  We examine holographic renormalization by the singular value decomposition
(SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical
Ising model at criticality. To take the continuous limit of the SVD enables us
to find the mathematical form of each SVD component by the inverse Mellin
transformation as well as the power-law behavior of the SVD spectrum. We find
that each SVD component is characterized by the two-point spin correlator with
a finite correlation length. Then, the continuous limit of the decomposition
index in the SVD corresponds to the inverse of the correlation length. These
features strongly suggest that the SVD contains mathematical structure the same
as the holographic renormalization.
