An L₁-and-L₂-Norm-Oriented Latent Factor Model for Recommender Systems

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 L₂ norm-oriented one, which ignores target data's characteristics described by other metrics like an L₁ norm-oriented one. To investigate this issue, this article proposes an L₁-and-L₂-norm-oriented LF (L³F) model. It adopts twofold ideas: 1) aggregating L₁ norm's robustness and L₂ norm's stability to form its Loss and 2) adaptively adjusting weights of L₁ and L₂ norms in its Loss. By doing so, it achieves fine aggregation effects with L₁ norm-oriented Loss's robustness and L₂ 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 L³F 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.