Optimality and sub-optimality of PCA I: Spiked random matrix models
PCA 的最优性与次优性之一：尖峰随机矩阵模型
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or “spike”) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Péché showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is…