scholarly journals Principal Component Analysis and Factor Analysis: differences and similarities in Nutritional Epidemiology application

2019 ◽  
Vol 22 ◽  
Author(s):  
Roberta de Oliveira Santos ◽  
Bartira Mendes Gorgulho ◽  
Michelle Alessandra de Castro ◽  
Regina Mara Fisberg ◽  
Dirce Maria Marchioni ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Factor Analysis ◽  
Statistical Methods ◽  
Principal Component ◽  
Component Analysis ◽  
Food Group ◽  
Correlated Data ◽  
Nutritional Epidemiology ◽  
Study Results ◽  
Nutritional Studies

ABSTRACT: Introduction: Statistical methods such as Principal Component Analysis (PCA) and Factor Analysis (FA) are increasingly popular in Nutritional Epidemiology studies. However, misunderstandings regarding the choice and application of these methods have been observed. Objectives: This study aims to compare and present the main differences and similarities between FA and PCA, focusing on their applicability to nutritional studies. Methods: PCA and FA were applied on a matrix of 34 variables expressing the mean food intake of 1,102 individuals from a population-based study. Results: Two factors were extracted and, together, they explained 57.66% of the common variance of food group variables, while five components were extracted, explaining 26.25% of the total variance of food group variables. Among the main differences of these two methods are: normality assumption, matrices of variance-covariance/correlation and its explained variance, factorial scores, and associated error. The similarities are: both analyses are used for data reduction, the sample size usually needs to be big, correlated data, and they are based on matrices of variance-covariance. Conclusion: PCA and FA should not be treated as equal statistical methods, given that the theoretical rationale and assumptions for using these methods as well as the interpretation of results are different.

Physical-oriented and machine learning-based emission modeling in a diesel compression ignition engine: Dimensionality reduction and regression

2022 ◽  
pp. 146808742110707
Author(s):  
Aran Mohammad ◽  
Reza Rezaei ◽  
Christopher Hayduk ◽  
Thaddaeus Delebinski ◽  
Saeid Shahpouri ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Support Vector Machine ◽  
Factor Analysis ◽  
Dimensionality Reduction ◽  
Principal Component ◽  
Component Analysis ◽  
Data Driven ◽  
Support Vector ◽  
Emission Models ◽  
Emission Modeling

The development of internal combustion engines is affected by the exhaust gas emissions legislation and the striving to increase performance. This demands for engine-out emission models that can be used for engine optimization for real driving emission controls. The prediction capability of physically and data-driven engine-out emission models is influenced by the system inputs, which are specified by the user and can lead to an improved accuracy with increasing number of inputs. Thereby the occurrence of irrelevant inputs becomes more probable, which have a low functional relation to the emissions and can lead to overfitting. Alternatively, data-driven methods can be used to detect irrelevant and redundant inputs. In this work, thermodynamic states are modeled based on 772 stationary measured test bench data from a commercial vehicle diesel engine. Afterward, 37 measured and modeled variables are led into a data-driven dimensionality reduction. For this purpose, approaches of supervised learning, such as lasso regression and linear support vector machine, and unsupervised learning methods like principal component analysis and factor analysis are applied to select and extract the relevant features. The selected and extracted features are used for regression by the support vector machine and the feedforward neural network to model the NOx, CO, HC, and soot emissions. This enables an evaluation of the modeling accuracy as a result of the dimensionality reduction. Using the methods in this work, the 37 variables are reduced to 25, 22, 11, and 16 inputs for NOx, CO, HC, and soot emission modeling while maintaining the accuracy. The features selected using the lasso algorithm provide more accurate learning of the regression models than the extracted features through principal component analysis and factor analysis. This results in test errors RMSETe for modeling NOx, CO, HC, and soot emissions 19.22 ppm, 6.46 ppm, 1.29 ppm, and 0.06 FSN, respectively.

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