# A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data

arXiv: https://arxiv.org/abs/1907.11970 · HTML: https://mlsanity.com/paper/1907.11970/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Exploratory Factor Analysis of Data on a Sphere](https://mlsanity.com/paper/2111.04940/) (2021)
- [A Hybrid Mixture of t-Factor Analyzers for Clustering High-dimensional Data](https://mlsanity.com/paper/2504.21120/) (2025)
- [A Hybrid Mixture Approach for Clustering and Characterizing Cancer Data](https://mlsanity.com/paper/2507.14380/) (2025)

## Abstract (arXiv)

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators and a control group.