Simultaneous diagonalization: the asymmetric, low-rank, and noisy settings

TL;DR

This paper extends algorithms for simultaneous matrix diagonalization to handle low-rank, asymmetric, and noisy matrices, broadening its applicability in machine learning tasks like source separation and latent variable estimation.

Contribution

The authors develop new algorithms and perturbation analysis for joint diagonalization applicable to low-rank, asymmetric, and noisy matrices, enabling new applications.

Findings

Extended diagonalization algorithms to low-rank, asymmetric matrices

Provided perturbation analysis for noisy settings

Enabled application in new machine learning scenarios

Abstract

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint diagonalization to low-rank and asymmetric matrices, and we also provide extensions to the perturbation analysis of these methods. Our results allow joint diagonalization to be applied in several new settings.