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Title: Principal components analysis with spline optimal transformations for continuous data
Authors: Lavado, N.
Calapez, T.
Keywords: CATPCA
Linear PCA
Nonlinear principal components analysis
Issue Date: 2011
Publisher: IAENG - International Association of Engineers
Abstract: A new approach to generalize Principal Components Analysis in order to handle nonlinear structures has been recently proposed by the authors: quasi-linear PCA (qlPCA). It includes spline transformation of the original variables and the qualifier quasi was chosen to emphasize the exclusive use of linear splines. Alternating least squares fitting of a suitable objective loss function is the mechanism for achieving spline optimal transformation and nonlinear principal components. Optimal transformations are explicitly known after convergence and allow a straightforward projection of new observations onto the nonlinear principal components space as well as reconstruction the original variables. QlPCA reports model summary in a linear PCA fashion and allows the introduction of the piecewise loadings concept. This paper provides further details on qlPCA and its properties. Results of a simulation study are also presented.
Peer reviewed: Sim
ISSN: 1992-9978
Publisher version: The definitive version is available at:
Appears in Collections:DINÂMIA'CET-RI - Artigo em revista científica internacional com arbitragem científica

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