论文标题
在几乎连续的正谱I中进行信号检测的现场理论方法：矩阵数据
Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data
论文作者
论文摘要
重新归一化的组技术被广泛用于现代物理学，以描述涉及大量自由度的系统的低能量相关方面。因此，当数据集非常大量时，这些技术被期望是解决数据分析中的开放问题的强大工具。目前，具有几乎连续光谱的协方差矩阵的信号检测和识别是这些开放问题之一。在[统计物理学杂志，第167期，第3-4期，第462-475页，（2017年）]和[Arxiv：2002.10574]中提出了第一项研究，这是从粗糙胶片和原理成分分析（PCA）之间的类比（PCA），即针对uv cutix cutix cutrix small off of same noise模式的分离。本文提出的领域理论框架是这些互补观点的综合，旨在成为理论研究和实验检测的一般和操作框架。我们的研究集中在信号检测上，并表现出实验证据，有利于对称性断裂与固有检测阈值的存在之间的联系。
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.
