# Enhancing Recommendation Accuracy of Item-Based Collaborative Filtering via Item-Variance Weighting
## 3 Proposed Approach
### Covering-Based Rating Prediction  
In the traditional IBCF, when predicting the rating score for a target item, items in the neighborhood of the target item will be assigned the same weight values; however, if most of the items in the neighborhood have characteristics that are similar to the target user's preference, the target item may also be preferred by the target user and should be assigned a relatively higher weight value. The weight differential will result in more accurate prediction results and better recommendations. For example, assume that items \(a\) and \(b\) are candidates for the target user and that, after sorting items  
Figure 3: Example of time factor used in different step of IBCF. (**a**) Most related approaches apply the time factor into rating prediction step; (**b**) the proposed approach applies the time factor into similarity computation step. in the neighborhood in descending order of similarity, the similarity values and rating scores for the items in item _a_'s neighborhood will be equal to those of item \(b\). However, most items in item _a_'s neighborhood are similar to the target user's preference and most items in item _b_'s neighborhood have very different characteristics. In traditional IBCF, items \(a\) and \(b\) will have the same predicted rating scores. However, because the characteristics of item _a_'s neighborhood are more similar to the target user's preference than those of item \(b\), it is more likely that the target user will prefer item \(a\). Thus, item \(a\) should have a higher predicted rating score than item \(b\). In other words, items whose characteristics are more similar to target user's preference should have higher weight. In this paper, to measure the relationship between items and the target user's preference, we present a niche covering degree function (Equation (6)) and further utilize it to propose a covering-based rating prediction method according to the theory of covering-based rough set. As illustrated in Figure 4, different from the traditional IBCF that utilizes the information of a target item's similar items to predicted rating scores (i.e., (a) of Figure 4), the proposed method further select neighborhood for each similar item of the target item (i.e., (b) of Figure 4) and utilizes proposed covering degree function to increase the weights of items that are closer to the target user's preference (i.e., (c) of Figure 4). First, we give the definitions of covering and the covering approximation space. More detailed information can be found in References [26; 27; 28; 29]. Let \(T\) be the domain of discourse and \(\{C_{i}\}(i=1,2,\ldots,n)\) be a family of subsets of \(T\). If \(C_{i}\
eq\varnothing\) and \(\cup C_{i}=T\), \(\{C_{i}\}\) is a covering of \(T\), denoted by C and we call the ordered pair \(\langle T,C\rangle\) a covering approximation space. In a covering approximation space \(\langle T,C\rangle\), the family sets  
\[Md(t)=\{K\in C\}\big{|}t\in K\wedge(\forall H\in C\wedge t\in H\wedge H\subseteq K \Rightarrow K=H)\big{]} \tag{4}\]  
is called the minimal description of \(t\), which represents a main characteristics description of element \(t\). In order to describe the relationship between an element \(t\in T\) with a set \(X\subseteq T\), [PERSON] and [PERSON] [26] present a roughness measure in classical rough sets induced by a covering, the definition is as follows. Let \(T\) be the domain of discourse, \(C\) be a covering of \(T\) and \(X\subseteq T\) be a subset of \(T\), for every element \(t\in T\), degree of rough membership of \(t\) in \(X\), denote by \(D(t,X)\), is defined by  
\[D(t,X)=\frac{card((\cap Md(t))\cap X)}{card(\cap Md(t))} \tag{5}\]  
Clearly, for any \(t\in T\), \(D(t,X)\in[0,\,1]\). In an RS, an item's neighborhood is most relevant to the item itself and can express common characteristics of the item. In addition, a target user's relevant item set can reflect this user's preference.