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arXiv · 2011.02376

Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data

Vincent Lahoche·Dine Ousmane Samary·Mohamed Tamaazousti
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Abstract

Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when data sets are very larges. Signal detection and recognition for covariance matrix having a nearly continuous spectra is currently one of these opened issues. First investigations in this direction has been proposed in [Journal of Statistical Physics, 167, Issue 3-4, pp 462-475, (2017)] and [arXiv:2002.10574], from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection, and exhibit experimental evidences in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

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Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti. 2021-11-18. Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data. https://doi.org/10.3390/e23091132

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