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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 matrixĈ 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.
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https://hal.archives-ouvertes.fr/hal-02971198
Contributor : Mohamed El Amine Seddik <>
Submitted on : Monday, October 19, 2020 - 12:05:47 PM
Last modification on : Monday, August 30, 2021 - 9:40:02 AM
Long-term archiving on: : Wednesday, January 20, 2021 - 6:35:34 PM

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Mohamed El Amine Seddik, Mohamed Tamaazousti, Romain Couillet. A kernel random matrix-based approach for sparse PCA. ICLR 2019 - International Conference on Learning Representations, 2019, New Orleans, United States. ⟨hal-02971198⟩

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