Identifying product shape relationships using principal component analysis

Product forms with multiple features, like automobiles, have traditionally accepted feature definitions and relationships between those features. These relationships drive how the product is created by focusing on expected, and accepted, feature development to push the form outside the traditional bounds. This paper uses principal component analysis to determine the fundamental characteristics within vehicle classes. The results of this analysis can then be considered by product designers to create new designs based upon the derived shape relationships. These new designs will be novel due to the non-traditional grouping of characteristics.     

A mechanism motion error sensitivity analysis method based on principal component analysis and artificial neural network

Present sensitivity analysis of motion error usually focuses on the trajectory deviation of the mechanism, which inevitably introduces an intractable time dependent problem. For efficiently and accurately measuring the motion error of the planar mechanism with dimension and clearance uncertainties by global sensitivity analysis (GSA), a novel method is proposed in this work. By applying the principal component analysis (PCA), the motion error is transformed into new vector output and cleverly avoids the time dependent problem. To ensure the accuracy of PCA in the case of small samples, the Bootstrap method is introduced. Based on the PCA results, the artificial neural network (ANN) surrogate model is established between the input variables and the vector output. Then the classical variance-based GSA method is applied to obtain the variable importance ranking for different PCs, and the synthesized GSA indices are introduced. Four representative examples are studied to demonstrate the versatility and effectiveness of the proposed method.     

The CHull procedure for selecting among multilevel component solutions

Recently, Timmerman [1] proposed a class of multilevel component models for the analysis of two-level multivariate data. These models consist of a separate component model for each level in the data. Specifically, the between-differences are captured by a between-component model and the within-differences by a within-component model. Within the class of multilevel component models a number of variants can be distinguished. These variants differ with respect to the within-component model, in that different sets of restrictions are imposed on the within-component loadings and on the variances and correlations of the within-component scores. The following question then may be raised: given a specific two-level data set, which of the multilevel component model variants should be selected, and with how many between- and within-components? We address this question by proposing a model selection procedure that builds on the CHull heuristic of Ceulemans and Kiers [2,3]. The results of an extensive simulation study show that the proposed CHull heuristic succeeds very well in assessing the number of between- and within-components. Tracing the underlying multilevel component model variant is more difficult: Whereas differences in within-loading matrices and differences in variances are very easy to detect, the precise correlational structure of the within-components is much harder to capture.     

Using principal component analysis to monitor spatial and temporal changes in water quality

Chemical, biological and physical data monitored at 12 locations along the Passaic River, New Jersey, during the year 1998 are analyzed. Principal component analysis (PCA) was used: (i) to extract the factors associated with the hydrochemistry variability; (ii) to obtain the spatial and temporal changes in the water quality. Solute content, temperature, nutrients and organics were the main patterns extracted. The spatial analysis isolated two stations showing a possible point or non-point source of pollution. This study shows the importance of environmental monitoring associated with simple but powerful statistics to better understand a complex water system.     

Simultaneous optimization of the microextraction of coffee volatiles using response surface methodology and principal component analysis

It is well known that no single experimental condition can be found under which the extraction of all the volatile compounds in a gas chromatographic analysis of roasted coffee beans by headspace-solid phase microextraction (HS-SPME) is maximized. This is due to the large number of peaks recorded. In this work, the scores vector of the first principal component obtained from PCA on chromatographic peak areas was used as the response to find the optimal conditions for simultaneous optimization of coffee volatiles extraction via response surface methodology (RSM). This strategy consists in compressing several highly correlated peak areas into a single response variable for a central composite design (CCD). RSM was used to identify an optimal factor combination that reflects a compromise between the partially conflicting behavior of the volatiles groups. This simultaneous optimization approach was compared with the desirability function method. The versatility of the PCA-RSM methodology allows it to be used in other chromatographic applications, resulting in an interpretable procedure to solve new analytical problems.     

主成分分析的入侵检测方法研究

直接将入侵检测算法应用在粗糙数据上,其入侵检测分析的效率非常低.为解决该问题,提出了一种基于主成分分析的入侵检测方法.该方法通过提取网络连接中的相关信息,对它进行解码,并将解码的网络连接记录与已知的网络连接记录数据进行比较,发现记录中的变化和连接记录分布的主成分,最后将机器学习方法和主成分分析方法结合实现入侵检测.实验结果表明该方法应用到各种不同KDD99入侵检测数据集中可以有效减少学习时间、降低各种数据集的表示空间,提高入侵检测效率.     

A fast method for robust principal components with applications to chemometrics

When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to eigenvectors of the sample covariance matrix. However, it is well-known that this covariance matrix is strongly affected by anomalous observations. It is therefore necessary to apply robust methods that are resistant to possible outliers.

Li and Chen [J. Am. Stat. Assoc. 80 (1985) 759] proposed a solution based on projection pursuit (PP). The idea is to search for the direction in which the projected observations have the largest robust scale. In subsequent steps, each new direction is constrained to be orthogonal to all previous directions. This method is very well suited for high-dimensional data, even when the number of variables p is higher than the number of observations n. However, the algorithm of Li and Chen has a high computational cost. In the references [C. Croux, A. Ruiz-Gazen, in COMPSTAT: Proceedings in Computational Statistics 1996, Physica-Verlag, Heidelberg, 1996, pp. 211–217; C. Croux and A. Ruiz-Gazen, High Breakdown Estimators for Principal Components: the Projection-Pursuit Approach Revisited, 2000, submitted for publication.], a computationally much more attractive method is presented, but in high dimensions (large p) it has a numerical accuracy problem and still consumes much computation time.

In this paper, we construct a faster two-step algorithm that is more stable numerically. The new algorithm is illustrated on a data set with four dimensions and on two chemometrical data sets with 1200 and 600 dimensions.     

Statistical validation of reproducibility of HPLC peptide mapping for the identity of an investigational drug compound based on principal component analysis

Peptide mapping is a key analytical method for studying the primary structure of proteins. The sensitivity of the peptide map to even the smallest change in the covalent structure of the protein makes it a valuable “fingerprint” for identity testing and process monitoring. We recently conducted a full method validation study of an optimized reverse-phase high-performance liquid chromatography (RP-HPLC) tryptic map of a therapeutic anti-CD4 monoclonal antibody. We have used this method routinely for over a year to test production lots for clinical trials and to support bioprocess development. One of the difficulties in the validation of the peptide mapping method is the lack of proper quantitative measures of its reproducibility. A reproducibility study may include method and system precision study, ruggedness study, and robustness study. In this paper, we discuss the use of principal component analysis (PCA) to quantitate peptide maps properly using its projected scores on the reduced dimensions. This approach allowed us not only to summarize the reproducibility study properly, but also to use the method as a diagnostic tool to investigate any troubles in the reproducibility validation process.     

基于互信息的主成分分析用于声场景分类

主成分分析是声场景分类中常用的特征选择方法。针对主成分分析的局限性,提出一种基于互信息的主成分分析方法。这一方法引入类别信息,用不同声场景条件下特征之间的互信息矩阵之和替代传统主成分分析中的协方差矩阵,计算其特征向量与特征值,特征向量表示由原始特征空间向新的主成分空间的转换系数,特征值则用于计算主成分的累计贡献率并判断主成分维数。声场景分类实验结果表明,该方法较之传统主成分分析方法降维效果更好,辅以神经网络分类器,计算得到的分类正确率更高。     

Improvement of mechanical properties of recycled plastic blends via optimizing processing parameters using the Taguchi method and principal component analysis

In this paper, the Taguchi method and principal component analysis (PCA) are used to improve the mechanical properties of recycled polypropylene (PP) blends in injection moulding procedure, with detailed assessments performed on each method and comparison was made based on results of both the methods. The experimental design was carried out by adopting a L9-3⁴ Taguchi orthodoxy array (OA), which has four controllable factors (i.e., melt temperature, mould temperature, injection speed and packing pressure) at three levels. Injection moulded specimens made from different compositions of virgin-recycled PP were tested to determine the optimal conditions for the injection moulding procedure. The effects of the processing parameters and the proportion of recycled plastic in composites on the mechanical properties were investigated, the optimal conditions for desired properties were obtained and then verified. The appropriate blending ratio of virgin and recycled plastic was evaluated. The results reveal that deteriorations in the mechanical properties of products produced from recycled plastic can be improved by optimizing the processing parameters during the injection moulding procedure.     

Multivariate process capability using principal component analysis

Wang and Chen (Qual. Eng. 1998; 11:21–27) have defined process capability indices (PCIs) for multivariate normal processes data using principal component analysis (PCA). Veevers (Statistical Process Monitoring and Optimization. Marcel Dekker: New York, NY, 1999; 241–256) has suggested a multivariate capability index based on the first principal component (PC). In this paper we demonstrate the problem in the definition of PCIs given by Wang and Chen (Qual. Eng. 1998; 11:21–27) and the non‐suitability of PCI given by Veevers (Statistical Process Monitoring and Optimization. Marcel Dekker: New York, NY, 1999; 241–256) through some examples. We also suggest an alternative method for assessing multivariate process capability based on the empirical probability distribution of PCs. This method has been performed on industrial and simulated data. Copyright © 2008 John Wiley & Sons, Ltd.     

基于模糊理论决策的双向二维PCA步态识别算法

针对步态识别中的平均步态能量图像系数矩阵维数过高和分类较困难的特点,提出一种基于模糊理论决策分类的双向二维主成分分析的步态识别算法.通过预处理技术得到平均步态能量图并将得到的图像分割为多个子图像,利用双向二维主成分分析来降低平均步态能量子图像的系数矩阵维数,加快识别速度.引入模糊理论决策的方法进行最近邻分类器的分类.最后在CASIA步态数据库上对所提出的算法进行实验,实验结果表明该算法具有较好的识别性能并有较强的鲁棒性.     

Improving automotive dimensional quality by using principal component analysis

Dimensional quality is a measure of conformance of the actual geometry of products with the designed geometry. In the automotive body assembly process, maintaining good dimensional quality is very difficult and critical to the product. In this paper, a dimensional quality analysis and diagnostic tool is developed based on principal component analysis (PCA). In quality analysis, the quality loss due to dimensional variation can be partitioned into a mean deviation and piece-to-piece variation. By using PCA, the piece-to-piece variation can be further decomposed into a set of independent geometrical variation modes. The features of these major variation modes help in identifying the underlying causes of dimensional variation in order to reduce the variation. The variation mode chart developed in this paper provides the explicit and exact geometrical interpretation of variation modes, making PCA easily understood. A case study using an automotive body assembly dimensional quality analysis will illustrate the value and power of this methodology in solving actual engineering problems in a practical manner.     

A least squares approach to principal component analysis for interval valued data

Principal Component Analysis (PCA) is a well-known technique, the aim of which is to synthesize huge amounts of numerical data by means of a low number of unobserved variables, called components. In this paper, an extension of PCA to deal with interval valued data is proposed. The method, called Midpoint Radius Principal Component Analysis (MR-PCA), recovers the underlying structure of interval valued data by using both the midpoints (or centers) and the radii (a measure of the interval width) information. In order to analyze how MR-PCA works, the results of a simulation study and two applications on chemical data are proposed.     

基于电容测量和PCA法的两相流相浓度检测方法

介绍利用电容层析成像系统阵列传感器结构和采样特点,引入主成分分析法(PCA)求取两相流相浓度的新方法.对大量测量值样本进行统计分析后,求出用测量值第一主成分求取相浓度的经验公式,仿真及静态实验表明:两者之间有着良好的对应关系,其测量结果不受两相流流型的影响,是一种有较好应用前景的测量方法.     

Principal alarms in multivariate statistical process control using independent component analysis

This article proposes a methodology that helps to predict the main mean shifts, denoted as principal alarms, in a non-normal multivariate process using the available in-control data. The analysis is based on the transformation of the observed correlated variables into independent factors using independent component analysis. These independent components allow us to simulate shifts preserving the covariance structure. The graphical representations of those simulated shifts are helpful in improving the design and control of the process. Two real manufacturing processes are presented showing the advantage of the proposed methodology.     

Kernel principal component analysis and support vector machines for stock price prediction

Technical indicators are used with two heuristic models, kernel principal component analysis and factor analysis in order to identify the most influential inputs for a forecasting model. Multilayer perceptron (MLP) networks and support vector regression (SVR) are used with different inputs. We assume that the future value of a stock price/return depends on the financial indicators although there is no parametric model to explain this relationship, which comes from the technical analysis. Comparison studies show that SVR and MLP networks require different inputs. Furthermore, proposed heuristic models produce better results than the studied data mining methods. In addition to this, we can say that there is no difference between MLP networks and SVR techniques when we compare their mean square error values.     

基于主成分分析的护听器优选方法研究

为了探究不同护听器对抽水蓄能电站内不同工作场所的降噪效果及适用情况,以便于工作人员根据不同需要选择合适的护听器,根据112种护听器的插入损失测试结果,应用主成分分析(Principal Component Analysis, PCA)对数据进行分析。结合某抽水蓄能电站10个工作场所的现场测试结果,得出文中所测试的112种护听器大部分适用于该蓄水电站中1#发电机隔声罩内、1#水车室外、1#水车室内、2#尾水锥管室外、2#尾水锥管检修门、3#尾水锥管室外和3#尾水锥管检修门7个工作场所,其他场所需要有针对性地选择适合的护听器。该文同时可以为其他不同工作场所情况下护听器的选择提供借鉴。     

State-space independent component analysis for nonlinear dynamic process monitoring

The cost effective benefits of process monitoring will never be over emphasised. Amongst monitoring techniques, the Independent Component Analysis (ICA) is an efficient tool to reveal hidden factors from process measurements, which follow non-Gaussian distributions. Conventionally, most ICA algorithms adopt the Principal Component Analysis (PCA) as a pre-processing tool for dimension reduction and de-correlation before extracting the independent components (ICs). However, due to the static nature of the PCA, such algorithms are not suitable for dynamic process monitoring. The dynamic extension of the ICA (DICA), similar to the dynamic PCA, is able to deal with dynamic processes, however unsatisfactorily. On the other hand, the Canonical Variate Analysis(CVA) is an ideal tool for dynamic process monitoring, however is not sufficient for nonlinear systems where most measurements follow non-Gaussian distributions. To improve the performance of nonlinear dynamic process monitoring, a state space based ICA (SSICA) approach is proposed in this work. Unlike the conventional ICA, the proposed algorithm employs the CVA as a dimension reduction tool to construct a state space, from where statistically independent components are extracted for process monitoring. The proposed SSICA is applied to the Tennessee Eastman Process Plant as a case study. It shows that the new SSICA provides better monitoring performance and detect some faults earlier than other approaches, such as the DICA and the CVA.     

Principal component transform — Outer product analysis in the PCA context

Outer product analysis is a method that permits the combination of two spectral domains with the aim of emphasizing co-evolutions of spectral regions. This data fusion technique consists in the product of all combinations of the variables that define each spectral domain. The main issue concerning the application of this technique is the very wide data matrix obtained which can be very hard to handle with multivariate techniques such as PCA or PLS, due to computer resources constraints. The present work presents an alternative way to perform outer product analysis in the PCA context without incurring into high demands on computational resources. This works shows that by decomposing each spectral domain with PCA and performing the outer product on the recovered scores, one can obtain the same results as if one calculated the outer product in the original variable space, but using much less computational resources. The results show that this approach will make possible to apply outer product analysis to very wide domains.