  Recently, the singular value decomposition (SVD) was applied to standard
Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale
invariance in the spectral fluctuations without performing any unfolding
procedure. Here, SVD is applied directly to the $\nu$-Hermite ensemble and to a
sparse matrix ensemble, decomposing the corresponding spectra in trend and
fluctuation modes. In correspondence with known results, we obtain that
fluctuation modes exhibit a cross-over between soft and rigid behavior. By
using the trend modes we performed a data-adaptive unfolding, and we calculate
traditional spectral fluctuation measures. Additionally, ensemble-averaged and
individual-spectrum averaged statistics are calculated consistently within the
same basis of normal modes.
