边界粒子法结合正则化技术求解Robin反问题

运用一种边界型无网格算法——边界粒子法求解Robin反问题,结合Tikhonov正则化技术消除反问题的不适定性。该方法仅需边界测量数据,计算精度高,特别适用于反问题的求解。数值算例显示该方法在求解Robin反问题上具有很好的稳定性和收敛性。     

基于广义交叉认证的多小波阈值的图像降噪

提出一种新的小波收缩阈值降噪方法,该方法是通过对噪声图像进行多小波变换,然后用广义交叉认证的方法来确定小波阈值参数．由于本文采用的是多小波变换,而多小波一般同时具有正交性和线性相位,另外广义交叉认证方法不需要对噪声的强度进行估计,所以这种方法有比较好的降噪效果．实验结果表明该方法与基于小波变换的广义交叉认证的图像降噪方法相比较,其降噪效果有一定的提高;同时也表明在一定的条件下,其降噪效果要明显好于传统的Wiener滤波方法．     

Application Des Réseaux de Neurones Avec la Régularisation Bayésienne pour la Modélisation de la Synthèse de l’hydroxyapatite Élaborée à Partir du Carbonate de Calcium et de L’acide Phosphorique

We have used a new, robust model mapping technique—a Bayesian-regularized neural network—to develop a quantitative relationships model for the synthesis of the phosphocalcic hydroxyapatite by precipitation from a calcium carbonate solution and a phosphoric acid solution. This model was preformed by using a set of factors consisting on the pH of reactional medium, the Ca/P molar ratio of the reagents, reaction time, and the initial concentration of calcium. The results show that the method is robust and gives satisfied results. The Levenberg–Marquardt's algorithm implemented in the neural network Matlab's toolbox allowed a drastic improvement of the performance of the model. Very satisfactory results are then obtained by testing the validity by cross-validation technique.

We have also turned our interests to the explanatory capacities of our methodology to explore the relative contribution and/or the contribution profile of the input factors by using Garson weight portioning method.     

Cross-Validating Non-Gaussian Data

Abstract

This article describes an appropriate way of implementing the generalized cross-validation method and some other least-squares-based smoothing parameter selection methods in penalized likelihood regression problems, and explains the rationales behind it. Simulations of limited scale are conducted to back up the semitheoretical analysis.     

Heuristic Parameter Choice Rules for Tikhonov Regularization with Weakly Bounded Noise

We study the choice of the regularization parameter for linear ill-posed problems in the presence of noise that is possibly unbounded but only finite in a weaker norm, and when the noise-level is unknown. For this task, we analyze several heuristic parameter choice rules, such as the quasi-optimality, heuristic discrepancy, and Hanke-Raus rules and adapt the latter two to the weakly bounded noise case. We prove convergence and convergence rates under certain noise conditions. Moreover, we analyze and provide conditions for the convergence of the parameter choice by the generalized cross-validation and predictive mean-square error rules.     

Merits of random forests emerge in evaluation of chemometric classifiers by external validation

Real-world applications will inevitably entail divergence between samples on which chemometric classifiers are trained and the unknowns requiring classification. This has long been recognized, but there is a shortage of empirical studies on which classifiers perform best in ‘external validation’ (EV), where the unknown samples are subject to sources of variation relative to the population used to train the classifier. Survey of 286 classification studies in analytical chemistry found only 6.6% that stated elements of variance between training and test samples. Instead, most tested classifiers using hold-outs or resampling (usually cross-validation) from the same population used in training. The present study evaluated a wide range of classifiers on NMR and mass spectra of plant and food materials, from four projects with different data properties (e.g., different numbers and prevalence of classes) and classification objectives. Use of cross-validation was found to be optimistic relative to EV on samples of different provenance to the training set (e.g., different genotypes, different growth conditions, different seasons of crop harvest). For classifier evaluations across the diverse tasks, we used ranks-based non-parametric comparisons, and permutation-based significance tests. Although latent variable methods (e.g., PLSDA) were used in 64% of the surveyed papers, they were among the less successful classifiers in EV, and orthogonal signal correction was counterproductive. Instead, the best EV performances were obtained with machine learning schemes that coped with the high dimensionality (914–1898 features). Random forests confirmed their resilience to high dimensionality, as best overall performers on the full data, despite being used in only 4.5% of the surveyed papers. Most other machine learning classifiers were improved by a feature selection filter (ReliefF), but still did not out-perform random forests.     

Influence Diagnostics in Partially Varying-Coefficient Models

When a real-world data set is fitted to a specific type of models,it is often encountered that oneor a set of observations have undue influence on the model fitting,which may lead to misleading conclusions.Therefore,it is necessary for data analysts to identify these influential observations and assess their impacton various aspects of model fitting.In this paper,one type of modified Cook's distances is defined to gaugethe influence of one or a set observations on the estimate of the constant coefficient part in partially varying-coefficient models,and the Cook's distances are expressed as functions of the corresponding residuals andleverages.Meanwhile,a bootstrap procedure is suggested to derive the reference values for the proposed Cook'sdistances.Some simulations are conducted,and a real-world data set is further analyzed to examine theperformance of the proposed method.The experimental results are satisfactory.