Alternative mathematical approaches to shade sorting

Shade sorting is the process of assigning samples of the same nominal color into groups having no significant color variation. Use of modern spectrophotometers and color measurement technology make it possible to obtain precise color differences between samples. When these color differences are viewed as distances between points, the shade sorting problem is seen to be equivalent to the clustering problem in the mathematical literature. Several mathematical techniques for clustering—complete linkage clustering, vertex labeling, and set covering—are explained and compared for their efficiency when applied to shade sorting. A particular implementation of complete linkage clustering called Clemson Color Clustering (CCC) is found to perform well as compared to the other reviewed methods. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 368–375, 2000     

采用主成分与聚类分析对市售保湿乳液感官评价的研究

以26款市售保湿乳液为研究对象,采用定量描述分析(QDA)法对保湿乳液手部使用结束后0,2和5 min 3个阶段的肤感进行评价。采用主成分(或主分量)分析(PCA)法和凝聚层次聚类(AHC)分析法对评价结果进一步分析。PCA的结果显示,本次考察的感官属性共提取出2个主成分,其特征值分别为4.182和2.611,前2个主成分累计方差贡献率达到84.91%。其中第1主成分描述了皮肤吸收,包括3个阶段的滋润感和柔软性;第2主成分描述了皮肤残留,包括3个阶段的黏滞感。结合AHC分析,结果表明26款市售产品可分为2类,第1和2类分别包含12和14款市售产品。该研究成功将26款市售保湿乳液分布在主成分图中,并对其进行了分类。     

Reconstruction of reflectance spectra using weighted principal component analysis

The weighted principal component analysis technique is employed for reconstruction of reflectance spectra of surface colors from the related tristimulus values. A dynamic eigenvector subspace based on applying certain weights to reflectance data of Munsell color chips has been formed for each particular sample and the color difference value between the target, and Munsell dataset is chosen as a criterion for determination of weighting factors. Implementation of this method enables one to increase the influence of samples which are closer to target on extracted principal eigenvectors and subsequently diminish the effect of those samples which benefit from higher amount of color difference. The performance of the suggested method is evaluated in spectral reflectance reconstruction of three different collections of colored samples by the use of the first three Munsell bases. The resulting spectra show considerable improvements in terms of root mean square error between the actual and reconstructed reflectance curves as well as CIELAB color difference under illuminant A in comparison to those obtained from the standard PCA method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 360–371, 2008     

Two‐step principal component analysis for dynamic processes monitoring

In this study, a two‐step principal component analysis (TS‐PCA) is proposed to handle the dynamic characteristics of chemical industrial processes in both steady state and unsteady state. Differently from the traditional dynamic PCA (DPCA) dealing with the static cross‐correlation structure and dynamic auto‐correlation structure in process data simultaneously, TS‐PCA handles them in two steps: it first identifies the dynamic structure by using the least squares algorithm, and then monitors the innovation component by using PCA. The innovation component is time uncorrelated and independent of the initial state of the process. As a result, TS‐PCA can monitor the process in both steady state and unsteady state, whereas all other reported dynamic approaches are limited to only processes in steady state. Even tested in steady state, TS‐PCA still can achieve better performance than the existing dynamic approaches.     

Performance of neural networks for predicting yarn properties using principal component analysis

In recent years, neural networks have been used as a tool for modeling an industrial process. An improvement in their performance may be expected either by divining more efficient training algorithms or by intelligently manipulating the data set. The second method is examined. The problem chosen is one of predicting the properties of cotton yarn from the fiber properties. When the input data are known to correlate with each other, principal component analysis can be used to improve the performance of neural networks. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1746–1751, 2004     

A review of principal component analysis and its applications to color technology

Principal component analysis, abbreviated PCA, has been an important and useful mathematical tool in color technology since the 1960s. Its uses have included defining tolerance intervals and ellipsoidal regions, estimating colorant spectral properties from mixtures, deriving CIE daylight, data reduction for large ensembles of spectra, and spectral imaging. Although PCA is a common topic in many engineering disciplines, statistics, and mathematics, many color‐technology professionals and color‐science students come from disciplines where this technique is not part of their curricula. It is from this perspective that this review publication was written. The purpose of this publication is to describe PCA and present examples in its use for colorant estimation, spectral data reduction, and defining multidimensional confidence regions for colorimetric scatter data. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 84–98, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20086     

A novel method for determination of compatibility of dyes by means of principal component analysis

A novel method for determination of the compatibility of dyes in mixtures based on the application of principal component analysis is presented. The well known dip‐test method is used to dye samples in different binary combinations of cationic dyestuffs. The spectral reflectance of different samples of each mixture that dyed with a given set of dyestuffs by dip‐test method has been measured and the corresponding K/S values are calculated. The actual dimensional properties of each mixture are evaluated by using principal component analysis technique and determination of cumulative percentage variance of the eigenvalues of proposed datasets. Ideally, the K/S spectral data of fully compatible pairs scatter around one dimension, while proportional to the degree of incompatibility of dyes in the mixture, other dimensions should be taken into account and cannot be ignored. Strong correlations are found between the calculated percentage variance and the traditional compatibility values of dyes shown by K value for cationic dyestuffs. The validity of suggested technique is also reconfirmed by normalization of spectral K/S data obtained from different dye sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Fault isolation in nonlinear systems with structured partial principal component analysis and clustering analysis

Partial principal component analysis (PCA) and parity relations are proven to be useful methods in fault isolation. To overcome the limitation of applying partial PCA to nonlinear problems, a new approach utilizing clustering analysis is proposed. By dividing a partial data set into smaller subsets, one can build more accurate PCA models with fewer principal components, and isolate faults with higher precision. Simulations on a 2 × 2 nonlinear system and the Tennessee Eastman (TE) process show the advantages of using the clustered partial PCA method over other nonlinear approaches.     

Prediction of emission spectra of fluorescence materials using principal component analysis

Fluorescent materials are now a critical field of research due to their unique excitation and emission properties that can be tailored to specific fluorescence detection technologies. In this work, a procedure is described to approximate the emission spectral data of fluorescent materials of different types from their excitation spectral data using principal component analysis (PCA) technique. First, PCA as a statistical and mathematical method was used to reconstruct the excitation and emission spectra of training dataset and then, the approximation was accomplished by multiple linear regression (MLR).The performance of obtained function was examined on testing dataset. Afterward, CIE tristimulus values of the fluorescent samples were calculated based on ASTM, E2152–12 standard test method. The colorimetric accuracy was then evaluated by calculating the geometric differences in CIE tristimulus values X, Y, and Z for the 1964 standard colorimetric observer under illuminant D65. The obtained results show a good curve fit between the actual emission spectra and recovered emission spectra. In addition, based on cumulative variance and root mean square (RMS), eight principal components were selected as optimum number of principal components for prediction of emission spectra data. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 16–21, 2016     

变量加权型主元分析算法及其在故障检测中的应用

传统主成分分析（PCA）算法旨在挖掘训练数据各变量间的相关性特征,已在数据驱动的故障检测领域得到了广泛的研究与应用。然而,传统PCA方法在建模过程中通常认为各个测量变量的重要性是一致的,因此不能有效而全面地描述出变量间相关性的差异。为此,提出一种变量加权型PCA（VWPCA）算法并将之应用于故障检测。首先,通过对训练数据进行加权处理,使处理后的数据能够充分体现出变量间相关性的差异。然后,在此基础上建立分布式的PCA故障检测模型。在线实施故障检测时,则通过贝叶斯准则将多组监测结果融合为一组概率指标。VWPCA方法通过相关性大小为各变量赋予不同的权值,从而将相关性差异考虑进了PCA的建模过程中,相应模型对训练数据特征的描述也就更全面。最后,通过在TE过程上的测试验证VWPCA方法用于故障检测的优越性。     

基于主成分分析结合灰色关联度的PPO/PA翼子板注射成型研究

以PPO/PA（聚苯醚/聚酰胺）翼子板为研究对象,在数值模拟基础上提出了一种主成分分析（PCA）结合灰色关联度（GRA）的研究方法,得到第一主成分方程、各项指标贡献度、各工艺参数对综合质量的影响程度及较优工艺参数组合,实现翼子板翘曲变形、体积收缩不均和缩痕等缺陷的优化。结果表明,各工艺参数对综合质量的影响程度为：冷却时间>模具温度>熔体温度>保压时间>保压压力;优化后,最大翘曲变形量、体积收缩率和缩痕长度分别由原来的11.29 mm、16.24 %、0.060 6 mm下降到10.21 mm、14.4 %、0.056 4 mm,分别下降了9.6 %、11.33 %和7 %。     

基于GC-MS和主成分分析的蜂蜡质量控制方法研究

目的:为确保蜂蜡质量稳定可控,建立建全蜂蜡的质量控制方法。方法:收集14个不同产地的蜂蜡,利用柱前衍生化气质联用技术对蜂蜡中成分进行分析,利用指纹图谱对14个不来源不同的蜂蜡样品进行鉴定分析,随后采用主成分分析进行结果验证,并找出引起质量差异的化合物,建立简单快捷的质量评价方法。结果:主成分(PCA)分析的结果表明,存在样品质量差别的最明显原因可能是由化合物2、6、9、14、17、21、22、24、29、33、37、39、44等造成。结论:蜂蜡质量标准应该控制总烷酸类含量的同时也控制烷烃及游离烷酸的含量。     

Analysis of rat haunch odor using dynamic solvent effect and principal component analysis

We used the dynamic solvent effect to sample rat haunch odor, which we then analyzed using principal component analysis. PCA, based on 22 volatile components, indicated that one axis clearly separated rat haunch odor samples according to sex and female reproductive condition (estrus and diestrus), explaining 79.5% of the variation in proportional peak area. We have therefore been able to separate odors along biologically meaningful lines.     

Detection of olive oil adulteration using principal component analysis applied on total and regio FA content

Principal component analysis (PCA) has been used to establish a new method for the detection of olive oil adulteration. The data set, composed of values obtained from the determination of the mole percentage of total FA and their regiospecific distribution in positions 1 and 3 in TG of oils (pure or mixtures) by GC analysis, was subjected to PCA. 3-D scatter plots showed clearly that it is possible to distinguish the pure oils from the mixtures. Moreover it is possible to discriminate the different types of seed oil used for the adulteration.     

Robust modeling of mixture probabilistic principal component analysis and process monitoring application

In this article, a robust modeling strategy for mixture probabilistic principal component analysis (PPCA) is proposed. Different from the traditional Gaussian distribution driven model such as PPCA, the multivariate student t‐distribution is adopted for probabilistic modeling to reduce the negative effect of outliers, which is very common in the process industry. Furthermore, for handling the missing data problem, a partially updating algorithm is developed for parameter learning in the robust mixture PPCA model. Therefore, the new robust model can simultaneously deal with outliers and missing data. For process monitoring, a Bayesian soft decision fusion strategy is developed which is combined with the robust local monitoring models under different operating conditions. Two case studies demonstrate that the new robust model shows enhanced modeling and monitoring performance in both outlier and missing data cases, compared to the mixture probabilistic principal analysis model. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2143–2157, 2014     

Applying metamer sets to investigate data dependency of principal component analysis method in recovery of spectral data

Principal component analysis (PCA) has been widely studied for reconstruction of spectral reflectance of a color sample from its tristimulus values. One of the most important factors that influences the recovery performance is the characteristic of the data set used for obtaining principal vectors. In this article, we investigated the influence of color similarities or color differences between the recovered and principal component (PC) data sets on the reconstruction error. For this purpose, two metamer sets that have similar color differences with the recovered samples, are used. The results show that two metamer sets can make completely different performance in recovery of specific color samples. It was shown that the most important factor that influences the recovery of spectral reflectance by PCA method is the characteristics of the data set used for obtaining PC vectors independent of the recovered samples. Another factor that influences the performance of PCA for spectral recovery is the characteristic of the sample that would be recovered. Some spectral data cannot be recovered precisely even applying different PC data sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Molecular reconstruction of complex hydrocarbon mixtures: An application of principal component analysis

Three methods for reconstruction of the detailed molecular composition of complex hydrocarbon mixtures, based on their global properties, are compared: a method based on the Shannon entropy criterion, an artificial neural network and a multiple linear regression model. In spite of the broad range of naphthas included in the training set, the application range of the last two methods proved to be limited. Principal component analysis allowed to identify their three‐dimensional ellipsoidal application range. In this subspace, the artificial neural network is more accurate than the multiple linear regression model and the Shannon entropy method. However, outside its application range, the performance of the neural network, as well as the regression model, decreases drastically. In contrast, the performance of the Shannon entropy method is not influenced by the characteristics of the considered naphtha, but rather depends on the number of available commercial indices. The Shannon entropy method yields comparable results to the artificial neural network, provided that a sufficient amount of distillation data is available to supply information on the carbon number distribution. Combining the reconstruction methods with a fundamental simulation model illustrates the necessity of having accurate feedstock reconstruction methods since they allow to capture the full power of fundamental simulation models for the simulation of industrial processes. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Effect of classification by competitive neural network on reconstruction of reflectance spectra using principal component analysis

The best way to describe a color is to study its reflectance spectrum, which provide the most useful information. Different methods were purposed for reflectance spectra reconstruction from CIE tristimulus values such as principal components analysis. In this study, the training samples were first divided into 3, 6, 9, and 12 subgroups by creating a competitive neural network. To do that, L*a*b*, L*C*h or L*a*b*C*h were introduced to neural network as input elements. In order to investigate the performance of reflectance spectra reconstruction, the color difference and RMS between actual and reconstructed data were obtained. The reconstruction of reflectance spectra were improved by using a six or nine‐neuron layer with L*a*b* input elements. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 182–188, 2017     

基于经验模式分解与主元分析的耐火材料声发射损伤分类

耐火材料微观结构十分复杂,其破坏形式呈现多样化、复杂化,如何对其损伤进行高效准确地判别十分重要。为此,借助声发射技术对镁碳质耐火材料受压过程进行了损伤声发射信号采集,针对海量声发射数据,首先采用了经验模式分解结合主元分析,对声发射信号进行了特征提取与参数化降维:在大量的声发射时域与频域参数中,选取前7个主元来表征损伤,其损伤贡献率可以达到99%;之后将主元作为支持向量机输入进行损伤分类,将损伤分为两个主要类型,基质相与界面相损伤;最后将分析结果与扫描电镜结果进行对比分析,发现两者结论可以较好地吻合,可为运用声发射手段检测耐火材料损伤提供一种高效准确的解决方案。