近连续正谱信号检测的场论方法II：张量数据
Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data
摘要：
张量主成分分析是普通主成分分析的推广，主要关注由张量而不是矩阵适当描述的数据。本文旨在基于协方差矩阵的轻微推广给出非微扰重整化群形式，以研究几乎连续谱的信号检测问题。重整化群允许构造有效的描述，仅保持低"能量“（即大本征值）限制中的相关特征，从而提供通用描述，允许将信号的存在与目标和可计算量相关联。其中，本文重点研究了真空期望值。我们展示的实验证据有利于对称性破缺和存在的内在检测阈值之间的连接，与我们的结论矩阵，提供了一个新的一步，在一个普遍的声明的方向。
英文摘要：
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.
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