3 research outputs found
Complex-valued neural networks for nonlinear complex principal component analysis
Principal component analysis (PCA) has been generalized to complex principal component analy-sis (CPCA), which has been widely applied to complex-valued data, 2-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 non-linear 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 ex-tract 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 2 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
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
Linear dimensionality reduction techniques, notably principal component
analysis, are widely used in climate data analysis as a means to aid in the
interpretation of datasets of high dimensionality. These linear methods may not
be appropriate for the analysis of data arising from nonlinear processes
occurring in the climate system. Numerous techniques for nonlinear
dimensionality reduction have been developed recently that may provide a
potentially useful tool for the identification of low-dimensional manifolds in
climate data sets arising from nonlinear dynamics. In this thesis I apply three
such techniques to the study of El Nino/Southern Oscillation variability in
tropical Pacific sea surface temperatures and thermocline depth, comparing
observational data with simulations from coupled atmosphere-ocean general
circulation models from the CMIP3 multi-model ensemble.
The three methods used here are a nonlinear principal component analysis
(NLPCA) approach based on neural networks, the Isomap isometric mapping
algorithm, and Hessian locally linear embedding. I use these three methods to
examine El Nino variability in the different data sets and assess the
suitability of these nonlinear dimensionality reduction approaches for climate
data analysis.
I conclude that although, for the application presented here, analysis using
NLPCA, Isomap and Hessian locally linear embedding does not provide additional
information beyond that already provided by principal component analysis, these
methods are effective tools for exploratory data analysis.Comment: 273 pages, 76 figures; University of Bristol Ph.D. thesis; version
with high-resolution figures available from
http://www.skybluetrades.net/thesis/ian-ross-thesis.pdf (52Mb download