Collaborative filtering recommendation algorithm based on the self-similarity matrix
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摘要: 针对推荐系统中存在的噪声问题，提出了一种基于自相似矩阵的协同过滤推荐算法.文中的自相似矩阵选取为原始矩阵，滑动窗口选取为评分值的行向量和列向量.通过建立评分值与自相似矩阵之间的线性关系，对原始评分矩阵进行预处理，得到新的评分矩阵.新评分矩阵既保留了原始矩阵的评分信息，同时也削弱了噪声数据对推荐系统的影响.实验表明，通过对原始矩阵的预处理，有效缓解了噪声数据在评分矩阵中所起的作用，提高了推荐系统的性能.Abstract: A collaborative filtering recommendation algorithm based on self-similar matrices is put forward for the noise problem in the proposed system. In this paper, self-similar matrices are selected as primitive matrices, and the sliding window is chosen as the row vector and column vector of the score. The new score matrix is obtained to preprocess the original scoring matrix to establish the linear relationship between the scoring value and the self-similar matrices. The new scoring matrix preserves the original matrix of scoring information, while weakening the impact of noise data on the recommended system. Experiments show that the pre-processing of the original matrix effectively alleviates the impact of noise in the scoring matrix and improves the performance of the proposed system.
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Key words:
- recommendation system /
- collaborative filtering /
- noise data /
- self-similarity matrix /
- pre-processing
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图 1 参数$\alpha $和$\beta $的比较($\theta=0.1^2$)
Fig. 1 Comparison of parameters $\alpha $ and $\beta $ ($\theta=0.1^2$)
图 2 参数$\alpha $和$\beta $的比较($\theta=0.2^2$)
Fig. 2 Comparison of parameters $\alpha $ and $\beta $ ($\theta=0.2^2$)
图 3 传统的方法和本文提出的方法之间的比较($\theta=0.1^2$)
Fig. 3 Comparison between traditional methods and the methods presented in this paper ($\theta=0.1^2$)
图 4 传统的方法和本文提出的方法之间的比较($\theta=0.2^2$)
Fig. 4 Comparison between traditional methods and the methods presented in this paper ($\theta=0.2^2$)
表 1 用户评分表
Tab. 1 User rating table
用户$\backslash$物品 $I_1$ $I_2$ $\cdots$ $I_n$ $U_1$ $r_{11}$ $r_{12}$ $\cdots$ $r_{1n}$ $U_2$ $r_{21}$ $r_{22}$ $\cdots$ $r_{2n}$ ${\cdots}$ ${\cdots}$ ${\cdots}$ ${\cdots}$ ${\cdots}$ $U_m$ $r_{m1}$ $r_{m2}$ $\cdots$ $r_{mn}$ 
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