The Study Of A Formal Concept Calcu-lation Algorithm Based On Attribute Topology

Formal concept analysis that a math method based on philosophy thought, and con-cept computing and the representation of the formal context is one of the important re-search context and hot topics in formal concept analysis. Formal context and formal con-cept analysis play an important role in knowledge discovery, data mining, machine learn-ing, pattern recognition and information processing. This paper formulates the fundamen-tal theory of formal concept analysis and mainly studies the follow area supported by thesetheories.Firstly, this paper analyses the pre-processing of the formal context. Some redundantobjects and attributes were reduced and merged to make formal context more adaptive toconcept computing, simplify formal context and reduce the operation process. Based onthe purifying formal context, this paper processes the classification of the attributes andsubmits a representation that used the attribute topology of formal context. The attributetopology is a representation of formal context which is based on graph theory. Theattribute topology makes use of adjacent matrix and incidence matrix to store andrepresent in order to make concept visualization and be able to be used in concept calcula-tion.Secondly, this paper analysises the algorithm of concept calculation basing on theattribute topology. Based on the top attributes’ properties proposed in the previous section,this paper comes up with an algorithm that puts the top attributes as the cores to decom-pose the topology into some sub-topologies, and make simple intersection and union cal-culation based on relationships among attribute objects in sub-topologies in order to get allthe formal concepts. However, this algorithm is not only difficult to calculate, but alsolack of logic and systematicness. To avoid these disadvantages, this paper puts forwardwith an improved concept calculation algorithm based on sub-topologies. This algorithmmakes use of the graph theory to reduce calculation and avoid generating pseudo-concepts.With further researching, we discover that the process of decomposing sub-topologies alsoneeds to raise the complexity. So we come up with a new method that calculates conceptsby full path searching using original topology. This method makes the calculation of for- mal concept simplicity. We can get the concept without repetition and missing. It alsoavoids generating pseudo-concepts. The algorithm was improved.Finally, because the preprocessing of formal context changed data in original formalcontext which will be used in formal concept calculation before calculation we need torecover the original context of the corresponding concepts. We add the deleted attributeobject to corresponding concept in order to get formal concept in original formal context.This method not only combine the presentation of formal context with formal conceptcomputing, but also make the calculation process visualized,providing a new thought ofthe theory of formal concept analysis.