# 科普篇 | 推荐系统之矩阵分解模型

《科普篇 | 推荐系统之矩阵分解模型》

《原理篇 | 推荐系统之矩阵分解模型》

《实践篇 | 推荐系统之矩阵分解模型》

1.一个具体的例子

1.1 收集数据，构造评分矩阵

1.2 分解评分矩阵

1.3 计算内积，排序，推荐

2.小结

(1)MF把用户对item的评分矩阵分解为User矩阵和Item矩阵，其中User矩阵每一行代表一个用户的向量，Item矩阵的每一列代表一个item的向量；

(2)用户对item的预测评分等于User矩阵的第行和Item矩阵的第列的内积，预测评分越大表示用户喜欢item的可能性越大；

(3)MF是把User矩阵和Item矩阵设为未知量，用它们来表示每个用户对每个item的预测评分，然后通过最小化预测评分和实际评分的差异学习出User矩阵和Item矩阵；

(4)MF是一种隐变量模型，它通过在隐类别的维度上去匹配用户和item来做推荐。

(5)MF是一种降维方法，它将用户或item的维度降低到隐类别个数的维度。

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