Isometric feature mapping (ISOMAP) is a nonlinear dimensionality reduction method and closely reflects the actual nonlinear distance by the view of tracing along the local linearity in the original nonlinear structure. Thus, the first leading 20 principal components (PCs) of low-dimensional space can reveal the characteristics of real structures and be utilized for clustering. In this study, a k-means algorithm was used to diagnose SST clustering based on ISOMAP. Warm and cold El Niño–Southern Oscillation events were subdivided into Central Pacific and Eastern Pacific types, and a two-dimensional cluster map was used to depict the relationship. The leading low-dimensional PCs of ISOMAP were considered as the orthogonal basis, and their trajectories demonstrated meaningful patterns that could be learned by machine learning algorithms. Predictions of SST in the Pacific Ocean were performed using support vector regression (SVR) and feedforward neural network (NN) models based on the low-dimensional PCs of ISOMAP. The forecast skills, the root-mean-square error (RMSE) and anomaly correlation coefficient (ACC), were comparable to those of current numerical models.

中文翻译：

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基于等距特征映射分析的太平洋海表温度聚类与预测

等距特征映射（ISOMAP）是一种非线性降维方法，通过沿着原始非线性结构中的局部线性追踪的观点，紧密地反映了实际的非线性距离。因此，低维空间的前20个主成分（PC）可以揭示真实结构的特征并用于聚类。本研究采用k-means算法来诊断基于ISOMAP的SST聚类。将厄尔尼诺-南方涛动暖冷事件细分为中太平洋和东太平洋类型，并采用二维聚类图来描绘其关系。ISOMAP 的领先低维 PC 被视为正交基础，它们的轨迹展示了可以通过机器学习算法学习的有意义的模式。使用基于 ISOMAP 低维 PC 的支持向量回归 (SVR) 和前馈神经网络 (NN) 模型对太平洋海表温度进行预测。预测技巧、均方根误差（RMSE）和异常相关系数（ACC）与当前数值模型相当。