Functional Data Analysis for Big Data: A Case Study on California Temperature Trends

In recent years, detailed historical records, remote sensing, genomics and medical imaging applications as well as the rise of the Internet-of-Things present novel data streams. Many of these data are instances where functions are more suitable data atoms than traditional multivariate vectors. Applied functional data analysis (FDA) presents a potentially fruitful but largely unexplored alternative analytics framework that can be incorporated directly into a general Big Data analytics suite. As an example, we present a modeling approach for the dynamics of a functional data set of climatic data. By decomposing functions via a functional principal component analysis and functional variance process analysis, a robust and informative characterization of the data can be derived; this provides insights into the relationship between the different modes of variation, their inherent variance process as well as their dependencies over time. The model is applied to historical data from the Global Historical Climatology Network in California, USA. The analysis reveals that climatic time-dependent information is jointly carried by the original processes as well as their noise/variance decomposition.