# 融合社交网络用户相似度的社会化推荐Social Recommendation with Social Network Users Similarity

Abstract: In view of the low accuracy of traditional social recommendation, a social recommendation algorithm SRSUS integrating social network user similarity was proposed based on the comprehensive consideration of social network user similarity factors, such as subgraph topology, user trust and user rating similarity. The algorithm takes traditional matrix decomposition as the framework. Firstly, the graph convolutional neural network is used to learn the user’s social network to obtain the user’s potential characteristics including the topology structure and connection relations of the social network subgraph. Then social relation is used to calculate user’s social trust and score data is used to calculate the user rating similarity. Finally, user potential characteristics, user trust and user rating similarity are comprehensively used to calculate social network user similarity and then integrate it into user rating matrix decomposition. In this way, the user's rating of the predicted item can be predicted. Experimental results on Epinions, Filmtrust, Ciao and other public data sets show that this algorithm is generally superior to other social recommendation algorithms.

1. 引言

2. 相关工作

3. 社交网络用户相似度计算

3.1. 社交网络用户潜在特征计算

Figure 1. Graph convolutional neural network propagation process

${H}^{\left(l+1\right)}=f\left({H}^{\left(l\right)},A\right)=\sigma \left({\stackrel{˜}{D}}^{-\frac{1}{2}}\stackrel{˜}{A}{\stackrel{˜}{D}}^{-\frac{1}{2}}{H}^{\left(l\right)}{W}^{\left(l\right)}\right)$ (1)

$si{m}_{social}\left({U}_{i},{U}_{j}\right)=\frac{\underset{d=1}{\overset{d}{\sum }}{U}_{id}×{U}_{jd}}{\sqrt{\underset{d=1}{\overset{d}{\sum }}{\left({U}_{id}\right)}^{2}}\sqrt{\underset{d=1}{\overset{d}{\sum }}{\left({U}_{jd}\right)}^{2}}}$ (2)

${U}_{id}$${U}_{jd}$ 为用户 ${U}_{i}$${U}_{j}$ 的第d维向量值。

3.2. 社交网络用户信任度计算

$T\left(u,v\right)=\frac{{W}_{u,v}}{f\left({U}_{u},{U}_{v}\right)}$ (3)

$Trust{p}_{i}\left({u}_{i},{v}_{i}\right)=\left(T\left({u}_{i},{a}_{i1}\right)+T\left({a}_{i1},{a}_{i2}\right)+\cdots +T\left({a}_{ij},{v}_{i}\right)\right)×{\text{e}}^{-\left(d-1\right)}$ (4)

$Trust\left(u,v\right)=\frac{{\sum }_{i\in n}Trust{p}_{i}\left({u}_{i},{v}_{i}\right)}{n}$ (5)

3.3. 用户评分相似度计算

${R}_{m×n}=\left(\begin{array}{ccc}{R}_{11}& \dots & {R}_{1n}\\ ⋮& \ddots & ⋮\\ {R}_{m1}& \cdots & {R}_{mn}\end{array}\right)$

$si{m}_{score}\left({U}_{i},{U}_{j}\right)=\frac{\underset{k=1}{\overset{n}{\sum }}{R}_{ik}×{R}_{jk}}{\sqrt{\underset{k=1}{\overset{n}{\sum }}{R}_{ik}^{2}}×\sqrt{\underset{k=1}{\overset{n}{\sum }}{R}_{jk}^{2}}}$ (6)

4. 社会化推荐算法SRSUS

4.1. 算法原理

$L=\frac{1}{2}\underset{i=1}{\overset{m}{\sum }}\underset{j=1}{\overset{n}{\sum }}{I}_{ij}{\left({R}_{ij}-{U}_{i}{V}_{j}^{\text{T}}\right)}^{2}+\frac{{\lambda }_{1}}{2}{‖U‖}_{F}^{2}+\frac{{\lambda }_{2}}{2}{‖V‖}_{F}^{2}\frac{{\lambda }_{3}}{2}\underset{i=1}{\overset{m}{\sum }}\underset{{U}_{j}\in F\left(i\right)}{\sum }sim\left({U}_{i},{U}_{j}\right){‖{U}_{i}-{U}_{j}‖}^{2}$ (7)

$sim\left({U}_{i},{U}_{j}\right)=\alpha si{m}_{social}\left({U}_{i},{U}_{j}\right)+\beta Trust\left({U}_{i},{U}_{j}\right)+\gamma si{m}_{score}\left({U}_{i},{U}_{j}\right)$ (8)

$\frac{\partial L}{\partial {U}_{i}}=\underset{i=1}{\overset{m}{\sum }}{I}_{ij}\left({R}_{ij}-{U}_{i}{V}_{j}^{\text{T}}\right){V}_{j}+{\lambda }_{1}{U}_{i}+{\lambda }_{3}\underset{i=1}{\overset{m}{\sum }}{Z}_{i}×{{Z}^{\prime }}_{i}$ (9)

$\frac{\partial L}{\partial {V}_{j}}=\underset{j=1}{\overset{n}{\sum }}{I}_{ij}\left({R}_{ij}-{U}_{i}{V}_{j}^{\text{T}}\right){U}_{i}+{\lambda }_{2}{V}_{j}$ (10)

4.2. 算法步骤

5. 实验结果与分析

5.1. 数据集

Table 1. Dataset information statistics

5.2. 评价指标

$\text{MAE}=\frac{{\sum }_{\left(i,j\right)\in N}|{R}_{ij}-{r}_{ij}|}{|N|}$ (11)

$\text{RMSE}=\sqrt{\frac{{\sum }_{\left(i,j\right)\in N}|{R}_{ij}-{r}_{ij}|}{|N|}}$ (12)

5.3. 实验结果与分析

Figure 2. RMSE and MAE values in different parameter $\alpha$

Figure 3. RMSE and MAE values in different number of similar users

Table 2. Performance comparison of different algorithms

6. 总结与展望

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