One phenomenon that has been recently observed online is the emergence of polarization among users on social networks, where the population gets divided in groups with opposite opinions. As recommender system algorithms become more selective in filtering what users see and discover, one important question arises: Could recommender system algorithms become more selective in filtering what users see and discover? In this paper, we study this question and propose a new counter-polarization approach for existing Matrix Factorization based recommender systems, that can be tuned by a user-controlled counter-polarization parameter which serves like a voluntary user anti-polarization or discovery dial.
Factorization objective function. Our counter-polarization approach is modulated by a usercontrolled counter-polarization parameter which acts like a user discovery dial to give the user the freedom to tune the severity of their filter bubbles as they wish.
The remainder of this paper is organized as follows. Section 3 presents our proposed methods for handling polarization, followed by experiments in Section 4, and conclusions in Section 5.
Research on polarization in recommender systems has emerged rapidly, in recent years, as an
important interdisciplinary topic [
Polarization has been investigated from a network perspective mainly using the social network
structure, the content and sentiment of discussions [
Despite the reasonableness of prior works, most current work on polarization has relied on textual content to detect sentiment and then polarization, or has been confined to specific domains within the context of political (or other controversial domain) news and blogs. In this paper, we are more interested in studying the emergence and aggravation of polarization as a result of using collaborative filtering recommender systems.
Our scope is within the context of classical collaborative filtering (CF) Recommendation algorithms that learn latent factor models, specifically Non-negative Matrix Factorization (NMF), to represent items and users based on a set of factors inferred from rating patterns.
Following the polarization definition in [
Definition 1 - Polarization-aware collaborative filtering recommendation : Given a set of ratings ∈ R× collected from a set of users ∈ R1× for a set of items ∈ R× 1, the problem of polarization-aware collaborative filtering recommendation (CF) can be modeled by the triplet (, , ), in a way that a recommender system should recommend a ranked item set 1, ..., ∈ according to 1) the relevance of the item to the user’s interest, and 2) the item’s polarization score. From definition 2, an instance from (, , ) can be denoted by (, , ) which means that user rated item with value .
The general problem of Non-negative matrix Factorization (NMF) is to decompose a non-negative data matrix with size × into two positive elements matrix factors and , with size × and × , respectively, such that ≪
min (, ) is a positive integer representing the
rank of matrices and [
where ⊙ is the I/O operator, meaning that user provides rating ′ for item ′
For the purpose of evaluation, we resort to a simulation scenario in this preliminary work
similar to [
We start by showing some experiments that illustrate examples of how an Interactive Recommender System (IRS) works in environment . In all of the examples, we set the number of factors in the latent space, , to 5 and we compute the list of top = 5 items to be recommended to each user. The user will give a rating for only one of the selected items at a time. In each iteration, we measure MSE from the training and testing phases. We also keep track of the items that a user decided to reacted to by providing a rating.
Figure 1 shows traces from the interactive recommendation system for user ∈ , which means the user likes red items more than blue items. We generate environment considering that the gap is 2. Figure 1, upper row, shows that NMF is always going to recommend red items, to which the user had previously shown more interest. Although the red items are relevant, the user Red is trapped in a filter bubble that does not allow them to explore any items from the opposite color/view. The second row shows the testing MSE decreases as the user provides new ratings in each iteration; hence, there are fewer unrated items for the user. Finally, the last row shows the NMF model’s objective or cost function’s convergence when using gradient descent optimization, where each line (or colored thread) represents the decrease of the objective function for an iteration of the interactive recommendation process.
Figure 2 shows the results of applying our proposed Polarization-aware Recommender Interactive System (PaRIS) in environment for user . As we can see, the user gets to see items from a diferent color/viewpoint even in a very polarized environment. The middle row shows the testing MSE error for user where there are some fluctuations in the testing MSE error which is due to the modification in the main updating function of NMF. Finally, the last row shows the contrast between the objective function evolution for varying polarization rates, compared to non polarization. Furthermore the error converges to a smaller value for higher polarization. We interpret this algorithmically, by the fact that the higher the polarization in the ratings, the larger the gap (extreme likes and dislikes) between the items’ ratings in the opposite viewpoints. Hence increased polarization leads to increased separation between the opposite viewpoint ratings, which, very naturally makes learning the ratings an easier task from a machine learning perspective.
We repeat the experiment with = 2 for two scenarios: (a) All users have the same , i.e. = ∀ ∈ , where c is a constant ∈ [0, 1]. (b) User u has his/her own unique , = for user u and = 0 ∀ ∈ − , where ∈ [0, 1], is a user defined constant. Then, we compute , and in two ways: (a) : the ratio of number of items from the opposite view to what the user has picked from the recommendation list, (b) : the ratio of number of items recommended to the user from an opposite view.
Table 1 shows that the higher the user-defined counter-polarization tuning parameter , the more they will be recommended items from the opposite view, again as desired by the user. Even though the traditional NMF-based algorithm achieves good accuracy in rating prediction, it is not able to recommend any item from the opposite view. In contrast, our proposed algorithm, PaRIS, recommends significantly more items ( ≤ 0.05) from the opposite view compared to the baseline approach, for all the degrees of user-defined discovery factors.
We proposed a polarization-aware recommender system based on Non-negative Matrix Factorization that succeeds to cover items from the opposite view after a few iterations and can broaden the viewpoint spectrum even faster if the user is more interested in discovering items from diferent viewpoints. Our work is limited by the simulation setting in the experiments, since inducing polarization and testing diferent new strategies in real life has ethical risks and legal ramifications. Future work should find a way to conduct tests on real users, after mitigating the risks involved.
This work was supported by the National Science Foundation through grant IIS-154998. [1] R. Baeza-Yates, Data and algorithmic bias in the web, in: Proceedings of the 8th ACM
Conference on Web Science, ACM, 2016, pp. 1–1. [2] J. Sanz-Cruzado, P. Castells, Enhancing structural diversity in social networks by recommending weak ties, in: Proceedings of the 12th ACM conference on recommender systems, 2018, pp. 233–241. [3] E. Bakshy, S. Messing, L. A. Adamic, Exposure to ideologically diverse news and opinion on facebook, Science 348 (2015) 1130–1132.