Please use this identifier to cite or link to this item:
http://hdl.handle.net/10071/10076
Author(s): | Lavado, N. Calapez, T. |
Date: | 2011 |
Title: | Principal components analysis with spline optimal transformations for continuous data |
Volume: | 41 |
Number: | 4 |
Pages: | 367-375 |
ISSN: | 1992-9978 |
Keywords: | CATPCA Linear PCA Nonlinear principal components analysis qLPCA |
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. |
Peerreviewed: | Sim |
Access type: | Embargoed Access |
Appears in Collections: | DINÂMIA'CET-RI - Artigos em revistas internacionais com arbitragem científica |
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