Eigenvalue Distribution

Eigenvalue distribution analysis investigates the statistical properties of eigenvalues derived from matrices representing data or model parameters, aiming to reveal underlying structure and relationships within complex systems. Current research focuses on applying this analysis to diverse areas, including deep learning (examining Jacobian matrices and autoencoder behavior), dimensionality reduction techniques like Partial Least Squares (PLS), and the characterization of real-world datasets using random matrix theory. These studies reveal connections between eigenvalue distributions and crucial properties like data correlation, model generalization, and representation quality, impacting fields ranging from machine learning to chemometrics.