Heterogeneous Learning of Functional Clustering Regression and Application to Chinese Air Pollution Data

Clustering algorithms are widely used to mine the heterogeneity between meteorological observations. However, traditional applications suffer from information loss due to data processing and pay little attention to the interaction between meteorological indicators. In this paper, we combine the ideas of functional data analysis and clustering regression, and propose a functional clustering regression heterogeneity learning model (FCR-HL), which respects the data generation process of meteorological data while incorporating the interaction between meteorological indicators into the analysis of meteorological data heterogeneity. In addition, we provide an algorithm for FCR-HL to automatically select the number of clusters, which has good statistical properties. In the later empirical study based on PM_2.5 concentrations and PM₁₀ concentrations in China, we found that the interaction between PM₁₀ and PM_2.5 varies significantly between regions, showing several types of significant patterns, which provide meteorologists with new perspectives to further study the effects between meteorological indicators.