Estimating Common Principal Components in High Dimensions

TL;DR

This paper introduces new majorization-minimization algorithms for estimating common principal components in high-dimensional data, addressing limitations of traditional methods like Flury in such settings.

Contribution

The paper develops simple, effective MM algorithms tailored for high-dimensional common principal component estimation, outperforming existing methods in convergence and computational efficiency.

Findings

Proposed algorithms are effective in high-dimensional settings.

Simulations show improved convergence over traditional methods.

Algorithms are computationally efficient for large datasets.

Abstract

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However, the Flury method is not effective for higher dimensional problems. We obtain several simple majorization-minizmation (MM) algorithms that provide solutions to this problem and are effective in higher dimensions. We then use simulated data to compare them with other approaches in terms of convergence and computational time.