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Analytical space for data representation and interactive analysis
Abstract
In the article the notion of analytical space is introduced and its application to data representation and interactive analysis is studied. Analytical space is defined through membership relation among its elements where each element is characterised by its extensional and intensional. All data element properties are derived from this fundamental relation. Inference in analytical space is thought of as finding mapping from one subspace into another and is carried out through propagation of information by means of deaggregation and aggregation operations. The general goal of data analysis is defined to be simplifying the form of representation with simultaneous retaining most of the data semantics. An interactive data analysis procedure is proposed, which is based on selecting interesting subspaces in analytical space, finding mapping from this space into the range of values by means of inference and finally visualising this mapping in an appropriate form.
In the paper the concept-oriented data model (COM) is described from the point of view of its hierarchical and multidimensional properties. The model consists of two levels: syntactic and semantic. At the syntactic level each element is defined as a combination of its superconcepts. At the semantic level each item is defined as a combination of its superitems. Such a definition has several general interpretations such as a hierarchical coordinate system or multidimensional categorization schema. The described approach can be applied to very different problems for dimensional modelling including database systems, knowledge based systems, ontologies, complex categorizations, knowledge sharing and semantics web.
We present new methods for analyzing geo-referenced statistical data. These methods combine visualization and direct manipulation techniques of exploratory data analysis and algorithms for data mining. The methods have been implemented by integrating two hitherto separate software tools: Descartes for interactive thematic mapping, and the data mining toolbox Kepler. In using these tools, data analysis may proceed as a steady interaction between visual inspiration and insights gained from mathematical–statistical calculations. After introducing the various components of the methods and tools, the paper guides the reader through in-depth examples of using the tools in the context of analysis of urban demographic data. In particular, it is shown how geography-based classifications of urban districts can be related to available thematic characteristics by applying the data mining algorithms classification tree derivation, attribute weighting, and subgroup discovery.