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A drawback of traditional data-mining methods is that they do not leverage prior knowledge of users. In prior work, we proposed a method that could discover unexpected patterns in data by using domain knowledge in a systematic manner. In this paper, we present new methods for discovering a minimal set of unexpected patterns by combining the two, independent concepts of minimality and unexpectedness, both of which have been well-studied in the KDD literature. We demonstrate the strengths of this approach experimentally using a case study in a marketing domain.