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

TL;DR

This paper introduces a tensorial renormalization group approach for signal detection in nearly continuous spectra, extending previous matrix-based methods to tensor data, and demonstrates a connection between symmetry breaking and detection thresholds.

Contribution

It generalizes the nonperturbative renormalization group formalism to tensor data for signal detection, revealing universal features and the link to symmetry breaking.

Findings

Experimental evidence links symmetry breaking to detection thresholds.

The approach provides universal descriptions for signal detection in tensor spectra.

Extension of matrix-based methods to tensorial principal component analysis.

Abstract

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.