Probabilistic formal concepts in some classification tasks

The definition of formal concepts as fixed points of implication is considered. On the basis of this definition, the notion of probability formal concepts is introduced by replacing implications with special, maximally specific probability rules for which it was previously proved that fixed points for them are logically consistent. The ProbClosure algorithm for detecting probabilistic formal concepts is defined. To develop algorithms for clustering and classification, the context is considered as a sample from the general population. Generalizing the algorithm ProbClosure, algorithms for clustering ConcClosure and StatClosure are defined by introducing various energy functionals that determine the degree of non-contradiction of the rules at a fixed point. Classification algorithms are obtained by applying clustering algorithms to new data. Classification algorithms obtained are compared with the decision trees C4.5, ID3 and the classification method based on the lattice of formal concepts. The comparison was made on the data of the UCI repository. The obtained results showed comparatively high accuracy of the developed algorithms in comparison with these methods.