Frequent subgraph mining in oceanographic multi-level directed graphs

We present an adaptation and application of frequent subgraph mining (FSM) in a time series of spatial multi-level directed graphs depicting probabilistic transitions of water masses between neighboring sea areas within a given time interval. The directed graphs are created from the results of the numerical model, the Mediterranean Ocean Forecasting System. We assign unique labels (geographical locations) to vertices of the multi-level directed graphs. Then, we add the edge labels as discretized values of the probabilities of transitions between vertices. This modification allows the use of the established algorithm gSpan to search for frequently directed subgraphs in the sequence of such directed graphs. Thus, we obtain both general and specific subgraphs, such as convergences, divergences, and paths of the ocean currents in the numerical model. The resulting substructures, revealed by directed subgraphs, match oceanographic structures (gyres, convergences/divergences, and paths) deduced from field observations, and can also serve as a tool for the validation of the numerical model of circulation in the sea.