Condensed Representations of Association Rules in n-Ary Relations

The problem of association rules mining has given rise to a rich literature, especially in classic binary bidimensional data. In particular, the representation of the set of rules without loss of information is well understood. This is not the case in multidimensional binary data. This paper shows that the knowledge of
$n-1$
components of every closed
$n$
-sets of a multidimensional Boolean tensor, as well as the cardinality of the remaining dimension, is enough to allow for the derivation of the confidence of every multidimensional association rule. This generalises well-known results in the bidimensional case. This paper provides experimental comparisons between the numbers of closed
$n$
-sets and frequent associations.