Low-Rank Principal Eigenmatrix Analysis
This is an incremental improvement for researchers in high-dimensional data analysis, offering a new method for a known bottleneck in sparse PCA.
The paper tackles the problem of high-dimensional data analysis by proposing low-rank principal eigenmatrix analysis, which assumes dominant eigenvectors have a low-rank structure when matricized, and demonstrates competitive empirical performance on synthetic datasets.
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a structure arises naturally in several practical cases: Indeed the top eigenvector of a circulant matrix, when matricized appropriately is a rank-1 matrix. We propose a matricized rank-truncated power method that could be efficiently implemented and establish its computational and statistical properties. Extensive experiments on several synthetic data sets demonstrate the competitive empirical performance of our method.