Social bookmark tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualisations are not formalised, but rather implicit. We present a new data mining task, the \emph{mining of all frequent tri-concepts}, together with an efficient algorithm, for discovering these implicit shared conceptualisations. Our approach extends the data mining task of discovering all closed itemsets to

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... mensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples. Abstract Social bookmark tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualisations are not formalised, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualisations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples.