On pattern setups and pattern multistructures
Order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a generic framework, called pattern structures, to formalize many types of patterns, such as itemsets, intervals, graphs, and sequence sets. Moreover, FCA provides generic algorithms to generate irredundantly all closed patterns, the only condition being that the pattern space is a meet-semilattice. This does not always hold, e.g. for sequential and graph patterns. Here, we discuss pattern setups consisting of descriptions making just a partial order. Such a framework can be too broad, causing several problems, so we propose a new model, dubbed pattern multistructures, lying between pattern setups and pattern structures, which relies on multilattices. Finally, we consider some techniques, namely completions, transforming pattern setups to pattern structures using sets/antichains of patterns.