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In this paper, we propose an efficient quantum algorithm for spectral regression which is a dimensionality reduction framework based on the regression and spectral graph analysis. The quantum algorithm involves two core subroutines: the quantum principal eigenvectors analysis and the quantum ridge regression algorithm. The quantum principal eigenvectors analysis can be performed by an efficient sparse Hamiltonian simulation. For the ridge regression, we propose a quantum algorithm that isdoi:10.1109/access.2018.2886581 fatcat:e6xo4ktntrf5jovzuzcoimzisy