# Exploratory Factor Analysis of Data on a Sphere

arXiv: https://arxiv.org/abs/2111.04940 · HTML: https://mlsanity.com/paper/2111.04940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 106 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [Bi-cross-validation for factor analysis](https://mlsanity.com/paper/1503.03515/) (2015)
- [A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data](https://mlsanity.com/paper/1907.11970/) (2019)
- [Small sphere distributions for directional data with application to medical imaging](https://mlsanity.com/paper/1705.10013/) (2017)

## Abstract (arXiv)

Data on high-dimensional spheres arise frequently in many disciplines either naturally or as a consequence of preliminary processing and can have intricate dependence structure that needs to be understood. We develop exploratory factor analysis of the projected normal distribution to explain the variability in such data using a few easily interpreted latent factors. Our methodology provides maximum likelihood estimates through a novel fast alternating expectation profile conditional maximization algorithm. Results on simulation experiments on a wide range of settings are uniformly excellent. Our methodology provides interpretable and insightful results when applied to tweets with the #MeToo hashtag in early December 2018, to time-course functional Magnetic Resonance Images of the average pre-teen brain at rest, to characterize handwritten digits, and to gene expression data from cancerous cells in the Cancer Genome Atlas.