EconPapers    
Economics at your fingertips  
 

Clustering, multicollinearity, and singular vectors

Hamid Usefi

Computational Statistics & Data Analysis, 2022, vol. 173, issue C

Abstract: Let A be a matrix with its Moore-Penrose pseudo-inverse A†. It is proved that, after re-ordering the columns of A, the projector P=I−A†A has a block-diagonal form, that is there is a permutation matrix Π such that ΠPΠT=diag(S1,S2,…,Sk). It is further proved that each block Si corresponds to a cluster of columns of A that are linearly dependent with each other. A clustering algorithm is provided that allows to partition the columns of A into clusters where columns in a cluster correlate only with columns within the same cluster. Some applications in supervised and unsupervised learning, specially feature selection, clustering, and sensitivity of solutions of least squares solutions are discussed.

Keywords: Collinearity; Clustering; Subset selection; Machine learning (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947322001037
Full text for ScienceDirect subscribers only.

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:eee:csdana:v:173:y:2022:i:c:s0167947322001037

DOI: 10.1016/j.csda.2022.107523

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-03-19
Handle: RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322001037