  The tensorial principal component analysis is a generalization of ordinary
principal component analysis, focusing on data which are suitably described by
tensors rather than matrices. This paper aims at giving the nonperturbative
renormalization group formalism based on a slight generalization of the
covariance matrix, to investigate signal detection for the difficult issue of
nearly continuous spectra. Renormalization group allows constructing effective
description keeping only relevant features in the low ``energy'' (i.e. large
eigenvalues) limit and thus provides universal descriptions allowing to
associate the presence of the signal with objectives and computable quantities.
Among them, in this paper, we focus on the vacuum expectation value. We exhibit
experimental evidence in favor of a connection between symmetry breaking and
the existence of an intrinsic detection threshold, in agreement with our
conclusions for matrices, providing a new step in the direction of a universal
statement.
