一种非线性表征的概率潜在因子张量模型

doi:10.16180/j.cnki.issn1007-7820.2025.03.002

电子科技 ›› 2025, Vol. 38 ›› Issue (3): 7-15.doi: 10.16180/j.cnki.issn1007-7820.2025.03.002

一种非线性表征的概率潜在因子张量模型

董佳英¹, 宋燕²(), 李明³

1.上海理工大学理学院,上海 200093
2.上海理工大学光电信息与计算机工程学院,上海 200093
3.江苏海洋大学计算机工程学院,江苏连云港 222005

收稿日期:2023-08-28 修回日期:2023-09-11 出版日期:2025-03-15 发布日期:2025-03-11
通讯作者: 宋燕(1979-),女,E-mail:sonya@usst.edu.cn,博士,教授。研究方向:模式识别、数据分析和预测控制等。
作者简介:董佳英(1999-),女,硕士研究生。研究方向:数据挖掘。
基金资助:
国家自然科学基金(62073223);上海市自然科学基金(22ZR1443400)

A Nonlinear Representation-Based Probabilistic Latent Factorization Tensor Model

DONG Jiaying¹, SONG Yan²(), LI Ming³

1. College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China
2. School of Optical-Electrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China
3. School of Computer Engineering,Jiangsu Ocean University,Lianyungang 222005,China

Received:2023-08-28 Revised:2023-09-11 Online:2025-03-15 Published:2025-03-11
Supported by:
National Natural Science Foundation of China(62073223);Natural Science Foundation of Shanghai(22ZR1443400)

摘要/Abstract

摘要：

针对具有极度稀疏和不平衡的非负不完整数据的填补问题,文中提出了一种非线性表征的概率潜在因子张量模型。通过合理假设数据的概率分布作为先验信息,缓解了数据的稀疏性。利用非线性映射实现对数据中每一非负元素的非线性表征,提高了模型的表征能力。考虑到数据的不平衡性,对传统正则化项添加基于实例频率的权重,增加了正则化项的有效性和针对性。实验结果表明,所提模型在补全精度和时间成本方面较现有模型具有明显提升。

关键词: 非线性表征, 概率潜在因子张量模型, 实例频率, 非线性映射, 数据稀疏性, CP分解, 不平衡分布, 正则项

Abstract:

In view of the filling problem of non-negative incomplete data with extremely sparse and unbalanced data, a probabilistic potential factor tensor model is proposed. The data sparsity is mitigated by reasonably assuming the probability distribution of the data as a priori information. Nonlinear mapping is used to realize nonlinear characterization of each non-negative element in the data and improve the characterization ability of the model. Considering the unbalance of data, the weights based on instance frequency are added to the traditional regularization terms to increase the effectiveness and pertinence of regularization terms. The experimental results show that the proposed model has obvious improvement over the existing model in terms of completion accuracy and time cost.

Key words: nonlinear representation, probabilistic factorization tensor model, frequency of known entries, nonlinear mapping, data sparsity, CP decomposition, unbalanced distribution, regular term

中图分类号:

TP393

董佳英, 宋燕, 李明. 一种非线性表征的概率潜在因子张量模型[J]. 电子科技, 2025, 38(3): 7-15.

DONG Jiaying, SONG Yan, LI Ming. A Nonlinear Representation-Based Probabilistic Latent Factorization Tensor Model[J]. Electronic Science and Technology, 2025, 38(3): 7-15.

图/表 11

输入:Λ,R,η,γ₁,γ₂,γ₃

初始化:

U -

V -

T -

初始化:l=1,max_l=L
while not converge and l≤L do
1. for each Y_ijk∈Λ

Y^i j k l

∑ r = 1 R

u - r i l

)f(

v - r j l

)f(

t - r k l

)
er

r i j k l

=Y_ijk-

Y^i j k l

end for
2.根据式(10)更新

u - r i l + 1

3.根据式(11)更新

v - r j l + 1

4.根据式(12)更新

t - r k l + 1

5.l=l+1
end while
6.根据式(13)更新u_ri、v_rj、t_rk

Θ((|I|+|J|+|K|)×R)
Θ(1)
×N
×|Λ|
Θ(R)
Θ(1)

Θ(Λ_i×|I|×R)
Θ(Λ_j×|J|×R)
Θ(Λ_k×|K|×R)
Θ(1)

Θ((|I|+|J|+|K|)×R)

输出:U,V,T

表1

表2

图1

图2

图3

表3

表4

表5

表6

表7

参考文献 25

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数据集	D₁	D₂
数据类型	电影评分	电影评分
用户数	6 040	27 221
项目数	3 706	19 367
时隙数	35	230
评分数	1 000 209	4 000 053
数据密度/%	0.130 0	0.003 3
评分范围	{1.0,2.0,…,5.0}	{0.5,1.0,…,5.0}

数据集	序号	训练-测试比/%	训练数据量	测试数据量	数据密度/%
D₁	D₁_.₁ D₁_.₂ D₁_.₃	10∶90 40∶60 70∶30	100 021 400 084 700 146	900 188 600 125 300 063	0.013 0 0.051 0 0.089 0
D₂	D₂_.₁ D₂_.₂ D₂_.₃	10∶90 40∶60 70∶30	400 006 1 600 022 2 800 037	3 600 047 2 400 031 1 200 016	0.000 3 0.001 3 0.002 3

数据集	η	β	γ
D₁_.₁	1.6×10^-4	2.3	2.0×10^-6
D₁_.₂	4.0×10^-5	2.3	2.0×10^-7
D₁_.₃	1.1×10^-5	2.3	3.0×10^-7
D₂_.₁	6.0×10^-4	2.3	2.0×10^-5
D₂_.₂	1.5×10^-4	2.3	4.0×10^-6
D₂_.₃	1.0×10^-4	2.3	1.5×10^-6

序号	名称	是否考虑概率分布	是否仅定义在已知数据上	是否考虑非负	是否为张量模型
M₁	BNLFT^[13]	否	是	是	是
M₂	NNCP^[4]	否	否	是	是
M₃	WSPred^[3]	否	否	否	是
M₄	NLF^[24]	否	是	是	否
M₅	PLFT	是	是	是	是

数据集	评价指标	M₁	M₂	M₃	M₄	M₅
D₁_.₁	MAE RMSE	1.061 3 1.425 4	3.579 2 3.749 5	8.248 5 12.056 8	4.089 3 16.085 1	1.060 9 1.342 5
D_1.2	MAE RMSE	1.097 3 1.489 4	3.498 1 3.668 8	6.113 8 7.757 1	2.205 9 8.173 6	1.072 8 1.369 0
D_1.3	MAE RMSE	1.102 8 1.496 7	3.406 6 3.578 8	6.509 1 8.210 4	1.653 2 5.954 7	1.093 0 1.388 2
D_2.1	MAE RMSE	2.670 1 2.852 1	16.888 2 32.291 1	6.816 4 9.137 4	5.352 4 26.023 9	1.096 7 1.401 8
D_2.2	MAE RMSE	2.666 8 2.847 7	3.291 0 3.448 8	6.283 1 7.901 3	2.037 7 11.578 8	1.102 2 1.409 8
D_2.3	MAE RMSE	2.667 2 2.847 9	3.517 0 3.671 4	6.041 0 7.603 9	1.483 2 7.823 7	1.084 5 1.388 9

一种非线性表征的概率潜在因子张量模型

A Nonlinear Representation-Based Probabilistic Latent Factorization Tensor Model

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参考文献 25

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数据集	评价指标	M₁	M₂	M₃	M₄	M₅
D₁_.₁	总耗时/s 单次迭代耗时/s 迭代次数	156 2.771 56	926 1.852 500	5 376 10.752 500	942 1.884 500	124 3.284 38
D_1.2	总耗时/s 单次迭代耗时/s 迭代次数	623 17.800 35	3,405 6.809 500	22,775 45.550 500	3,903 7.805 500	515 13.271 39
D_1.3	总耗时/s 单次迭代耗时s 迭代次数	893 29.767 30	5 908 11.817 500	33 788 67.575 500	4,187 8.373 500	330 22.630 15
D_2.1	总耗时/s 单次迭代耗时/s 迭代次数	2 545 55.324 46	12 088 24.176 500	19 278 38.557 500	22 855 45.709 500	1 010 31.959 32
D_2.2	总耗时/s 单次迭代耗时/s 迭代次数	11 888 258.433 46	62 759 125.519 500	81 501 163.002 500	87 127 174.254 500	4 273 164.350 26
D_2.3	总耗时/s 单次迭代耗时/s 迭代次数	20 236 439.921 46	109 709 219.418 500	138 219 276.439 500	117 500 235.000 500	14 894 273.788 54