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
$L_{2}$
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.