Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Fully Complex Multi-Layer Perceptron Network for Nonlinear Signal Processing
Journal of VLSI Signal Processing Systems
Limitations of nonlinear PCA as performed with generic neural networks
IEEE Transactions on Neural Networks
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Quasi-objective nonlinear principal component analysis
Neural Networks
A genetic algorithm based heuristic to the multi-period fixed charge distribution problem
Applied Soft Computing
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Principal component analysis (PCA) has been generalized to complex principal component analysis (CPCA), which has been widely applied to complex-valued data, two-dimensional vector fields, and complexified real data through the Hilbert transform. Nonlinear PCA (NLPCA) can also be performed using auto-associative feed-forward neural network (NN) models, which allows the extraction of nonlinear features in the data set. This paper introduces a nonlinear complex PCA (NLCPCA) method, which allows nonlinear feature extraction and dimension reduction in complex-valued data sets. The NLCPCA uses the architecture of the NLPCA network, but with complex variables (including complex weight and bias parameters). The application of NLCPCA on test problems confirms its ability to extract nonlinear features missed by the CPCA. For similar number of model parameters, the NLCPCA captures more variance of a data set than the alternative real approach (i.e. replacing each complex variable by two real variables and applying NLPCA). The NLCPCA is also used to perform nonlinear Hilbert PCA (NLHPCA) on complexified real data. The NLHPCA applied to the tropical Pacific sea surface temperatures extracts the El Niño-Southern Oscillation signal better than the linear Hilbert PCA.