# SO(3)-invariant PCA with application to molecular data

arXiv: https://arxiv.org/abs/2510.18827 · HTML: https://mlsanity.com/paper/2510.18827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [Fast Steerable Principal Component Analysis](https://mlsanity.com/paper/1412.0781/) (2014)
- [Denoising and Covariance Estimation of Single Particle Cryo-EM Images](https://mlsanity.com/paper/1602.06632/) (2016)

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

- [Group Invariant Spectral Embedding](https://mlsanity.com/paper/2607.08987/) (2026)

## Abstract (arXiv)

Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant challenges. A naive approach requires augmenting the dataset with many rotated copies of each sample, incurring prohibitive computational costs. In this paper, we extend PCA to 3D volumetric datasets with unknown orientations by developing an efficient and principled framework for SO(3)-invariant PCA that implicitly accounts for all rotations without explicit data augmentation. By exploiting underlying algebraic structure, we demonstrate that the computation involves only the square root of the total number of covariance entries, resulting in a substantial reduction in complexity. We validate the method on real-world molecular datasets, demonstrating its effectiveness and opening up new possibilities for large-scale, high-dimensional reconstruction problems.