Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Vincent Lahoche (1) , Mohamed Ouerfelli (1) , Dine Ousmane Samary (1, 2) , Mohamed Tamaazousti (1)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
2 UAC - Université d’Abomey-Calavi = University of Abomey Calavi

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 an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing 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.

Mots clés: renormalization group; field theory; phase transition; random tensors; big data; renormalization group: nonperturbative; principal component analysis; tensorial principal component analysis; signal detection; symmetry breaking; covariance

Domaines: Physique Générale [physics.gen-ph]

Vincent Lahoche, Mohamed Ouerfelli, Dine Ousmane Samary, Mohamed Tamaazousti. Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data. Entropy, 2021, 23 (7), pp.795. ⟨10.3390/e23070795⟩. ⟨hal-03098843⟩