Fluctuations of Spiked Random Matrix Models and Failure Diagnosis in Sensor Networks
Fluctuations of Spiked Random Matrix Models and Failure Diagnosis in Sensor Networks
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DOI：
10.1109/tit.2012.2218572
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发表时间：
2013-01-01
影响因子：
2.5
通讯作者：
Hachem, Walid
中科院分区：
文献类型：
--
作者：
Couillet, Romain;Hachem, Walid
本文分析了高维样本协方差矩阵是单位矩阵的有限秩扰动时，高维样本协方差矩阵的极值和特征向量的联合起伏，对应于随机矩阵理论中的尖峰模型。随着矩阵大小的增大，渐近涨落与高斯么正系综中的矩阵密切相关。当尖峰种群本征值具有单位重数时，涨落遵循中心极限定理。这一结果被用来开发一个原始的框架，用于检测和诊断大型传感器网络中的局部故障，对于已知或未知的故障程度。
In this paper, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample co-variance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity matrix, corresponding to the so-called spiked model in random matrix theory. The asymptotic fluctuations, as the matrix size grows large, are shown to be intimately linked with matrices from the Gaussian unitary ensemble. When the spiked population eigenvalues have unit multiplicity, the fluctuations follow a central limit theorem. This result is used to develop an original framework for the detection and diagnosis of local failures in large sensor networks, for known or unknown failure magnitude.