Application of nonlinear principal component analysis in industrial product quality assessment

Abstract

This thesis examines the use of nonlinear PCA in data analysis, aiming to reduce information loss during dimensionality reduction while preserving essential data patterns. The study utilizes the wine dataset, selected for its relevance to customer segmentation, containing 14 variables that present a challenging test case for evaluating nonlinear PCA techniques on high-dimensional data. The dataset’s complexity and practical significance in the wine industry add considerable value to the research outcomes. Data visualization using Python revealed that traditional PCA produced mixed clusters, whereas Kernel PCA generated distinct clusters, highlighting its superior performance. The dataset matrix exhibited a high condition number of 16251.1265, indicating poor conditioning. Standard PCA resulted in a condition number of 1.502, pointing to sensitivity issues. Conversely, Kernel PCA achieved a lower condition number of 1.42, reflecting its better handling of poorly conditioned datasets and reduced information loss. The research highlights Kernel PCA’s potential to enhance data analysis and quality assessment in industrial settings. The thesis concludes by suggesting further research to explore the practical applications of nonlinear PCA across various industrial domains, contributing to the fields of applied mathematics and industrial engineering.