Abstract
Given a Boolean matrix and a threshold t, a subset of the columns is frequent if there are at least t rows having a 1 entry in each corresponding position. This concept is used in the algorithmic, combinatorial approach to knowledge discovery and data mining. We consider the complexity aspects of frequent sets. An explicit family of subsets is given that requires exponentially many rows to be represented as the family of frequent sets of a matrix, with any threshold. Examples are given of families that can be represented by a small matrix with threshold t, but that require a significantly larger matrix if the threshold is less than t. We also discuss the connections of these problems to circuit complexity and the existence of efficient listing algorithms.
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Sloan, R.H., Takata, K. & Turán, G. On frequent sets of Boolean matrices. Annals of Mathematics and Artificial Intelligence 24, 193–209 (1998). https://doi.org/10.1023/A:1018905417023
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DOI: https://doi.org/10.1023/A:1018905417023