Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph Laplacian regularization was proposed, which treats the prediction problem of the recommendation system as a reconstruction issue of small samples of the graph signal under the same graph model. Such a technique takes into account both known and unknown labeled samples information, thereby obtaining good prediction accuracy. However, when the data size is large, solving the reconstruction model is computationally expensive even with an approximate strategy. In this paper, we propose an equivalent reconstruction model that can be solved exactly with extremely low computational cost. Finally, a final prediction algorithm is proposed. We find in the experiments that the proposed method significantly reduces the computational cost while maintaining a good prediction accuracy.

翻译：推荐算法在推荐系统（RS）中扮演着重要角色，它根据用户的已知信息预测用户对特定项目的兴趣和偏好。近年来，一种基于图拉普拉斯正则化的推荐算法被提出，该算法将推荐系统的预测问题视为同一图模型下图信号小样本的重建问题。这种技术同时考虑了已知和未知标记样本的信息，从而获得了良好的预测准确性。然而，当数据规模较大时，即使采用近似策略，求解该重构模型的计算代价仍然很高。在本文中，我们提出一个等价的、能以极低计算代价精确求解的重构模型。最后，我们提出了一个最终的预测算法。实验发现，所提出的方法在保持良好预测准确性的同时，显著降低了计算成本。