Identification of Co-Clusters with Coherent Trends in Geo-Referenced Time Series

Several studies have worked on co-clustering analysis of spatio-temporal data. However, most of them search for co-clusters with similar values and are unable to identify co-clusters with coherent trends, defined as exhibiting similar tendencies in the attributes. In this study, we present the Bregman co-clustering algorithm with minimum sum-squared residue (BCC_MSSR), which uses the residue to quantify coherent trends and enables the identification of co-clusters with coherent trends in geo-referenced time series. Dutch monthly temperatures over 20 years at 28 stations were used as the case study dataset. Station-clusters, month-clusters, and co-clusters in the BCC_MSSR results were showed and compared with co-clusters of similar values. A total of 112 co-clusters with different temperature variations were identified in the Results, and 16 representative co-clusters were illustrated, and seven types of coherent temperature trends were summarized: (1) increasing; (2) decreasing; (3) first increasing and then decreasing; (4) first decreasing and then increasing; (5) first increasing, then decreasing, and finally increasing; (6) first decreasing, then increasing, and finally decreasing; and (7) first decreasing, then increasing, decreasing, and finally increasing. Comparisons with co-clusters of similar values show that BCC_MSSR explored coherent spatio-temporal patterns in regions and certain time periods. However, the selection of the suitable co-clustering methods depends on the objective of specific tasks.