Text

Eigenvectors from Eigenvalues Sparse Principal Component Analysis

We present a novel technique for sparse principal component analysis. This method, named eigenvectors from eigenvalues sparse principal component analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a Hermitian matrix from the eigenvalues of the full matrix and associated sub-matrices. We explore two versions of the EESPCA method: a version that uses a fixed threshold for inducing sparsity and a version that selects the threshold via cross-validation. Relative to the state-of-the-art sparse PCA methods of Witten et al., Yuan and Zhang, and Tan et al., the fixed threshold EESPCA technique offers an order-of-magnitude improvement in computational speed, does not require estimation of tuning parameters via cross-validation, and can more accurately identify true zero principal component loadings across a range of data matrix sizes and covariance structures. Importantly, the EESPCA method achieves these benefits while maintaining out-of-sample reconstruction error and PC estimation error close to the lowest error generated by all evaluated approaches. EESPCA is a practical and effective technique for sparse PCA with particular relevance to computationally demanding statistical problems such as the analysis of high-dimensional datasets or application of statistical techniques like resampling that involve the repeated calculation of sparse PCs. Supplementary materials for this article are available online.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS; Vol.31 No.2 June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 486-501

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

PRINCIPAL COMPONENT ANALYSIS
SPARSE PRINCIPAL COMPONENT ANALYSIS
EIGENVECTOR-EIGENVALUE IDENTITY
SPARSE EIGENVALUE DECOMPOSITION

Info Detail Spesifik

https://doi.org/10.1080/10618600.2021.1987254

Pernyataan Tanggungjawab

H. Robert Frost

Versi lain/terkait

Lampiran Berkas

Komentar