Nonlinear complex principal component analysis and its applications

Complex principal component analysis (CPCA) is a linear multivariate technique commonly applied to complex variables or 2D vector fields such as winds or currents. A new nonlinear CPCA (NLCPCA) method has been developed via complex-valued multi-layer perceptron neural networks. NLCPCA is applied to the tropical Pacific wind field to study the interannual variability. Compared to the CPCA mode 1, the NLCPCA mode 1 is found to explain more variance and reveal the asymmetry in the wind anomalies between warm (El Nino) and cool (La Nina) states. NLCPCA can also be used to nonlinearly generalize Hilbert PCA (where real data is complexified prior to performing CPCA). An example is provided from the nearshore bathymetry at Egmond, Netherlands, where sand bars propagate offshore, and unlike the CPCA mode 1, the NLCPCA mode 1 detects asymmetry between the bars and the troughs.