Triclustering Georeferenced Time Series for Analyzing Patterns of Intra-Annual Variability in Temperature

Clustering is often used to explore patterns in georeferenced time series (GTS). Most clustering studies, however, only analyze GTS from one or two dimension(s) and are not capable of the simultaneous analysis of the data from three dimensions: spatial, temporal, and any third (e.g., attribute) dimension. Here we develop a novel clustering algorithm called the Bregman cuboid average triclustering algorithm with I-divergence (BCAT_I), which enables the complete partitional analysis of 3D GTS. BCAT_I simultaneously groups the data along its dimensions to form regular triclusters. These triclusters are subsequently refined using k means to fully capture spatiotemporal patterns in the data. By applying BCAT_I to time series of daily average temperature in The Netherlands (twenty-eight weather stations from 1992 to 2011), we identified the refined triclusters with similar temperature values along the spatial dimension (weather stations that represent locations) and two nested temporal dimensions (year and day). Geovisualization techniques were then used to display the patterns of intra-annual variability in temperature. Our results show that in the last two thirds of the study period, there is an intense variability of spring and winter temperatures in the northeast and center of The Netherlands. For the same period, an intense variability of spring temperatures is also visible in the southeast of the country. Our results also show that summer temperatures are homogenous across the country for most of the study period. This particular application demonstrates that BCAT_I enables a complete analysis of 3D GTS and, as such, it contributes to a better understanding of complex patterns in spatiotemporal data.