2017/10/07 by Roy Mitz, Nir Sharon, Mitz, Roy +3
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optical Network Technologies
paper · pdf · doi:10.48550/arxiv.1710.02774
openalex publication_date 2017/10/07 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28
Rank-one update of the spectrum of a matrix is a fundamental problem in\nclassical perturbation theory. In this paper, we consider its variant where\nonly part of the spectrum is known. We address this variant using an efficient\nscheme for updating the known eigenpairs with guaranteed error bounds. Then, we\napply our scheme to the extension of the top eigenvectors of the graph\nLaplacian to a new data sample. In particular, we model this extension as a\nperturbation problem and show how to solve it using our rank-one updating\nscheme. We provide a theoretical analysis of this extension method, and back it\nup with numerical results that illustrate its advantages.\n