Overview of the Collaborative Filtering Process

The goal of a collaborative filtering algorithm is to suggest new items or to predict the utility of a certain item for a particular user based on the user's previous likings and the opinions of other like-minded users. In a typical CF scenario, there is a list of m users ${\cal{U}} = \{u_1,u_2, \ldots, u_m\}$ and a list of n items ${\cal{I}} = \{i_1,i_2, \ldots, i_n\}$. Each user u_i has a list of items I_ui, which the user has expressed his/her opinions about. Opinions can be explicitly given by the user as a rating score, generally within a certain numerical scale, or can be implicitly derived from purchase records, by analyzing timing logs, by mining web hyperlinks and so on [28,16]. Note that $I_{u_i} \subseteq {\cal{I}}$ and it is possible for I_ui to be a null-set. There exists a distinguished user $u_a \in {\cal{U}}$called the active user for whom the task of a collaborative filtering algorithm is to find an item likeliness that can be of two forms.

• Prediction is a numerical value, P_a,j, expressing the predicted likeliness of item $i_j \not \in I_{u_a}$ for the active user u_a. This predicted value is within the same scale (e.g., from 1 to 5) as the opinion values provided by u_a.
• Recommendation is a list of N items, $I_r \subset {\cal{I}}$, that the active user will like the most. Note that the recommended list must be on items not already purchased by the active user, i.e., $I_r \cap I_{u_a} = \Phi$. This interface of CF algorithms is also known as Top-N recommendation.

  

Figure 1: The Collaborative Filtering Process.

Figure 1 shows the schematic diagram of the collaborative filtering process. CF algorithms represent the entire $m \times n$user-item data as a ratings matrix, $\cal {A}$. Each entry a_i,j in $\cal {A}$ represent the preference score (ratings) of the ith user on the jth item. Each individual ratings is within a numerical scale and it can as well be 0 indicating that the user has not yet rated that item. Researchers have devised a number of collaborative filtering algorithms that can be divided into two main categories-Memory-based (user-based) and Model-based (item-based) algorithms [6]. In this section we provide a detailed analysis of CF-based recommender system algorithms.

 

• Memory-based Collaborative Filtering Algorithms.
• Model-based Collaborative Filtering Algorithms.