Spectral dimensionality reduction methods have recently emerged as powerful tools for various applications in pattern recognition, data mining and computer vision. These methods use information contained in the eigenvectors of a data affinity (i.e., item-item similarity) matrix to reveal the low dimensional structure of the high dimensional data. One of the limitations of various spectral dimen...

We study joint eigenvector distributions for large symmetric matrices in the presence of weak noise. Our main result asserts that every submatrix orthogonal matrix eigenvectors converges to a multidimensional Gaussian distribution. The proof involves analyzing stochastic eigenstate equation (SEE) (Bourgade and Yau Comm Math Phys, 2013) which describes Lie group valued flow induced by Brownian m...