PaRIS: Polarization-aware Recommender Interactive System Mahsa Badami1 , Olfa Nasraoui1 1 Knowledge Discovery and Web Mining Lab, Computer Engineering and Computer Science Department, University of Louisville, 132 Eastern Parkway, Louisville, Kentucky, USA, 40292 Abstract 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 recom- mender 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. Keywords Recommender System, Polarization, Algorithmic bias, Filter Bubble, Echo Chamber 1. Introduction More than two-thirds of Americans get their news from online social media platforms 1 . At the same time, social media services (e.g. Facebook) automatically filter and sort the order of items on a user’s home feed, in many cases without an explicit request from the user to do so [1]. As information filtering algorithms become more and more targeted and selective in filtering what users see and discover, one important question arise: Could these algorithms filter too much information? Despite the numerous benefits of personalized recommender systems, narrow-minded over-specialization, resulting from positive feedback loops, can exacerbate "echo chamber" and "filter bubble" by not expanding, or even restricting, the users’ exposure to more diverse and non-obvious options [2, 3, 4, 5]. These two effects get even more extreme in polarized environments leading to an even worse polarized environment [6, 7, 8]. The goal of our work is to expand the domain of recommended options and expand the discovery potential for humans, and thus reducing the users’ chance of getting locked in on an online platform. We aim to achieve this goal by designing a recommendation system that not only recommends relevant items but also includes opposite views in case the user is interested in discovering the opposite view. To do so, we propose a novel polarization-aware recommender interactive system (PaRIS) which learns using a modified Non-Negative Matrix OHARS’21: Second Workshop on Online Misinformation- and Harm-Aware Recommender Systems, October 2, 2021, Amsterdam, Netherlands " Mahsa.Badami@louisville.edu (M. Badami); Olfa.Nasraoui@louisville.edu (O. Nasraoui) ~ http://webmining.spd.louisville.edu (O. Nasraoui) © 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings CEUR Workshop Proceedings (CEUR-WS.org) http://ceur-ws.org ISSN 1613-0073 1 https://www.theatlantic.com/technology/archive/2018/04/mark-zuckerberg-atlantic-exclusive/557489/ 68 Factorization objective function. Our counter-polarization approach is modulated by a user- controlled 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. 2. Related Work Research on polarization in recommender systems has emerged rapidly, in recent years, as an important interdisciplinary topic [9, 10, 5], with efforts to formulate a richer understanding of the potential characteristics of this Phenomenon and to decrease online polarization, especially in recommender systems [10, 3, 11, 12]. Polarization has been investigated from a network perspective mainly using the social network structure, the content and sentiment of discussions [13, 6], where as others studied polarization based on the ratings provided by users on items, within the context of a recommender system [13, 14]. Even though some researchers showed echo chambers in social media are somewhat inevitable by design, other studies proposed strategies to mitigate such effects[15, 16, 17]. Badami et al. proposed a counter-polarization methodology for combating over-specialization in polarized environments [16]. In another research, Tintarev el al. used visual explanations, i.e., chord diagrams and bar charts [18] to address polarization. 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. 3. Proposed Method Our scope is within the context of classical collaborative filtering (CF) Recommendation algo- rithms 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. 3.1. Problem Definition Following the polarization definition in [13], we define polarization-aware collaborative filtering as follows: Definition 1 - Polarization-aware collaborative filtering recommendation: Given a set of ratings 𝑅 ∈ R𝑚×𝑛 collected from a set of users 𝑈 ∈ R1×𝑛 for a set of items 𝐼 ∈ R𝑚×1 , the problem of polarization-aware collaborative filtering recommendation (CF) can be modeled by the triplet (𝑈, 𝐼, 𝑅), in a way that a recommender system should recommend a ranked item set 𝑖1 , ..., 𝑖𝑡 ∈ 𝐼 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 (𝑈, 𝐼, 𝑅) can be denoted by (𝑢, 𝑖, 𝑟) which means that user 𝑢 rated item 𝑖 with value 𝑟. 69 3.2. Polarization-aware Recommender Interactive System - (PaRIS) The general problem of Non-negative matrix Factorization (NMF) is to decompose a non-negative data matrix 𝑅 with size 𝑚 × 𝑛 into two positive elements matrix factors 𝑃 and 𝑄, with size 𝑚 × 𝑘 and 𝑘 × 𝑛, respectively, such that 𝑘 ≪ min (𝑛, 𝑚) is a positive integer representing the rank of matrices 𝑃 and 𝑄 [19]. Here, our goal is to design a recommendation system which not only recommends relevant items but also includes opposite views in case the user is interested to discover new items. A classical NMF predicts the overall rating 𝑟^𝑖𝑗 = 𝑝𝑖 .𝑞𝑗 by minimizing ||𝑟𝑖𝑗 − 𝑝𝑖 .𝑞𝑗 ||2 . However, the item rating alone is not able to fully consider the polarization phenomenon. Hence, in order to estimate 𝑅 from (𝑈, 𝐼) such that the system considers both relevance and polarization, we propose to minimize the objective function: ∑︁ ∑︁ (︁ min 𝒥𝑃 𝑎𝑅𝐼𝑆 = (1 − 𝜆𝑢 ) × ||𝑟𝑢𝑖 − 𝑝𝑢 𝑞𝑖 ||2 + 𝑝𝑢 , 𝑞 𝑖 𝑢 ∈𝑈 𝑖 ∈𝐼 )︁ ′ 𝜆𝑢 × ||𝑟𝑢𝑖 − 𝑝𝑢 𝑞𝑖 ||2 (1) 𝑔𝑖 ′ 𝑟𝑢𝑖 = 𝑟𝑢𝑖 − 𝜆𝑢 × (𝑟¯ + ) × Φ𝜆𝑖 𝑢 +𝑟𝑢𝑖 if 𝑟𝑢𝑖 ≥ 𝛿 𝑔𝑚𝑎𝑥 𝑔𝑖 ′ 𝑟𝑢𝑖 = 𝑟𝑢𝑖 + 𝜆𝑢 × (𝑟¯ − ) × Φ𝜆𝑖 𝑢 +𝑟𝑢𝑖 if 𝑟𝑢𝑖 < 𝛿 𝑔𝑚𝑎𝑥 where 𝜆𝑢 is user u’s discovery factor, Φ𝑖 is item i’s polarization score, computed using the Polarization Detection Classifier proposed in [13], 𝑔𝑖 measures how extreme the different viewpoints are, 𝛿 is a threshold that indicates which ratings are considered as liked versus disliked. 𝑔𝑖 ∈ [0, 1] indicates the gap between the two rating extreme ranges for a polarized item; in other words, it measures how polarized the user population’s ratings are for item 𝑖. We use the gap 𝑔𝑖 as the difference between an item’s typical minimum rating when it is liked and its typical maximum rating when it is disliked. 𝑔𝑚𝑎𝑥 is the difference between the maximum and minimum rating that a typical user can provide for any item, using the system’s rating scale. The more polarized a population gets, the higher 𝑔𝑖 gets. 𝛿 is a threshold that indicates which ratings are considered as liked versus disliked. By minimizing the objective function in (1), we estimate 𝑅 from (𝑈, 𝐼) such that the system considers both relevance and polarization, but to different degrees. The first part of the optimization objective is the classical NMF optimization criterion; while the second part is the counter-polarization component. The intuition behind the second part is to bring a user and an item closer in the latent space, if the user is interested in discovering more and the item happens to be polarized. The new incremental stochastic Gradient Descent update equations at iteration 𝑡 + 1, after each new input 𝑟𝑢𝑖 , can be derived as shown below, where 𝑒𝑢𝑖 (𝑒𝑢𝑖 ) are the ratings’ (depolarized ratings’) reconstruction errors. 𝑒𝑢𝑖 = 𝑟𝑢𝑖 − 𝑝𝑡𝑢 𝑞𝑖𝑡 (2) 𝑒′𝑢𝑖 = 𝑟𝑢𝑖 ′ − 𝑝𝑡𝑢 𝑞𝑖𝑡 𝜕𝒥𝑃 𝑎𝑅𝐼𝑆 = 2(1 − 𝜆𝑢 ) × 𝑒𝑢𝑖 × (−𝑞𝑖 ) + 2𝜆𝑢 × 𝑒′𝑢𝑖 × (−𝑞𝑖 ) 𝜕𝑝𝑢 (3) 𝜕𝒥𝑃 𝑎𝑅𝐼𝑆 = 2(1 − 𝜆𝑢 ) × 𝑒𝑢𝑖 × (−𝑝𝑢 ) + 2𝜆𝑢 × 𝑒′𝑢𝑖 × (−𝑝𝑢 ) 𝜕𝑞𝑖 70 𝑝𝑡+1 = 𝑝𝑡𝑢 + 𝜂 2𝑞𝑖𝑡 ((1 − 𝜆𝑢 )𝑒𝑢𝑖 + 𝜆𝑢 × 𝑒′𝑢𝑖 ) (︀ )︀ 𝑢 (4) 𝑞𝑗𝑡+1 = 𝑞𝑖𝑡 + 𝜂 2𝑝𝑡𝑢 ((1 − 𝜆𝑢 )𝑒𝑢𝑖 + 𝜆𝑢 × 𝑒′𝑢𝑖 ) (︀ )︀ The steps for the PaRIS algorithm are listed in Algorithm 1. Algorithm 1 Polarization-aware Recommender Interactive System - ( PaRIS ) Input: initial user-item matrix (𝑅𝑡𝑟𝑎𝑖𝑛 ), 𝑓𝑃 𝐷𝐶 ( Polarization classifier function [13]) Output: final user-item matrix 𝑅 1: For each user 𝑢 ∈ 𝑈 : 2: Repeat While 𝑢 rates unrated items: 3: Update model 𝑃 , 𝑄 using input data 𝑅 by optimizing objective function (1) 4: with the parameter set of 𝜆𝑢 , Φ𝑖 , 𝑔𝑖 5: ¯ ← 𝑃𝑄 𝑅 6: Find 𝑆𝑢 which is the set of items sorted in descending order of predicted rating 7: Select the top 𝑘𝑡 items from S and recommend them to 𝑢 8: User picks an item 𝑖′ randomly and gives it rating 𝑟𝑢𝑖′ 9: 𝑅 ← 𝑅 ⊙ 𝑟𝑢𝑖′ 𝑓 𝑜𝑟 𝑖′ ∈ 𝑆𝑢 10: where ⊙ is the I/O operator, meaning that user 𝑢 provides rating 𝑟𝑢𝑖′ for item 𝑖′ 4. Experiments For the purpose of evaluation, we resort to a simulation scenario in this preliminary work similar to [16]. We evaluate the performance of our approach in terms of rating prediction accuracy, using the Mean Squared Error (MSE) [19] and the Opposite View Hit Rate (OVHR) ratio based on the ratio of the number of items from the opposite view to the total number of recommended items [16]. We consider the following simple environment: Let 𝐺 = (𝑈, 𝐼, 𝑅) be an environment where user 𝑢 ∈ 𝑈 can rate item 𝑖 ∈ 𝐼 with rating 𝑟𝑢𝑖 ∈ 𝑅 on a scale of 𝑥 to 𝑦. We generate a rating environment with 50 users and 200 items where items are evenly divided in two opposite viewpoint sets (red items and blue items). Users are also divided into two groups based on whether they like red or blue items. In order to make the environment polarized, we assume that user 𝑢𝑎 ∈ 𝐺𝑟𝑜𝑢𝑝𝐴 likes red items more and user 𝑢𝑏 ∈ 𝐺𝑟𝑜𝑢𝑝𝐵 likes blue items more than red ones. Finally, we generated environment 𝐺 with different values of polarization gaps and user discovery factors. We start by showing some experiments that illustrate examples of how an Interactive Recom- mender System (IRS) works in environment 𝐺. In all of the examples, we set the number of factors in the latent space, 𝑘𝑓 , to 5 and we compute the list of top 𝑘𝑡 = 5 items to be recom- mended 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 𝑢 ∈ 𝐺𝑟𝑜𝑢𝑝𝐴, 71 Figure 1: Traces of the Interactive Recommendation NMF-based RS in environment 𝐺 with different polarization ratio and gap values, for user 𝑢𝑎 . Polarization increases acutely with Gap. The error drops sharply in the more polarized case, making it easier for the Machine Learning model. which means the user likes red items more than blue items. We generate environment 𝐺 considering that the gap 𝑔𝑖 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 Inter- active System (PaRIS) in environment 𝐺 for user 𝑢𝑎 . As we can see, the user gets to see items from a different color/viewpoint even in a very polarized environment. The middle row shows the testing MSE error for user 𝑢𝑎 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 72 Figure 2: Traces of the Interactive Recommendation process with the polarization-aware recommender system ( PaRIS ) in environment 𝐺 with different polarization ratio and gap values, for user 𝑢𝑎 who had liked red items more than blue items. Polarization is reduced relative to NMF in Fig. 1 (top row). As Gap increases, the prediction error drops according to two modes: one as sharp as the unmitigated polarized case of NMF, and another decreasing more slowly like the unpolarized case at Gap = 0). 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 𝑔𝑎𝑝 = 2 for two scenarios: (a) All users have the same 𝜆, i.e. 𝜆𝑢 = 𝑐 ∀𝑢 ∈ 𝑈 , where c is a constant ∈ [0, 1]. (b) User u has his/her own unique 𝜆, 𝜆𝑢 = 𝑐𝑢 for user u and 𝜆𝑢 = 0 ∀𝑢 ∈ 𝑈 − 𝑢, where 𝑐𝑢 ∈ [0, 1], is a user defined constant. Then, we compute 𝑀 𝑆𝐸𝑡𝑒𝑠𝑡 , 𝑀 𝑆𝐸𝑡𝑟𝑎𝑖𝑛 and 𝑂𝑉 𝐻𝑅 in two ways: (a) 𝑂𝑉 𝐻𝑅𝑢 : the ratio of number of items from the opposite view to what the user has picked from the recommendation list, (b) 𝑂𝑉 𝐻𝑅𝑡𝑘 : 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 𝜆, 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, 73 Table 1 Comparison of PaRIS with the classical NMF RS in terms of accuracy and opposite view ratio (𝑂𝑉 𝐻𝑅𝑢 ,𝑂𝑉 𝐻𝑅𝑡𝑘 ) Opposite View Ratio 𝑀 𝑆𝐸𝑇 𝑟𝑎𝑖𝑛 𝑀 𝑆𝐸𝑇 𝑒𝑠𝑡 𝑂𝑉 𝐻𝑅𝑢 𝑂𝑉 𝐻𝑅𝑡𝑘 mean, std mean, std mean, std mean, std Classic NMF 0.0 ± 0.00 22.02 ± 5.27 138.96 ± 12.55 𝜆𝑖 = 0.2 0.0% ± 0.00 0.0% ± 0.00 57.63 ± 14.35 223.31 ± 32.14 𝜆𝑖 = 0.5 0.0% ± 0.00 0.0% ± 0.00 146.51 ± 41.73 632.21 ± 57.73 Scenario (a) 𝜆𝑖 = 1.0 48.0% ± 0.17 32.0% ± 0.12 383.80 ± 108.52 2015.85 ± 167.46 PaRIS 𝜆𝑖 = 0.2 5.4% ± 0.073 4.9% ± 0.021 123.92 ± 36.76 813.01 ± 36.76 𝜆𝑖 = 0.5 6.0% ± 0.08 18.1% ± 0.21 124.46 ± 37.29 299.82 ± 76.01 Scenario (b) 𝜆𝑖 = 1.0 67.0% ± 0.24 68.0% ± 0.24 361.77 ± 102.74 1883.50 ± 237.83 PaRIS, recommends significantly more items (𝑝 ≤ 0.05) from the opposite view compared to the baseline approach, for all the degrees of user-defined discovery factors. 5. 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