  Matrix Factorization (MF) is a very popular method for recommendation
systems. It assumes that the underneath rating matrix is low-rank. However,
this assumption can be too restrictive to capture complex relationships and
interactions among users and items. Recently, Local LOw-Rank Matrix
Approximation (LLORMA) has been shown to be very successful in addressing this
issue. It just assumes the rating matrix is composed of a number of low-rank
submatrices constructed from subsets of similar users and items. Although
LLORMA outperforms MF, how to construct such submatrices remains a big problem.
Motivated by the availability of rich social connections in today's
recommendation systems, we propose a novel framework, i.e., Social LOcal
low-rank Matrix Approximation (SLOMA), to address this problem. To the best of
our knowledge, SLOMA is the first work to incorporate social connections into
the local low-rank framework. Furthermore, we enhance SLOMA by applying social
regularization to submatrices factorization, denoted as SLOMA++. Therefore, the
proposed model can benefit from both social recommendation and the local
low-rank assumption. Experimental results from two real-world datasets, Yelp
and Douban, demonstrate the superiority of the proposed models over LLORMA and
MF.
