Algebraic relational approach for geospatial feature correlation

In Geometry in Action: Cartography and geographic Information Systems David Eppstein [6] lists several important problems of computational geometry for cartography and GIS. This paper considers two of them: (1) matching/correlating similar features from different geospatial databases (the conflation problem), and (2) handling approximate and inconsistent data. These problems are of great practical importance for end users -defense and intelligence analysts, geologists, geographers, ecologists and others. An adequate mathematical formulation and solution of these problems is still an open question due their complexity. This paper analyzes relations between these problems and topics in computational topology and geometry. This analysis concludes that a fundamentally new mathematical approach is needed. The paper develops such new approach based on the general concept of an abstract algebraic system. Such a system can uniformly express all major algebraic constructs such as groups, fields, algebras and models. We also show the benefit of developing a fundamentally new approach -algebraic invariants for geospatial data analysis and correlation using this concept.