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A new method to compute the principal components from self-organizing maps: an application to monsoon intraseasonal oscillations



The study develops a self-organizing map (SOM)-based local principal component analysis (PCA) to obtain the linearly decorrelated principal components (PCs) of monsoon intraseasonal oscillations (MISOs). Although the SOM-derived feature maps are not orthogonal like empirical orthogonal function (EOFs), we show that in the case of MISOs simple mathematical substitution can make the SOM-derived PCs linearly decorrelated to each other. Thus, the SOM-based local PCA is seen also to be statistically equivalent to extended EOF analysis when applied to MISO analysis. The life cycle and phase evolution of MISO through SOM-based PCA is robust and conforms to the results based on extended EOFs besides having potential to give new information. The remarkable similarity of results with the symmetric SOM configurations shows the effectiveness of these methods for use as empirical reduction models for climate patterns. The asymmetric SOM lattice configurations derive similar phase evolution as compared to a symmetric lattice, but asymmetric temporal evolutions in the PC-defined phase space. The results once again endorse the mathematical basis of PCA through SOM for geophysical applications.