南京大学学报(自然科学版) ›› 2022, Vol. 58 ›› Issue (1): 135–142.doi: 10.13232/j.cnki.jnju.2022.01.013

• • 上一篇    

一种可解释性泛化矩阵分解推荐算法

吕亚兰, 徐媛媛, 张恒汝()   

  1. 西南石油大学计算机科学学院,成都,610500
  • 收稿日期:2021-08-03 出版日期:2022-01-30 发布日期:2022-02-22
  • 通讯作者: 张恒汝 E-mail:zhanghrswpu@163.com
  • 作者简介:E⁃mail:zhanghrswpu@163.com
  • 基金资助:
    国家自然科学基金(61902328);四川省科技厅应用基础研究项目(2019YJ0314);四川省青年科技创新研究团队(2019JDTD0017);浙江省海洋大数据挖掘与应用重点实验室开放课题(OBDMA202005)

An explainable generalized matrix factorization recommendation algorithm

Lü Yalan, Yuanyuan Xu, Hengru Zhang()   

  1. School of Computer Science,Southwest Petroleum University,Chengdu,610500,China
  • Received:2021-08-03 Online:2022-01-30 Published:2022-02-22
  • Contact: Hengru Zhang E-mail:zhanghrswpu@163.com

摘要:

可解释性矩阵分解解决了概率矩阵分解缺乏可解释性的问题,然而概率矩阵分解假设评分数据是服从正态分布的,这与实际场景有一定的偏差.针对该问题,提出一种可解释性泛化矩阵分解推荐算法.首先采用一种新型的变换函数使原始评分近似服从正态分布,然后通过可解释性矩阵分解获得预测评分,最后利用对应的逆变换函数将预测评分映射回原始评分区间.在三个数据集上进行实验,结果表明,与多个主流矩阵分解算法相比,提出的算法在多个评价指标上占优.

关键词: 推荐系统, 可解释性矩阵分解, 变换函数, 正态分布

Abstract:

Explainable matrix factorization solves the problem of the lack of explainability of probabilistic matrix factorization. However,this method assumes that the ratings obey the normal distribution,which is different from the real scenario. In this paper,we propose an explainable generalized matrix factorization recommendation algorithm. First,we use a novel transformation function to make the original ratings obey the normal distribution. Then,we predict ratings by explainable matrix factorization. Finally,we use the corresponding inverse transformation function to map the predicted ratings back to the original rating interval. The superiority of our method is substantiated by experiments on three datasets,as compared with state?of?the?art matrix factorization methods.

Key words: recommender system, explainable matrix factorization, transformation function, normal distribution

中图分类号: 

  • TP181

图1

EGMF算法"

表1

符号系统"

符号说明
N用户数
M项目数
R评分矩阵
RG新评分区间上的评分矩阵
PG新评分区间上的预测评分矩阵
P预测评分矩阵
rij用户i对项目j的评分
rijG新评分区间上用户i对项目j的评分
pijG新评分区间上用户i对项目j的预测评分
pij用户i对项目j的预测评分
D潜在因子数
xi用户i的特征向量
yj项目j的特征向量
X用户特征矩阵
Y项目特征矩阵
?GLT变换函数
?*GLT逆变换函数

表2

本文实验采用的数据集"

数据集用户数量项目数量评分数量
Jester1_1249831001810455
Jester1_2235001001708993
Jester1_324938100616912

表3

本文采用的评价指标"

评价指标公式
MAEMAE=1Τi,jΤpij-rij
RMSERMSE=1Τi,jΤpij-rij2
RecallRec=ηp?ηη
PrecisionPre=ηp?ηηp
F1F1=21Rec+1Pre

表4

EGMF和对比算法在Jester1_1数据集上的实验结果"

EGMF (ours)GPMFEMFPMFSVD
MAE3.02313.0626↑1.29%3.0626↑0.27%3.1261↑3.29%3.1414↑3.77%
RMSE4.04284.1115↑1.67%4.0699↑0.67%4.1182↑1.83%4.1417↑2.39%
Rec0.78210.7729↑1.19%0.7425↑5.33%0.7297↑7.18%0.7280↑7.43%
Pre0.74360.7375↑0.83%0.7576↑1.85%0.7592↓2.05%0.7590↓2.03%
F10.76240.7548↑1.01%0.7499↑1.67%0.7441↑2.46%0.7432↑2.58%

表5

EGMF和对比算法在Jester1_2数据集上的实验结果"

EGMF (ours)GPMFEMFPMFSVD
MAE3.04473.0748↑0.98%3.0683↑0.77%3.1514↑3.39%3.1629↑3.74%
RMSE4.09314.1528↑1.44%4.1005↑0.18%4.1739↑1.94%4.1841↑2.17%
Rec0.77330.7635↑1.28%0.7703↑0.39%0.7208↑7.28%0.7165↑7.93%
Pre0.73870.7372↑0.20%0.7332↑0.75%0.7185↑2.81%0.7552↓2.18%
F10.75560.7501↑0.73%0.7513↑0.57%0.7371↑2.51%0.7353↑2.76%

表6

EGMF和对比算法在Jester1_3数据集上的实验结果"

EGMF (ours)GPMFEMFPMFSVD
MAE3.38233.3985↑0.48%3.3901↑0.23%3.4973↑3.29%3.5235↑4.01%
RMSE4.45244.4705↑0.40%4.4639↑0.62%4.4753↑0.51%4.5119↑1.32%
Rec0.71700.7001↑2.41%0.7091↑1.11%0.6704↑6.95%0.6456↑11.06%
Pre0.69130.6857↑0.82%0.6881↑0.47%0.6879↑0.49%0.7306↓5.38%
F10.70390.6928↑1.60%0.6984↑0.79%0.6791↑3.65%0.6854↑2.70%

图2

不同α,β,λ对MAE和RMSE的影响"

图3

本文算法在Jester1_1上的运行时间"

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