Principal component analysis constrained by layered simple structures

The paper proposes a procedure for principal component analysis called layered principal component analysis (LPCA) to produce a simple and interpretable loading matrix. The novelty of LPCA is that a loading matrix is constrained as a sum of matrices with simple structures called layers, and the resu...

Full description

Saved in:
Bibliographic Details
Published in:Advances in data analysis and classification 2023-06, Vol.17 (2), p.347-367
Main Author: Yamashita, Naoto
Format: Article
Language:English
Subjects:
Applied statistics
Chemistry and Earth Sciences
Computer Science
Data Mining and Knowledge Discovery
Economics
Finance
Health Sciences
Humanities
Insurance
Law
Management
Mathematics and Statistics
Medicine
Parameters
Physics
Principal components analysis
Regular Article
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The paper proposes a procedure for principal component analysis called layered principal component analysis (LPCA) to produce a simple and interpretable loading matrix. The novelty of LPCA is that a loading matrix is constrained as a sum of matrices with simple structures called layers, and the resulting simplicity of the LPCA solution is controlled by how many layers are used. LPCA is a generalization of disjoint PCA proposed as reported by Ferrara (in: Giommi (ed) Topics in theoretical and applied statistics, Springer, Cham 2016). The number of layers controls the balance of simplicity and the fit to the data, and the user can choose the desired level of simplicity between the most restrictive but simplest case with a single layer or multiple layers with better fit to the data. The optimal number of layers is specified in terms of explained variance and two information criteria. Two simulation studies were conducted to evaluate how accurately the LPCA procedure recovers the true parameter values. The results showed that LPCA was effective for parameter recovery. The paper presents three examples of LPCA applied to real data, which show the potential of LPCA for producing simple and interpretable loading matrices.
ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-022-00503-9