Principal component analysis of interval data: a symbolic data analysis approach

2000 ◽  
Vol 15 (1) ◽  
pp. 73-87 ◽  
Author(s):  
Carlo N. Lauro ◽  
Francesco Palumbo
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Principal Component ◽  
Interval Data ◽  
Component Analysis ◽  
Analysis Approach ◽  
Symbolic Data Analysis ◽  
Symbolic Data

Component Analysis: An Aid to the Interpretation of Data

1969 ◽  
Vol 5 (2) ◽  
pp. 151-164 ◽  
Author(s):  
D. A. Holland
Keyword(s):  
Principal Component Analysis ◽  
Statistical Study ◽  
Principal Component ◽  
Component Analysis ◽  
Linear Functions ◽  
Analysis Approach ◽  
Specific Technique ◽  
Mathematical Technique ◽  
Biological Concepts ◽  
General Component

SummaryPrincipal component analysis is a mathematical technique for summarizing a set of related measurements as a set of derived variates, frequently fewer in number, which are definable as independent linear functions of the original measurements. Consideration of their mathematical nature shows that they do not, themselves, necessarily correspond to sensible biological concepts, though they are more amenable to statistical study than the original measurements. Further, by assessing the extent to which they are in accordance with biological hypotheses, or with the results of other, similar, analyses, they can be transformed into other linear functions which are meaningful in the biological sense, or consistent with other results. Thus the specific technique of principal component analysis is developed into a more general component analysis approach. With proper regard for the purpose the analysis is intended to serve and for the mathematical restrictions involved, this approach can lead to a useful condensation of a mass of data, a better under-standing of the observed individuals as entities rather than collections of isolated measurements, and to the formulation of new hypotheses for subsequent examination.

Uncertain Nonlinear Process Monitoring Using Interval Ensemble Kernel Principal Component Analysis

2021 ◽  
Vol 25 (1) ◽  
pp. 101-109
Author(s):  
Xianrui Wang ◽  
Guoxin Zhao ◽  
Yu Liu ◽  
Shujie Yang ◽  
◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Process Monitoring ◽  
Principal Component ◽  
Nonlinear Process ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Gaussian Kernel ◽  
Bayesian Decision ◽  
Symbolic Data ◽  
Nonlinear Process Monitoring

To solve uncertainties in industrial processes, interval kernel principal component analysis (IKPCA) has been proposed based on symbolic data analysis. However, it is experimentally discovered that the performance of IKPCA is worse than that of other algorithms. To improve the IKPCA algorithm, interval ensemble kernel principal component analysis (IEKPCA) is proposed. By optimizing the width parameters of the Gaussian kernel function, IEKPCA yields better performances. Ensemble learning is incorporated in the IEKPCA algorithm to build submodels with different width parameters. However, the multiple submodels will yield a large number of results, which will complicate the algorithm. To simplify the algorithm, a Bayesian decision is used to convert the result into fault probability. The final result is obtained via a weighting strategy. To verify the method, IEKPCA is applied to the Tennessee Eastman (TE) process. The false alarm rate, fault detection rate, accuracy, and other indicators used in the IEKPCA are compared with those of other algorithms. The results show that the IEKPCA improves the accuracy of uncertain nonlinear process monitoring.

Reaction Monitoring in Explorative Organic Synthesis Using Fiber-Optical NIR Spectroscopy and Principal Component Analysis

1996 ◽  
Vol 50 (12) ◽  
pp. 1541-1544 ◽  
Author(s):  
Hans-René Bjørsvik
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Latent Variables ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Component Analysis ◽  
Quantitative Information ◽  
Chemistry Laboratory ◽  
Reaction Profile

A method of combining spectroscopy and multivariate data analysis for obtaining quantitative information on how a reaction proceeds is presented. The method is an approach for the explorative synthetic organic laboratory rather than the analytical chemistry laboratory. The method implements near-infrared spectroscopy with an optical fiber transreflectance probe as instrumentation. The data analysis consists of decomposition of the spectral data, which are recorded during the course of a reaction by using principal component analysis to obtain latent variables, scores, and loading. From the scores and the corresponding reaction time, it is possible to obtain a reaction profile. This reaction profile can easily be recalculated to obtain the concentration profile over time. This calculation is based on only two quantitative measurements, which can be (1) measurement from the work-up of the reaction or (2) chromatographic analysis from two withdrawn samples during the reaction. The method is applied to the synthesis of 3-amino-propan-1,2-diol.

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