A hybrid high-dimensional matrix-free approach for Mixture of t-factor analyzers

Music City Center 

Traditional MFA models, which rely on Gaussian assumptions, are sensitive to outliers and heavy-tailed distributions, making them less robust in complex real-world scenarios. The Mixture of t-Factor Analyzers (MtFA) model extends this framework by incorporating multivariate t-distributions, offering improved robustness to non-Gaussian data. Despite its advantages, the MtFA model faces computational challenges, particularly in high-dimensional settings, where the estimation of large covariance matrices and the iterative nature of Expectation-Maximization (EM) algorithms lead to scalability issues. In this work, we present a hybrid approach that integrates a matrix-free algorithm into the EM framework to efficiently estimate the parameters of the MtFA model. By leveraging the structure of the t-distribution within a factor analysis framework, our method retains the interpretability of traditional MFA while improving robustness to heavy-tailed noise and localized anomalies. We demonstrate the effectiveness of our approach through simulations and real-world datasets, showcasing its superior computational efficiency, resilience against outliers, while preserving clustering accuracy.

Mixture of factor analyzers

data clustering

matrix-free computations

expectation-maximization algorithm

dimensionality reduction

factor analysis 

Section on Statistical Computing