Discrete matrix factorization (DMF) has been a promising solution to improve the inferring efficiency of matrix factorization (MF) against the rapidly growing numbers of users and items. However, DMF suffers from a serious encoding loss due to its oversimplified modeling on the original data geometry. In this article, we propose a semi-discrete matrix factorization (SDMF) model to combine the predicting efficacy of MF with the inferring efficiency of DMF. It first learns real-valued latent features by MF, and then, taking them as group-wise and point-wise smoothness, learns binary codes in the DMF framework, for preserving the geometrical structures collectively hidden in users and items, as well as aligning binary codes originated from Hamming space with their real-valued counterparts learned from vector space. Particularly, we devise a computationally efficient optimization algorithm to estimate model parameters. Extensive evaluations on three real-world datasets clearly demonstrate the superiority of our SDMF model over state-of-the-art hash-based recommendation methods.

中文翻译：

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半离散矩阵分解

离散矩阵分解 (DMF) 一直是一种很有前途的解决方案，可以提高矩阵分解 (MF) 对快速增长的用户和项目数量的推理效率。然而，DMF 由于其对原始数据几何结构的过度简化建模而遭受严重的编码损失。在本文中，我们提出了一种半离散矩阵分解（SDMF）模型，将 MF 的预测效率与 DMF 的推理效率相结合。它首先通过 MF 学习实值潜在特征，然后将它们作为分组和点的平滑度，在 DMF 框架中学习二进制代码，用于保留集体隐藏在用户和项目中的几何结构，以及对齐二进制代码源自汉明空间，其实值对应物从向量空间中学习。特别，我们设计了一种计算效率高的优化算法来估计模型参数。对三个真实世界数据集的广泛评估清楚地证明了我们的 SDMF 模型优于最先进的基于哈希的推荐方法。