Identifying Coherent Anomalies in Multi-Scale Spatio-Temporal Data using Markov Random Fields

Abstract: Many physical processes involve spatio-temporal observations, which can be studied at different spatial and temporal scales. For example, rainfall data measured daily by rain gauges can be considered at daily, monthly or annual temporal scales, and local, grid-wise, region-wise or country-wise spatial scales. In this work, we focus on detection of anomalies in such multi-scale spatio-temporal data. We consider an anomaly as an event where the measured values over a spatio-temporally extended region are significantly different from their long-term means. However we aim to avoid setting any thresholds on the measured values and spatio-temporal sizes, because not only are thresholds subjective but also the long-term mean values often vary spatially and temporally. For this purpose we use spatio-Temporal Markov Random Field, where latent states indicate anomaly type (positive anomaly, negative anomaly, no anomaly/normal). Spatio-temporal coherence is maintained through suitable edge potentials. The model is extended to multiple spatio-temporal scales to achieve our second goal: anomalies at any scale should be defined both on the data at that scale, and also on anomalies at other scales. This allows us to trace an anomaly at a coarse scale to finer scales. For example, whether rainfall in a particular year is anomalous over a region should depend not only on the total volume of rainfall over the entire region, but also on whether there were such anomalies at the grid-scale, and the monthly scale. We use this approach to study rainfall anomalies over India -extremely diverse with respect to rainfall- for the period 1901-2011, and show its benefits over existing approaches.