Nonlinear Principal Component Analysis: Tropical Indo–Pacific Sea Surface Temperature and Sea Level Pressure

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Abstract
Nonlinear principal component analysis (NLPCA) is a generalization of traditional principal component analysis (PCA) that allows for the detection and characterization of low-dimensional nonlinear structure in multivariate datasets. The authors consider the application of NLPCA to two datasets: tropical Pacific sea surface temperature (SST) and tropical Indo–Pacific sea level pressure (SLP). It is found that for the SST data, the low-dimensional NLPCA approximations characterize the data better than do PCA approximations of the same dimensionality. In particular, the one-dimensional NLPCA approximation characterizes the asymmetry between spatial patterns characteristic of average El Niño and La Niña events, which the 1D PCA approximation cannot. The differences between NLPCA and PCA results are more modest for the SLP data, indicating that the lower-dimensional structures of this dataset are nearly linear. Abstract Nonlinear principal component analysis (NLPCA) is a generalization of traditional principal component analysis (PCA) that allows for the detection and characterization of low-dimensional nonlinear structure in multivariate datasets. The authors consider the application of NLPCA to two datasets: tropical Pacific sea surface temperature (SST) and tropical Indo–Pacific sea level pressure (SLP). It is found that for the SST data, the low-dimensional NLPCA approximations characterize the data better than do PCA approximations of the same dimensionality. In particular, the one-dimensional NLPCA approximation characterizes the asymmetry between spatial patterns characteristic of average El Niño and La Niña events, which the 1D PCA approximation cannot. The differences between NLPCA and PCA results are more modest for the SLP data, indicating that the lower-dimensional structures of this dataset are nearly linear.

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