气候数据分析中的非线性降维方法
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
摘要：
线性降维技术，特别是主成分分析，被广泛用于气候数据分析作为一种手段，以帮助解释高维数据集。这些线性方法可能不适合于分析气候系统中发生的非线性过程所产生的数据。近年来，非线性降维技术的发展为识别非线性动力学引起的气候数据中的低维流形提供了一个潜在的有用工具。在这篇论文中，我应用了三种这样的技术来研究热带太平洋海表温度和温跃层深度的厄尔尼诺/南方涛动变化，将观测数据与CMIP 3多模式集合的耦合大气-海洋环流模型的模拟进行比较。这里使用的三种方法是基于神经网络的非线性主成分分析（NLPCA）方法、Isomap等距映射算法和Hessian局部线性嵌入。我使用这三种方法来检查厄尔尼诺变化在不同的数据集，并评估这些非线性降维方法的气候数据分析的适用性。我的结论是，虽然，对于这里提出的应用程序，使用NLPCA，Isomap和Hessian局部线性嵌入分析不提供额外的信息以外，已经提供了主成分分析，这些方法是探索性数据分析的有效工具。
英文摘要：
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mapping algorithm, and Hessian locally linear embedding. I use these three methods to examine El Nino variability in the different data sets and assess the suitability of these nonlinear dimensionality reduction approaches for climate data analysis. I conclude that although, for the application presented here, analysis using NLPCA, Isomap and Hessian locally linear embedding does not provide additional information beyond that already provided by principal component analysis, these methods are effective tools for exploratory data analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
