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