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- Title
Principal Components Analysis with Spline Optimal Transformations for Continuous Data.
- Authors
Lavado, Nuno; Calapez, Teresa
- 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.
- Subjects
PRINCIPAL components analysis; DATA analysis; CONTINUOUS functions; MATHEMATICAL variables; STOCHASTIC convergence; SIMULATION methods &; models; LEAST squares
- Publication
IAENG International Journal of Applied Mathematics, 2011, Vol 41, Issue 4, p367
- ISSN
1992-9978
- Publication type
Article