A recommender system (RS) is highly efficient in filtering people’s desired information from high-dimensional and sparse (HiDS) data. To date, a latent factor (LF)-based approach becomes highly popular when implementing a RS. However, current LF models mostly adopt single distance-oriented Loss like an $L_{2}$ norm-oriented one, which ignores target data’s characteristics described by other metrics like an $L_{1}$ norm-oriented one. To investigate this issue, this article proposes an $L_{1}$ -and- $L_{2}$ -norm-oriented LF ( $\text{L}^{3}\text{F}$ ) model. It adopts twofold ideas: 1) aggregating $L_{1}$ norm’s robustness and $L_{2}$ norm’s stability to form its Loss and 2) adaptively adjusting weights of $L_{1}$ and $L_{2}$ norms in its Loss. By doing so, it achieves fine aggregation effects with $L_{1}$ norm-oriented Loss ’s robustness and $L_{2}$ norm-oriented Loss ’s stability to precisely describe HiDS data with outliers. Experimental results on nine HiDS datasets generated by real systems show that an $\text{L}^{3}\text{F}$ model significantly outperforms state-of-the-art models in prediction accuracy for missing data of an HiDS dataset. Its computational efficiency is also comparable with the most efficient LF models. Hence, it has good potential for addressing HiDS data from real applications.

中文翻译：

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推荐系统的面向 L 1 和 L 2 范数的潜在因子模型


推荐系统（RS）可以高效地从高维稀疏（HiDS）数据中过滤人们想要的信息。迄今为止，基于潜在因素 (LF) 的方法在实现 RS 时变得非常流行。然而，当前的 LF 模型大多采用单一的面向距离的损失，例如 $L_{2}$ 范数导向的损失，它忽略了其他指标（例如 $L_{1}$ 范数导向的损失）描述的目标数据的特征。为了研究这个问题，本文提出了一个 $L_{1}$ -and- $L_{2}$ -范数导向的 LF ( $\text{L}^{3}\text{F}$ ) 模型。它采用双重思想：1）聚合$L_{1}$范数的鲁棒性和$L_{2}$范数的稳定性以形成其损失；2）自适应调整$L_{1}$和$L_{2}$范数的权重在它的损失中。通过这样做，它实现了良好的聚合效果，具有 $L_{1}$ 面向范数的 Loss 的鲁棒性和 $L_{2}$ 面向范数的 Loss 的稳定性，以精确描述带有异常值的 HiDS 数据。在真实系统生成的九个 HiDS 数据集上的实验结果表明，$\text{L}^{3}\text{F}$ 模型在 HiDS 数据集缺失数据的预测精度方面显着优于最先进的模型。其计算效率也可与最高效的 LF 模型相媲美。因此，它在处理实际应用中的 HiDS 数据方面具有良好的潜力。