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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (3): 14-26.doi: 10.6040/j.issn.1671-9352.7.2023.9950

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模糊概念集的启发式构造方法及其推荐应用

刘忠慧1(),姜帅1,闵帆1,2,*()   

  1. 1. 西南石油大学计算机科学学院，四川 成都 610500
    2. 西南石油大学人工智能研究院，四川 成都 610500
  • 收稿日期:2023-04-28 出版日期:2024-03-20 发布日期:2024-03-06
  • 通讯作者: 闵帆 E-mail:lz_hui@126.com;minfan@swpu.edu.cn
  • 作者简介:刘忠慧(1980—)，女，教授，硕士生导师，硕士，研究方向为机器学习、形式概念分析与粗糙集等. E-mail: lz_hui@126.com
  • 基金资助:
    国家自然科学基金资助项目(61976245);中央引导地方科技发展专项资助项目(2021ZYD0003)

Heuristic construction method of fuzzy concept set and its recommended application

Zhonghui LIU1(),Shuai JIANG1,Fan MIN1,2,*()   

  1. 1. School of Computer Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China
    2. Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, Sichuan, China
  • Received:2023-04-28 Online:2024-03-20 Published:2024-03-06
  • Contact: Fan MIN E-mail:lz_hui@126.com;minfan@swpu.edu.cn

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摘要：

针对模糊形式概念分析在推荐应用中难以用于大规模数据集的问题，提出了一种基于模糊概念集启发式构造的推荐方法。根据用户之间的相似度，为每个用户构建子背景，在子背景上采用新的启发式信息，分别以用户和项目为线索生成模糊概念。利用模糊概念内部信息，设计了融入用户权重的推荐置信度，实现了对用户的个性化推荐。在6个真实数据集上进行试验，本方法的推荐效率较高，与经典的协同过滤算法相比，在稀疏的数据集上能够取得更好的推荐效果。

关键词: 形式概念分析, 模糊概念, 概念构造, 推荐系统, 用户相似度

Abstract:

Aiming at the problem that fuzzy formal concept analysis is difficult to apply to large-scale datasets in recommendation applications, a recommendation method based on a heuristic construction of fuzzy concept set is proposed. Sub-contexts are constructed for each user based on the similarity between users. Then, new heuristic information is used on the sub-contexts to generate fuzzy concepts with users and items as clues, respectively. Finally, using the internal information of fuzzy concepts, a recommendation confidence integrated with user weights is designed to achieve personalized recommendations for users. The experimental results on six real datasets show that the proposed method has higher recommendation efficiency, and can achieve better recommendation results on sparse data sets compared with classical collaborative filtering algorithms.

Key words: formal concept analysis, fuzzy concept, concept construction, recommender system, user similarity

中图分类号: 

  • TP181

表1

主要符号"

符号 含义 符号 含义
U 用户集 C 概念集合
M 属性集 Hu=(Uu, Mu, Ĩu) 用户u子背景
I 二元关系 D(u1, u2) 用户相似度
K=(U, M, I) 形式背景 S(c) 模糊概念大小
Ĩ 模糊关系 wc(u1, u2) 用户权重
H=(U, M, Ĩ) 模糊形式背景 Rc(u, m) 推荐置信度
μ(*) 隶属度 Au 用户u线索集合
φ(*) 模糊集 Bm 项目m线索集合
c=(φ(A), B) 模糊概念 L 推荐矩阵

表2

形式背景"

UM
m1 m2 m3 m4 m5
u1 1 1 1 0 0
u2 1 1 1 1 1
u3 1 0 1 0 1
u4 1 1 0 1 0
u5 0 0 1 0 0

表3

模糊形式背景"

UM
m1 m2 m3 m4 m5
u1 1.0 0.2 0.6 0.0 0.0
u2 0.8 0.4 0.8 0.6 0.8
u3 0.6 0.0 0.2 0.0 0.4
u4 0.6 0.2 0.0 0.6 0.0
u5 0.0 0.0 0.6 0.0 0.0

表4

u1的子背景"

Uu1Mu1
m1 m2 m3
u1 1.0 0.2 0.6
u2 0.8 0.4 0.8
u3 0.6 0.0 0.2
u4 0.6 0.2 0.0

表5

在u1子背景下以用户为线索生成概念过程"

Au φ(Au**) Au* S(c)
{u1} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6
{u1, u2} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6
{u1, u2, u3} {(u1, 0.6), (u2, 0.8), (u3, 0.2)} {m1, m3} 0.9
{u1, u2, u3, u4} {(u1, 1.0), (u2, 0.8), (u3, 0.6), (u4, 0.6)} {m1} 0.7

表6

在u1子背景下以项目为线索生成概念过程"

Bu φ(Bu*) Bu** S(c)
{m1} {(u1, 1.0), (u2, 0.8), (u3, 0.6), (u4, 0.6)} {m1} 0.7
{m1, m2} {(u1, 0.2), (u2, 0.4), (u4, 0.2)} {m1, m2} 0.9
{m1, m2, m3} {(u1, 0.2), (u2, 0.4)} {m1, m2, m3} 0.6

表7

试验数据集"

数据集 用户数 项目数 评分数 稠密度
movielens-100k 943 1 682 100 000 0.063 0
movielens-1m 6 040 3 952 1 000 000 0.041 9
eachmovie-2ku 2 000 1 628 38 571 0.011 8
eachmovie-3ku 3 000 1 628 59 247 0.012 1
filmtrust 1 508 2 071 35 497 0.011 3
jester-s 8 000 100 577 379 0.721 7

图1

不同θ对概念生成时间与F1的影响"

图2

不同α对F1的影响"

图3

不同λ对F1的影响"

表8

RFCS与其他算法推荐效果对比"

数据集 算法 Pprecision Precall F1
movielens-100k RFCS 0.248 7 0.243 9 0.246 2
CSBR 0.192 5 0.239 3 0.213 2
kNN 0.199 4 0.344 2 0.252 5
IBCF 0.203 8 0.406 1 0.271 4
GreConD-kNN 0.199 6 0.342 4 0.252 1
NCF 0.194 6 0.335 2 0.246 1
movielens-1m RFCS 0.216 0 0.186 4 0.200 0
CSBR 0.142 1 0.204 0 0.167 6
kNN 0.188 3 0.339 0 0.242 0
IBCF 0.200 1 0.394 2 0.265 5
GreConD-kNN 0.188 5 0.338 0 0.242 1
NCF 0.139 5 0.359 3 0.200 8
eachmovie-2ku RFCS 0.223 6 0.251 8 0.236 8
CSBR 0.187 5 0.227 2 0.205 2
kNN 0.201 4 0.272 9 0.231 8
IBCF 0.148 6 0.352 0 0.208 9
GreConD-kNN 0.199 0 0.269 8 0.229 1
NCF 0.129 7 0.317 8 0.184 1
eachmovie-3ku RFCS 0.231 5 0.271 3 0.249 7
CSBR 0.203 0 0.236 2 0.218 3
kNN 0.112 3 0.276 8 0.159 6
IBCF 0.151 0 0.389 4 0.217 7
GreConD-kNN 0.104 3 0.247 8 0.146 6
NCF 0.131 9 0.363 2 0.193 4
filmtrust RFCS 0.486 2 0.477 6 0.481 4
CSBR 0.360 2 0.641 7 0.461 2
kNN 0.438 6 0.441 8 0.441 0
IBCF 0.182 6 0.532 8 0.271 7
GreConD-kNN 0.467 9 0.406 6 0.435 0
NCF 0.207 9 0.742 2 0.324 7
jester-s RFCS 0.714 8 0.846 9 0.775 3
CSBR 0.572 7 0.839 7 0.681 0
kNN 0.880 3 0.902 9 0.891 5
IBCF 0.891 0 0.851 7 0.870 9
GreConD-kNN 0.895 2 0.614 0 0.728 4
NCF 0.971 0 0.853 4 0.908 4
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