Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the location for a function's value. Gaussian processes are a generalization of the multivariate normal distribution to function space and, in this paper, they are used to shed light on coastal rainfall patterns in British Columbia (BC). Specifically, this work addressed the question over how one should carry out an exploratory cluster analysis for the BC, or any similar, coastal rainfall data. An approach is developed for clustering multiple processes observed on a comparable interval, based on how similar their underlying covariance kernel is. This approach provides interesting insights into the BC data, and these insights can be framed in terms of El Ni\~{n}o and La Ni\~{n}a; however, the result is not simply one cluster representing El Ni\~{n}o years and another for La Ni\~{n}a years. From one perspective, the results show that clustering annual rainfall can potentially be used to identify extreme weather patterns.

中文翻译：

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通过聚类高斯过程检测不列颠哥伦比亚省沿海降雨模式

功能数据分析是一种统计框架，其中假设数据遵循某种功能形式。这种分析方法通常应用于时间序列数据，其中连续或以离散间隔测量的时间用作函数值的位置。高斯过程是多元正态分布到函数空间的推广，在本文中，它们用于阐明不列颠哥伦比亚省 (BC) 的沿海降雨模式。具体而言，这项工作解决了如何对 BC 或任何类似的沿海降雨数据进行探索性聚类分析的问题。开发了一种方法来聚类在可比区间上观察到的多个过程，基于它们的底层协方差内核的相似程度。这种方法提供了对 BC 数据的有趣见解，这些见解可以用 El Ni\~{n}o 和 La Ni\~{n}a 来描述；然而，结果不仅仅是一个代表厄尔尼\~{n}年的星团和另一个代表拉尼\~{n}年的星团。从一个角度来看，结果表明聚类年降雨量可用于识别极端天气模式。