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Application of Multivariate Statistical Analysis for Quality Control of Food Products
Published in Surajbhan Sevda, Anoop Singh, Mathematical and Statistical Applications in Food Engineering, 2020
Partial least squares regression (PLSR) is a statistical technique which is related to principal components regression. It develops a linear regression model by projecting the observed variables and the projected variables to a new space. It is used to find the fundamental relations between two matrices (X and Y). A PLS model will try to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the Y space. Instead of finding the major variation in X and Y, it looks for a direction in both which is good for correlating the X score with the Y score. PLS regression is particularly suited when the variables in the predictors’ matrix are higher than the matrix of observations, and when there is multicollinearity among X values.
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Published in Tesfay Gebretsadkan Gebremicael, Understanding the Impact of Human Interventions on the Hydrology of Nile Basin Headwaters, the Case of Upper Tekeze Catchments, 2019
Tesfay Gebretsadkan Gebremicael
This approach is essential to ascertain whether the observed change in LULC was large enough to cause the change in streamflow dynamics. The relation between each LULC type and hydrological components was computed using the pair-wise Pearson correlation whilst the contribution of their change to the streamflow was quantified using the PLSR model. The PLSR is a robust multivariate regression technique that is appropriate when the response (dependent variables) exhibit collinearity with many predictors (independent) variables (Woldesenbet et al., 2017; Shi et al., 2013). It combines features from principal component analysis and multiple regressions that is appropriate when predictors exhibit multicollinearity (Yan et al., 2016). In this study, the independent variables are the different LULC types (Table 5.1) while the dependent variables are hydrological components (total runoff, wet and dry season flow, actual evapotranspiration (AET) and SWS). Detailed information on PLSR algorithms can be found in the literature (Shi et al., 2013; Abdi, 2010) and hence only a brief description is given here. The PLSR is a linear model specifies the relationship between a response variable, Y, and a set of predictor variables X’s given in Equation 6.12. () Y=a0+a1X1+a2X2+a3X3+⋯+aiXi
Partial Least Squares Regression
Published in N.C. Basantia, Leo M.L. Nollet, Mohammed Kamruzzaman, Hyperspectral Imaging Analysis and Applications for Food Quality, 2018
Partial least squares regression (PLS regression—PLSR) is a statistical method, a multivariate calibration technique that bears some relationship with principal components regression. PLS finds a linear regression model by projecting the predicted variables and the observable variables to a new space. Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models. PLS discriminant analysis (PLS-DA) is a variant used when the Y is categorical.
Floc sensor prototype tested in the municipal wastewater treatment plant
Published in Cogent Engineering, 2018
N. Sivchenko, K. Kvaal, H. Ratnaweera
The resulted data matrix was processed in statistical software The Unscrambler® X 10.3 (CAMO Software AS, Norway) and in MATLAB using PLS toolbox (Eigenvector Research, Inc., USA). Principal component analysis (PCA) was performed to find the relationships between water quality parameters and images of flocs – GLCM feature vectors. PCA is a statistical data analysis technique to reduce the dimensionality of the data-set, overview and describe the interrelationships among variables and to find so-called hidden structures in the data. Partial least squares regression (PLSR) was performed to predict coagulant dosage based on the combination of water quality parameters and GLCM texture features. PLSR is a statistical regression method to model the response variable using a large number of predictor variables while those variables may highly correlate.
Hyperspectral data for predicting moisture content and distribution in scallops during continuous and intermittent drying
Published in Drying Technology, 2022
Jialiang Sun, Xueyu Zhang, Xinjing Qiu, Xinyu Zhu, Tao Zhang, Jixin Yang, Xu Zhang, Yan Lv, Huihui Wang
PLSR as a common linear regression analysis algorithm, combines the functions of multiple regression analysis and principal component analysis.[38] It can be used in the case of serious multicultural of independent variables and linear correlation when the number of variables is larger than the number of samples. PLSR can process the data of X variable and Y variable at the same time, optimize the covariance of X variable and Y variable, and extract important information from these two sets of data.[39] PLSR regression models were built on Unscrambler X 10.1 (Camo AS, Oslo, Norway) and leave-one-out cross-validation procedures were conducted.