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International Journal of Machine Learning and Cybernetics
Erschienen in: International Journal of Machine Learning and Cybernetics 6/2013

01.12.2013 | Original Article

Principal component analysis using QR decomposition

verfasst von: Alok Sharma, Kuldip K. Paliwal, Seiya Imoto, Satoru Miyano

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 6/2013

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Abstract

In this paper we present QR based principal component analysis (PCA) method. Similar to the singular value decomposition (SVD) based PCA method this method is numerically stable. We have carried out analytical comparison as well as numerical comparison (on Matlab software) to investigate the performance (in terms of computational complexity) of our method. The computational complexity of SVD based PCA is around \( 14dn^{2} \) flops (where d is the dimensionality of feature space and n is the number of training feature vectors); whereas the computational complexity of QR based PCA is around \( 2dn^{2} \, + \,2dth \) flops (where t is the rank of data covariance matrix and h is the dimensionality of reduced feature space). It is observed that the QR based PCA is more efficient in terms of computational complexity.
Vorheriger Artikel New approach to MCDM under interval-valued intuitionistic fuzzy environment
Nächster Artikel Properties of two types of covering-based rough sets

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Fußnoten
1
To deal with higher order matrices, other variants of PCA have been proposed in the literature. See the following references for details [23‐27]
 
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Metadaten
Titel
Principal component analysis using QR decomposition
verfasst von
Alok Sharma
Kuldip K. Paliwal
Seiya Imoto
Satoru Miyano
Publikationsdatum
01.12.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 6/2013
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-012-0131-7

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