形式概念中對象概念與屬性概念的識別算法探討

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摘要
形式概念分析(Formal Concept Analysis，F(xiàn)CA)是Wille提出的一種從形式背景進行數(shù)據(jù)分析和規(guī)則提取的強有力工具，形式概念分析建立在數(shù)學基礎之上，對組成本體的概念、屬性以及關系等用形式化的語境表述出來，然后根據(jù)語境，構造出概念格(concept lattice),即本體，從而清楚地表達出本體的結構。形式概念分析強調(diào)以人的認知為中心，提供了一種與傳統(tǒng)的、統(tǒng)計的數(shù)據(jù)分析和知識表示完全不同的方法，成為了人工智能學科的重要研究對象,在機器學習、數(shù)據(jù)挖掘、信息檢索等領域得到了廣泛的應用。
為了進一步提高數(shù)據(jù)表示的效率以及數(shù)據(jù)挖掘的效率，分別對兩類特殊概念即對象概念和屬性概念進行了研究。分析了對象概念和屬性概念與不可約元的關系。根據(jù)對象概念是上確界不可約元，上確界不可約元一定是對象概念；對偶的，屬性概念是下確界不可約元，下確界不可約元一定是屬性概念，提出相對簡便的對象概念和屬性概念的識別算法；并順帶討論了以屬性概念為遞歸終止條件的內(nèi)涵縮減的遞歸計算和屬性排序與關聯(lián)規(guī)則的提取。
本次設計采用VS2010開發(fā)平臺，C++程序設計語言，對對象概念和屬性概念的識別算法，以及對象概念和屬性概念的比較和排序行了實例測試。并測試了內(nèi)涵縮減的遞歸計算和關聯(lián)規(guī)則的提取。

關鍵詞：形式概念分析 對象概念 屬性概念 內(nèi)涵縮減 關聯(lián)規(guī)則


Summary
Formal concept analysis (Formal Concept Analysis, FCA) is a powerful tool Wille proposed by data analysis and rule extraction from formal context, formal concept analysis based on the mathematical basis, the concept of body composition, properties, and relationships out with the context of the formal presentation, and then according to the context, to construct a concept lattice (concept lattice), that body, in order to clearly express the structure of the body. Formal Concept Analysis emphasizes human cognition center, offers a traditional, statistical data analysis and knowledge representation completely different approach, the study of artificial intelligence has become an important subject in machine learning, data mining, information retrieva l and other fields has been widely used.
In order to further improve the efficiency of data representation and the efficiency of data mining, namely the concept of two special attributes that object concepts and concepts were studied. Analyzes the relationship between object concepts and attributes of the concept of irreducible element. Depending on the object concept is the supremum irreducible element, the supremum irreducible element must be the object concept; duality, property concept is infimum irreducible element, infimum irreducible element must be the property of the concept, put forward a relatively simple concepts and properties of the object recognition algorithm concept; and incidentally discussed the concept of recursive calculations to attribute meaning to recursion termination condition reduced sorting and extracting attributes associated with the rule.
In this paper, VS2010 development platform, C++ programming language, concepts and properties of the concept of object recognition algorithms, as well as the concept of object concepts and attributes to compare and sort the list instances tested. And test the extract reduced the recursive calculation connotation and association rules.

Key Words：Formal Concept Analysis Object concept Property concept
Connotation reduction Association rules


目錄
第一章 緒論 7
1.1 國內(nèi)外研究現(xiàn)狀 7
1.2 選題意義 7
1.3 課題研究內(nèi)容 8
1.3.1 主要內(nèi)容 8
1.3.2 設計過程 8
1.4 論文結構安排 9
第二章 背景與經(jīng)典概念格理論 10
2.1形式背景 10
2.2 概念格及其定理 12
2.3半序集理論和完全格 13
第三章 對象概念和屬性概念的識別 15
3.1 上下確界不可約元與子概念 15
3.2 對象概念與屬性概念 16
3.3 對象概念的識別 16
3.3.1 概念識別定理 16
3.3.2 概念格中對象概念的識別算法 16
3.3.3 對象概念的排序 24
3.4 屬性概念的識別 25
3.4.1 屬性概念的識別算法 25
3.4.2 屬性概念的識別算法的實現(xiàn) 26
3.4.3 屬性概念的排序 28
第四章 內(nèi)涵縮減的遞歸計算 30
4.1 內(nèi)涵縮減的定義 30
4.2內(nèi)涵縮減的遞歸計算公式 31
第五章 屬性排序與關聯(lián)規(guī)則的提取 37
5.1 規(guī)則的置信度 37
5.2 屬性的可比性與關聯(lián)規(guī)則 37
結論 39
致謝 40
參考文獻 41