A Kernel Random Matrix-Based Approach for Sparse PCA
Mohamed El Amine Seddik, Mohamed Tamaazousti, Romain Couillet
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.
BibTeX
@inproceedings{
seddik2018a,
title={A Kernel Random Matrix-Based Approach for Sparse {PCA}},
author={Mohamed El Amine Seddik and Mohamed Tamaazousti and Romain Couillet},
booktitle={International Conference on Learning Representations},
year={2019},
url={https://openreview.net/forum?id=rkgBHoCqYX},
}