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Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data.

Vincent Lahoche1, Dine Ousmane Samary1,2, Mohamed Tamaazousti1

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Summary

Renormalization group techniques offer a novel approach to signal detection in highly correlated data. This study connects symmetry breaking to an intrinsic detection threshold, advancing data analysis methods.

Keywords:
big datafield theoryinformation theoryphase transitionprincipal component analysisrenormalization groupsignal detection

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Area of Science:

  • Statistical Physics
  • Data Analysis
  • Signal Processing

Background:

  • Renormalization group (RG) techniques are crucial for understanding complex systems with many degrees of freedom.
  • Highly correlated datasets present challenges in traditional data analysis, particularly in signal detection.
  • Existing methods draw analogies between coarse-graining and principal component analysis (PCA) for noise separation.

Purpose of the Study:

  • To develop a general and operational field-theoretical framework for signal detection in systems with correlated data.
  • To synthesize existing viewpoints on noise separation and eigenvalue analysis within a unified framework.
  • To investigate the specific application of this framework to signal detection problems.

Main Methods:

  • Application of renormalization group techniques to the problem of signal detection.
  • Development of a field-theoretical framework integrating coarse-graining and PCA concepts.
  • Numerical investigations to explore the relationship between theoretical predictions and empirical data.

Main Results:

  • The proposed framework provides a unified approach for theoretical and experimental signal detection.
  • Numerical investigations reveal a significant connection between symmetry breaking and the presence of a detection threshold.
  • The study demonstrates the efficacy of RG techniques in identifying intrinsic detection limits.

Conclusions:

  • Renormalization group techniques offer a powerful tool for analyzing highly correlated datasets and detecting signals.
  • Symmetry breaking is identified as a key factor influencing the existence of an intrinsic detection threshold.
  • The developed framework is applicable to both theoretical research and practical experimental detection scenarios.