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Export Reference (APA) 
Lavado, N & Calapez, T. (2011). Principal components analysis with spline optimal transformations for continuous data. IAENG International Journal of Applied Mathematics. 41 (4), 367-375
Export Reference (IEEE) 
N. F. Lavado and M. T. Calapez,  "Principal components analysis with spline optimal transformations for continuous data", in IAENG Int. Journal of Applied Mathematics, vol. 41, no. 4, pp. 367-375, 2011
Export BibTeX 
@article{lavado2011_1769466350552,
	author = "Lavado, N and Calapez, T.",
	title = "Principal components analysis with spline optimal transformations for continuous data",
	journal = "IAENG International Journal of Applied Mathematics",
	year = "2011",
	volume = "41",
	number = "4",
	pages = "367-375",
	url = "http://www.iaeng.org/IJAM/issues_v41/issue_4/IJAM_41_4_14.pdf"
}
Export RIS 
TY  - JOUR
TI  - Principal components analysis with spline optimal transformations for continuous data
T2  - IAENG International Journal of Applied Mathematics
VL  - 41
IS  - 4
AU  - Lavado, N
AU  - Calapez, T.
PY  - 2011
SP  - 367-375
SN  - 1992-9986
UR  - http://www.iaeng.org/IJAM/issues_v41/issue_4/IJAM_41_4_14.pdf
AB  - 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.
ER  -