There are di erent types of information systems, such as those that perform group recommendations and market segmentations, which operate with groups of users. In order to combine the individual preferences and properly address suggestions to users, group modeling strategies are employed. Nowadays, data is characterized by large amounts in terms of volume, speed, and variety (the so-called big data issue). In this paper, we are going to tackle the problem of modeling group preferences in big data scenarios. This study will present the existing strategies, and we are going to present criteria to design the algorithms that implement them when big amounts of data have to be combined. Moreover, a set of best practices discusses under which conditions the presented strategies can be adopted in big data scenarios.
Combining the preferences of individual users is a central problem for the
information systems that operate with groups. The most challenging and widely
studied, both by the industry and the academia, are the group recommender [
The task of aggregating the individual preferences into a single model is
known as group modeling, and several strategies have been studied in the
literature [
In this paper, we tackle the novel problem of studying criteria for applicable and e cient design of group modeling algorithms in big data scenarios. More speci cally, we are going to answer the following research question: which group modeling strategies can actually be employed in real-world contexts characterized by big data? In order to answer this question, we rst present the existing group modeling strategies (Section 2), then we propose design guidelines to e ciently implement these strategies in big data scenarios, and discuss with a set of best practices which strategies are applicable in real-world big data contexts (Section 3). Our aim is to guide future research in this area towards the development of approaches that are e cient and e ective at the same time. This study is concluded with a summary of the proposed criteria and with perspectives for future work in this research area (Section 4). 2
Group modeling [
Here, we present an example of how each group modeling strategy operates. We consider three users (denoted as u1, u2, and u3), who rate ten items (i1, ..., i10) with a rating from 1 to 10. Table 1 reports the output of the strategies that combine individual ratings, while tables 2, 3, and 4, show how the Borda Count, Copeland Rule, and Plurality Voting strategies respectively work (these tables are based on the ratings in Table 1). 2.2
The individual ratings for each item are summed and a list of items ranked by sum is created. The list produced by each strategy is the same that would be generated when averaging the individual ratings, so it is also called `Average strategy'. An example of how the strategy works is given in Table 1 (AU line).
The strategy has proven to be e ective in di erent contexts [
The ratings given by the users for each item are multiplied and a ranked list of items is produced. An example of how the strategy works is given in Table 1 (M U line).
This strategy was employed in the music recommendation domain by [
This strategy was implemented in [
It is a form of majority voting that sorts the items according to their Copeland index, which is calculated as the number of times in which an alternative beats i6 + 0 + + + 0 + + + + +8 4 i1 i1, i10 i10 i1, i10 i7 + 0 + + 0 + + + +4 i8 0 0 -8 5 i3 i3 i3 i3 i9 0 0 -8 6 i8 i8, i9 i9 i8, i9 i10 0 + + + 0 -2 u1 u2 u3 Group i1 0 + + + 0 -2 the others, minus the number of times it loses against the other alternatives. In the example in Table 3, item i2 beats item i1, since it received a higher rating by both users u1 and u2.
The approach proposed in [
Each user votes for her/his favorite option. The one that receives the highest number of votes wins. If more than one alternative needs to be selected, the options that received the highest number of votes are selected. An example of how the strategy works is given in Table 4.
This strategy was implemented and tested by [
Each user votes for as many items as she/he wants, and a point is assigned to all the ones a user likes. To show how the strategy works, in the example in Table 1 (AV line) we suppose that each user votes for all the items with a rating above a threshold (for example, 5). A group preference is obtained by adding the individual points of an item.
To choose the pages to recommend to a group, Let's Browse [
The group rating produced for an item is the lowest rating expressed for that item by any of the users in the group. This strategy usually models small groups, to make sure that every member is satis ed. A drawback is that if the majority of the group really likes something, but one person does not, the item will not to be recommended to the group. This is what happens in Table 1 for the items i2 and i7. An example of how the strategy works is given in Table 1 (LM line).
This strategy is used by [
The rating assigned to an item for a group is the highest one expressed for that item by a member of a group. An example of how the strategy works is given in Table 1 (M P line).
This strategy is used by [
The rating assigned to an item for a group is the average of the ratings given by each user. All the items that received a rating under a certain threshold by a user are not included in the group model (in the example in Table 1 - AW M line, the threshold rating is 4).
In order to model a group to decide the music to play in a gym, in [
This strategy is based on the idea that users can be recommended something they do not like, as long as they also get recommended something they like. This is done by allowing each user to choose her/his favorite item. If two items have the same rating, the choice is based on the other users' preferences. This is done until everyone made a choice. Next, everyone chooses a second item, starting from the person who chose last the rst time.
If in the example in Table 1, we suppose that user u1 chose rst, she/he would consider i2, i4, and i7, and would choose i4, because it has the highest average considering the other users' ratings. Next, u2 would choose between i2 and i6 and would select i6 for the same reason. Then, u3 would choose item i10. Since everyone chose an item, it would be u3's turn again and i5 would be chosen. User u2 would choose i2, which has the highest rating along with i6 (which was already chosen). Then, u1 would choose i7, which is the one with the highest rating and was not chosen yet. The nal sequence of items that models the group would be: i4, i6, i10, i5, i2, i7, i1, i3, i9, i8.
This strategy is adopted by [
This strategy is adopted to select tourist attractions advantaging the users
with particular needs [
This section presents design criteria to implement the strategies presented in the previous section in scenarios characterized by big data. In Section 3.1, we are going to present design criteria from an algorithmic point of view, while in Section 3.2 we are going to study the nature of each strategy to evaluate their applicability in real-world scenarios characterized by big data. 3.1
Each strategy is fairly trivial to implement in an e cient way, by adopting data structures that can be quickly accessed. A possible way to implement a group model might be a hash table that stores the item ids as keys and the group rating as values. Each time a new individual rating arrives, the hash table can be e ciently updated with average complexity O(1).
In order to suggest the items to the users, the items in the group model have
to be sorted by group rating. An e cient sorting algorithm for big data, known as
two-way replacement selection, has been proposed in [
Here, we present a set of best practices related to the applicability of the
previously presented group modeling strategies in big data scenarios. Most of these
best practices are derived from a case-study conducted in the group
recommendation domain and presented in [
The main argument against the deployment of a strategy in a big data scenario will be represented by a high computational cost of performing inserts and updates of ratings in large sets of data. More precisely, it is assumed that group ratings, resulting from the application of a speci c strategy on a set of user ratings, are stored for later use in order to save computation power, and that a recalculation of group ratings is required following the insertion or update of user ratings. This evaluation takes into account the computational cost of updating group ratings. Furthermore, for the sake of completeness, it will also be noted when a strategy is simply inadequate for modeling large groups of users, regardless of any di culties in handling large amounts of data.
The Additive Utilitarian strategy can be easily employed in big data scenarios, as the only operation required to update the group model is to add the rating expressed by a user for an item to the existing group rating for that item.
Likewise, the Multiplicative Utilitarian would be very simple to implement. However, it would not be advisable to employ it in presence of large groups, as an over ow would most certainly occur when the original user ratings are multiplied1. Moreover, given the large amounts of operations that the strategy would perform for such a group, rating normalization to avoid the problem would lead to a loss in precision and to a drop in the accuracy of the system.
Borda Count, Copeland Rule, Plurality Voting, and Fairness require to update the individual model of each user each time she/he assigns a new rating. After the individual model is updated, the group model can be updated accordingly. Therefore, these strategies would not be e ciently applicable in big data scenarios.
The Average Without Misery, Approval Voting, Least Misery, and Most Pleasure strategies, can apparently be easily and e ciently adapted in big data scenarios, as they only require to calculate an average, the maximum, or the minimum of the individual ratings given to each item. However, they should not be adopted in big data due to their nature. Indeed, Average Without Misery discards a group rating if at least a user has given to an item a rating lower than the considered threshold. Therefore, even with a small threshold value, like 2, the vast majority of the items would not be modeled by the strategy in a context in which groups are large (the larger is the group, the higher is the number of times an item is rated, and higher is the probability that at least one user did not like the item). Considering the Approval Voting strategy with high threshold values (for example, 5), too many ratings would be discarded by the model because only the items with a high rating (i.e., with a rating above 5), would be considered. The other two strategies (i.e., Least Misery and Most Pleasure) are usually employed to model small groups; indeed, if a group is large, the group model would contain respectively only low or high ratings, which would not represent the preferences of the group as a whole.
Lastly, in case a person that guides the group or whose preferences align with most of the group exists, the Most Respected Person strategy would be at the same time e ective and e cient to employ. 1 Given 60 users who expressed a very low rating (like 2) for an item, a 64 bit machine would not be able to handle the group rating, since it cannot process numbers higher that 252.
In this paper, we analyzed the existing group modeling strategies and presented criteria for applicable design in real-world scenarios characterized by big data. As a result of this study, we can say that the vast majority of the strategies do not present limitations from an algorithmic point of view and could be e ciently implemented. However, due to how the strategies operate, their e ectiveness is a ected in big data scenarios. Indeed, some of them do not consider a group rating if a user or a part of the group has given a low rating to an item, or some others would lead the group model to be composed just with low or high ratings, blurring the knowledge on what the users in the group like or do not like. In conclusion, in presence of big data, a simple but very e ective strategy, like Additive Utilitarian, which considers all the users and all the ratings given by them, should be preferred. Future work will be devoted at experimenting these strategies in the real-world scenarios characterized by big data to analyze their applicability and validate these design criteria.