Pattern mining started with mining itemset patterns, however many applicd problems of data mining make researchers face more complex data like numerical intervals, strings, graphs, geometric figures, etc. Like in itemset mining closed patterns proved to be very important for concise representations of association rules and other types of dependencies. An acknowledged approach to representing closed patterns was formulated in terms of Pattern Structures [3, 5], which were implemented for various description spaces, among them tupies of intervals [7], convex polygons [2], partitions [4], graphs [6], and strings [1]. Pattern structures, however, require that the description space makes a complete semilattice. Pattern setups is a generalization of pattern structures that allows for a partially ordered description space. We consider various examples of pattern structures and pattern setups arising in different applicd domains, together with approximation schemes based on kernel operators and efficient algorithms for computing closed patterns and dependencies based on them.
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