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UBC Theses and Dissertations

Nonlinear complex principal component analysis : applications to tropical Pacific wind velocity anomalies Rattan, Sanjay S.P.

Abstract

Principal component analysis (PCA) has been generalized to complex principal component analysis (CPCA), which has been widely applied to complex-valued data, 2-D 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 dataset. This thesis introduces a nonlinear complex PCA (NLCPCA) method, which allows nonlinear feature extraction and dimension reduction in complexvalued datasets. The NLCPCA uses the architecture of the NLPCA network, but with complex variables (including complex weight and bias parameters). Applications of NLCPCA to two test problems confirm its ability to extract nonlinear features missed by the CPCA. With complexified real data, the NLCPCA performs well as nonlinear. Hilbert PCA. The NLCPCA is also applied to the tropical Pacific wind velocity data to study the nonlinear seasonal, interannual, decadal and decadal variability of El Niño and La Niña. The nonlinear mode of NLCPCA for the analysis of data at all these frequencies is found to be explaining more variance and features simultaneously than the equivalent linear approach of CPCA with the same dimensionality. For the interannual variability the NLCPCA mode 1 is able to characterise the whole ENSO phenomenon in a single mode whereas it took CPCA to do the same with at least 2 modes. The variances explained by NLCPCA (17.4%) is certainly higher than CPCA mode 1 (15.3%). The data set with the seasonal variability is found to show a nonlinear mode that explains the full seasonal cycle. The CPCA, in contrast, has the winter/summer stationary anomaly pattterns manifested in the first mode whereas the second mode is the signal for the stationary spring/fall anomaly patterns. The interdecadal background wind velocity anomaly patterns are also found to be more pronounced in the NLCPCA output. The NLCPCA mode 1 analysis of pre- and post-interdecadal regime shift shows that the El Niño structure and amplitude have changes while there has been no significant differences in the La Niña.

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