An alternating minimization algorithm for Factor Analysis

TL;DR

This paper introduces a fast, projection-based alternating minimization algorithm for decomposing covariance matrices into low-rank and diagonal components, demonstrating strong performance on large datasets and real-world benchmarks.

Contribution

The paper presents a novel, efficient algorithm for factor analysis that outperforms existing methods in speed and scalability, with proven local convergence.

Findings

Algorithm performs extremely well and is very fast on large covariance matrices.

Simulation studies confirm the effectiveness of the method.

Application to real datasets demonstrates practical utility.

Abstract

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem. This algorithm appears to perform extremely well and is extremely fast even when the given covariance matrix has a very large dimension. The effectiveness of the algorithm is assessed through simulation studies and by applications to three real datasets that are considered as benchmark for the problem. A local convergence analysis of the algorithm is also presented.