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.

中文翻译：

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关于模式设置和模式多结构

秩序和格理论为模式挖掘提供了方便的数学工具，特别是模式空间的压缩非冗余表示及其有效生成。形式概念分析 (FCA) 提供了一个称为模式结构的通用框架，以形式化多种类型的模式，例如项集、区间、图和序列集。此外，FCA 提供了通用算法来生成无冗余的所有闭合模式，唯一的条件是模式空间是一个相遇半格。这并不总是成立，例如对于顺序和图形模式。在这里，我们讨论由仅构成偏序的描述组成的模式设置。这样的框架可能过于宽泛，会导致一些问题，因此我们提出了一种新模型，称为模式多结构，介于模式设置和模式结构之间，它依赖于多晶格。最后，我们考虑一些技术，即完成，使用模式集/反链将模式设置转换为模式结构。