Statistics of Min-max Normalized Eigenvalues in Random Matrices
This work addresses the analysis of normalized data in machine learning and data science, but it is incremental as it builds on prior theoretical frameworks.
The study investigated the statistical properties of min-max normalized eigenvalues in random matrices, deriving a scaling law for the cumulative distribution and the residual error in matrix factorization, with numerical experiments confirming theoretical predictions.
Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenvalues in random matrices. Previously, the effective distribution for such normalized eigenvalues has been proposed. In this study, we apply it to evaluate a scaling law of the cumulative distribution. Furthermore, we derive the residual error that arises during matrix factorization of random matrices. We conducted numerical experiments to verify these theoretical predictions.