Validation of nonlinear PCA

Details Validation of nonlinear PCA Validation of nonlinear PCA

2012-04-03

arxiv.org/abs/1204.0684v1

Neural Processing Letters, 2012

Computer Science

Learning

12 pages, 5 figures

Scientific paper

10.1007/s11063-012-9220-6

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.

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