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2016 Reconstruction of a high-dimensional low-rank matrix
Kazuyoshi Yata, Makoto Aoshima
Electron. J. Statist. 10(1): 895-917 (2016). DOI: 10.1214/16-EJS1128


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.


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Kazuyoshi Yata. Makoto Aoshima. "Reconstruction of a high-dimensional low-rank matrix." Electron. J. Statist. 10 (1) 895 - 917, 2016.


Received: 1 October 2015; Published: 2016
First available in Project Euclid: 8 April 2016

zbMATH: 1341.62170
MathSciNet: MR3486420
Digital Object Identifier: 10.1214/16-EJS1128

Primary: 62H25
Secondary: 62F12

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.10 • No. 1 • 2016
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