Local classification: Locally weighted–partial least squares-discriminant analysis (LW–PLS-DA)

The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW–PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones.     

Data-fusion for multiplatform characterization of an italian craft beer aimed at its authentication

Five different instrumental techniques: thermogravimetry, mid-infrared, near-infrared, ultra-violet and visible spectroscopies, have been used to characterize a high quality beer (Reale) from an Italian craft brewery (Birra del Borgo) and to differentiate it from other competing and lower quality products. Chemometric classification models were built on the separate blocks using soft independent modeling of class analogies (SIMCA) and partial least squares-discriminant analysis (PLS-DA) obtaining good predictive ability on an external test set (75% or higher depending on the technique). The use of data fusion strategies – in particular, the mid-level one – to integrate the data from the different platforms allowed the correct classification of all the training and validation samples.     

Sensitive and selective cocaine electrochemical detection using disposable sensors

This paper describes the voltammetric determination of cocaine in presence of three different interferences that could be found in street samples using disposable sensors. The electrochemical analysis of this alkaloid can be affected by the presence of codeine, paracetamol or caffeine, whose oxidation peaks may overlap and lead to false positives. This work describes two different solutions to this problem. On one hand, the modification of disposable carbon sensors with carbon nanotubes allows the voltammetric quantification of cocaine by using ordinary least squares regressions in the concentration range from 10 to 155 μmol L⁻¹, with a reproducibility of 5.6% (RSD, n = 7. On the other hand, partial least squares regressions are used for the resolution of the overlapped voltammetric signals when using screen-printed carbon electrodes without any modification. Both procedures have been successfully applied to the evaluation of the purity of cocaine street samples.     

A strategy that iteratively retains informative variables for selecting optimal variable subset in multivariate calibration

Nowadays, with a high dimensionality of dataset, it faces a great challenge in the creation of effective methods which can select an optimal variables subset. In this study, a strategy that considers the possible interaction effect among variables through random combinations was proposed, called iteratively retaining informative variables (IRIV). Moreover, the variables are classified into four categories as strongly informative, weakly informative, uninformative and interfering variables. On this basis, IRIV retains both the strongly and weakly informative variables in every iterative round until no uninformative and interfering variables exist. Three datasets were employed to investigate the performance of IRIV coupled with partial least squares (PLS). The results show that IRIV is a good alternative for variable selection strategy when compared with three outstanding and frequently used variable selection methods such as genetic algorithm-PLS, Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS) and competitive adaptive reweighted sampling (CARS). The MATLAB source code of IRIV can be freely downloaded for academy research at the website: http://code.google.com/p/multivariate-calibration/downloads/list.     

Parameter Estimation of Multivariate Regression Model with Fuzzy Random Errors

In many real-world problems, observations are usually described by approximate values due to fuzzy uncertainty, unlikeprobabilistic uncertainty that has nothing to do with experimentation. The combination of statistical model and fuzzy set theory is helpful to improve the identification and analysis of complex systems. As an extension ofstatistical techniques, this study is an investigation of the relationship between fuzzy multiple explanatory variables and fuzzy response with numeric coefficients and the fuzzy random error term. In this work we describe a parameter estimation procedure carrying out the least-squares method in a complete metric space of fuzzy numbers to determine the coefficients based on the extension principle. We demonstrate how the fuzzy least squares estimators present large sample statistical properties, including asymptotic normality, strong consistency and confidence region. The estimators are also examined via asymptotic relative efficiency concerning traditional least squares estimators. Different from the construction of error term in Kim et al.\cite{21}, it is more reasonable in the proposed model since the problems of inconsistency in referring to fuzzy variable and producing the negative spreads may be avoided. The experimental study verifies that the proposed fuzzy least squares estimators achieve the meaning consistent with the theory identification for large sample data set and better generalization regarding one single variable model.     

半变系数模型研究美国爱荷华州埃姆斯市的房价问题

近年来房地产业发展迅猛,房价快速走高,对经济发展和社会稳定产生了重大影响,因此房价研究具有重要的社会价值和经济意义.文章通过散点图及其拟合曲线展示不同协变量和响应变量之间的相关关系,提出半变系数模型建模美国埃姆斯市的房价问题.文章采用剖面最小二乘法研究7个协变量:地面以上的居住面积、地面以上的房间总数(不包括卫生间)、卫生间总数、房屋整体建材质量和品质、地下室面积、车库面积、建造年份与埃姆斯市房价之间的回归关系,为房价预测研究作准备.研究结果表明半变系数模型在探索美国爱荷华州埃姆斯市房价方面表现较好.因此,文章提供了一种利用半变系数模型同时学习高维数据线性和交互关系的有效方法.     

基于个人超出值的模糊联盟合作博弈最小二乘预核仁

本文给出了基于个人超出值的无限模糊联盟合作博弈最小二乘预核仁的求解模型,得到该模型的显式解析解,并研究该解的若干重要性质。证明了:本文给出的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的相等解(The equalizer solution),基于个人超出值的字典序解三者相等。进一步证明了:基于Owen线性多维扩展的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的经典合作博弈最小二乘预核仁相等。最后,通过数值实例说明本文提出的无限模糊联盟合作博弈求解模型的实用性与有效性。     

土壤重金属砷的高光谱估算模型

砷是严重危害人体的重金属之一。利用高光谱技术进行土壤重金属砷含量的估测具有很大的应用潜力,但受区域和土壤背景的影响,估算模型适用性和精度都会有很大的差异。针对石家庄市地表水源地保护区土壤砷含量的高光谱估算,在水源地保护区的主要采矿地和冶炼企业进行了土壤实地采样和实验室重金属分析,对土壤样本的原始光谱反射率采用Savitzky-Golay 7点平滑处理,进行一阶微分（FD）、二阶微分（SD）、倒数（RT）、倒数一阶微分（RTFD）、倒数二阶微分（RTSD）、倒数对数（AT）、倒数对数一阶微分（ATFD）、倒数对数二阶微分（ATSD）、连续统去除（CR）9种光谱变换后,再对重金属砷实测含量与经光谱变换后的光谱指标进行相关分析,并提取各光谱指标的最大敏感波段。运用多元线性逐步回归（MLSR）、单光谱变换指标偏最小二乘回归（U-PLSR）和多光谱变换指标偏最小二乘回归（M-PLSR）方法构建土壤重金属砷含量估算模型,最后通过相关系数r、均方根误差（root mean square error, RMSE）和统计值F来比对建模效果。结果表明：研究区部分土壤样本重金属砷含量已经出现了轻度污染,大部分样本处于污染的临界状态;经连续统去除变换后的光谱特征与砷的相关性最大,一阶微分与砷含量存在最大负相关性;相较于多元线性逐步回归和单光谱变换指标偏最小二乘回归,采取多光谱变换指标偏最小二乘回归方法土壤重金属砷含量模型估算值与实测值最为接近,建模R2达到0.852,RMSE和F值分别达到0.147和32.384,多光谱变换指标建模集成效果显著。因此研究结果可以为石家庄水源地保护区主要采矿地和冶炼企业重金属砷污染高光谱快速监测提供科学依据。     

不同颜色冬枣可溶性固形物可见-近红外光谱分析模型构建

冬枣品质受其品种和生长环境等因素的影响,引起采后化转红指数不同,导致果实的颜色差异较大,从而影响其可溶性固形物（SSC）检测模型的分析精度。采用可见-近红外（Vis-NIR）光谱结合Norris-Williams平滑（NWS）、连续小波导数（CWD）、多元散射校正（MSC）、标准正态变量变换（SNV）和NWS-MSC五种光谱预处理方法构建不同颜色（红绿相间MJ,绿色GJ和红色RJ）冬枣SSC的偏最小二乘（PLS）定量分析模型,分别采用MJ,GJ,RJ,MJ-GJ和MJ-GJ-RJ五个样品集合建立冬枣SSC的定量分析模型,并采用由MJ-GJ-RJ三种颜色冬枣样品组成的测试集进行模型的评价;以不同建模样品集（校正集）的校正相关系数（R_c）和交互验证均方根误差（RMSECV）作为构建最优模型的评价指标;测试集的预测相关系数（R_p）和预测均方根误差（RMSEP）用于模型预测精度的评价。研究结果表明：分别采用MJ,GJ和RJ的独立样品集进行建模时,模型仅对具有相同颜色的冬枣样品的SSC实现了较好的预测;分别在MJ样品中加入GJ和GJ-RJ样品进行MJ-GJ和MJ-GJ-RJ两个混合样品集的定量模型的构建时,MJ-GJ模型对MJ和GJ样品的SSC具有较好的预测效果,其RMSECV,R_c,RMSEP,R_p分别为1.108,0.698,0.980,0.724和1.108,0.698,0.983,0.822,而对RJ样品的预测误差较大,模型的RMSECV,R_c,RMSEP,R_p为1.108,0.698,1.928,0.597;而MJ-GJ-RJ模型对三种颜色的冬枣SSC均有较好的预测结果：MJ-GJ-RJ模型对MJ样品的SSC模型的RMSECV,R_c,RMSEP,R_p为1.158,0.796,1.077,0.668;对GJ样品的SSC模型的RMSECV,R_c,RMSEP,R_p为1.158,0.796,0.881,0.861;对RJ样品的SSC模型的RMSECV,R_c,RMSEP,R_p为1.158,0.796,1.140,0.841;采用蒙特卡罗无信息变量消除（MCUVE）方法进一步对MJ-GJ-RJ样品集光谱的特征变量进行优选后,模型的R_c和R_p分别由原来的0.796和0.864提高到0.884和0.922,模型的RMSECV和RMSEP分别由1.158和0.946减小到0.886和0.721,模型具有较好的分析精度。采用可见-近红外光谱对不同颜色冬枣的SSC进行分析时,当建模集样品与测试集样品颜色属性相似或选择性质相似的建模变量进行模型构建时,模型具有更好的通用性。     

高光谱定量反演火龙果茎枝叶绿素含量的研究

火龙果是近年来引进我国的营养价值高、经济效益好的新型水果,肉质茎枝是其主要光合器官,与常见果树具有较大差异。为探索以茎枝为光合作用器官的植被的光谱特征及其生化组分的估测方法,以火龙果为研究对象,在贵州省典型种植区罗甸县开展了4个氮肥梯度田间试验,同步测定不同养分丰缺程度下的火龙果茎枝高光谱和相应叶绿素含量数据;然后分析火龙果茎枝光谱数据的演化规律,并采用数学变换、连续小波变换算法并结合相关性分析算法处理分析火龙果茎枝光谱数据,提取并筛选特征波段;最后利用偏最小二乘算法构建火龙果茎枝叶绿素含量估测模型。研究结果表明：（1）火龙果肉质茎枝的原始光谱曲线整体趋势与常见绿叶植物相似,但随施氮量的增加,火龙果近红外处的光谱反射率逐渐降低,变化趋势与常见绿叶植物相反,茎枝光谱的吸收峰（谷）随施氮量的增加呈升高（加深）的趋势。（2）数学变换中的一阶微分与在L₁-L₅尺度内的连续小波变换能有效提升光谱对叶绿素含量的敏感性,火龙果茎枝原始光谱与叶绿素含量的敏感区域主要位于730～1 400 nm,数学变换与连续小波变换均能提升光谱对叶绿素含量的敏感性。与常见绿叶植物相比,火龙果茎枝敏感波段分布相对分散,且多位于730 nm附近与近红外区域（1 100～1 600 nm）。（3）数学变换和连续小波变换能明显提升光谱对火龙果茎枝叶绿素含量的估测能力,其中基于一阶微分的估测模型与基于连续小波变换L₁与L₄的估测模型分别为数学变换与连续小波变换的最优模型,其验证精度分别为R2_验证=0.625,RMSE=0.048,RPD=1.238（一阶微分）;R2_验证=0.678,RMSE=0.037,RPD=1.652（连续小波变换）;表明高光谱技术可以作为火龙果茎枝叶绿素含量和营养诊断的无损监测手段。该研究为完善不同植被类型基于高光谱指数的叶绿素反演提供了补充。