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Top1. Introduction
The increasing number of items featured by online websites led to the necessity to assist users and help them reach relevant resources. Recommender Systems (RS) address this issue by automatically suggesting to users, all along their navigations, the most relevant items according to their needs and preferences. RS are, as defined in (Burke, 2002), systems that can provide custom recommendations and guide the user to find interesting resources in a large data space. In other words, their purpose is to filter information according to the interest of users.
While traditional RS focus only on users and items to compute predictions, another trend suggests considering additional information relative to the context within the user experienced the items, such as time, weather, or accompanying persons. These systems are called Context Aware Recommender Systems (CARS). Indeed, research proved that in situation where context matters, including contextual information when computing recommendation improves its accuracy (Herlocker & Konstan, 2001). Thus, a user may be interested in completely different items according to its situation. For example, a user may choose a restaurant for a business lunch but would prefer another one when he is with his family.
A common RS task is to predict ratings for unobserved interactions between users and items. Thus, the goal is to define a target function 
, called utility function, from the set 
to 
where 
the set of users, 
the set of items, and 
and 
are the number of users and items respectively, so that: 
and 
is the predicted rating of user 
on item 
. While only users and items are involved, this is called a two-dimensional recommendation (Adomavicius, Sankaranarayanan, Sen, & Tuzhilin, 2005).
In contrast, CARS assume that additional information affect ratings like Mood or Accompanying Person. Thus, the goal in CARS is to define a utility function from the set 
to 
, where 
are the different sets of context that influence rating behavior. For example, 
could be the Mood, 
could be the Accompanying Person and so on. Because additional dimensions are involved, CARS are called multi-dimensional recommendation (Adomavicius et al., 2005).
In the literature (Adomavicius, Mobasher, Ricci, & Tuzhilin, 2011), CARS algorithms are classified in either: