流域面积、主沟长、切割度、沟口高程、流域高差和沟床比降等,一起用最小平方距离法(LSD)进行了初步处理分析之探讨:建立了线性相关的回归方程,并与用最小二乘法(LS)得到的线性回归方程进行比较,一些参数的估计值得到了改善。     

苹果糖度的光谱图像无损检测技术研究

应用光谱图像技术进行了苹果内部品质无损检测技术的研究。通过采集不同波长(分别为632 nm,650 nm,670 nm,780 nm,850 nm和900 nm)的光谱图像,对所采集的光谱图像灰度分布进行洛伦兹分布(LD)、高斯分布(GD)、指数分布(ED)函数的拟合,通过比较发现洛伦兹分布为最优灰度分布拟合函数。将苹果的糖度与洛伦兹分布函数拟合所得参量分别进行多元线性回归,建立最佳单波长、最佳双波长组合、最佳三波长组合和最佳四波长组合的校正方程,相关系数R分别为0.622、0.776、0.831、0.813。实验表明,利用光谱图像技术无损检测苹果糖度是可行性的,为计算机图像对水果进行内部品质的无损检测提供技术依据。