Theoretical backgrounds of Boolean reasoning-based binary n-clustering

摘要

Biclustering is a two-dimensional data analysis technique, where submatrices of a given data matrix are looked for. Its extension into three-dimensional data is called triclustering. In the paper, a new generalized look into n-dimensional binary data n-clustering is presented. The searching is performed in terms of the Boolean reasoning paradigm, where the original case (the data) is coded into the Boolean formula and its prime implicants are equivalent to the solutions of the original issue. The correctness (finding n-clusters containing only 0s or 1s) and maximality (the n-cluster cannot be expanded in any dimension without the correctness requirement violation) of such an approach have strong mathematical foundations. The paper also shows the application of Boolean reasoning-based n-clustering for small three- and four-dimensional artificial data as well as for some biomedical ones.