Finding maximal frequent and minimal infrequent sets in partially ordered data

Relevant issues of time costs reducing in the logical analysis of data with elements from the Cartesian product of finite partially ordered sets are investigated. An original method based on solving a complex discrete problem called dualization over the product of partial orders is proposed for the problem of finding maximal frequent and minimal infrequent sets in the transaction database. The proposed method is a synthesis of two other known methods, one of which is quite obvious and the other uses the idea of an incremental enumeration of target sets and is, therefore, mainly of theoretical interest. An experimental study of the considered approaches in the case of the product of finite chains is carried out and conditions for their effectiveness are revealed. The expediency of applying asymptotically optimal dualization algorithms over the product of partial orders is shown.