On order determination by predictor augmentation

L. U.O. Wei, L. I. Bing

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that if the predictor is augmented by an artificially generated random vector, then the parts of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.

Original languageEnglish (US)
Pages (from-to)557-574
Number of pages18
Issue number3
StatePublished - Sep 1 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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