# On Pattern Setups and Pattern Multistructures

## TL;DR

This paper introduces the concept of pattern multistructures based on multilattices, expanding the formal framework for pattern mining beyond traditional pattern structures, and discusses techniques for transforming pattern setups into pattern structures.

## Contribution

It proposes a new model called pattern multistructure that bridges the gap between pattern setups and pattern structures, addressing limitations in existing FCA-based pattern generation.

## Key findings

- Pattern multistructures rely on multilattices for broader pattern representation.
- Techniques for transforming pattern setups into pattern structures are discussed.
- The framework extends FCA applicability to sequential and graph patterns.

## Abstract

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.