一种跨区域跨评分协同过滤推荐算法

于旭; 彭庆龙; 詹定佳; 杜军威; 刘金环; 林俊宇; 巩敦卫; 张子迎; 于婕

doi:10.7544/issn1000-1239.202330017

一种跨区域跨评分协同过滤推荐算法

于旭^{1, 2, 3,},
彭庆龙¹,
詹定佳¹,
杜军威¹,
刘金环¹,
林俊宇^4, ,,
巩敦卫^{1, 5},
张子迎⁶,
于婕¹

1.
青岛科技大学信息科学技术学院　山东青岛　266061
2.
中国石油大学（华东）计算机科学与技术学院　山东青岛　266580
3.
符号计算与知识工程教育部重点实验室（吉林大学）　长春　130012
4.
中国科学院信息工程研究所　北京　100093
5.
中国矿业大学信息与控制工程学院　江苏徐州　221116
6.
嘉应学院计算机学院　广东梅州　514011

基金项目: 国家自然科学基金项目（62472441，62172249，61773384，62202253）；山东省自然科学基金项目（ZR2021MF092，ZR2019MF014，ZR2021QF074）；中央高校基本科研业务费专项资金（93K172022K01）

详细信息

作者简介:
于旭: 1982年生. 博士，教授. CCF高级会员. 主要研究方向为推荐算法、迁移学习、智能软件工程

彭庆龙: 1997年生. 硕士研究生. 主要研究方向为推荐算法、迁移学习、智能软件工程

詹定佳: 1996年生. 硕士研究生. 主要研究方向为推荐算法、迁移学习、智能软件工程

杜军威: 1974年生. 博士，教授. CCF高级会员. 主要研究方向为推荐算法、迁移学习、智能软件工程

刘金环: 1990年生. 博士，硕士生导师. 主要研究方向为推荐算法、信息检索

林俊宇: 1981年生. 博士，高级工程师. CCF杰出会员. 主要研究方向为人工智能、内容安全、科技伦理

巩敦卫: 1970年生. 博士，教授. CCF杰出会员. 主要研究方向为智能优化与控制、基于搜索的软件工程

张子迎: 1973年生. 博士，副教授. 主要研究方向为模式识别、人工智能以及人工智能在网络安全中的应用

于婕: 1999年生. 硕士研究生. 主要研究方向为推荐算法、迁移学习、智能软件工程

通讯作者:
林俊宇（linjunyu@fudan.edu.cn）

中图分类号: TP391
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出版历程
- 收稿日期: 2023-04-09
- 修回日期: 2023-12-21
- 网络出版日期: 2024-05-16
- 刊出日期: 2024-11-30

A Cross-Region and Cross-Rating Collaborative Filtering Recommendation Algorithm

Yu Xu^{1, 2, 3,},
Peng Qinglong¹,
Zhan Dingjia¹,
Du Junwei¹,
Liu Jinhuan¹,
Lin Junyu^4, ,,
Gong Dunwei^{1, 5},
Zhang Ziying⁶,
Yu Jie¹

1.
College of Information Science and Technology, Qingdao University of Science and Technology, Qingdao, Shandong 266061
2.
College of Computer Science and Technology, China University of Petroleum (East China), Qingdao, Shandong 266580
3.
Key Laboratory of Symbol Computation and Knowledge Engineering (Jilin University), Ministry of Education, Changchun 130012
4.
Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093
5.
School of Information and Control Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116
6.
College of Computer Science, Jiaying University, Meizhou, Guangdong 514011

Funds: This work was supported by the National Natural Science Foundation of China (62472441, 62172249, 61773384, 62202253), the Natural Science Foundation of Shandong Province (ZR2021MF092, ZR2019MF014, ZR2021QF074), and the Fundamental Research Funds for the Central Universities (93K172022K01).

More Information

Author Bio:
Yu Xu: born in 1982. PhD, professor. Senior member of CCF. His main research interests include recommendation algorithms, transfer learning, and intelligent software engineering

Peng Qinglong: born in 1997. Master candidate. His main research interests include recommendation algorithms, transfer learning, and intelligent software engineering

Zhan Dingjia: born in 1996. Master candidate. His main research interests include recommendation algorithms, transfer learning, and intelligent software engineering

Du Junwei: born in 1974. PhD, professor. Senior member of CCF. His main research interests include recommendation algorithms, transfer learning, and intelligent software engineering

Liu Jinhuan: born in 1990. PhD, master supervisor. Her main research interests include recommendation algorithms and information retrieval

Lin Junyu: born in 1981. PhD, senior engineer. Distinguished member of CCF. His main research interests include artificial intelligence, content security, and ethics of science and technology

Gong Dunwei: born in 1970. PhD, professor. Distinguished member of CCF. His main research interests include intelligent optimization and control, and search-based software engineering

Zhang Ziying: born in 1973. PhD, associate professor. His main research interests include pattern recognition, and artificial intelligence and its application in network security

Yu Jie: born in 1999. Master candidate. Her main research interests include recommendation algorithms, transfer learning, and intelligent software engineering

摘要

摘要:
传统跨评分协同过滤范式忽视了目标域中评分密度对用户和项目隐向量精度的影响，导致评分稀疏区域评分预测不够准确. 为克服区域评分密度对评分预测的影响，基于迁移学习思想提出一种跨区域跨评分协同过滤推荐算法（cross-rating collaborative filtering recommendation algorithm，CRCRCF），相对于传统跨评分协同过滤范式，该算法不仅能有效挖掘辅助域重要知识，而且可以挖掘目标域中评分密集区域的重要知识，进一步提升目标域整体，尤其是评分稀疏区域的评分预测精度. 首先，针对用户和项目，分别进行活跃用户和非活跃用户、热门项目和非热门项目的划分. 利用图卷积矩阵补全算法提取目标域活跃用户和热门项目、辅助域中全体用户和项目的隐向量. 其次，对活跃用户和热门项目分别构建基于自教学习的深度回归网络学习目标域和辅助域中隐向量的映射关系. 然后，将映射关系泛化到全局，利用非活跃用户和非热门项目在辅助域上相对较准确的隐向量推导其目标域上的隐向量，依次实现了跨区域映射关系迁移和跨评分的隐向量信息迁移. 最后，以求得的非活跃用户和非热门项目在目标域上的隐向量为约束，提出受限图卷积矩阵补全模型，并给出相应推荐结果. 在MovieLens和Netflix数据集上的仿真实验显示CRCRCF算法较其他最先进算法具有明显优势.
- 协同过滤 /
- 跨区域跨评分推荐 /
- 图卷积矩阵补全 /
- 自教学习 /
- 深度回归网络 /
- 受限图卷积矩阵补全
Abstract:
Traditional cross-rating collaborative filtering paradigm ignores the influence of rating density in the target domain on the accuracy of user and item latent vectors, resulting in less accurate rating prediction in regions with sparse ratings. To overcome the influence of regional rating density on rating prediction, based on the thought of transfer learning, a cross-region and cross-rating collaborative filtering recommendation algorithm (CRCRCF) is proposed. Compared with the traditional cross-rating collaborative filtering paradigm, CRCRCF algorithm can effectively exploit not only the important knowledge from the auxiliary domain, but also the important knowledge from the rating-dense regions in the target domain, which can further improve the rating prediction accuracy of the whole target domain, especially the rating-sparse regions. Firstly, for users and items, active users and inactive users, popular items and unpopular items are divided respectively. Graph convolution matrix complementation algorithm is used to extract the latent vectors of active users and popular items in the target domain and all users and items in the auxiliary domain. Secondly, for users and items in rating-dense regions, deep regression models based on self-taught learning are constructed to learn the mapping relationships between latent vectors in the target domain and in the auxiliary domain, respectively. Then the mapping relationships are generalized to the whole target domain, and the relatively accurate latent vectors of inactive users and unpopular items in the auxiliary domain are used to derive their latent vectors in the target domain, which achieves the cross-region mapping relationships transfer and cross-rating latent vector information transfer successively. Finally, the restricted graph convolutional matrix completion model is proposed with the obtained latent vectors of inactive users and non-popular items in the target domain as constraints, and the corresponding recommendation results are given. The simulation experiments on MovieLens and Netflix datasets show that the CRCRCF algorithm has obvious advantages over other state-of-the-art algorithms.

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图 1 目标域用户和项目的划分

Figure 1. Division of users and items in the target domain

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图 2 CRCRCF模型结构图

Figure 2. Structure diagram of CRCRCF model

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图 3 跨区域跨评分推荐场景

Figure 3. The cross-region cross-rating recommendation scenario

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图 4 利用非活跃用户的辅助域隐向量训练SDAE模型

Figure 4. Training the SDAE model with the latent vectors of inactive users in the auxiliary domain

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图 5 训练深度回归网络

Figure 5. Training the deep regression network

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GC-MC算法不同 $k$ 和 $d$ 组合对应的MAE均值

Figure 6. Average values of MAE corresponding to different combinations of k and d for GC-MC algorithm

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用户侧栈式降噪自编码器参数 ${k_2}$ ， ${k_3}$ 不同组合对应的MAE均值

Average values of MAE corresponding to different combinations of ${k_2}$ and ${k_3}$ for SDAE parameters on user-side

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项目侧栈式降噪自编码器参数 ${k_2}$ ， ${k_3}$ 不同组合对应的MAE均值

Average values of MAE corresponding to different combinations of ${k_2}$ and ${k_3}$ for SDAE parameters on item-side

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${\mu _1}$ = ${\mu _{\text{2}}}$ = 5%时Restricted-GC-MC不同 $\lambda$ 对应的MAE均值

Average values of MAE corresponding to different $\lambda$ for Restricted-GC-MC when ${\mu _1}$ and ${\mu _{\text{2}}}$ equal to 5%

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表 1 数据集统计信息

Table 1 Statistics of the Datasets

数据集	域名	用户数	项目数	评分格式	评分个数	评分密度/%
ML10M	目标域	5 000	5 000	[0.5, 5]间隔为0.5	253 673	1.01
ML10M	辅助域	5 000	5 000	{0, 1}	2 536 729	10.15
Netflix	目标域	3 000	3 000	[1, 5]间隔为1	55 024	0.61
Netflix	辅助域	3 000	3 000	{0, 1}	574 880	6.39

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表 2 在Netflix数据集上的GC-MC最优参数取值

Table 2 Optimal Parameters Values of GC-MC for Netflix Dataset

参数	目标域				辅助域
参数	TR₉₀	TR₈₀	TR₇₀	TR₆₀	辅助域
$\rho$	0.6	0.7	0.5	0.6	0.6
$d$	45	45	45	45	80
$k$	100	500	500	300	700

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表 3 Netflix数据集不同阈值下用户侧和项目侧栈式降噪自编码器最优参数

Table 3 The Optimal Parameters of SDAE on User-Side and Item-Side with Different Thresholds for Netflix Dataset

维度	µ₁						µ₂
维度	5%	10%	15%	20%	25%	30%	5%	10%	15%	20%	25%	30%
k₂	30	35	40	45	35	45	30	35	30	45	35	50
k₃	15	20	10	25	20	25	20	20	25	20	25	15

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表 4 ML10M数据集上不同活跃度阈值和热门度阈值对应的MAE值

Table 4 Values of MAE Corresponding to Different Activity Thresholds and Popularity Thresholds for ML10M Dataset

${\mu _1}$	${\mu _2}$	MAE				MAE均值	${\mu _1}$	${\mu _2}$	MAE				MAE均值
${\mu _1}$	${\mu _2}$	TE₁₀	TE₂₀	TE₃₀	TE₄₀	MAE均值	${\mu _1}$	${\mu _2}$	TE₁₀	TE₂₀	TE₃₀	TE₄₀	MAE均值
5%	5%	0.6953	0.7011	0.7028	0.7017	0.7002	20%	5%	0.6939	0.7012	0.7045	0.7056	0.7013
5%	10%	0.6969	0.7188	0.7299	0.7443	0.7225	20%	10%	0.6971	0.7202	0.7298	0.7268	0.7185
5%	15%	0.6965	0.7001	0.7036	0.7359	0.7090	20%	15%	0.6966	0.7006	0.7038	0.7086	0.7024
5%	20%	0.6981	0.6998	0.7029	0.7333	0.7085	20%	20%	0.6993	0.6926	0.7013	0.7003	0.6984
5%	25%	0.7001	0.6995	0.7028	0.7456	0.7120	20%	25%	0.6971	0.6992	0.7001	0.7068	0.7008
5%	30%	0.6962	0.6992	0.7013	0.7061	0.7007	20%	30%	0.6912	0.6968	0.6983	0.7055	0.6980
10%	5%	0.6952	0.7006	0.7038	0.7041	0.7009	25%	5%	0.6871	0.7066	0.7026	0.7055	0.7005
10%	10%	0.6953	0.7189	0.7301	0.7512	0.7239	25%	10%	0.6898	0.7202	0.7311	0.7289	0.7175
10%	15%	0.6986	0.7022	0.7038	0.7086	0.7033	25%	15%	0.6995	0.7021	0.7039	0.7286	0.7085
10%	20%	0.7011	0.6995	0.7032	0.6998	0.7009	25%	20%	0.7028	0.7035	0.7151	0.7269	0.7121
10%	25%	0.6698	0.6735	0.6751	0.6826	0.6753	25%	25%	0.7008	0.7019	0.7177	0.7282	0.7122
10%	30%	0.6801	0.6887	0.6866	0.6978	0.6883	25%	30%	0.6987	0.7026	0.7089	0.7198	0.7075
15%	5%	0.6986	0.7033	0.7038	0.7046	0.7026	30%	5%	0.6925	0.6995	0.7249	0.7272	0.7110
15%	10%	0.6956	0.7189	0.7302	0.7669	0.7279	30%	10%	0.6991	0.7193	0.7297	0.7289	0.7193
15%	15%	0.6985	0.7012	0.6992	0.7063	0.7013	30%	15%	0.7001	0.6986	0.7031	0.7082	0.7025
15%	20%	0.6978	0.697	0.6993	0.7051	0.6998	30%	20%	0.7011	0.6956	0.7115	0.7253	0.7084
15%	25%	0.7003	0.699	0.7022	0.7101	0.7029	30%	25%	0.7026	0.7001	0.7058	0.7088	0.7043
15%	30%	0.7017	0.7008	0.7029	0.7089	0.7036	30%	30%	0.7088	0.7001	0.7056	0.7086	0.7058
注：黑体数值表示在ML10M数据集上最优阈值组合结果.

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表 5 Netflix数据集上不同活跃度阈值和热门度阈值对应的MAE值

Table 5 Values of MAE Corresponding to Different Activity Thresholds and Popularity Thresholds for Netflix Dataset

${\mu _1}$	$\mu_{2}$	MAE				MAE均值	$\mu_1$	$\mu_{2}$	MAE				MAE均值
${\mu _1}$	$\mu_{2}$	TE₁₀	TE₂₀	TE₃₀	TE₄₀	MAE均值	$\mu_1$	$\mu_{2}$	TE₁₀	TE₂₀	TE₃₀	TE₄₀	MAE均值
5%	5%	0.8343	0.8396	0.8621	0.8811	0.8543	20%	5%	0.8085	0.8101	0.8286	0.8305	0.8194
5%	10%	0.8328	0.8369	0.8699	0.8655	0.8513	20%	10%	0.8026	0.8035	0.8202	0.8245	0.8127
5%	15%	0.8288	0.8403	0.8698	0.8683	0.8518	20%	15%	0.8345	0.8315	0.8398	0.8446	0.8376
5%	20%	0.8281	0.8388	0.8679	0.8856	0.8551	20%	20%	0.8356	0.8337	0.8406	0.8419	0.8380
5%	25%	0.8372	0.8368	0.8403	0.8919	0.8516	20%	25%	0.8329	0.8353	0.8405	0.8478	0.8391
5%	30%	0.8351	0.8326	0.8788	0.8968	0.8608	20%	30%	0.8219	0.8347	0.8302	0.8418	0.8322
10%	5%	0.8301	0.8322	0.8359	0.8826	0.8452	25%	5%	0.8303	0.8329	0.8377	0.8326	0.8334
10%	10%	0.8281	0.8306	0.8399	0.887	0.8464	25%	10%	0.8326	0.8356	0.8386	0.8578	0.8412
10%	15%	0.8306	0.8329	0.8782	0.8699	0.8529	25%	15%	0.8313	0.8369	0.8403	0.8609	0.8424
10%	20%	0.8349	0.8311	0.8409	0.8618	0.8422	25%	20%	0.8301	0.8298	0.8377	0.8499	0.8369
10%	25%	0.8326	0.8345	0.8591	0.8687	0.8487	25%	25%	0.8336	0.8368	0.8402	0.8587	0.8423
10%	30%	0.8335	0.8338	0.8369	0.8651	0.8423	25%	30%	0.8324	0.8359	0.8371	0.8524	0.8395
15%	5%	0.8276	0.8352	0.8349	0.8401	0.8345	30%	5%	0.8349	0.8336	0.8382	0.8809	0.8469
15%	10%	0.8303	0.8346	0.8386	0.8343	0.8345	30%	10%	0.8321	0.8359	0.8411	0.8863	0.8489
15%	15%	0.8306	0.8329	0.8399	0.8468	0.8376	30%	15%	0.8312	0.8355	0.8401	0.8869	0.8484
15%	20%	0.8293	0.8297	0.8421	0.8295	0.8327	30%	20%	0.8311	0.8326	0.8403	0.8717	0.8439
15%	25%	0.8335	0.8329	0.8386	0.8398	0.8362	30%	25%	0.8346	0.8298	0.8387	0.8933	0.8491
15%	30%	0.8278	0.8353	0.8388	0.8601	0.8405	30%	30%	0.8367	0.8477	0.8609	0.8971	0.8606
注：黑体数值表示在Netflix数据集上最优阈值组合结果.

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表 6 ML10M数据集上不同算法的MAE和RMSE值

Table 6 MAE and RMSE Values of Different Algorithms on ML10M Dataset

算法	MAE				RMSE				p值
算法	TE₁₀	TE₂₀	TE₃₀	TE₄₀	TE₁₀	TE₂₀	TE₃₀	TE₄₀	p值
GC-MC	0.7807	0.7819	0.7913	0.7965	0.9971	0.9994	1.0098	1.0146	0.0048
CSVD	0.7101	0.7180	0.7285	0.7294	0.9110	0.9189	0.9318	0.9359	0.0039
TMF	0.7207	0.7240	0.7337	0.7387	0.9272	0.9290	0.9414	0.9475	0.0031
DLSCF-S	0.7069	0.7105	0.7181	0.7186	0.9063	0.9084	0.9178	0.9195	0.0049
EKT	0.7147	0.7174	0.7238	0.7260	0.9147	0.9182	0.9219	0.9313	0.0040
CRCRCF_sv	0.7266	0.7293	0.7382	0.7402	0.9301	0.9328	0.9459	0.9517	0.0027
CRCRCF_direct	0.7133	0.7192	0.7301	0.7299	0.9151	0.9223	0.9339	0.9377	0.0037
CRCRCF（本文）	0.6698	0.6735	0.6751	0.6826	0.8607	0.8756	0.8792	0.8863
注：黑体数值表示在ML10M数据集上最优的性能指标数据，下划线数字表示次优的性能指标数据.

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表 7 Netflix数据集上不同算法的MAE和RMSE值

Table 7 MAE and RMSE Values of Different Algorithms on Netflix Dataset

算法	MAE				RMSE				p值
算法	TE₁₀	TE₂₀	TE₃₀	TE₄₀	TE₁₀	TE₂₀	TE₃₀	TE₄₀	p值
GC-MC	0.9037	0.9108	0.9113	0.9347	1.1218	1.1362	1.1383	1.1669	0.0069
CSVD	0.8462	0.8522	0.8574	0.8656	1.0651	1.0728	1.0756	1.0885	0.0038
TMF	0.8740	0.8776	0.8825	0.9005	1.0982	1.1106	1.1177	1.1402	0.0016
DLSCF-S	0.8413	0.8451	0.8491	0.8617	1.0533	1.0626	1.0657	1.0802	0.0045
EKT	0.8438	0.8511	0.8526	0.8634	1.0587	1.0699	1.0697	1.0857	0.0041
CRCRCF_sv	0.8782	0.8815	0.8876	0.9028	1.1036	1.1219	1.1265	1.1431	0.0014
CRCRCF_direct	0.8498	0.8571	0.8599	0.8682	1.0694	1.0806	1.0812	1.0921	0.0034
CRCRCF（本文）	0.8026	0.8035	0.8202	0.8245	1.0062	1.0078	1.0239	1.0276
注：黑体数值表示在Netflix数据集上最优的性能指标数据，下划线数字表示次优的性能指标数据.

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表 8 ML10M数据集评分非密集区域上不同算法的MAE和RMSE值

Table 8 MAE and RMSE Values of Different Algorithms on Non-Rating-Dense Region of ML10M Dataset

算法	MAE				RMSE				p值
算法	TE₁₀	TE₂₀	TE₃₀	TE₄₀	TE₁₀	TE₂₀	TE₃₀	TE₄₀	p值
GC-MC	0.8198	0.8209	0.8292	0.8415	1.0391	1.0442	1.0497	1.0659	0.0021
CSVD	0.7434	0.7453	0.7572	0.7670	0.9528	0.9543	0.9682	0.9845	0.0023
TMF	0.7500	0.7612	0.7771	0.7781	0.9547	0.9774	0.9981	1.0255	0.0015
DLSCF-S	0.7355	0.7401	0.7499	0.7545	0.9379	0.9460	0.9585	0.9742	0.0030
EKT	0.7399	0.7417	0.7551	0.7623	0.9493	0.95	0.9652	0.9803	0.0026
CRCRCF_sv	0.7588	0.7695	0.7809	0.7851	0.9628	0.9856	1.0049	1.0345	0.0012
CRCRCF_direct	0.7466	0.7437	0.7601	0.7699	0.9572	0.9513	0.9721	0.9887	0.0022
CRCRCF（本文）	0.6795	0.6846	0.6852	0.6931	0.8789	0.8801	0.9025	0.9133
注：黑体数值表示在ML10M数据集评分非密集区域上最优的性能指标数据，下划线数字表示次优的性能指标数据.

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表 9 Netflix数据集评分非密集区域上不同算法的MAE和RMSE值

Table 9 MAE and RMSE Values of Different Algorithms on Non-Rating-Dense Region of Netflix Dataset

算法	MAE				RMSE				p值
算法	TE₁₀	TE₂₀	TE₃₀	TE₄₀	TE₁₀	TE₂₀	TE₃₀	TE₄₀	p值
GC-MC	0.9351	0.9457	0.9768	1.0311	1.1948	1.1976	1.3394	1.3561	0.0033
CSVD	0.8956	0.8977	0.9090	0.9153	1.1137	1.1181	1.1293	1.1364	0.0027
TMF	0.8977	0.9100	0.9245	0.9321	1.1290	1.1470	1.1477	1.1508	0.0019
DLSCF-S	0.8884	0.8946	0.9047	0.9117	1.1102	1.1165	1.1254	1.1321	0.0030
EKT	0.8894	0.8963	0.9081	0.9131	1.1120	1.1167	1.1284	1.1341	0.0029
CRCRCF_sv	0.9029	0.9201	0.9333	0.9412	1.1368	1.1608	1.1567	1.1601	0.0015
CRCRCF_direct	0.9022	0.9089	0.9205	0.9238	1.1221	1.1312	1.1421	1.1355	0.0021
CRCRCF（本文）	0.8221	0.8293	0.8380	0.8429	1.0511	1.0572	1.0629	1.0683
注：黑体数值表示在Netflix数据集评分非密集区域上最优的性能指标数据，下划线数字表示次优的性能指标数据.

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