Multi-level directed graphs for analysis of spatial data

Boris Petelin (2014) Multi-level directed graphs for analysis of spatial data. PhD thesis.

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Abstract

The dissertation provides a contribution to the field of spatial-temporal data mining, which is a response to the enormous amount of data collected in operational and research databases worldwide. The advantage of spatial-temporal data mining compared to traditional methods is the appropriate treatment of spatial and temporal attributes and consequently the ability to discover hidden information which is contained in databases. The dissertation is limited to spatial-temporal data mining in the earth sciences, or more precisely, we have developed a methodology that upgrades methods of the Lagrangian particle tracking of moving virtual water parcels in the ocean. By using classic Lagrangian analysis, we examine paths or trajectories of simulated water parcels by visual inspection or by using various statistical methods as well as other approaches (i.e. dynamic system theory, stochastic modeling etc.). In the field of oceanography, which is the primary data source for the dissertation, high-quality numerical modeling is becoming increasingly important. Based on the velocity fields in the results of such a model, we first produce a number of trajectories of virtual particles (typically around 100,000). In the next step, we subdivide the model domain into smaller areas and search for spatial-temporal association rules that enable us to obtain the probability of the transition of virtual particles from individual sea areas to neighboring ones within the specified time interval. We visualize the resulting rules in the form of multi-level directed graphs with different granulation in space and time. We can add any attributes to the edges and vertices in such graphs, which represent aggregated or statistical information, or oceanographic or other material. The resulting multi-level directed graphs are open to numerous algorithms that are used for graph mining. Our contribution is the algorithms for searching significant structures (paths and cycles) in these graphs. First we uncover simple cycles that occur in short periods of time (one month) within one graph, though more realistic paths and cycles occur over longer periods, that is, several months or even years. In the dissertation, we deal with paths and cycles that extend into periods of several months but less than one year. We deal with simulations which are too short to detect longer term processes and this results in dynamic paths. For the construction of these paths and cycles, we must take into account that the weights of graphs change over time, so the resulting paths and cycles are called dynamic. We perform hierarchical clustering of the resulting dynamic paths and cycles based on the distance between them and obtain dynamic fuzzy paths and cycles and compare them with the structures that are known from oceanographic observations provided by domain experts. The results in the dissertation show the significant similarity of obtained dynamic fuzzy paths and cycles with the observations and prior knowledge of oceanographic experts. The methodology, described in the dissertation, is a solid basis for the development of applications that upgrade the established methods used by oceanographic experts. In chapter 6 of the dissertation, we present some examples of successful applications of multi-level directed graphs. Thus, we show that the movement of water masses in the Mediterranean Sea has a seasonal nature with a period of 12 months. In addition, by using multi-level directed graphs we present long-term transient phenomena such as the circulation reversal in the Ionian Sea, which occurs approximately every 10 years. By using additional attributes (e.g. wind power) in multi-level directed graphs, we show the correlation of the probability of movements of water masses with these attributes. Finally, multi-level directed graphs are a solid basis for modeling the dispersal of biological species.

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