摘要:协同过滤推荐算法中的矩阵分解因其简单、易于实现，得到了广泛的应用.但是矩阵分解通过简单的线性内积建模用户和物品之间的非线性交互关系，限制了模型的表达能力.为此，He等人提出了广义矩阵分解模型，通过非线性激活函数和连接权重，将矩阵分解推广到广义矩阵分解，为模型赋予建模用户和物品间的二阶非线性交互关系的能力.但是广义矩阵分解模型是一个浅层模型，并不能很好地建模用户和物品间高阶交互关系，一定程度上可能会影响模型性能.受广义矩阵分解模型启发，提出了深度矩阵分解模型（deep matrix factorization，简称DMF），在广义矩阵分解模型的基础上引入隐藏层，利用深层神经网络来学习用户和物品间高阶交互关系.深度矩阵分解模型不仅解决了简单内积的线性问题，同时还能够建模用户和物品间的高阶交互，具有很好的表达能力.此外，在MovieLens和Anime两个数据集上进行了大量丰富的对比实验，验证了模型的可行性和有效性；同时，通过实验确定了模型的最优参数.



Abstract:Matrix factorization in collaborative filtering recommendation algorithms is widely used because of its simplicity and facility of implementation, but matrix factorization utilizes a simple linear inner product to model the non-linear interaction between the user and the item, which limits the model's expressive power. He et al. proposed a generalized matrix factorization model, which extended the matrix factorization to the generalized matrix factorization through a non-linear activation function and connection weights, and gave the model the ability to model second-order non-linear interactions between users and items. Nevertheless, the generalized matrix factorization model is a shallow model and does not model the high-order interaction between users and items, which may affect the performance of the model to a certain extent. Inspired by the generalized matrix factorization model, this study proposes a deep matrix factorization model, abbreviated as DMF. Based on the generalized matrix factorization model, a hidden layer is introduced, and a deep neural network is used to learn the higher-order interaction between users and items. The deep matrix factorization model, which has a good expression ability, not only solves the linear problem of simple inner product, but also models high-order interactions between users and items. In addition, a lot of rich comparative experiments are performed on two datasets, MovieLens and Anime, and the results confirm its feasibility and effectiveness. Meanwhile the optimal parameters of the model were determined through experiments.



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