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     

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     

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     

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     

The total colorant sensitivity of a color matching recipe: An approach to colorant weighting and tinctorial strength errors

The repeatability of the recipe color can be affected by several different types of inevitable inaccuracies in the coloration process. Two of the major causes of poor target‐color reproducibility are the (random) weighing and (proportional) strength errors. This article describes alternative definitions of colorant strength sensitivity and total colorant sensitivity of a dyeing recipe. The influences of the maximal colorant weighing and strength errors are taken into account in order to bring the magnitudes of the two treated types of sensitivity into a mutually realistic balance between each other. The quantifications of precision and accuracy of a color matching recipe are also developed and combined into a single‐number measure of recipe quality. The listed quantities are expected to be useful in selecting the most reliable one(s) among the different formulations for the same standard color. The methods are presented for calculating numerical estimates of the newly introduced quantities. The precision and accuracy of the coloration process are investigated in laboratory experiments involving repeated dyeings. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 300–306, 2008.     

基于主元子空间富信息重构的过程监测方法

作为一种经典的多元投影方法,主元分析（PCA）已在多变量统计过程监测领域得到了广泛应用。然而,传统的主元挑选方法往往选择方差较大的主元以表征建模样本中包含的较大信息量,但当过程信息发生变化时,方差较小的主元所表现出来的变异性可能更为明显,即包含的信息量更为丰富,也更有利于故障检出。为此,提出一种基于主元子空间富信息重构的过程监测方法（informative PCA,Info-PCA）。该方法通过计算过程数据在各主元方向上累积T²统计量的变化率,选择变化较为明显的主元以重构主元子空间。在此基础上,建立相应的统计监测模型。最后,通过实例验证该方法用于过程监测的可行性与有效性。     

主元空间中的故障分离与识别方法

主元分析 (PCA)作为数据驱动的一种统计建模方法,在化工产品质量控制与故障诊断方面得到广泛研究和应用.在故障重构技术的基础上,研究了基于T²统计量的故障分离和识别问题,分别获得了主元空间中故障可分离和识别的理论条件.以双效蒸发过程为例,对该生产过程中的10种不同故障进行仿真监测分析,证实了所获理论结果的有效性.     

基于稀疏核主元分析的在线非线性过程监控

核主元分析(KPCA)适合非线性过程的监控,但存在计算量大、实时性差等缺点。提出一种基于稀疏KPCA(SKPCA)的过程监控方法,先使用SKPCA对正常建模数据进行加权,少数权值大的数据基本能代表全部正常数据的信息,因此稀化了建模数据,然后根据稀化后的正常数据建立过程的KPCA模型,并提出监控指标,大大减少了计算量,提高了监控的实时性,最后以化工分离过程为对象,就KPCA与SKPCA的监控效果和实时性进行了详细的对比研究,结果表明了基于SKPCA监控方法的优越性。     

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。     

Process monitoring using principal components in parallel coordinates

Parallel coordinates is a recognized visualization technique in which data points, each defined by multiple coordinates, are represented by an unlimited number of adjoining parallel axes. This type of visualization technique is suitable for process monitoring applications in industrial facilities where a significant number of sensors are used to detect and identify abnormal operating conditions. This work makes use of principal component monitoring methods implemented in parallel coordinates plots, named PC². The PC² capabilities to visualize confidence regions of operations, evaluate models with different number of principal components, compare faulty events and determine the frequency of false alarms are here demonstrated. The monitoring visualization technology presented by PC² was successfully used for early detection of compressor surge and column flooding using actual process data. © 2012 American Institute of Chemical Engineers AIChE J, 59: 445–456, 2013     

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     

A non‐PC look at principal components

Two principal‐component methods are used in color science. For a given data set of spectra, one method finds the best‐fitting subspace about the mean spectrum, and the other finds the best‐fitting subspace about the zero spectrum. The first of these was originally developed for illuminants and the second for reflectance analysis. Yet there seems to be no strong argument for choosing one method over the other, in either case. Hence it is urged that each of us declares which one we are using, even if making that discrimination is considered “non‐PC” (i.e., not “politically correct”). © 2002 Wiley Periodicals, Inc. Col Res Appl, 28, 69–71, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

基于非线性主元分析和符号有向图的故障诊断方法

Nonlinear principal component analysis（NLPCA）fault detection method achieves good detection results especially in a nonlinear process.Signed directed graph（SDG）model is based on deep-going information,which excels in fault interpretation.In this work,an NLPCA-SDG fault diagnosis method was proposed.SDG model was used to interpret the residual contributions produced by NLPCA.This method could overcome the shortcomings of traditional principal component analysis（PCA）method in fault detection of a nonlinear process and the shortcomings of traditional SDG method in single variable statistics in discriminating node conditions and threshold values.The application to a distillation unit of a petrochemical plant illustrated its validity in nonlinear process fault diagnosis.     

一种基于改进MPCA的间歇过程监控与故障诊断方法

针对基于不同展开方式的多向主元分析(MPCA)方法在线应用时各自存在的缺陷,提出一种改进的基于变量展开的MPCA方法,实现间歇过程的在线监控与故障诊断。该方法采用随时间更新的主元协方差代替固定的主元协方差进行T²统计量的计算,充分考虑了主元得分向量的动态特性;同时引入主元显著相关变量残差统计量,避免SPE统计量的保守性,且该统计量能提供更详细的过程变化信息,对正常工况改变或过程故障引起的T²监控图变化有一定的识别能力;最后提出一种随时间变化的贡献图计算方法用于在线故障诊断。该方法和MPCA方法的监控性能在一个青霉素发酵仿真系统上进行了比较。仿真结果表明：该方法具有较好的监控性能,能及时检测出过程存在的故障,且具有一定的故障识别和诊断能力。     

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.     

基于核主角的故障检测方法

基于主元分析（PCA）的统计检测方法已经被广泛应用于各种化工过程的故障检测和识别.移动主元分析（moving principal component analysis,简称MPCA）算法基于PCA,根据主元子空间的变化来判断故障是否发生.然而,基于主元分析的统计检测方法是线性方法,无法有效应用于非线性系统.因此,提出一种适合于非线性系统的故障检测方法——基于核主角(kernel principal angle,简称KPA)的故障检测方法,其基本思想与MPCA相似,主要内容包括构建特征子空间和核主角测量两部分.TE过程故障检测仿真实验证明,基于核主角的故障检测方法优于传统的多元统计检测方法（cMSPC）和MPCA.     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

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。     

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