Document Type
Lecture
Publication Date
3-26-2026
Abstract
Principal component analysis (PCA) is a statistical technique for the dimensionality reduction of data, minimizing information loss and increasing interpretability. It does so by first extracting new uncorrelated variables which successively maximize variance in the remaining data spaces and then cutting off principal components (PCs) corresponding to small singular values.
However, for various applications, certain PCs must be eliminated to enhance the stability and reliability, although the corresponding singular values are not small. This article introduces an innovative statistical criterion for the selection of reliable PCs, called the α-Test.
The proposed test is analyzed, and effective computational algorithms are discussed for an automatic picking of reliable PCs. The effectiveness of the α-Test is verified with numerous synthetic systems in regression analysis and also with real datasets.
Relational Format
presentation
Recommended Citation
Kim, Seongjai, "The α-Test: A New Statistical Test for the Selection of Reliable Principal Components" (2026). Probability & Statistics Seminar. 77.
https://egrove.olemiss.edu/math_statistics/77
Accessibility Status
Searchable text