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• W4313256323 abstract "•Users surf on online recommendation networks to explore information•ICs widely exist in online recommendation networks suppressing system efficiency•Application of similarity-based recommendation techniques gives rise to ICs•Introducing flexibility to recommendation prevents ICs and improves efficiency Social media and online navigation bring us enjoyable experiences in accessing information, and simultaneously create information cocoons (ICs) in which we are unconsciously trapped with limited and biased information. We provide a formal definition of IC in the scenario of online navigation. Subsequently, by analyzing real recommendation networks extracted from Science, PNAS, and Amazon websites, and testing mainstream algorithms in disparate recommender systems, we demonstrate that similarity-based recommendation techniques result in ICs, which suppress the system navigability by hundreds of times. We further propose a flexible recommendation strategy that addresses the IC-induced problem and improves retrieval accuracy in navigation, which are demonstrated by simulations on real data and online experiments on the largest video website in China. This paper quantifies the challenge of ICs in recommender systems and presents a viable solution, which offer insights into the industrial design of algorithms, future scientific studies, as well as policy making. Social media and online navigation bring us enjoyable experiences in accessing information, and simultaneously create information cocoons (ICs) in which we are unconsciously trapped with limited and biased information. We provide a formal definition of IC in the scenario of online navigation. Subsequently, by analyzing real recommendation networks extracted from Science, PNAS, and Amazon websites, and testing mainstream algorithms in disparate recommender systems, we demonstrate that similarity-based recommendation techniques result in ICs, which suppress the system navigability by hundreds of times. We further propose a flexible recommendation strategy that addresses the IC-induced problem and improves retrieval accuracy in navigation, which are demonstrated by simulations on real data and online experiments on the largest video website in China. This paper quantifies the challenge of ICs in recommender systems and presents a viable solution, which offer insights into the industrial design of algorithms, future scientific studies, as well as policy making. The explosive development of information technologies and services, in particular the emergence of portal sites, recommender systems, search engines, and social media, has led us to a world of abundant information. We access diverse information via increasing sources, yet it is widely believed that information cocoons (ICs) are very often emerged in which we are unconsciously trapped with limited and biased information.1Sunstein C.R. Infotopia: How Many Minds Produce Knowledge. Oxford University Press, 2006Google Scholar The proliferation of ICs may result in an increase in social fragmentation, polarization, and extremism, and eventually intensify segregation and threaten democracy.1Sunstein C.R. Infotopia: How Many Minds Produce Knowledge. Oxford University Press, 2006Google Scholar,2Stroud N.J. Polarization and partisan selective exposure.J. Commun. 2010; 60: 556-576Crossref Scopus (722) Google Scholar,3Sunstein C.R. Is social media good or bad for democracy.Int. J. Hum. Rights. 2018; 27: 83-89Google Scholar,4Shi F. Shi Y. Dokshin F.A. Evans J.A. Macy M.W. Millions of online book co-purchases reveal partisan differences in the consumption of science.Nat. Hum. Behav. 2017; 1: 0079Crossref Scopus (36) Google Scholar,5Sülflow M. Schäfer S. Winter S. Selective attention in the news feed: an eye-tracking study on the perception and selection of political news posts on Facebook.New Media Soc. 2019; 21: 168-190Crossref Scopus (45) Google Scholar,6Romenskyy M. Spaiser V. Ihle T. Lobaskin V. Polarized Ukraine 2014: opinion and territorial split demonstrated with the bounded confidence XY model, parametrized by Twitter data.R. Soc. Open Sci. 2018; 5: 171935Crossref PubMed Scopus (9) Google Scholar Contributing factors to ICs are various, which can be roughly classified into two categories, namely active selection and passive choice. Individuals tend to access and produce information with similar opinions but overlook different voices.7Cowan S.K. Baldassarri D. It could turn ugly: selective disclosure of attitudes in political discussion networks.Soc. Networks. 2018; 52: 1-17Crossref Scopus (57) Google Scholar,8Wihbey J. Joseph K. Lazer D. The social silos of journalism? Twitter, news media and partisan segregation.New Media Soc. 2019; 21: 815-835Crossref Scopus (9) Google Scholar,9Cinelli M. De Francisci Morales G. Galeazzi A. Quattrociocchi W. Starnini M. The echo chamber effect on social media.Proc. Natl. Acad. Sci. USA. 2021; 118 (e2023301118)Crossref PubMed Scopus (348) Google Scholar The social network formed by like-minded people is also enhancing such information segregation that individuals are more often exposed to information communicated by his/her chosen friends.10Hu J. Zhang Q.M. Zhou T. Segregation in religion networks.EPJ Data Sci. 2019; 8: 6Crossref Scopus (14) Google Scholar,11Bakshy E. Messing S. Adamic L.A. Exposure to ideologically diverse news and opinion on Facebook.Science. 2015; 348: 1130-1132Crossref PubMed Scopus (1461) Google Scholar,12Mosleh M. Martel C. Eckles D. Rand D.G. Shared partisanship dramatically increases social tie formation in a Twitter field experiment.Proc. Natl. Acad. Sci. USA. 2021; 118 (e2022761118)Crossref Scopus (27) Google Scholar,13Chen W. Pacheco D. Yang K.C. Menczer F. Neutral bots probe political bias on social media.Nat. Commun. 2021; 12: 5580Crossref PubMed Scopus (23) Google Scholar,14Vasconcelos V.V. Levin S.A. Pinheiro F.L. Consensus and polarization in competing complex contagion processes.J. R. Soc. Interface. 2019; 16: 20190196Crossref PubMed Scopus (21) Google Scholar,15Tokita C.K. Tarnita C.E. Social influence and interaction bias can drive emergent behavioural specialization and modular social networks across systems.J. R. Soc. Interface. 2020; 17: 20190564Crossref PubMed Scopus (8) Google Scholar,16Ou Y. Guo Q. Liu J. Identifying spreading influence nodes for social networks.Front. Eng. Manag. 2022; 9: 520-549Crossref Scopus (3) Google Scholar As such, each person is at risk to be positioned in virtual “cocoons” consisting of self-selected information, leading to an echo chamber effect. Although ICs induced by active selection are of one’s own choice, either intentionally or unintentionally, people also struggle with ICs of passive choice. Search engines and recommender systems are nowadays widely implemented to feed information to users according to their past records. Such feed may be very homogeneous, creating filter bubbles that narrow users’ navigation scopes.17Zhou T. Kuscsik Z. Liu J.G. Medo M. Wakeling J.R. Zhang Y.C. Solving the apparent diversity-accuracy dilemma of recommender systems.Proc. Natl. Acad. Sci. USA. 2010; 107: 4511-4515Crossref PubMed Scopus (737) Google Scholar,18Pariser E. The Filter Bubble: What the Internet Is Hiding from You. Penguin, 2011Google Scholar,19Helberger N. Karppinen K. D'acunto L. Exposure diversity as a design principle for recommender systems.Inf. Commun. Soc. 2018; 21: 191-207Crossref Scopus (148) Google Scholar For example, a news website may recommend only conservative or liberal news to a target user based on the analytical assumption of his/her political view, or recommend friends who have very similar political views. Consequently, the behaviors of active selection and passive choice may coact and reinforce ICs via friend recommendations20Aiello L.M. Barrat A. Schifanella R. Cattuto C. Markines B. Menczer F. Friendship prediction and homophily in social media.ACM Trans. Web. 2012; 6: 1-33Crossref Scopus (303) Google Scholar,21Huszár F. Ktena S.I. O’Brien C. Belli L. Schlaikjer A. Hardt M. Algorithmic amplification of politics on Twitter.Proc. Natl. Acad. Sci. USA. 2022; 119 (e2025334119)Crossref PubMed Scopus (44) Google Scholar and news recommendations.22Beam M.A. Automating the news: how personalized news recommender system design choices impact news reception.Commun. Res. 2014; 41: 1019-1041Crossref Scopus (89) Google Scholar,23Santos F.P. Lelkes Y. Levin S.A. Link recommendation algorithms and dynamics of polarization in online social networks.Proc. Natl. Acad. Sci. USA. 2021; 118 (e2102141118)Crossref Scopus (34) Google Scholar,24Ohme J. Algorithmic social media use and its relationship to attitude reinforcement and issue-specific political participation–The case of the 2015 European Immigration movements.J. Inf. Technol. Politics. 2021; 18: 36-54Crossref Scopus (19) Google Scholar Although IC-related issues are under the spotlight of investigation and heated debates,11Bakshy E. Messing S. Adamic L.A. Exposure to ideologically diverse news and opinion on Facebook.Science. 2015; 348: 1130-1132Crossref PubMed Scopus (1461) Google Scholar,25Yang T. Majó-Vázquez S. Nielsen R.K. González-Bailón S. Exposure to news grows less fragmented with an increase in mobile access.Proc. Natl. Acad. Sci. USA. 2020; 117: 28678-28683Crossref PubMed Scopus (24) Google Scholar,26ZuiderveenBorgesius F.J. Trilling D. Möller J. Bodó B. De Vreese C.H. Helberger N. Should we worry about filter bubbles?.Internet Policy Review. 2016; 5: 1-14Google Scholar,27Guess A. Nyhan B. Lyons B. Reifler J. Avoiding the Echo Chamber about Echo Chambers.2. Knight Foundation, 2018: 1-25Google Scholar,28Bruns A. Are Filter Bubbles Real?. John Wiley & Sons, 2019Google Scholar,29Eady G. Nagler J. Guess A. Zilinsky J. Tucker J.A. How Many People Live in Political Bubbles on Social Media? Evidence from Linked Survey and Twitter Data. 9. Sage Open, 2019Google Scholar,30Powers E. My news feed is filtered? Awareness of news personalization among college students.Digit.Journal. 2017; 5: 1315-1335Google Scholar,31Puschmann C. Beyond the bubble: assessing the diversity of political search results.Digit.Journal. 2019; 7: 824-843Google Scholar quantitative studies about the existence and influence of ICs are rare, largely because of the lack of an explicit definition of IC and subsequently a benchmark for quantitative analyses. Here we provide a mathematically formal definition of IC in a common scenario of online navigation, namely the recommendation network (RN) that connects similar contents with hyperlinks (URL links) according to algorithmic evaluations32Lü L. Medo M. Yeung C.H. Zhang Y.C. Zhang Z.K. Zhou T. Recommender systems.Phys. Rep. 2012; 519: 1-49Crossref Scopus (830) Google Scholar,33Oestreicher-Singer G. Sundararajan A. Recommendation networks and the long tail of electronic commerce.MIS Q. 2012; 36: 65-83Crossref Scopus (168) Google Scholar,34Kumar A. Hosanagar K. Measuring the value of recommendation links on product demand.Inf. Syst. Res. 2019; 30: 819-838Crossref Scopus (16) Google Scholar (Figure 1, Figure S1). Denoting G(V,E) a directed RN where V and E are a set of nodes (objects) and a set of directed links (hyperlinks), then an IC is defined as a subset C∈V such that (1) the subgraph G[C] induced by C is strongly connected, and (2) there is no outgoing link from a node in C to a node outside C. A node belonging to an IC is called an IC node (note, a node at most belongs to one IC) and the number of nodes in an IC is called its size. With such a definition, the aim of this paper is threefold: (1) To quantify the impact of ICs on the efficiency of online navigation systems; (2) to unfold the mechanism underlying the emergence of ICs; and (3) to provide a solution to ease IC-induced problems. We firstly examine three empirical RNs, namely the Science RN of articles, PNAS RN of articles, and Amazon RN of kindle books, which are collected from the three mentioned websites (see method details for description of data collection). Figure 1 illustrates the case of Amazon. In the website of Amazon, the page of each kindle book lists several recommended books with hyperlinks embedded (Figure 1A). These hyperlinks constitute the Amazon RN (Figure 1B), aiming to help users explore relevant information. Table 1 presents fundamental statistics of the three empirical RNs. In such RNs, the in-degree of a node k largely describes how often the article/kindle book gets recommended by others, and thus well links with its visibility in the network for the surfing users. As shown in Figure 2A , the in-degree distributions of empirical RNs show heavy-tailed patterns. Although most nodes barely get recommended, there are hub nodes that frequently show up in others’ recommendation lists, and thus have much higher chances to be visited by users. In particular, according to the definition, 96, 79, and 1181 ICs in Science, PNAS, and Amazon RNs have been identified, respectively (Figures 1C–1F reveal four typical ICs in Amazon RN, see method details for the identification of ICs). Most ICs in empirical RNs are of rather small sizes (Table S1). This is largely owing to the strict definition, because a large subgraph is unlikely to be strongly connected.Table 1Statistics for the studied recommendation networksRN#Objects#ICs#IC nodesIC trafficNavigabilityEmpirical RNsScience7,7309635094.77%0.44%PNAS59,4797941596.98%0.67%Amazon119,6361,18110,85995.81%0.07%Derived RNsSteam10,97810.00113.7099.99%0.06%Yelp60,7858.90164.9022.85%0.09%Epinions61,2733.0046.3099.98%0.05%MovieLens33,6701.008.0099.99%0.03%The symbol # stands for the number of and IC traffic means the percentage of visits on IC nodes during an N-steps random walk. The results regarding derived RNs are averaged over 20 realizations, and the standard deviations among different realizations are reported in Table S3. Open table in a new tab The symbol # stands for the number of and IC traffic means the percentage of visits on IC nodes during an N-steps random walk. The results regarding derived RNs are averaged over 20 realizations, and the standard deviations among different realizations are reported in Table S3. We apply randomwalks35Masuda N. Porter M.A. Lambiotte R. Random walks and diffusion on networks.Phys. Rep. 2017; 716–717: 1-58Crossref Scopus (365) Google Scholar to simulate users’ surfing activities. Generally, the more nodes being visited within a given number of clicks, the more diverse information could be accessed. Such a quantity can be well characterized by network navigability.36De Domenico M. Solé-Ribalta A. Gómez S. Arenas A. Navigability of interconnected networks under random failures.Proc. Natl. Acad. Sci. USA. 2014; 111: 8351-8356Crossref PubMed Scopus (309) Google Scholar Given an RN with N nodes, its navigability Ω(G) can be defined as the expected coverage of distinct nodes being visited during an N-steps random walk from a randomly selected starting node. Accordingly, a higher navigability suggests higher diversity of information access from the RN. Denoting n(t) the expected number of distinct nodes being visited during a t-steps random walk, for a completely random network, the growth of n(t) follows the dynamicsddtn(t)=1−1Nn(t),(Equation 1) and, thus, we haven(t)=N(1−e−t/N)(Equation 2) Hence, the corresponding navigability isΩ=n(N)N=1−1e≈63.21%.(Equation 3) To validate the above prediction, we create random RNs with N=5×104 nodes by letting each node connects to L=5 others randomly. As shown in Figure 2B, simulations in random RNs well follow such prediction. However, to our surprise, navigabilities of the three empirical RNs are all less than 1% (see Figure 2C), whereas IC nodes monopolize most traffic (generally ≥95%, see Table 1). As in-degree distributions of the three RNs are heavy-tailed, it is also possible that hub nodes with large in-degrees dominate the traffic. To separate effects from ICs and hub nodes, we apply the link-crossing operations sufficiently many times to get first-order null networks.37Maslov S. Sneppen K. Specificity and stability in topology of protein networks.Science. 2002; 296: 910-913Crossref PubMed Scopus (2293) Google Scholar In each operation, two links, say a→b and c→d, are randomly selected and switched as a→d and c→b. The selection ensures the avoidance of multiple links and loops. In a null network, the degree sequence keeps unchanged while ICs are absent. As shown in Figure 2C, in despite of the presence of hub nodes, n(t) curves for null networks closely follow the prediction of random networks, suggesting that IC nodes rather than hub nodes result in poor navigabilities. To further demonstrate the impact of ICs on navigability, we insert ICs to completely random RNs where each node connects to Lrandom others. To insert an IC to the RN, we randomly select a node as the target, remove all out-going links of its L recommending nodes, and reconnect the target and its L recommending nodes to form a fully connected network. Then we obtain an IC of size S=L+1. By manipulating the number of inserted ICs, the number of IC nodes, denoted as c, can be controlled accordingly. Assuming c>0 IC nodes are inserted into a random RN. The random walk in this network can thus be regarded as a Bernoulli process, where at each step, the walker has a probability of ρ=c/N to visit an IC node, and thereby fall into an IC. The number of steps until falling into an IC for the first time, denoted as s0, follows a Geometric distribution as p(s0=t)=ρ(1−ρ)t. Consequently, the expected number of steps until falling into an IC is ⟨s0⟩=1/ρ=N/c. Once the walker falls into an IC, only the nodes within this IC can be visited. Therefore, the number of distinct visited objects during an N-steps random walk can be calculated by summing up two parts: visited nodes before and after falling into an IC. Accordingly, we haven(N)=n(t=s0)+S−1=N(1−e−s0N)+S−1.(Equation 4) Taking s0=N/c into the above equation, the navigability of a random RN with c IC nodes is thusΩ=n(N)N=1−e−1c+S−1N.(Equation 5) As shown in Figure 2D, the simulation in random RNs with manipulated ICs suggests the rapid decrease of navigability as predicted. Impressively, with even one IC inserted, the navigability dramatically drops to 14.19%. With more ICs being inserted, the navigability further decreases. Therefore, we conclude that the existence of ICs largely causes to the poor navigability of RNs. Though it is very likely that links in empirical RNs connect similar objects, we do not know the exact mechanism underlying empirical RNs. Therefore, we next generate RNs by implementing mainstream recommendation algorithms based on datasets of real user-object interactions. We consider four real datasets (Steam, Yelp, Epinions, and MovieLens, see method details), each of which can be described by a bipartite network GB(U,O,EB) where U={u1,u2,⋯,uM} is the set of users, O={o1,o2,⋯,oN} is the set of objects, and EB is the set of links between users and objects.38Zhou T. Ren J. Medo M. Zhang Y.C. Bipartite network projection and personal recommendation.Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2007; 76: 046115Crossref PubMed Scopus (891) Google Scholar,39Shang M.S. Lü L. Zhang Y.C. Zhou T. Empirical analysis of web-based user-object bipartite networks.Europhys.Lett. 2010; 90: 48006Crossref Google Scholar According to many widely applied similarity-based recommendation techniques, a recommendation network G can be generated by linking each object to its top-L most similar objects with pairwise similarity being defined based on GB. We adopt the common neighbor index40Liben-Nowell D. Kleinberg J. The link prediction problem for social networks.J. Am. Soc. Inf. Sci. Tec. 2007; 58: 1019-1031Crossref Scopus (3033) Google Scholar,41Lü L. Zhou T. Link prediction in complex networks: a survey.Phys. A Stat. Mech. Appl. 2011; 390: 1150-1170Crossref Scopus (1972) Google Scholar,42Liu J.G. Hou L. Pan X. Guo Q. Zhou T. Stability of similarity measurements for bipartite networks.Sci. Rep. 2016; 6: 18653Crossref PubMed Scopus (44) Google Scholarsαβ=∑u∈Ubuαbuβ+ϵ,(Equation 6) where ϵ→0 is a tiny random number used to remove degeneracy caused by same similarity scores and B(M×N) is the adjacency matrix of GB with buo=1 if user u connects with object o and buo=0 otherwise. Analogous to the empirical RNs, all four derived RNs have heavy-tailed in-degree distributions (see Figure 3A ), suggesting that the similarity-based recommendation technique tends to emphasis on some particular objects, making them frequently recommended. A few ICs also emerged in derived RNs. Though generally with very small sizes (Table S2), these ICs monopolize a significantly large amount of traffic (see Table 1). In particular, as shown in Figure 3B, derived RNs have much lower navigabilities in comparison with random RNs. An N-steps random walk can only find 0.06%, 0.09%, 0.05%, and 0.03% objects in Steam, Yelp, Epinions, and MovieLens RNs respectively. The results for other well-known similarity indices are close (see Table S3 for results of Jaccard index,41Lü L. Zhou T. Link prediction in complex networks: a survey.Phys. A Stat. Mech. Appl. 2011; 390: 1150-1170Crossref Scopus (1972) Google Scholar,42Liu J.G. Hou L. Pan X. Guo Q. Zhou T. Stability of similarity measurements for bipartite networks.Sci. Rep. 2016; 6: 18653Crossref PubMed Scopus (44) Google Scholar Salton index,41Lü L. Zhou T. Link prediction in complex networks: a survey.Phys. A Stat. Mech. Appl. 2011; 390: 1150-1170Crossref Scopus (1972) Google Scholar,42Liu J.G. Hou L. Pan X. Guo Q. Zhou T. Stability of similarity measurements for bipartite networks.Sci. Rep. 2016; 6: 18653Crossref PubMed Scopus (44) Google Scholar and heat conduction index17Zhou T. Kuscsik Z. Liu J.G. Medo M. Wakeling J.R. Zhang Y.C. Solving the apparent diversity-accuracy dilemma of recommender systems.Proc. Natl. Acad. Sci. USA. 2010; 107: 4511-4515Crossref PubMed Scopus (737) Google Scholar,43Zhang Y.C. Blattner M. Yu Y.K. Heat conduction process on community networks as a recommendation model.Phys. Rev. Lett. 2007; 99: 154301Crossref PubMed Scopus (233) Google Scholar). In a word, the similarity-based recommendation algorithms can generate ICs and thus lead to poor navigability. A possible cause of ICs is the similarity reciprocity (i.e., if α is among the most similar objects to β, then β is likely among the most similar objects to α) and similarity transitivity (i.e., if both α and β are among the most similar objects to γ, then α and β are likely to be very similar to each other). This subsequently leads to the formation of local clusters if we simply pick up the top-L most similar objects to construct the RN, and ICs are an extreme type of such clusters. To break ICs and thus improve navigability, we suggest a flexible recommendation strategy that selects the L recommended objects of each object from its top-λL (λ>1) most similar objects (see Figure 4A for an illustration). As shown in Figures 4B, S6, and S7, the increasing λ quickly reduces ICs and largely improves navigability. Meanwhile, we should also consider the effect of λ on the ability to hit a user’s interest. To quantify such ability, in each user-object interaction dataset, users are randomly divided into a training group and a testing group, and only the information of training users is used to construct the RN. Each testing user u then performs a random walk starting from one of u's selected objects. After t steps, the hit rate of u's interest isru(t)=hu(t)/(ku−1),(Equation 7) where ku is the number of selected objects of u (i.e., the degree of u in the original user-object bipartite network) and hu(t) is the number of visited objects among the ku−1 selected objects (except for the starting object) during the t-step random walk. The overall retrieval accuracy r(t) is the average of hit rates over all testing users. As shown in Figure 4C and Figure S8, the optimal value of λsubject to the largest r(t) is larger than 1 unless t is very small, and there exists a huge area in the (λ,t) plane wherein the navigability and retrieval accuracy can be simultaneously improved. We further tested whether the flexible recommendation strategy is effective in a real scenario of online navigation. The experiment was carried out in AiQiYi (NASDAQ: IQ), the largest video website in China with about 1.5×108 daily active users and 5×108 monthly active users (about 2/3 users use mobile app). To fill a recommendation position, relevant videos are selected by a series of recall algorithms from all candidates and then sorted by a ranking model. The top item that can pass the final regulation (to filter out violent, porno, and brand-conflicting videos) will be exhibited (see Figure S10 for an illustration of the structure of AiQiYi’s recommender system). The item-based collaborative filtering (ICF) is a major recall algorithm, which finds out the most relevant videos according to recently clicked videos of the target user. Upon each request, the original ICF returns the top-5 most relevant videos. In our experiment, for users in the treatment group, it randomly returns 5 videos from the top-10 most relevant ones, analogous to the flexible recommendation strategy with λ=2. The experiment was conducted in the first two positions of the Guess You Like column on the landing page, which are the hottest positions attracting about 1.5×108 clicks from about 8×107 distinct users per day. To evaluate the performance, we employ two widely used metrics in industry, playing rate (PR) and playing duration (PD). The former is the ratio of playing to clicking of recommended videos, and the latter is the average playing duration (see method details). The experiment lasted one week from November 3 to November 9 in 2020 (daily results are presented in Table S4), with average PR and PD over seven days being 73.22% and 61.37 min for the treatment group (5% users, randomly selected), and 73.12% and 61.33 min for the control group (95% users). Our experiment only made a minute alteration of an elaborately designed and well trained recommender system in industry but brought about 150,000 more video plays per day (the change of PR is statistically significant, see t-test in method details), indicating the effectiveness of the flexible recommendation strategy. Despite ongoing and heated debates on the harm of ICs,11Bakshy E. Messing S. Adamic L.A. Exposure to ideologically diverse news and opinion on Facebook.Science. 2015; 348: 1130-1132Crossref PubMed Scopus (1461) Google Scholar,25Yang T. Majó-Vázquez S. Nielsen R.K. González-Bailón S. Exposure to news grows less fragmented with an increase in mobile access.Proc. Natl. Acad. Sci. USA. 2020; 117: 28678-28683Crossref PubMed Scopus (24) Google Scholar,26ZuiderveenBorgesius F.J. Trilling D. Möller J. Bodó B. De Vreese C.H. Helberger N. Should we worry about filter bubbles?.Internet Policy Review. 2016; 5: 1-14Google Scholar,27Guess A. Nyhan B. Lyons B. Reifler J. Avoiding the Echo Chamber about Echo Chambers.2. Knight Foundation, 2018: 1-25Google Scholar,28Bruns A. Are Filter Bubbles Real?. John Wiley & Sons, 2019Google Scholar,29Eady G. Nagler J. Guess A. Zilinsky J. Tucker J.A. How Many People Live in Political Bubbles on Social Media? Evidence from Linked Survey and Twitter Data. 9. Sage Open, 2019Google Scholar,30Powers E. My news feed is filtered? Awareness of news personalization among college students.Digit.Journal. 2017; 5: 1315-1335Google Scholar,31Puschmann C. Beyond the bubble: assessing the diversity of political search results.Digit.Journal. 2019; 7: 824-843Google Scholar a formal definition of IC is lacking. The primary contribution of this paper is to provide a mathematically explicit definition of IC, and to demonstrate the existence and notably negative impact on the navigability of ICs in both empirical and derived recommendation networks. The definition may appear to be too strict and thus less applicable; however, based on the essence of our research, it can be extended to characterize more generalized substructures of directed networks. For example, the extent a strongly connected subgraphG[C] induced by a node set C is likely to form an IC can be measured by its escaping probability pe(C), defined as the ratio of escaping links (i.e., links from nodes in C to nodes outside C) to all links starting from nodes in C. Then, a strongly connected subgraph with a pe no more than a preset threshold can be treated as a quasi-IC (QIC, see Figure S11). Such an escaping probability of QIC is also closely linked with the system navigability (see method details), which improves the explanation power. For example, as shown in Figure S12, the two QICs in Yelp, respectively of escaping probabilities 0.0111 and 0.0118, dominate 71.86% of the random walk traffic. The remarkably lower IC traffic of Yelp in Table 1 can thus be well explained. Similarity based recommendation algorithms used to be popular and are still important modules in industrial recommender systems up to date.32Lü L. Medo M. Yeung C.H. Zhang Y.C. Zhang Z.K. Zhou T. Recommender systems.Phys. Rep. 2012; 519: 1-49Crossref Scopus (830) Google Scholar,44Smith B. Linden G. Two decades of recommender systems at amazon.com.IEEE Internet Comput. 2017; 21: 12-18Crossref Scopus (338) Google Scholar Present simulations on similarity-based algorithms indicate that recommender systems, by nature of their design, tend to insulate users from exposure to diverse content. Recent ethical studies19Helberger N. Karppinen K. D'acunto L. Exposure diversity as a design principle for recommender systems.Inf. Commun. Soc. 2018; 21: 191-207Crossref Scopus (148) Google Scholar,45Milano S. Taddeo M. Floridi L. Recommender systems and their ethical challenges.AI Soc. 2020; 35: 957" @default.
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• W4313256323 title "Information cocoons in online navigation" @default.
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