Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric reprensentations
Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric reprensentations
复制标题
适用于高维、低样本量数据的有效 PCA，并通过几何表示降低噪声
DOI：
10.1016/j.jmva.2011.09.002
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M.
中科院分区：
文献类型：
--
作者：
Yata;K.;Aoshima;M.
在这篇文章中，我们提出了一种新的估计方法来处理高维，低样本量（HDLSS）数据的PCA。我们首先证明了HDLSS数据集具有不同的几何表示，这取决于ρ-混合类型依赖是否出现在变量中。当变量之间存在ρ-混合型依赖关系时，HDLSS数据随维数的增加而收敛到单位球面的n维曲面上。我们特别关注这一现象。我们提出了一种称为降噪方法的方法来估计HDLSS数据集的特征值。我们表明，特征值估计持有一致性沿着其极限分布在HDLSS上下文中。我们考虑PC方向的一致性。我们应用降噪方法来估计PC分数。我们也给出了一个应用程序中的判别分析HDLSS数据集通过使用逆协方差矩阵估计引起的噪声降低的方法。
In this article, we propose a new estimation methodology to deal with PCA for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS datasets have different geometric representations depending on whether a ρ-mixing-type dependency appears in variables or not. When the ρ-mixing-type dependency appears in variables, the HDLSS data converge to an n-dimensional surface of unit sphere with increasing dimension. We pay special attention to this phenomenon. We propose a method called the noise-reduction methodology to estimate eigenvalues of a HDLSS dataset. We show that the eigenvalue estimator holds consistency properties along with its limiting distribution in HDLSS context. We consider consistency properties of PC directions. We apply the noise-reduction methodology to estimating PC scores. We also give an application in the discriminant analysis for HDLSS datasets by using the inverse covariance matrix estimator induced by the noise-reduction methodology.