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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 52-62.doi: 10.6040/j.issn.1671-9352.4.2022.7343

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三支概念的恢复集

陈曜琦(),徐伟华*(),蒋宗颖   

  1. 西南大学人工智能学院, 重庆 400715
  • 收稿日期:2022-08-12 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 徐伟华 E-mail:1312941662@qq.com;chxuwh@gmail.com
  • 作者简介:陈曜琦(1998—)，女，硕士研究生，研究方向为粒计算、认知计算. E-mail: 1312941662@qq.com
  • 基金资助:
    国家自然科学基金资助项目(62376229);重庆市研究生科研创新项目(CYS21133)

Recovery set of three-way concept

Yaoqi CHEN(),Weihua XU*(),Zongying JIANG   

  1. School of Artificial Intelligence, Southwest University, Chongqing 400715, China
  • Received:2022-08-12 Online:2023-12-20 Published:2023-12-19
  • Contact: Weihua XU E-mail:1312941662@qq.com;chxuwh@gmail.com

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摘要：

将三支形式概念分析这一工具引入到数据恢复领域，通过定义三支概念的恢复集和恢复度，研究三支概念间的隐藏信息，提出了一种有效的形式背景恢复算法。同时，针对三支概念恢复集问题，研究三支概念对形式背景二元关系的约束，设计了恢复集的合取范式化简(conjunctive normal form simplification，CNFS) 算法，进一步给出了恢复集的动态更新算法，以适应形式背景的不断变化。最后，使用UCI机器学习数据库中的数据集对CNFS算法进行了测试。实验结果表明，CNFS算法在形式背景恢复方面具有较高的准确性和有效性，同时也验证了不同概念对认知的重要程度是不同的。

关键词: 合取范式, 动态更新, 三支概念, 形式概念分析

Abstract:

The theory of three-way formal concept analysis is introduced into the field of data recovery in this paper. By defining the recovery set and recovery degree of three-way concept, it explores the hidden information from three-way concepts, and proposes an effective formal context recovery algorithm. Additionally, to solve the three-way concept recovery set problem, the constraints of three-way concept are considered on formal context binary relations, and a conjunctive normal form simplification algorithm is designed for the recovery set (CNFS). Furthermore, a dynamic update algorithm is provided for the recovery set to adapt to the continuous changes of the formal context. Finally, some numerical experiments on public datasets from the UCI perform the effectiveness of our proposed method. Experimental results indicate that the proposed algorithm has high accuracy and effectiveness in formal context recovery, and also verifies that different concepts have different important degrees in cognition.

Key words: conjunctive normal form, dynamic update, three-way concept, formal context analysis

中图分类号: 

  • TP181

表1

生物与水形式背景"

OB a1 a2 a3 a4 a5 a6 a7 a8 a9
o1 1 1 0 0 0 0 1 0 0
o2 1 1 0 0 0 0 1 1 0
o3 1 1 1 0 0 0 1 1 0
o4 1 0 1 0 0 0 1 1 1
o5 1 1 0 1 0 1 0 0 0
o6 1 1 1 1 0 1 0 0 0
o7 1 0 1 1 1 0 0 0 0
o8 1 0 1 1 0 1 0 0 0

图1

例4进行算法1的流程图"

图2

例5进行算法2的流程图"

表3

实验数据集描述"

编号 数据集 对象数 属性数 概念数
1 生物与水[35] 8 9 43
2 西瓜数据集3.0 [40] 14 7 878
3 Acuteinflammations [40] 120 6 48
4 Shuttle_landing_control [40] 15 16 2 752

表4

生物与水形式背景概念数与恢复度"

概念个数比例/% 概念个数 平均恢复度/% 最大恢复度/% 最小恢复度/%
5 2 32.14 47.22 19.44
10 4 56.53 77.78 37.50
15 6 73.28 93.06 50.00
20 9 90.83 100.00 70.83
30 13 96.56 100.00 87.50
50 21 99.58 100.00 94.44

表5

西瓜数据集3.0概念数与恢复度"

概念个数比例/% 概念个数 平均恢复度/% 最大恢复度/% 最小恢复度/%
5 44 98.27 100.00 95.75
10 88 99.94 100.00 99.35
15 132 99.99 100.00 99.67
20 176 100.00 100.00 100.00
30 236 100.00 100.00 100.00
50 439 100.00 100.00 100.00

表6

Acute inflammations概念数与恢复度"

概念个数比例/% 概念个数 平均恢复度/% 最大恢复度/% 最小恢复度/%
5 2 26.64 38.89 8.33
10 5 55.89 73.37 32.78
15 7 70.37 81.53 55.14
20 9 79.99 94.44 62.08
30 14 93.62 100.00 81.94
50 24 99.55 100.00 94.31

表7

Shuttle_landing_control概念数与恢复度"

概念个数比例/% 概念个数 平均恢复度/% 最大恢复度/% 最小恢复度/%
5 138 99.92 100.00 99.17
10 275 100.00 100.00 100.00
15 413 100.00 100.00 100.00
20 550 100.00 100.00 100.00
30 826 100.00 100.00 100.00
50 1 376 100.00 100.00 100.00
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