  Context-aware recommendation algorithms focus on refining recommendations by
considering additional information, available to the system. This topic has
gained a lot of attention recently. Among others, several factorization methods
were proposed to solve the problem, although most of them assume explicit
feedback which strongly limits their real-world applicability. While these
algorithms apply various loss functions and optimization strategies, the
preference modeling under context is less explored due to the lack of tools
allowing for easy experimentation with various models. As context dimensions
are introduced beyond users and items, the space of possible preference models
and the importance of proper modeling largely increases.
  In this paper we propose a General Factorization Framework (GFF), a single
flexible algorithm that takes the preference model as an input and computes
latent feature matrices for the input dimensions. GFF allows us to easily
experiment with various linear models on any context-aware recommendation task,
be it explicit or implicit feedback based. The scaling properties makes it
usable under real life circumstances as well.
  We demonstrate the framework's potential by exploring various preference
models on a 4-dimensional context-aware problem with contexts that are
available for almost any real life datasets. We show in our experiments --
performed on five real life, implicit feedback datasets -- that proper
preference modelling significantly increases recommendation accuracy, and
previously unused models outperform the traditional ones. Novel models in GFF
also outperform state-of-the-art factorization algorithms.
  We also extend the method to be fully compliant to the Multidimensional
Dataspace Model, one of the most extensive data models of context-enriched
data. Extended GFF allows the seamless incorporation of information into the
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