Grant: Discovery Grants Program - Individual

Most methods of knowledge-discovery and data mining assume parameters outside the observed data such asprior probabilities, belief functions or statistical distributions, the origin of which is not always clear or justifiable. On the other hand, there are qualitative or ""non-invasive"" methods of temporal/spatial data analysis (such as rough sets or concept lattices) that take into account only the given data without stringent additional model assumptions. Using fewer model assumptions results in more generality, wider applicability, less de-contextualization, and reduced costs and time.The main aim of my research is the investigation of the algebraic and logical aspects of qualitative reasoningmethods and to supplement such reasoning by statistical and information theoretic tools that enable it tofunction as a reliable tool of temporal/spatial data analysis. I will concentrate on a specific application area, namely, qualitative temporal und spatial reasoning with the aim to describe the behavior of perceptual systems. Using optimal Rough-Quadtrees (ORQT) as the basic representation - and multiple instances of ORQTs in time and space - it is possible to determine complex temporal/spatial features to set up an object definition ""on the fly"" assuming a few structural mechanisms only. Using this basic framework I will aim to describe invariant properties like ''objects'', ''contact'', ''approaching'' or ''time-to-contact'' in terms of a rigid logical/algebraical data model.