be very low(because only five distinct items are recommended across all users) Higher diversity(both individual and aggregate), however, can come at the expense of accuracy. The example in Table 1(based on the Movie lens dataset that is publicly available at grouplens. org) shows that it is possible to obtain higher diversity simply by recommending less popular items; however, the loss of recommendation accuracy in this case can be substantial. Some prior work(Adomavicius and Kwon 2008) has attempted to overcome this accuracy-diversity trade-off by filtering out less promising recommendations; as a result, however, such approaches often can offer only a fraction of possible recommendations to users. In contrast, we explore new recommendation approaches that can increase the diversity of recommendations with only a minimal (negligible) accuracy loss using different recommendation ranking techniques, without losing any recommendations. While the traditional recommender systems typically rank the relevant items by their predicted rating and recommend the most highly predicted item to each user, resulting in high accuracy, the proposed approaches consider additional factors, such as item popularity, when ranking the recommended item list to substantially increase recommendation diversity while maintaining comparable levels of accuracy 2 Related work Recommender systems typically operate in a two dimensional space of users and items. Let U be the set of users of a recommender system, and let I be the set of all possible items that can be recommended to users. Then, the utility function that represents the preference of item iel by user ue U is often defined as R: Ux/Rating, where Rating typically represents some numeric scale used by the users to evaluate each item. Also, we use the r(u, i)notation to represent a known rating(i.e, the actual rating that user u gave to item i), and the r*(u, i) notation to represent the system-predicted rating for item i and user u Numerous metrics have been employed for measuring the accuracy of recommendations(Herlocker et al 004). In particular, precision is one of the most popular decision-support metrics that measures the percentage of truly " high"ratings among those that were predicted to be high" by the recommender system. The ratings in the data that we used for our experiments are integers between I and 5, inclusive and accordingly we define the items with ratings greater than 3.5( threshold for "high "ratings, denoted by TH) as"highly-ranked", and the ratings less than 3.5 as"non-highly-ranked " Furthermore, in real world settings, recommender systems typically recommend the most highly-ranked N items since users are usually interested in only several most relevant recommendations, and this list of N items for user u can be defined as Lm(u)=il,., iN), where R (u, ik)> TH for all kE(1, 2,,N. Therefore, in our paper, we evaluate the recommendation accuracy based on the percentage of truly "highly-ranked"ratings, denoted by correct(LN(u), among those that were predicted to be the n most relevant"highly ranked""items for each user, i.e., using the precision-in-top-N metric(Herlocker et al. 2004), as written formally as follows precision-m-m-N=∑ I correct(L2(m/∑|L(m) where correct(LM(u))=(iEL(u)I R(u, i> TH). However, as mentioned earlier, relying on the accuracy of recommendations alone may not be enough to find the most relevant items for a user(McNee et al. 2006) and another important aspect can be measured by the diversity of recommendations. Since we intend to measure the recommendation quality based on the top-N recommendation lists that the system provides to ers,in this paper we use the total number of distinct items recommended across all users aggregate diversity measure, which we will refer to as diversity-in-top-N and can formally express as diversity-in-top-N=U L(u) 3. Improving Diversity By Re-Ranking Recommendation List As mentioned earlier, traditional recommender systems recommend to user u a list of top-N items, LM(u), selected according to some ranking criterion. More formally, item i is ranked ahead of item iy(i.e,ix iy)if rank(i)<rank(i, ) where rank: 1>R is a function representing the ranking criterion. The vast majority of current recommender systems use the predicted rating value as the ranking criterion (i.e rankstandard), and it shares the motivation with the widely accepted probability ranking p rinciple in 19th Workshop on Information Technologies and Systemsbe very low (because only five distinct items are recommended across all users). Higher diversity (both individual and aggregate), however, can come at the expense of accuracy. The example in Table 1 (based on the MovieLens dataset that is publicly available at grouplens.org) shows that it is possible to obtain higher diversity simply by recommending less popular items; however, the loss of recommendation accuracy in this case can be substantial. Some prior work (Adomavicius and Kwon 2008) has attempted to overcome this accuracy-diversity trade-off by filtering out less promising recommendations; as a result, however, such approaches often can offer only a fraction of possible recommendations to users. In contrast, we explore new recommendation approaches that can increase the diversity of recommendations with only a minimal (negligible) accuracy loss using different recommendation ranking techniques, without losing any recommendations. While the traditional recommender systems typically rank the relevant items by their predicted rating and recommend the most highly predicted item to each user, resulting in high accuracy, the proposed approaches consider additional factors, such as item popularity, when ranking the recommended item list to substantially increase recommendation diversity while maintaining comparable levels of accuracy. 2. Related Work Recommender systems typically operate in a two dimensional space of users and items. Let U be the set of users of a recommender system, and let I be the set of all possible items that can be recommended to users. Then, the utility function that represents the preference of item i∈I by user u∈U is often defined as R:U×I→Rating, where Rating typically represents some numeric scale used by the users to evaluate each item. Also, we use the R(u, i) notation to represent a known rating (i.e., the actual rating that user u gave to item i), and the R*(u, i) notation to represent the system-predicted rating for item i and user u. Numerous metrics have been employed for measuring the accuracy of recommendations (Herlocker et al. 2004). In particular, precision is one of the most popular decision-support metrics that measures the percentage of truly “high” ratings among those that were predicted to be “high” by the recommender system. The ratings in the data that we used for our experiments are integers between 1 and 5, inclusive, and accordingly we define the items with ratings greater than 3.5 (threshold for “high” ratings, denoted by TH) as “highly-ranked”, and the ratings less than 3.5 as “non-highly-ranked.” Furthermore, in real world settings, recommender systems typically recommend the most highly-ranked N items since users are usually interested in only several most relevant recommendations, and this list of N items for user u can be defined as LN(u) = {i1, …, iN}, where R*(u, ik) ≥ TH for all k∈{1, 2,.., N}. Therefore, in our paper, we evaluate the recommendation accuracy based on the percentage of truly “highly-ranked” ratings, denoted by correct(LN(u)), among those that were predicted to be the N most relevant “highly ranked” items for each user, i.e., using the precision-in-top-N metric (Herlocker et al. 2004), as written formally as follows: - - - | ( ( )) | | ( ) | N N uU uU precision in top N correct L u L u ∈ ∈ = ∑ ∑ , where correct(LN(u)) = {i∈LN(u) | R(u, i) ≥ TH}. However, as mentioned earlier, relying on the accuracy of recommendations alone may not be enough to find the most relevant items for a user (McNee et al. 2006), and another important aspect can be measured by the diversity of recommendations. Since we intend to measure the recommendation quality based on the top-N recommendation lists that the system provides to its users, in this paper we use the total number of distinct items recommended across all users as an aggregate diversity measure, which we will refer to as diversity-in-top-N and can formally express as: - - - () N u U diversity in top N L u ∈ = ∪ . 3. Improving Diversity By Re-Ranking Recommendation List As mentioned earlier, traditional recommender systems recommend to user u a list of top-N items, LN(u), selected according to some ranking criterion. More formally, item ix is ranked ahead of item iy (i.e., ix ≺ iy) if rank(ix) < rank(iy), where rank: I → R is a function representing the ranking criterion. The vast majority of current recommender systems use the predicted rating value as the ranking criterion (i.e., rankStandard), and it shares the motivation with the widely accepted probability ranking p rinciple in 80 19th Workshop on Information Technologies and Systems