A Sparse Singular Value Decomposition Method for High-Dimensional Data

By Dan Yang, Zongming Ma, Andreas Buja. 2014

43 citations recorded by the source corpus.

We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors simultaneously, rather than successively as in competing proposals. We introduce novel ways to estimate thresholding parameters, which obviate the need for computationally expensive cross-validation. We also introduce a way to sparsely initialize the algorithm for computational savings that allow our algorithm to outperform the vanilla singular value decomposition (SVD) on the full data table when the signal is sparse. A comparison with two existing sparse SVD methods suggests that our algorithm is computationally always faster and statistically always at least comparable to the better of the two competing algorithms. Supplementary materials for the article are available in an online appendix. An R package ssvd implementing the algorithms introduced in this article is available on CRAN.

Subfields: Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

1. Serena Ng
2. Jushan Bai
3. Mark W. Watson
4. Liangjun Su
5. James H. Stock
6. In Choi
7. Jianqing Fan
8. Pierre Perron

Citations in the corpus

• Principal Components and Regularized Estimation of Factor Models (2017, background): “..N to index cross-section units and t = 1,...T to index time series observations. Let Xi = (Xi1,...XiT )′ be a T ×1 vector of random variables. The T ×N data matrix is denoted Agarwal et al. (2012), Yang et al. (2014), Hastie et al. (2015). 2 X = (X1,X2,...,XN). The factor representation of the dat”