西安电子科技大学学报 ›› 2022, Vol. 49 ›› Issue (3): 171-182.doi: 10.19665/j.issn1001-2400.2022.03.019
收稿日期:
2021-03-08
修回日期:
2021-12-01
出版日期:
2022-06-20
发布日期:
2022-07-04
作者简介:
史加荣(1979—),男,教授,博士,E-mail: 基金资助:
Received:
2021-03-08
Revised:
2021-12-01
Online:
2022-06-20
Published:
2022-07-04
摘要:
个性化推荐在网络消费平台上发挥着越来越重要的角色。低秩和深度矩阵分解已广泛应用于推荐系统,并使推荐性能得以优化。为了克服传统矩阵分解的双线性性,深度矩阵分解基于用户和项目的特征向量,建立深度神经网络模型。现有方法在数据规模较大且稀疏性较高时,表现出性能不佳及运行时间较长。为此,提出了一种新型深度矩阵分解模型。该模型的输入为用户和项目的隐特征向量,网络结构由两个并行的多层感知机和一个用于预测的加权内积算子组成。对于所建立的模型,设计了两阶段求解方法。先利用低秩矩阵拟合算法对缺失数据进行补全,从而确定了两个隐特征矩阵。再将所构建的特征工程作为深度神经网络的输入,建立输出为预测评分的非线性映射。在公开的推荐数据集上验证了所提模型的有效性。实验结果表明:与传统矩阵分解方法相比,所提方法极大地提高了推荐性能;与现有的深度矩阵分解方法相比,运行时间得到显著降低。
中图分类号:
史加荣,李金红. 新型深度矩阵分解及其在推荐系统中的应用[J]. 西安电子科技大学学报, 2022, 49(3): 171-182.
SHI Jiarong,LI Jinhong. Novel deep matrix factorization and its application in the recommendation system[J]. Journal of Xidian University, 2022, 49(3): 171-182.
表2
不同推荐方法在ml-100k上的性能比较"
算法 | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) |
---|---|---|---|---|
MF | 1.094 4 | 0.897 2 | 1.089 5 | 0.892 3 |
PMF | 1.094 1 | 0.897 9 | 1.098 6 | 0.900 8 |
Bias-SVD | 0.959 8 | 0.769 2 | 0.964 8 | 0.772 6 |
SVD++ | 0.963 9 | 0.773 6 | 0.961 0 | 0.769 8 |
LMaFit | 0.118 7 | 0.068 7 | 2.057 6 | 1.595 5 |
MC-by-DMF | 0.266 9 | 0.169 3 | 1.590 5 | 1.202 2 |
DMF1 | 0.815 0 | 0.639 1 | 0.931 4 | 0.730 9 |
DMF2 | 0.831 3 | 0.651 3 | 0.896 6 | 0.703 1 |
LMaFit +DMF | 0.401 1 | 0.323 6 | 0.398 9 | 0.338 1 |
表6
数据集sushi下不同优化器的实验结果"
优化器 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) | Total time/s |
---|---|---|---|---|---|---|
Adadelta | 4 438.232 9 | 0.939 5 | 0.761 8 | 0.767 9 | 0.556 1 | 39.978 0 |
Adagrad | 4 259.258 8 | 0.920 3 | 0.737 8 | 0.750 8 | 0.539 3 | 38.829 1 |
Adam | 1 460.785 8 | 0.537 2 | 0.357 5 | 0.555 1 | 0.461 9 | 39.126 0 |
RMSProp | 1 455.512 5 | 0.537 3 | 0.358 6 | 0.553 5 | 0.462 1 | 39.069 3 |
表7
数据集jester下不同优化器的实验结果"
优化器 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) | Total time/s |
---|---|---|---|---|---|---|
Adadelta | 15 053.592 3 | 0.773 3 | 0.657 2 | 0.863 4 | 0.765 1 | 375.934 8 |
Adagrad | 10 762.330 1 | 0.652 9 | 0.542 9 | 0.740 8 | 0.662 4 | 383.168 1 |
Adam | 4 177.764 9 | 0.405 8 | 0.383 7 | 0.413 3 | 0.394 8 | 388.597 8 |
RMSProp | 4 151.930 7 | 0.406 0 | 0.383 8 | 0.413 5 | 0.393 1 | 389.326 0 |
表8
数据集ml-100k下不同优化器的实验结果"
优化器 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) | Total time/s |
---|---|---|---|---|---|---|
Adadelta | 533.496 5 | 0.731 5 | 0.610 4 | 0.777 5 | 0.642 5 | 9.987 5 |
Adagrad | 487.218 1 | 0.698 0 | 0.568 1 | 0.733 1 | 0.594 5 | 9.867 5 |
Adam | 39.151 1 | 0.157 2 | 0.096 4 | 0.571 6 | 0.476 0 | 9.976 2 |
RMSProp | 32.372 8 | 0.157 2 | 0.099 1 | 0.570 6 | 0.475 3 | 10.169 4 |
表9
数据集ml-1m下不同优化器的实验结果"
优化器 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) | Total time/s |
---|---|---|---|---|---|---|
Adadelta | 2 414.897 0 | 1.063 7 | 0.889 7 | 0.865 9 | 0.720 4 | 59.257 8 |
Adagrad | 1 855.704 3 | 0.926 7 | 0.733 5 | 0.735 9 | 0.582 4 | 57.587 4 |
Adam | 679.423 8 | 0.547 7 | 0.352 9 | 0.503 4 | 0.375 9 | 59.545 5 |
RMSProp | 658.356 8 | 0.548 0 | 0.356 4 | 0.499 9 | 0.376 5 | 58.288 2 |
表10
数据集sushi下不同特征维数的实验结果"
误差 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) |
---|---|---|---|---|---|
K1=30,K2=30 | 2 192.029 5 | 0.661 0 | 0.410 2 | 0.567 8 | 0.411 6 |
K1=30,K2=50 | 2 198.657 5 | 0.660 9 | 0.409 8 | 0.567 8 | 0.411 4 |
K1=30,K2=100 | 2 214.651 9 | 0.660 9 | 0.410 0 | 0.568 0 | 0.411 6 |
K1=50,K2=30 | 1 488.368 2 | 0.543 7 | 0.365 2 | 0.497 1 | 0.387 7 |
K1=50,K2=50 | 1 493.476 9 | 0.543 4 | 0.364 7 | 0.497 0 | 0.387 6 |
K1=50,K2=100 | 1 510.461 1 | 0.543 1 | 0.364 6 | 0.496 9 | 0.387 6 |
K1=80,K2=30 | 1 455.386 7 | 0.537 3 | 0.358 0 | 0.555 1 | 0.462 0 |
K1=80,K2=50 | 1 460.785 8 | 0.527 2 | 0.357 5 | 0.555 1 | 0.461 9 |
K1=80,K2=100 | 1 485.411 5 | 0.536 9 | 0.357 2 | 0.555 1 | 0.461 9 |
表11
数据集jester下不同特征维数的实验结果"
误差 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) |
---|---|---|---|---|---|
K1=30,K2=30 | 4 244.512 2 | 0.411 8 | 0.394 2 | 0.430 4 | 0.417 5 |
K1=30,K2=50 | 4 253.303 5 | 0.411 8 | 0.394 2 | 0.430 4 | 0.417 6 |
K1=30,K2=100 | 4 275.875 0 | 0.411 8 | 0.394 1 | 0.430 2 | 0.417 7 |
K1=50,K2=30 | 4 629.877 2 | 0.430 1 | 0.415 6 | 0.450 8 | 0.440 3 |
K1=50,K2=50 | 4 638.375 5 | 0.430 0 | 0.415 6 | 0.451 0 | 0.440 4 |
K1=50,K2=100 | 4 665.692 1 | 0.430 0 | 0.415 5 | 0.450 8 | 0.440 2 |
K1=80,K2=30 | 4 134.036 6 | 0.406 0 | 0.383 9 | 0.413 5 | 0.394 9 |
K1=80,K2=50 | 4 145.002 7 | 0.405 9 | 0.383 9 | 0.413 6 | 0.395 0 |
K1=80,K2=100 | 4 177.764 9 | 0.405 8 | 0.383 7 | 0.413 3 | 0.394 8 |
表12
数据集ml-100k下不同特征维数的实验结果"
误差 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) |
---|---|---|---|---|---|
K1=50,K2=30 | 43.295 0 | 0.195 4 | 0.130 6 | 0.525 5 | 0.443 8 |
K1=50,K2=50 | 47.092 1 | 0.195 3 | 0.130 5 | 0.525 5 | 0.443 8 |
K1=50,K2=100 | 60.205 8 | 0.195 3 | 0.130 5 | 0.525 5 | 0.443 8 |
K1=100,K2=30 | 36.899 4 | 0.166 8 | 0.098 5 | 0.571 6 | 0.475 9 |
K1=100,K2=50 | 39.151 1 | 0.157 2 | 0.096 4 | 0.571 8 | 0.476 0 |
K1=100,K2=100 | 55.598 8 | 0.157 2 | 0.096 4 | 0.571 7 | 0.476 0 |
K1=300,K2=30 | 27.520 6 | 0.096 6 | 0.051 5 | 0.660 8 | 0.521 1 |
K1=300,K2=50 | 38.436 9 | 0.096 4 | 0.051 4 | 0.660 9 | 0.521 2 |
K1=300,K2=100 | 74.406 8 | 0.096 4 | 0.051 3 | 0.660 8 | 0.521 2 |
表13
数据集ml-1m下不同特征维数的实验结果"
误差 | Loss | RMSE(Train) | MAE(Train) | RMSE(Test) | MAE(Test) |
---|---|---|---|---|---|
K1=100,K2=30 | 3 421.744 1 | 1.291 7 | 1.036 2 | 0.919 8 | 0.808 5 |
K1=100,K2=50 | 3 415.197 5 | 1.288 3 | 1.032 7 | 0.920 6 | 0.809 2 |
K1=100,K2=100 | 3 443.585 2 | 1.287 3 | 1.030 6 | 0.919 3 | 0.807 6 |
K1=300,K2=30 | 818.631 3 | 0.619 5 | 0.350 8 | 0.546 9 | 0.369 9 |
K1=300,K2=50 | 828.196 0 | 0.616 5 | 0.349 1 | 0.548 6 | 0.370 3 |
K1=300,K2=100 | 879.735 0 | 0.616 3 | 0.348 8 | 0.549 0 | 0.370 4 |
K1=500,K2=30 | 661.818 4 | 0.548 5 | 0.353 8 | 0.503 4 | 0.375 9 |
K1=500,K2=50 | 679.423 8 | 0.547 7 | 0.352 9 | 0.503 4 | 0.375 9 |
K1=500,K2=100 | 754.771 4 | 0.547 5 | 0.352 3 | 0.503 4 | 0.375 9 |
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