2019/06/07 by Aimene Belfodil, Belfodil, Aimene, Sergei O. Kuznetsov +5
Computer Science · #Advanced Algebra and Logic #Data Mining Algorithms and Applications #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Rough Sets and Fuzzy Logic #cs.DM
paper · pdf · doi:10.48550/arxiv.1906.02963
arxiv created 2019/06/07 · openalex publication_date 2019/06/07 · arxiv updated 2019/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modern 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, graph 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 multistructure, 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.