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The tensorial principal component analysis is a generalization of ordinaryprincipal component analysis, focusing on data which are suitably described bytensors rather than matrices. This paper aims at giving the nonperturbativerenormalization group formalism based on a slight generalization of thecovariance matrix, to investigate signal detection for the difficult issue ofnearly continuous spectra. Renormalization group allows constructing effectivedescription keeping only relevant features in the low ``energy'' (i.e. largeeigenvalues) limit and thus provides universal descriptions allowing toassociate the presence of the signal with objectives and computable quantities.Among them, in this paper, we focus on the vacuum expectation value. We exhibitexperimental evidence in favor of a connection between symmetry breaking andthe existence of an intrinsic detection threshold, in agreement with ourconclusions for matrices, providing a new step in the direction of a universalstatement.

Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data