# Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation

arXiv: https://arxiv.org/abs/2601.03326 · HTML: https://mlsanity.com/paper/2601.03326/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Adaptive exponential power distribution with moving estimator for nonstationary time series](https://mlsanity.com/paper/2003.02149/) (2020)
- [Rapid parametric density estimation](https://mlsanity.com/paper/1702.02144/) (2017)
- [Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals](https://mlsanity.com/paper/2305.09478/) (2023)
- [Normalized rotation shape descriptors and lossy compression of molecular shape](https://mlsanity.com/paper/1509.09211/) (2015)
- [Polynomial-based rotation invariant features](https://mlsanity.com/paper/1801.01058/) (2018)
- [Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional propagation of values and densities](https://mlsanity.com/paper/2405.05097/) (2024)

## Abstract (arXiv)

PCA can be used for rotation invariant features, describing a shape with its pab=E[(xi-E[xa])(xb-E[xb])] covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real shapes are usually much more complicated, hence there is proposed its extension to e.g. pabc=E[(xa-E[xa])(xb-E[xb])(xc-E[xc])] order-3 or higher tensors describing central moments, or polynomial times Gaussian allowing decodable shape descriptors of arbitrarily high accuracy, and their analogous rotation invariants. Its practical applications could be rotation-invariant features to include shape modulo rotation e.g. for molecular shape descriptors, or for up to rotation object recognition in 2D images/3D scans maybe also for 3D scene understanding, or shape similarity metric allowing inexpensive comparison of objects modulo rotation avoiding costly optimization over rotations.