# A generalized spatial sign covariance matrix

arXiv: https://arxiv.org/abs/1805.01417 · HTML: https://mlsanity.com/paper/1805.01417/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2018.

## Built on by (most cited first, 2 of 2)

- [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)

The well-known spatial sign covariance matrix (SSCM) carries out a radial transform which moves all data points to a sphere, followed by computing the classical covariance matrix of the transformed data. Its popularity stems from its robustness to outliers, fast computation, and applications to correlation and principal component analysis. In this paper we study more general radial functions. It is shown that the eigenvectors of the generalized SSCM are still consistent and the ranks of the eigenvalues are preserved. The influence function of the resulting scatter matrix is derived, and it is shown that its breakdown value is as high as that of the original SSCM. A simulation study indicates that the best results are obtained when the inner half of the data points are not transformed and points lying far away are moved to the center.