Inverse Matrix Problem in Regression for High-Dimensional Data Sets

Forhigh-dimensional chemometric data, the inverse matrix XtX−1 problem in regression models is a difficulty. Multicollinearity and identification result from the inverse matrix problem. The usage of the least absolute shrinkage and selection operator (LASSO) and partial least squares are two existin...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2023-01, Vol.2023 (1)
Main Authors: Shakeel, Namra, Mehmood, Tahir
Format: Article
Language:English
Subjects:
Chemometrics
Datasets
Dough
Fatty acids
Infrared analysis
Infrared spectra
Linear equations
Methods
Near infrared radiation
Raman spectra
Regression analysis
Regression models
Spectrum analysis
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Forhigh-dimensional chemometric data, the inverse matrix XtX−1 problem in regression models is a difficulty. Multicollinearity and identification result from the inverse matrix problem. The usage of the least absolute shrinkage and selection operator (LASSO) and partial least squares are two existing ways of dealing with the inverse matrix problem (PLS). For regressing the chemometric data sets, we used extended inverse and beta cube regression. The existing and proposed methods are compared over near-infrared spectra of biscuit dough and Raman spectra analysis of contents of polyunsaturated fatty acids (PUFA). For reliable estimation, Monte Carlo cross-validation has been used. The proposed methods outperform based on the root mean square error, indicating that cube regression and inverse regression are reliable and can be used for diverse high-dimensional data sets.
ISSN:1024-123X
1563-5147
DOI:10.1155/2023/2308541