用数学结构分析对象间的共性与差异，助力变异性研究
Formal Concept Analysis: a Structural Framework for Variability Extraction and Analysis
- 基于属性关系构建分层概念结构，自动组织相似对象
- 通过概念格的层级关系揭示对象间的共性与变异性模式
- 适合软件工程、知识管理等需挖掘共性与差异的场景
形式概念分析（FCA）是一种数学化的知识表示与发现框架，通过对一组由属性描述的对象进行层次聚类，生成概念结构，使对象按共享属性被组织。该结构自然凸显相似对象之间的共性与变异性，通过分组和层级排列展现相似性，特别适用于变异性提取与分析。尽管FCA潜力显著，但其哪些特性可用于变异性任务及其具体应用方式并不总是清晰，部分原因在于其基础文献具有较强的数学性。本文旨在填补这一空白，梳理对变异性分析至关重要的若干FCA性质，并说明如何利用这些性质解释概念结构中蕴含的多样化变异性信息。
原文摘要 · Abstract (English)
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects are organized depending on the attributes they share. These conceptual structures naturally highlight commonalities and variabilities among similar objects by categorizing them into groups which are then arranged by similarity, making it particularly appropriate for variability extraction and analysis. Despite the potential of FCA, determining which of its properties can be leveraged for variability-related tasks (and how) is not always straightforward, partly due to the mathematical orientation of its foundational literature. This paper attempts to bridge part of this gap by gathering a selection of properties of the framework which are essential to variability analysis, and how they can be used to interpret diverse variability information within the resulting conceptual structures.
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