Functional Renormalization Group Approach for Signal Detection

Abstract

This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be viewed as a maximum entropy model. In particular and exploiting universality arguments, we justify the ${\mathbb{Z}}_2$-symmetry of the classical action and we stress the existence of a large-scale (local) regime and of a small-scale (nonlocal) regime. Secondly and related to noise models, we observe the universal relation between phase transition and symmetry breaking in the vicinity of the detection threshold. Finally, we discuss the issue of defining the covariance matrix for tensorial-like data. Based on the cutting graph prescription, we note the superiority of definitions based on complete graphs of large size for data analysis.

In this new version, we have improved the clarity of certain passages and corrected a few typos. The results remain unchanged

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Cited by in corpus (1)

• Functional Renormalization for Signal Detection: Dimensional Analysis and Dimensional Phase Transition for Nearly Continuous Spectra Effective Field Theory