New Interpretation of Principal Components Analysis

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Authors
Gniazdowski, Zenon
Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Warszawska Wyższa Szkoła Informatyki
License
Creative Commons License
Creative Commons Attribution-NoDerivs 3.0 Poland License
Abstract
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of easy-tounderstand basic geometric structures was shown. As a result of the analysis of these structures it was proposed to enrich the classical PCA. In particular, it was proposed a new criterion for the selection of important principal components and a new algorithm for clustering primary variables by their level of similarity to the principal components. Virtual and real data spaces, as well as tensor operations on data, have also been identified.The anisotropy of the data was identified too.
Description
Keywords
determination coefficient    geometric interpretation of PCA    selection of principal components    clustering of variables    tensor data mining    anisotropy of data
Citation
Gniazdowski, Zenon. (2017). New Interpretation of Principal Components Analysis. Zeszyty Naukowe WWSI. 11. 43-65. 10.26348/znwwsi.16.43.
URI
https://depot.ceon.pl/handle/123456789/21799
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Artykuły / Articles