Open AccessConvergence of sample eigenvalues, eigenvectors, and principal component scores for ultra-high dimensional data
Author(s) -
Seunggeun Lee,
Fei Zou,
Fred A. Wright
Publication year - 2014
Publication title -
biometrika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.307
H-Index - 122
eISSN - 1464-3510
pISSN - 0006-3444
DOI - 10.1093/biomet/ast064
Subject(s) - principal component analysis , eigenvalues and eigenvectors , mathematics , sample size determination , sample (material) , dimension (graph theory) , convergence (economics) , high dimensional , embedding , large sample , statistics , combinatorics , artificial intelligence , computer science , physics , quantum mechanics , economics , thermodynamics , economic growth
The development of high-throughput biomedical technologies has led to increased interest in the analysis of high-dimensional data where the number of features is much larger than the sample size. In this paper, we investigate principal component analysis under the ultra-high dimensional regime, where both the number of features and the sample size increase as the ratio of the two quantities also increases. We bridge the existing results from the finite and the high-dimension low sample size regimes, embedding the two regimes in a more general framework. We also numerically demonstrate the universal application of the results from the finite regime.