# Enhancing Recommendation Accuracy of Item-Based Collaborative Filtering via Item-Variance Weighting
## 3 Proposed Approach
### Time-Aware Similarity Computation  
In an RS, user preferences may change as time goes on, so ratings rated in different period should be assigned different weight [18; 19; 20]. For example, consider movies 1, 2 and 3 rated by a single person with the same rating scores, where movie 1 was rated one year ago and movies 2 and 3 were rated one day ago. Recall that, in the traditional IBCF, rating weights are equal; thus, here, the similarity between movies 1 and 2 will be the same as that between movies 2 and 3. However, although the ratings have equal values, they may have different contributions because user preferences may change over time. Here, if this user's preferences have changed, even though movies 1 and 2 are assigned the same rating scores, they may have very different characteristics. Typically, preferences do not change over a single day; thus, movies 2 and 3 should have high similarity. In a similar period, we assume that item ratings can reflect correlation between items more precisely. Therefore, when computing similarity, an effective CF algorithm should gradually reduce the influence of ratings relative to time, that is, recent ratings should be assigned greater weight. To express the degree of correlation between two items over time, a number of time functions were proposed but most related approaches applied time factor to rating prediction of traditional IBCF (e.g., (a) of Figure 3). However, in this case, the time function was ineffective because, in practical applications, RS must handle a large amount of data that include significant numbers of users and items. Here, each user has rated only a small number of items compared to the huge number of unrated items. Thus, most RSs have sparse datasets. In the IBCF approach, to maintain real-time performance, the neighborhood size must be limited [23; 24; 25], that is, the number of items available to rate is limited. The time function is only applied to items that the target user has rated in the target item's neighborhood; therefore, it is applied to only a few items and cannot efficiently reduce the weight of item ratings given over a long period. To express the degree of correlation between two items over time more effectively, we propose the following time-related correlation degree in (Equation (3)) that computes time weights for different items such that smaller weight values are assigned to items rated in the past and apply it to the similarity computation in traditional IBCF because, when computing the similarity between each item, it is easy to find two items rated by the same user (e.g., (b) of Figure 3); thus, we can take full advantage of the time-related correlation degree, which is expressed as  
\[f(u,x,y)=e^{-\lambda\cdot u\eta_{u,x}-t_{u,y}t}, \tag{3}\]  
where \(\lambda=\frac{1}{t_{0}}\) is the decay rate. Here, if \(T_{0}=30\) days, the time weight is reduced by one month. \(f(u,x,y)\) is a gradually decreasing function that tracks the degree of correlation between items \(x\) and \(y\) for target user \(u\). The behavior of the function \(f(u,x,y)\) differs with different values for parameter \(T_{0}\) Thus, we should select different \(T_{0}\) values under different circumstances. For example, consider a dataset with a long-time span (10 years). If we set \(T_{0}\) to one day, most time function values will be 0 and the meaning of the time weight will be lost. In contrast, if a dataset has a short time span (two months) and \(T_{0}\) is set to 30 days, most time function values will be close to 1 and the effect of the time function will be limited. Generally, user preferences do not change significantly over a short period. Thus, for a single user, the score assigned to an item rated at approximately the same time as the target item will make a greater contribution to effective similarity computation. With the function \(f(u,x,y)\), as the times at which two items were rated by the target user become closer and the value of \(\left|t_{u,x}-t_{u,y}\right|\) becomes smaller, the degree of correlation between the two items increases.