A Kernel Random Matrix-Based Approach for Sparse PCA
Abstract
In this paper, we present a random matrix approach to recover sparse principal components from n p-dimensional vectors. Specifically, considering the large dimensional setting where n, p → ∞ with p/n → c ∈ (0, ∞) and under Gaussian vector observations, we study kernel random matrices of the type f (Ĉ), where f is a three-times continuously differentiable function applied entry-wise to the sample covariance matrix Ĉ of the data. Then, assuming that the principal components are sparse, we show that taking f in such a way that f'(0) = f''(0) = 0 allows for powerful recovery of the principal components, thereby generalizing previous ideas involving more specific f functions such as the soft-thresholding function.
Cite
Text
Seddik et al. "A Kernel Random Matrix-Based Approach for Sparse PCA." International Conference on Learning Representations, 2019.Markdown
[Seddik et al. "A Kernel Random Matrix-Based Approach for Sparse PCA." International Conference on Learning Representations, 2019.](https://mlanthology.org/iclr/2019/seddik2019iclr-kernel/)BibTeX
@inproceedings{seddik2019iclr-kernel,
title = {{A Kernel Random Matrix-Based Approach for Sparse PCA}},
author = {Seddik, Mohamed El Amine and Tamaazousti, Mohamed and Couillet, Romain},
booktitle = {International Conference on Learning Representations},
year = {2019},
url = {https://mlanthology.org/iclr/2019/seddik2019iclr-kernel/}
}