Key words: Hierarchical Reasoning, Multidimensional Model, Spatiotemporal Analysis
Geographic phenomena often exhibit different characteristics depending on the scale of the observations. Hierarchical reasoning enables the understanding of scale and categorization effects in data analysis. This research focuses on the computational support that is required for reasoning about data at various levels and at multiple dimensions. The model proposed within this framework enables researchers to obtain insights into information in data repositories by enabling access to a wide range of views of the data along dimensions relevant to the application domain. The framework is characterized by its focus on the multidimensional data cube as the logical model for spatiotemporal analysis. This logical data structure supports functionality that is crucial to exploratory analysis such as calculations and modelling across dimensions, through hierarchies, over temporal intervals and derivation of relevant subsets of the data. Data subsets are extracted by flexible operations for 'slicing' and 'dicing' through the multidimensional cube; 'roll-up' and 'drill-down' enable aggregation at required levels of consolidation; and 'pivoting' to view the data from different perspectives. The research challenges inherent in the analysis of spatiotemporal data have also been recognized in other application domains such as scientific and statistical databases where similar requirements arise for advanced classification structures, dynamic hierarchies, and the need for dimension reduction of data through high level abstractions.
Hierarchy theory has been proposed as a means for dealing with complex systems. It has also been noted that hierarchies, especially nested hierarchies, occur frequently in nature and most such systems display common, generic behaviour. Ecologists and geographic scientists have become interested in the problems associated with scale in spatiotemporal information. In this context, questions that arise relate to whether spatial analysis and aggregation are scale dependent or not, and the design of appropriate representational and computational models to enable reasoning about the effects of changes in scale. In ecological modelling and analysis, a related problem is concerned with how the wealth of small-scale observational data sets can be used to reason about large-scale, long-term phenomena. Frequently, a natural hierarchy exists when dealing with geographic phenomena and related processes. For example, in the oceanographic domain, different temporal scales apply - hourly, daily, seasonal, and long-term - when considering hydrographic processes that may be related to wind speed, tidal effects, seasonal temperature changes, and changes in the polar ice caps, respectively. Each phenomenon has is own characteristic space-time scale and computational support for dealing with the space-time hierarchy needs to be provided.
The theme of the research described involves the design of a generic computational framework to facilitate hierarchical reasoning. There are many ways of tackling this problem; the approach adopted is informed by developments in on-line analytical processing (OLAP) and scientific and statistical database (SSDM) systems, specifically in the area of multidimensional consolidation and aggregation. It consists of a representational technique and tools that enable properties of data categorization and scale-oriented processes to be quantified. The proposed hierarchical cube structure is an extension of the cube operator that has now been included in the latest version of the standard database query language SQL1999. By incorporating dimension hierarchies, the hierarchical cube enables subaggregates or partitioned aggregation to be realized and indirectly provides more efficient support for exploring summary values at different abstraction levels. The paper will illustrate the model with examples using space-time referenced data sets.