Denoising Data with Random Matrix Theory  

作　　者：Nathan Jiang Nathan Jiang(Department of Mathematics, Columbia University, New York, NY, USA)

机构地区：[1]Department of Mathematics, Columbia University, New York, NY, USA

出　　处：《Journal of Applied Mathematics and Physics》2024年第11期3902-3911,共10页应用数学与应用物理（英文）

摘　　要：Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries, the introduction of noise, and the size of the matrix, the resulting eigenvalue and eigenvector distributions remain relatively unchanged. However, when there are certain anomalous eigenvalues and their corresponding eigenvectors that do not follow the predicted distributions, it could indicate that there’s an underlying non-random signal inside the data. As data and matrices become more important in the sciences and computing, so too will the importance of processing them with the principles of random matrix theory.Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries, the introduction of noise, and the size of the matrix, the resulting eigenvalue and eigenvector distributions remain relatively unchanged. However, when there are certain anomalous eigenvalues and their corresponding eigenvectors that do not follow the predicted distributions, it could indicate that there’s an underlying non-random signal inside the data. As data and matrices become more important in the sciences and computing, so too will the importance of processing them with the principles of random matrix theory.

关 键 词：Random Matrix Theory UNIVERSALITY Wishart Matrices Marchenko-Pastur (M-P) Distribution Noise SPARSITY SIGNALING Linear Sketching 

分 类 号：O17[理学—数学]