文章基本信息

标题：Reconstruction of a high-dimensional low-rank matrix
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作者：Kazuyoshi Yata ; Makoto Aoshima
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：1
页码：895-917
DOI：10.1214/16-EJS1128
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of recovering a low-rank signal matrix in high-dimensional situations. The main issue is how to estimate the signal matrix in the presence of huge noise. We introduce the power spiked model to describe the structure of singular values of a huge data matrix. We first consider the conventional PCA to recover the signal matrix and show that the estimation of the signal matrix holds consistency properties under severe conditions. The conventional PCA is heavily subjected to the noise. In order to reduce the noise we apply the noise-reduction (NR) methodology and propose a new estimation of the signal matrix. We show that the proposed estimation by the NR method holds the consistency properties under mild conditions and improves the error rate of the conventional PCA effectively. Finally, we demonstrate the reconstruction procedures by using a microarray data set.
关键词：Eigenstructure;HDLSS;noise-reduction me thodology;PCA;singular value decomposition.