# Generalized Spherical Principal Component Analysis

arXiv: https://arxiv.org/abs/2303.05836 · HTML: https://mlsanity.com/paper/2303.05836/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2023.

## Built on by (most cited first, 3 of 3)

- [Sparse outlier-robust PCA for multi-source data](https://mlsanity.com/paper/2407.16299/) (2024)
- [Robust and Differentially Private Principal Component Analysis](https://mlsanity.com/paper/2507.15232/) (2025)
- [Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustness](https://mlsanity.com/paper/2502.16391/) (2025)

## Abstract (arXiv)

Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal component analysis, a new robust version of principal component analysis that is based on the generalized spatial sign covariance matrix. Supporting theoretical properties of the proposed method including influence functions, breakdown values and asymptotic efficiencies are studied, and a simulation study is conducted to compare our new method to existing methods. We also propose an adjustment of the generalized spatial sign covariance matrix to achieve better Fisher consistency properties. We illustrate that generalized spherical principal component analysis, depending on a chosen radial function, has both great robustness and efficiency properties in addition to a low computational cost.