Simultaneous diagonalization: the asymmetric, low-rank, and noisy settings
Provides theoretical and algorithmic extensions for joint diagonalization, benefiting practitioners in blind source separation and latent variable models.
The paper extends simultaneous matrix diagonalization to low-rank and asymmetric matrices, with perturbation analysis, enabling new applications in machine learning.
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.