The Equivalence Between Principal Component Analysis and Nearest Flat in the Least Square Sense

Yuan-Hai Shao () and Nai-Yang Deng ()
Additional contact information
Yuan-Hai Shao: Zhejiang University of Technology
Nai-Yang Deng: China Agricultural University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 13, 278-284

Abstract: Abstract In this paper, we declare the equivalence between the principal component analysis and the nearest q-flat in the least square sense by showing that, for given m data points, the linear manifold with nearest distance is identical to the linear manifold with largest variance. Furthermore, from this observation, we give a new simpler proof for the approach to find the nearest q-flat.

Keywords: Linear manifold; Unsupervised learning; Nearest q-flat; Principal component analysis; Eigenvalue decomposition; 15A18; 58C40 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-014-0647-y 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:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0647-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-014-0647-y

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().