3. A Granular Description of Data: A Study in Evolvable Systems

A human-centric way of data analysis, especially when dealing with data distributed in space and time, is concerned with data representation in an interpretable way where a perspective from which the data are analyzed is actively established by the user. Being motivated by this essential feature of data analysis, in the study we present a granular way of data analysis where the data and relationships therein are described through a collection of information granules defined in the spatial and temporal domain. We show that the data, expressed in a relational fashion, can be effectively described through a collection of Cartesian products of information granules forming a collection of semantically meaningful data descriptors. The design of the codebooks (vocabularies) of such information granules used to describe the data is guided through a process of information granulation and degranulation. This scheme comes with a certain performance index whose minimization becomes instrumental in the optimization of the codebooks. A description of logical relationships between elements of the codebooks used in the granular description of spatiotemporal data present in consecutive time frames is elaborated on as well.