Incorporating Bayesian inference with random walk for friend recommendations
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摘要: 随机游走是一种应对推荐应用中用户规模庞大、数据稀疏等问题的有效方法.鉴于社交网络用户间亲密度差异、反向社交影响力等因素对基于随机游走的推荐具有积极影响，提出了一种引入频繁项挖掘来计算用户社交亲密度，进而优化转移概率矩阵，并与局部反向游走相结合的随机游走改进模型.此外，为了有效利用用户属性信息，提出了一种用户潜在好友关系推断的贝叶斯推理模型，并与随机游走改进模型协同应用，进一步提升了好友推荐性能.真实数据集上的对比实验验证了提出算法的有效性.Abstract: Random walk is an effective strategy for dealing with a large user base as well as data sparsity in recommendation problems. However, the current work on recommendation problems do not take full account of the impact implied by both the intimacy difference between users and the reverse social influence. This paper presents an optimized friend recommendation model based on random walk, which introduces frequent pattern mining to capture user intimacy and to optimize the transition probability matrix, and is combined with local reverse search to implement recommendations. In order to make full use of users' attribute information, a Bayesian inference model is proposed for analyzing users' potential friend relationships and combined with random walk to provide better recommendation services. Experiments on real datasets demonstrated the effectiveness of the proposed method.
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Key words:
- friend recommendations /
- random walk /
- Bayesian inference
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图 1 社交网络图与用户关系推理贝叶斯网络
Fig. 1 User network with attributes and friendship inference Bayesian network
$\textbf{算法1}$ 融合贝叶斯推理和随机游走的好友推荐算法(BN-IRRWR). $\textbf{输入:}$ 社交网络数据集$D$; 目标节点$i$; 前向搜索长度$q$; 反向搜索最大/最小长度$l_{\max}/l_{\min}$; 推荐列表长度$k$; 用户属性集合$A=\{a_1, a_2, \cdots, a_n\}$ $\textbf{输出:}$ $k$个推荐用户集合$L_k$ 1: 对$D$进行扫描, 找到频繁的用户项, 建立FP-tree结构; 2: 对FP-tree中的每一个节点, 构建条件FP-tree, 并基于公式(3)计算置信度$c(m, n)$; 3: 将$c(m, n)$与社交网络图$G(V, E)$的对应边关联, 基于公式(4)构建转移概率矩阵$P$; 4: $\textbf{for}$ $t$ from 1 to $q$ $\textbf{do}$ 5: $x_i^{(t)}=\alpha x_i^{(t-1)}\cdot P'+(1-\alpha)x_i^{(0)}$; 6: $\textbf{end for}$ 7: $x_i^\text {Reverse}=\{0\}$; 8: $\textbf{for}$ $l$ from $l_{\min}$ to $l_{\max}$ $\textbf{do}$ 9: $x_i^\text {Reverse}=x_i^\text {Reverse}+x_{i, l}^\text {Reverse}$, 10: $\textbf{end for}$ 11: $x_i^\text {Reverse}=x_i^\text {Reverse}/(l_{\max}-l_{\min}+1)$; 12: 根据数据集$D$和属性集合$A$构建贝叶斯网络BN$_D$; 13: $\textbf{for}$ each $j\in V$, $j\neq i$ $\textbf{do}$ 14: 在BN$_D$中计算$p_{f(i, j)}$; 15: Rec$_i(j)=\delta \beta x_i(j)+\delta(1-\beta)x_i^\text {Revese}(j)+(1-\delta)p_{f|A}(i, j)$; 16: $\textbf{end for}$ 17: 从Rec$_i$中移除与$i$有直接连接的节点; 18: 将Rec$_i$中节点按照其值进行降序排序, 将前$k$个节点对应的用户加入到$L_k$中; 19: $\textbf{return}$ $L_k$; 
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