On the asymptotic normality and efficiency of Kronecker envelope principal component analysis
type: Item
instance of: scholarly article
title: On the asymptotic normality and efficiency of Kronecker envelope principal component analysis
zbMATH Open document ID: 1467.62107
author: Shih-Hao Huang
author: Suyun Huang
published in: Journal of Multivariate Analysis
publication date: 2021-06-22T00:00:00Z
review text: This paper is a study on the asymptotic analysis. The authors show the multilinear principal component analysis (PCA) theory and the notion of the Kronecker envelope and proposed dimension folding estimators for supervised dimension reduction. The authors review the asymptotic normality of the principal component (PC) estimators of ordinary PCA, they derive the asymptotic normality of the PC estimators of Kronecker envelope PCA. The authors show that Kronecker envelope PCA is asymptotically more efficient than ordinary PCA. They then illustrate with real data example of cryo-EM image clustering and a simulation experiments to conclusion their results.
reviewed by: Glauber Márcio Silveira Pereira
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62P35
Mathematics Subject Classification ID: 92E10
zbMATH DE Number: 7361744
zbMATH Keywords: cryogenic electron microscopy
zbMATH Keywords: dimension reduction
zbMATH Keywords: Kronecker envelope
zbMATH Keywords: multilinear principal component analysis
zbMATH Keywords: principal component analysis
zbMATH Keywords: tensor data
MaRDI profile type: Publication
full work available at URL: j.jmva.2021.104761
OpenAlex ID: W3156476091
cites work: \(\gamma\)-SUP: a clustering algorithm for cryo-electron microscopy images of asymmetric particles
cites work: Complete class results for the moment matrices of designs over permutation-invariant sets
cites work: Two-stage dimension reduction for noisy high-dimensional images and application to cryogenic electron microscopy
cites work: On multilinear principal component analysis of order-two tensors
cites work: On dimension folding of matrix- or array-valued statistical objects
cites work: The commutation matrix: Some properties and applications
cites work: Inequalities: theory of majorization and its applications
cites work: Tests for Kronecker envelope models in multilinear principal components analysis
cites work: Q3048082
cites work: Asymptotic inference for eigenvectors
cites work: PCA consistency for the power spiked model in high-dimensional settings
DOI: 10.1016/J.JMVA.2021.104761
description: scientific article; zbMATH DE number 7361744