  Exploiting low-rank structure of the user-item rating matrix has been the
crux of many recommendation engines. However, existing recommendation engines
force raters with heterogeneous behavior profiles to map their intrinsic rating
scales to a common rating scale (e.g. 1-5). This non-linear transformation of
the rating scale shatters the low-rank structure of the rating matrix,
therefore resulting in a poor fit and consequentially, poor recommendations. In
this paper, we propose Clustered Monotone Transforms for Rating Factorization
(CMTRF), a novel approach to perform regression up to unknown monotonic
transforms over unknown population segments. Essentially, for recommendation
systems, the technique searches for monotonic transformations of the rating
scales resulting in a better fit. This is combined with an underlying matrix
factorization regression model that couples the user-wise ratings to exploit
shared low dimensional structure. The rating scale transformations can be
generated for each user, for a cluster of users, or for all the users at once,
forming the basis of three simple and efficient algorithms proposed in this
paper, all of which alternate between transformation of the rating scales and
matrix factorization regression. Despite the non-convexity, CMTRF is
theoretically shown to recover a unique solution under mild conditions.
Experimental results on two synthetic and seven real-world datasets show that
CMTRF outperforms other state-of-the-art baselines.
