# Principal Ellipsoid Analysis (PEA): Efficient non-linear dimension reduction & clustering

arXiv: https://arxiv.org/abs/2008.07110 · HTML: https://mlsanity.com/paper/2008.07110/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

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

- [Robust Principal Component Analysis: A Median of Means Approach](https://mlsanity.com/paper/2102.03403/) (2021)
- [Ellipsoid fitting with the Cayley transform](https://mlsanity.com/paper/2304.10630/) (2023)

## Abstract (arXiv)

Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination of simplicity, interpretability and computational efficiency. The focus of this article is on improving upon PCA and k-means, by allowing non-linear relations in the data and more flexible cluster shapes, without sacrificing the key advantages. The key contribution is a new framework for Principal Elliptical Analysis (PEA), defining a simple and computationally efficient alternative to PCA that fits the best elliptical approximation through the data. We provide theoretical guarantees on the proposed PEA algorithm using Vapnik-Chervonenkis (VC) theory to show strong consistency and uniform concentration bounds. Toy experiments illustrate the performance of PEA, and the ability to adapt to non-linear structure and complex cluster shapes. In a rich variety of real data clustering applications, PEA is shown to do as well as k-means for simple datasets, while dramatically improving performance in more complex settings.