Principal component analysis and clustering on manifolds
type: Item
instance of: scholarly article
title: Principal component analysis and clustering on manifolds
author: Kanti V. Mardia
author: Henrik Wiechers
author: Benjamin Eltzner
author: Stephan F. Huckemann
published in: Journal of Multivariate Analysis
publication date: 2022-01-03T00:00:00Z
review text: The paper studies the problem of principal component analysis (PCA) and clustering on manifolds. The authors review related literature and depict advances in the important topics of PCA and clustering on manifolds. They deal here mostly with two key manifolds, namely spheres and tori. The paper is organized as follows. After introducing notation and terminology in Section 2, a comprehensive introduction to torus PCA is given in Section 3, which is followed by the description of a new method of clustering for manifold data, namely MINCE post AGE (Mode huntIng on the main principle Nested small Circle of prE-clusters post Adaptive linkaGe clustEring), in Section 4 where the authors cover three typical applications. The first two address SARS-CoV-2 structure clustering on the microscopic level of backbone suites using torus PCA and on a mesoscopic level using PNS (Principal Nested Shape analysis) on lifts to the pre-shape sphere of shape spaces. Using simulated data from a benchmark algorithm, the last application illustrates how to apply the method to Euclidean data. One of the simplest model based methods for torus PCA is to use the wrapped multivariate normal distribution following indirectly a multivariate normal formulation for Euclidean PCA. However, this method is not yet well explored. This is briefly presented in Section 5. The paper is concluded with an overview addressing some important research questions.
Mathematics Subject Classification ID: 62R30
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62H11
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 7451367
zbMATH Keywords: adaptive linkage clustering
zbMATH Keywords: circular mode hunting
zbMATH Keywords: dimension reduction
zbMATH Keywords: multivariate wrapped normal
zbMATH Keywords: SARS-CoV-2 geometry
zbMATH Keywords: stratified spheres
zbMATH Keywords: torus PCA
reviewed by: Joseph Melamed
describes a project that uses: dynamicTreeCut
describes a project that uses: SiZer
MaRDI profile type: Publication
full work available at URL: j.jmva.2021.104862
OpenAlex ID: W3214068148
cites work: Means in complete manifolds: uniqueness and approximation
cites work: SiZer for Exploration of Structures in Curves
cites work: Scale space view of curve estimation.
cites work: Principal nested shape space analysis of molecular dynamics data
cites work: Q3842168
cites work: Multiscale inference about a density
cites work: A smeary central limit theorem for manifolds with application to high-dimensional spheres
cites work: Torus principal component analysis with applications to RNA structure
cites work: Sur la liaison et la division des points d'un ensemble fini
cites work: Generalized Procrustes analysis
cites work: Comments on: ``Recent advances in directional statistics''
cites work: Backward nested descriptors asymptotics with inference on stem cell differentiation
cites work: Q3405558
cites work: The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation
cites work: Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces
cites work: Analysis of principal nested spheres
cites work: Generalized Gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space
cites work: Q3836517
cites work: Q3870155
cites work: Principal Flows
cites work: Barycentric subspace analysis on manifolds
cites work: Recent advances in directional statistics
cites work: Two-Sample Bootstrap Hypothesis Tests for Three-Dimensional Labelled Landmark Data
cites work: Horizontal Dimensionality Reduction and Iterated Frame Bundle Development
cites work: On the folded normal distribution
cites work: Principal Boundary on Riemannian Manifolds
DOI: 10.1016/J.JMVA.2021.104862
description: scientific article; zbMATH DE number 7451367