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Visualizing data with formal concept analysis

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2003
Diner, Çağrı
In this thesis, we wanted to stress the tendency to the geometry of data. This should be applicable in almost every branch of science, where data are of great importance, and also in every kind of industry, economy, medicine etc. Since machine's hard-disk capacities which is used for storing datas and the amount of data you can reach through internet is increasing day by day, there should be a need to turn this information into knowledge. This is one of the reasons for studying formal concept analysis. We wanted to point out how this application is related with algebra and logic. The beginning of the first chapter emphasis the relation between closure systems, galois connections, lattice theory as a mathematical structure and concept analysis. Then it describes the basic step in the formalization: An elementary form of the representation of data is defined mathematically. Second chapter explains the logic of formal concept analysis. It also shows how implications, which can be regard as special formulas on a set,between attributes can be shown by fewer implications, so called generating set for implications. These mathematical tools are then used in the last chapter, in order to describe complex 'concept' lattices by means of decomposition methods in examples.