Lattice theory for machine learning

We represent theoretical foundations for similarity-based machine learning system construction. The key technique is Formal Concept Analysis, a modern branch of Lattice Theory. We introduce bitset encoding algorithms for objects described by both discrete and continuous attributes. Then we discuss Markov chain Monte Carlo method. After presentations of main steps of machine learning we provide a result on sufficient number of hypotheses to generate. We conclude with discussion of results of experimental approbation of our approach with respect to several datasets from UCI Machine Learning repository.