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

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 Nino and La Nina 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.

[1]  A. Barnston,et al.  Classification, seasonality and persistence of low-frequency atmospheric circulation patterns , 1987 .

[2]  David B. Stephenson,et al.  The “normality” of El Niño , 1999 .

[3]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[4]  Ralph J. Slutz,et al.  A Comprehensive Ocean-Atmosphere Data Set , 1987 .

[5]  Prashant D. Sardeshmukh,et al.  The Optimal Growth of Tropical Sea Surface Temperature Anomalies , 1995 .

[6]  Ferdinand Hergert,et al.  Improving model selection by nonconvergent methods , 1993, Neural Networks.

[7]  Thomas M. Smith,et al.  Reconstruction of Historical Sea Surface Temperatures Using Empirical Orthogonal Functions , 1996 .

[8]  William W. Hsieh,et al.  Applying Neural Network Models to Prediction and Data Analysis in Meteorology and Oceanography. , 1998 .

[9]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.

[10]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[11]  Bin Wang,et al.  Interdecadal changes in El Niño onset in the last four decades , 1995 .

[12]  A. Barnston.  Linear Statistical Short-Term Climate Predictive Skill in the Northern Hemisphere , 1994 .

[13]  E. C. Malthouse,et al.  Limitations of nonlinear PCA as performed with generic neural networks , 1998, IEEE Trans. Neural Networks.

[14]  Yuval.  Neural Network Training for Prediction of Climatological Time Series, Regularized by Minimization of the Generalized Cross-Validation Function , 2000 .

[15]  F. Tangang,et al.  Forecasting ENSO Events: A Neural Network–Extended EOF Approach. , 1998 .

[16]  M. Kramer.  Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[17]  S. Sengupta,et al.  Nonlinear principal component analysis of climate data , 1995 .

[18]  Min Zhong,et al.  El Niño, La Niña, and the Nonlinearity of Their Teleconnections , 1997 .

[19]  Adam H. Monahan,et al.  Nonlinear Principal Component Analysis by Neural Networks: Theory and Application to the Lorenz System , 2000 .