一种新的预报策略

本文提出一种新的预报策略，将校准和预报的测量数据结合在一起进行主成分分解，找到校准和预报的共同的正交投影空间。这种新策略用于确定主成分数的交叉验证时只需一次主成分分解，因此速度很快；用于定量预报时，模型稳定性好，预报准确度令人满意。     

气相色谱-质谱法鉴别香水样品真伪

建立气相色谱-质谱法鉴别香水样品真伪的方法。利用气相色谱-质谱联用法测定香水中化学成分及其含量，按照商品不同价位将分析数据分组进行主成分分析以及偏最小二乘分析，并通过模型载荷图与变量投影重要性分析，判断影响香水真假的主要差别成分。结果显示，主成分分析构建的模型可行性优于偏最小二乘-判别分析构建的模型，影响香水真假的主要差别成分为芳樟醇。该方法可用于真假香水的鉴别。     

基于PCA-BP神经网络的香精香料识别方法研究

主成分分析(PCA)结合BP神经网络是一种新型香料识别法。先利用质谱分析仪对香精香料进行测量,得到质荷比以及对应浓度数值;再使用主成分分析(PCA)方法对原始数据进行处理;同时创建BP神经网络训练数据;最后将对照组数据输入神经网络得到识别结果并与标准比对。结果表明主成分分析的采用对实验效率提高有巨大帮助,使用PCA-BP方法可以有效识别香精香料,测试识别率高达96.7%。     

主成分分光光度法中主成分的选择

主成分分析是全光谱分析度分析中常用的校正方法。本文提出第一主成分并不是与因最线性相关的主成分。为此，我们利用扫描算法众多主成分中选择与因变量（浓度）最相关的主成分，从而使计算结果更准确可信。本文还对单因变量和多因变量两种情况下主成分选择的统计量进行了讨论。     

一种测定中药复方制剂中活性成分的计算分析方法

提出了一种测定中药复方制剂中活性成分含量的计算分析新方法。该方法将主 成分分析和广义秩消因子分析集成用于处理HPLC／DAD数据，并改进了传统的IND因 子指示函数，适用于定量计算分析复杂混和物体系中的待测成分。将其用于测定复 方丹参制剂中三七皂苷R1的含量，计算分析结果表明，本方法明显优于广义秩消因 子法，同时证明IND函数的改进提高了计算分析准确度。     

基于料酒的三维同步荧光光谱模式识别研究

提出了一种应用同步荧光光谱技术无损快速鉴别料酒品牌的新方法.利用主成分分解法和小波变换法对料酒样品的同步荧光光谱信号进行了压缩处理,分别采用同步荧光光谱数据的第一主成分和小波细节系数为特征变量进行主成分分析和聚类分析,分类结果表明小波系数作为料酒的特征变量对料酒品牌分类正确率更高.利用偏最小二乘和径向基人工神经网络方法...     

基于小波变换平滑主成分分析

小波变换具有很强的信号分离能力,很容易把随机噪音从信号中分离出来,从而提高信号的信噪比。本文把小波变换引入到因子分析中,提出了基于小波变换平滑主成分分析,该算法既保留普通主成分分析的正交分解,又具备了小波变换的信号分离能力。模拟数据和实验数据的结果表明,该算法具有从低信噪比的数据中提取出有用信息,并提高信号的信噪比。迭代目标变换因子分析处理实验数据的结果表明,基于小波变换平滑主成分分析的处理结果优     

稳健算法及其在红外光谱分析中的应用

总结了稳健主成分分析、稳健主成分回归、稳健偏最小二乘回归和稳健连续回归等各种稳健算法的新近成果. 研究表明,稳健算法可以检测并规避异常值的影响. 稳健算法应用红外光谱分析中可望优化定性、定量预测模型.     

基于光谱融合-特征提取的海洛因及其添加剂无损分类研究

在近年来的多数治安案件中,有不少是由形形色色的毒品所引起的。为了提高检验的效率,降低检验成本,实现对海洛因样本主成分及添加剂的无损分类,提出了一种基于光谱融合,主成分分析和判别分析的鉴别方法。采集并获取了不同质量分数和添加剂共计45个海洛因样本的红外光谱,选择一阶求导、多元散射校正、Savitzky-Golay平滑和峰面积归一化开展预处理工作,并利用主成分分析进行特征变量提取和采用Fisher判别分析构建判别分类模型。实验对单独的原始光谱数据,一阶导数光谱数据和融合后的光谱数据进行比较。无论是对海洛因主成分的质量分数进行分类,还是对海洛因的添加剂分类,单一的分类模型都仅能实现66.7%～88.9%的准确区分。结果表明,基于融合的光谱数据构建的判别模型分类准确率更高,对主成分质量分数和海洛因添加剂的分类,均能达到100.0%。利用红外光谱数据融合技术结合主成分分析和判别分析达到了降低检验成本且无损的目的,能够最大程度的限制毒品的流动,对今后的毒品检测和维护社会治安稳定具有一定的贡献。     

基于多元统计学的青稞HPLC指纹图谱研究

为了筛选品质良好的青稞,选择不同产地的10批青稞样品,建立了青稞的高效液相指纹图谱,并进行了聚类分析和主成分分析,测定了儿茶素、表儿茶素和芦丁3种指标成分的含量。首先采用高效液相色谱法测得了10批青稞的色谱图,建立其共有模式,确定了11个共有峰,蓝青稞指标成分含量均高于白青稞。对共有峰数据进行聚类分析和主成分分析,10批青稞被分为两类,主成分分析得到了3个主成分,方差累积达82.266%,综合得分最高的三个样品分别为S4、S3、S1,均为西藏地区的蓝青稞,与指标成分含量测定的结果一致。指纹图谱、聚类分析结合主成分分析为青稞的指标筛选和综合评价提供了新的方法。     

Comparative study between three methods of outlying detection on experimental results

This paper describes experimental results through multivariate statistical methods that might reveal outliers that are rarely taken into account by analysts. The results were submitted to three procedures to detect outliers: Mahalanobis distance, MD, cluster analysis, CA, and principal component analysis, PCA. The results showed that although CA is one of the procedures most often used to identify outliers, it can fail by not showing the samples that are easily identified as outliers by other methods, like MD. Mahalanobis distance proved to be the simpler application, with sensitive procedures to identify outliers in multivariate datasets.     

Spectral pattern recognition using self-organizing MAPS

A Kohonen neural network is an iterative technique used to map multivariate data. The network is able to learn and display the topology of the data. Self-organizing maps have advantages as well as drawbacks when compared to principal component plots. One advantage is that data preprocessing is usually minimal. Another is that an outlier will only affect one map unit and its neighborhood. However, outliers can have a drastic and disproportionate effect on principal component plots. Removing them does not always solve the problem for as soon as the worst outliers are deleted, other data points may appear in this role. The advantage of using self-organizing maps for spectral pattern recognition is demonstrated by way of two studies recently completed in our laboratory. In the first study, Raman spectroscopy and self-organizing maps were used to differentiate six common household plastics by type for recycling purposes. The second study involves the development of a potential method to differentiate acceptable lots from unacceptable lots of avicel using diffuse reflectance near-infrared spectroscopy and self-organizing maps.     

Peak alignment and robust principal component analysis of gas chromatograms of fatty acid methyl esters and volatiles

Gas chromatograms of fatty acid methyl esters and of volatile lipid oxidation products from fish lipid extracts are analyzed by multivariate data analysis [principal component analysis (PCA)]. Peak alignment is necessary in order to include all sampled points of the chromatograms in the data set. The ability of robust algorithms to deal with outlier problems, including both sample-wise and element-wise outliers, and the advantages and drawbacks of two robust PCA methods, robust PCA (ROBPCA) and robust singular value decomposition when analysing these GC data were investigated. The results show that the usage of ROPCA is advantageous, compared with traditional PCA, when analysing the entire profile of chromatographic data in cases of sub-optimally aligned data. It also demonstrates how choosing the most robust PCA (sample or element-wise) depends on the type of outliers present in the data set.     

Rime samples characterization and comparison using classical and fuzzy principal components analysis

The main objective of this paper is to introduce principal component analysis and two robust fuzzy principal component algorithms as useful tools in characterizing and comparing rime samples collected in different locations in Poland (2004–2007). The efficiency of the applied procedures was illustrated on a data set containing 108 rime samples and concentration of anions, cations, HCHO, as well as pH and conductivity. The fuzzy principal component algorithms achieved better results mainly because they are more compressible than classical PCA and very robust to outliers. For example, a three component model, fuzzy principal component analysis-first component (FPCA-1) accounts for 62.37% of the total variance and fuzzy principal component analysis-orthogonal (FPCA-o) 90.11%; PCA accounts only for 58.30%. The first two principal components explain 51.41% of the total variance in the case of FPCA-1 and 79.59% in the case of FPCA-o as compared to only 47.55% for PCA. As a direct consequence, PCA showed only a partial differentiation of rime samples onto the plane or in the space described by different combination of two or three principal components, whereas a much sharper differentiation of the samples, regarding their origin and location, is observed when FPCAs are applied.      

Principal component analysis versus fuzzy principal component analysis A case study: the quality of danube water (1985-1996)

Principal component analysis (PCA) is a favorite tool in environmetrics for data compression and information extraction. PCA finds linear combinations of the original measurement variables that describe the significant variations in the data. However, it is well-known that PCA, as with any other multivariate statistical method, is sensitive to outliers, missing data, and poor linear correlation between variables due to poorly distributed variables. As a result data transformations have a large impact upon PCA. In this regard one of the most powerful approach to improve PCA appears to be the fuzzification of the matrix data, thus diminishing the influence of the outliers. In this paper we discuss and apply a robust fuzzy PCA algorithm (FPCA). The efficiency of the new algorithm is illustrated on a data set concerning the water quality of the Danube River for a period of 11 consecutive years. Considering, for example, a two component model, FPCA accounts for 91.7% of the total variance and PCA accounts only for 39.8%. Much more, PCA showed only a partial separation of the variables and no separation of scores (samples) onto the plane described by the first two principal components, whereas a much sharper differentiation of the variables and scores is observed when FPCA is applied.     

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Median absolute deviation (MAD) is a well‐established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F‐tests, extensive calibration tables, time‐consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

主成分分析同时测定多组分金属离子

将主成分分析用于同时单点pH络合滴定,可同时测定多组分金属离子。讨论了方法原理、pH值的选择,建立了主成分分析常数矩阵。对四元金属离子混合样进行了多次测定,均获得满意结果。