EconPapers    
Economics at your fingertips  
 

Sparse principal component regression via singular value decomposition approach

Shuichi Kawano ()
Additional contact information
Shuichi Kawano: The University of Electro-Communications

Advances in Data Analysis and Classification, 2021, vol. 15, issue 3, No 10, 795-823

Abstract: Abstract Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage builds a regression model whose explanatory variables are the principal components obtained in the first stage. Since PCA is performed using only explanatory variables, the principal components have no information about the response variable. To address this problem, we present a one-stage procedure for PCR based on a singular value decomposition approach. Our approach is based upon two loss functions, which are a regression loss and a PCA loss from the singular value decomposition, with sparse regularization. The proposed method enables us to obtain principal component loadings that include information about both explanatory variables and a response variable. An estimation algorithm is developed by using the alternating direction method of multipliers. We conduct numerical studies to show the effectiveness of the proposed method.

Keywords: ADMM; Lasso; One-stage procedure; Singular value decomposition; Principal component analysis; 62H25; 62J07; 62J05 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11634-020-00435-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00435-2

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-020-00435-2

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from Springer, German Classification Society - Gesellschaft für Klassifikation (GfKl), Japanese Classification Society (JCS), Classification and Data Analysis Group of the Italian Statistical Society (CLADAG), International Federation of Classification Societies (IFCS)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2025-03-20
Handle: RePEc:spr:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00435-2