Neural networks have been extensively used in recommender systems. Embedding layers are not only necessary but also crucial for neural models in recommendation as a typical discrete task. In this article, we argue that the widely used l 2 regularization for normal neural layers (e.g., fully connected layers) is not ideal for embedding layers from the perspective of regularization theory in Reproducing Kernel Hilbert Space. More specifically, the l 2 regularization corresponds to the inner product and the distance in the Euclidean space where correlations between discrete objects (e.g., items) are not well captured. Inspired by this observation, we propose a graph-based regularization approach to serve as a counterpart of the l 2 regularization for embedding layers. The proposed regularization incurs almost no extra computational overhead especially when being trained with mini-batches. We also discuss its relationships to other approaches (namely, data augmentation, graph convolution, and joint learning) theoretically. We conducted extensive experiments on five publicly available datasets from various domains with two state-of-the-art recommendation models. Results show that given a kNN (k-nearest neighbor) graph constructed directly from training data without external information, the proposed approach significantly outperforms the l 2 regularization on all the datasets and achieves more notable improvements for long-tail users and items.

中文翻译：

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用于推荐的嵌入层的基于图的正则化

神经网络已广泛用于推荐系统。嵌入层不仅是必要的，而且对于推荐中的神经模型作为典型的离散任务也是至关重要的。在本文中，我们认为广泛使用的l 2从再现内核希尔伯特空间中的正则化理论的角度来看，正常神经层（例如，全连接层）的正则化对于嵌入层并不理想。更具体地说，l 2正则化对应于内积和欧几里得空间中的距离，其中离散对象（例如，项目）之间的相关性没有得到很好的捕捉。受这一观察的启发，我们提出了一种基于图的正则化方法，作为l 2嵌入层的正则化。提议的正则化几乎不会产生额外的计算开销，尤其是在使用小批量训练时。我们还在理论上讨论了它与其他方法（即数据增强、图卷积和联合学习）的关系。我们使用两个最先进的推荐模型对来自不同领域的五个公开可用的数据集进行了广泛的实验。结果表明，在没有外部信息的情况下直接从训练数据构建的 kNN（k-最近邻）图，所提出的方法显着优于l 2对所有数据集进行正则化，并为长尾用户和项目实现更显着的改进。