Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 10, Number 1 (2016), 895-917.
Reconstruction of a high-dimensional low-rank matrix
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.
Electron. J. Statist. Volume 10, Number 1 (2016), 895-917.
Received: October 2015
First available in Project Euclid: 8 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62F12: Asymptotic properties of estimators
Yata, Kazuyoshi; Aoshima, Makoto. Reconstruction of a high-dimensional low-rank matrix. Electron. J. Statist. 10 (2016), no. 1, 895--917. doi:10.1214/16-EJS1128. https://projecteuclid.org/euclid.ejs/1460141647