# A generalized information criterion for high-dimensional PCA rank selection

arXiv: https://arxiv.org/abs/2004.13914 · HTML: https://mlsanity.com/paper/2004.13914/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis](https://mlsanity.com/paper/2606.08188/) (2026)

## Abstract (arXiv)

Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) are among the most widely used rank selection methods. Both use the number of free parameters for assessing model complexity. In this work, we adopt the generalized information criterion (GIC) to propose a new method for PCA rank selection under the high-dimensional framework. The GIC model complexity takes into account the sizes of covariance eigenvalues and can be better adaptive to practical applications. Asymptotic properties of GIC are derived and the selection consistency is established under the generalized spiked covariance model.