Academic literature on the topic 'Nonlinear PCA (NLPCA)'

Abstract. Principal Component Analysis (PCA) is one of the popular statistical methods for feature extraction. The neural network model has been performed on the PCA to obtain nonlinear principal component analysis (NLPCA), which allows the extraction of nonlinear features in the dataset missed by the PCA. NLPCA is applied to the monthly Sea Surface Temperature (SST) data from the eastern tropical Atlantic Ocean (29° W–21° E, 25° S–7° N) for the period 1982–2005. The focus is on the differences between SST inter-annual variability patterns; either extracted through traditional PCA or the NLPCA methods.The first mode of NLPCA explains 45.5% of the total variance of SST anomaly compared to 42% explained by the first PCA. Results from previous studies that detected the Atlantic cold tongue (ACT) as the main mode are confirmed. It is observed that the maximum signal in the Gulf of Guinea (GOG) is located along coastal Angola. In agreement with composite analysis, NLPCA exhibits two types of ACT, referred to as weak and strong Atlantic cold tongues. These two events are not totally symmetrical. NLPCA thus explains the results given by both PCA and composite analysis. A particular area observed along the northern boundary between 13 and 5° W vanishes in the strong ACT case and reaches maximum extension to the west in the weak ACT case. It is also observed that the original SST data correlates well with NLPCA and PCA, but with a stronger correlation on ACT area for NLPCA and southwest in the case of PCA.

Abstract. The spatial coherence of a measured variable (e.g. temperature or pressure) is often studied to determine the regions of high variability or to find teleconnections, i.e. correlations between specific regions. While usual methods to find spatial patterns, such as Principal Components Analysis (PCA), are constrained by linear symmetries, the dependence of variables such as temperature or pressure at different locations is generally nonlinear. In particular, large deviations from the sample mean are expected to be strongly affected by such nonlinearities. Here we apply a newly developed nonlinear technique (Maxima of Cumulant Function, MCF) for detection of typical spatial patterns that largely deviate from the mean. In order to test the technique and to introduce the methodology, we focus on the El Niño/Southern Oscillation and its spatial patterns. We find nonsymmetric temperature patterns corresponding to El Niño and La Niña, and we compare the results of MCF with other techniques, such as the symmetric solutions of PCA, and the nonsymmetric solutions of Nonlinear PCA (NLPCA). We found that MCF solutions are more reliable than the NLPCA fits, and can capture mixtures of principal components. Finally, we apply Extreme Value Theory on the temporal variations extracted from our methodology. We find that the tails of the distribution of extreme temperatures during La Niña episodes is bounded, while the tail during El Niños is less likely to be bounded. This implies that the mean spatial patterns of the two phases are asymmetric, as well as the behaviour of their extremes.