Behavior patterns of online users and the effect on information filtering

Behavior patterns of online users and the e ff ect on information filtering Cheng-Jun Zhang , An Zeng , ∗ Department of Physics, Univer sity of F ribour g , Chemin du Mus ´ ee 3, CH-1700 F ribour g, Swi tzerland Abstract Understand ing the s tructure and e volution of web-based user -object bipartite netw orks is an important task si nce they play a fu ndamen tal role in online infor mation filtering. In this paper, we focus on in vestigating the patterns of online users’ beha vior and the e ff ect on recommen dation process. Empirical analysis o n the e -commer cial systems s how that users hav e significant taste diversity and the ir interests for niche items highly overlap. Additionally , r ecommend ation process are in vestigated on both the real networks and the re shu ffl ed n etworks in w hich real users’ behavior patterns can be gradually destroyed. Our results shows that the perf ormance of personalized r ecommen dation metho ds is strongly related to the real n etwork structur e. Detail study on each item shows tha t recomm endation accuracy fo r hot items is almo st maximum an d q uite robust to th e resh u ffl ing process. Howe ver , niche items ca nnot be accurately recommen ded after removin g users’ beh avior patter ns. Our work also is meaningful in p ractical sense since it reveals an e ff ectiv e direction to improve the accu racy an d the robustness o f the existing recommender systems. K e y wor ds: bipartite networks, reshu ffl ing process, information filtering 1. Introduction Complex n etworks have been studied intensively for more than a decade. The rapid development of network science has greatly helped us to under stand and m odel real systems [1]. So far, many systems have been d escribed by networks includin g th e transpo rtation system [2], neura l sy stem [3], social system [4], p ower gr id [5] an d so on. Some oth er systems coupled by two di ff eren t elements a re m odeled by the b ipartite ne tworks. For example, the online commercia l systems [6] and the scientific collaborative systems [7] are well represented by such networks. W ith the help of the network structure , many novel meth ods h av e been proposed to improve the fu nction of real systems. Th e on line comm ercial system is a good examp le. Now adays, we can simply ord er boo ks, movies, clothes from the online retailer even at ho me. Howe ver , like a coin has both sides, internet also brings us overab undan t informa tion so that we always have too many cand idate pr oducts to compar e. In o rder to solve the p roblem, ma ny recommen dation algorithm s such as co llaborative filtering [8], conten t-based ana lysis [ 9], spectral analysis [10] and iterativ e self- consistent refinemen t [1 1] w ere developed to filter irr elev ant info rmation. Recently , so me physical dy- namics on the bipartite networks, includin g mass d i ff usion [12] and heat con duction proce ss [13], have been applied to d esign reco mmend ation algorithms. Hybrid of these so -called ne twork-based infer ence method s (NBI) is shown to hav e sign ificant improvement in bo th recommen dation accu racy and item diversity compar ed to the tradition al methods [14, 15]. When stu dying the recomm endation, most o f the previous works are dev oted to imp rove th e pe rforman ce o f the recomme ndation a lgorithms by examin ing their method s o n some stand ard d atasets [1 6]. However , the n etwork structure pro perties will inevitably a ff ect the recomm endation proc ess [ 17]. For example, given a recom mendation method, its the per forman ce would change from one netw ork to an other . Actually , how much do the recommend ation method rely on typical d ata are still unclear . T o answer su ch question , it is useful to investigate the users’ online behaviors in di ff e rent real systems. Previous works have fou nd th at peop le’ s behavior ar e far di ff erent from rando m ∗ Correspondi ng author Email addr esses: an.zeng@ unifr.ch (An Zeng) Prep rint submitted to Elsevi er Septembe r 27, 2018 100 200 300 10 0 10 1 10 2 10 3 (a) Movielens d p(d) 0 300 600 900 1200 10 0 10 1 10 2 10 3 10 4 (b) Netflix d p(d) 0 500 1000 10 0 10 2 10 1 10 3 10 4 10 5 (c) Delicious d p(d) 500 1000 1500 2000 10 0 10 2 10 4 10 6 (d) Amazon d p(d) real data reshuffled real data reshuffled real data reshuffled real data reshuffled Figure 1: (Color online) T he distrib ution P ( d ) in real systems where d is the avera ge degre e of selected items for each user . and ob ey certain predictable rules [ 18]. Therefor e, the user s’ on line b ehavior will emerge som e typical statistical patterns o n th e n etwork structure. Consequ ently , these pattern s will influ ence the recom mendation proce ss ba sed on the networks. In this p aper, we focus on u nderstand ing online users’ statistical behavior pattern and the re lated e ff e ct on in for- mation filtering. W e will co mpare the real b ipartite networks w ith the rando mized coun terpart n etworks (i. e. the reshu ffl ed ne tworks) in which re al users’ behavior pattern a re d estroyed. Ac tually , some spec ific pro perties of the real networks has been disco vered by the comparison to the reshu ffl ed networks such as the loop distrib ution [19 , 20], rich club [ 21, 2 2], commu nity stru cture [ 23], assortative [ 24] a nd motifs [2 5]. Here, we find tha t on line users have significant taste diversity and their interests for niche items h ighly overlap. Add itionally , recommen dation process are in vestigated o n both the rea l networks and the reshu ffl ed networks. W e fin d that the per forman ce o f popularity -based recommen dation methods don’t rely on the r eal network structur e while the perform ance of personalized recommen - dation methods is strongly related to it. Detail study on the personalized methods in dicate that r ecommen dation accu- racy f or hot items is alm ost maximum and quite ro bust to the reshu ffl ing process. On the contrary , niche items cannot be accur ately reco mmende d witho ut real users’ behavior prope rties. Moreover , our work is meanin gful in p ractical aspect since it r ev eals an e ff ec ti ve direction to improve the accur acy and the robustness of th e existing rec ommend er systems. 2. Statistical behavior pattern of online users T able 1: Propertie s of the used datasets network Users Items Links Sparsity Movielens 943 1 , 682 82 , 520 5 . 20 · 10 − 2 Netflix 3 , 000 3 , 000 197 , 248 2 . 19 · 10 − 2 Delicious 10 , 000 232 , 657 1 , 233 , 997 5 . 30 · 10 − 4 Amazon 99 , 622 645 , 056 2 , 036 , 091 3 . 17 · 10 − 5 In this paper, the datasets that we will u se are the su bsets of data ob tained from four online system s: Movie- lens (http: // www .g rouplen s.com / ), Netflix (http: / / www .n etflixprize.co m / ), Delicious ( http: // www .delicious.com / ) and 2 10 1 0 20 40 60 80 100 120 (a) Movielens user degree ˜ S 10 1 0 100 200 300 400 (b) Netflix user degree ˜ S 10 0 10 1 10 2 0 2 4 6 (c) Delicious user degree ˜ S 10 0 10 2 10 1 0 0.5 1 1.5 2 (d) Amazon user degree ˜ S real data reshuffled real data reshuffled real data reshuffled real data reshuffled Figure 2: (Color online ) The inter-si milarity e S among all the selected items for each user vs user’ s degree . For a give n x , its corresponding e S is obtaine d by av eraging ov er al l the it ems whose de grees are in t he rang e of [ a ( x 2 − x ) , a ( x 2 + x )], where a is chosen as 1 2 log 5 for a bette r illustration. Amazon (http: // www .amazon.com / ). These data are r andom samplings of t he whole records of user acti vities in these websites, the descriptions of data are gi ven in T able I. T o inv estigate u sers’ behavior p attern, we will comp are th e real b ipartite n etworks with the re shu ffl ed networks. In each step of the reshu ffl in g process, we first rando mly pick two links from the real n etwork, for examp le, one is from user i to item α an d the other is from u ser j to item β (thro ughou t this paper we use Gr eek and Latin letter s, respectively , for ob ject- and user-related indic es). T hen we rewire the se two links b y i to β and j to α . Hence, the degree o f the users and items would not be ch anged by this reshu ffl in g p rocess while the links in this reshu ffl ed networks are random ized. D enoting T as the reshu ffl ing times and L as the total link s in the networks, we fix T / L = 3 in the following analysis. After the reshu ffl ing pro cess, user s’ degree and items’ degree are preserved while the c orrelation b etween users and item s are destroyed. T o begin our comparison, we focus on the a verage d egree of users’ selected items. Sup pose a user i selects m item s with degree k α ( α = 1 , 2 , .. ., m ) , we calculate the a verage d egree of the item s that he / she selected as d i = P m α = 1 k α m . Actually , the distribution of d reflects t he taste div ersity of the users. Wh en all th e users p refer the same type of items, u sers’ d will be the same to each other . Consequen tly , the distribution o f d will be extremely n arrow . On the con trary , the distribution of d will be quite flat if all th e users seek fo r d i ff erent items. W e then compa re the distribution P ( d ) in real networks and th eir reshu ffl e d networks. As sh own in fig. 1, P ( d ) in r eal networks inde ed are much boarder than that in the reshu ffl ed networks. Obvious, users hav e obvious t aste diversity in r eal systems. Secondly , fo r each user we study the inter-similarity am ong all his / her selected items. Th e similarity of tw o items is ca lculated by the comm on neighb or here [ 26]. Suppo se a u ser i selects m items an d th e similarity between item α and β is d enoted a s s αβ , the in ter-similarity among a ll th ese m items can be obtained b y e S i = 2 P m α = 2 P α β = 1 s αβ m ( m − 1) . In fact, e S indicates the taste diversity fo r ea ch single user . Specifically , when a user always select for the sam e kind of items, e S f or him / her will be high. On the o ther hand, if the interest of a user cha nges from time to time, his / her e S will be very low . A s shown in fig. 2, com pared to the r eshu ffl ed networks, the inactive users (i.e . u sers with small d egree) in real systems show a higher e S while the active u sers (i.e. u sers with large degree) are with lower e S . Actua lly , since the inactiv e users in real n etworks do not have m uch experience in seeking for their own interested objects, they tend to co nservati vely choose several most popular o bjects. Hen ce, th eir selected items are very similar . On the c ontrary , activ e users in real system s are more likely to explore an d try di ff erent kin ds of u npop ular obje cts. The refore, their selected items are with low e S . Similarly , for ea ch item we in vestigate the inter-similarity amon g all the users who selecte d it. Assume a item α is cho sen by n users and the similarity b etween user i and j is den oted as s i j , the in ter-similarity am ong all these 3 10 0 10 1 0 20 40 60 80 (a) Movielens item degree ˜ S 10 0 10 1 10 2 0 20 40 60 (b) Netflix item degree ˜ S 10 0 10 2 10 1 0 2 4 6 8 10 12 (c) Delicious item degree ˜ S 10 0 10 2 10 1 0 1 2 3 4 5 (d) Amazon item degree ˜ S real data reshuffled real data reshuffled real data reshuffled real data reshuffled Figure 3: (Color online) The int er-simil arity e S among all the select ing users for each item vs ite m’ s degree. The e S is av eraged by the same proc ess in fig.2. users can b e calcu lated b y e S α = 2 P n i = 2 P i j = 1 s i j n ( n − 1) . Actually , e S r eflects wheth er a specific item is selected by the same group o f users. In fig.3, we stud y e S α in th e real networks and the re shu ffl ed n etworks. For hot items (i.e. item with large degree), th eir selecto rs in real networks have a lower e S than those in th e reshu ffl ed networks. Howe ver , th e selectors of niche items (i.e. item w ith small degree) enjoy a hig her inter-similarity in the real networks than tho se in the reshu ffl ed networks. As we k now , the personalized recomme ndation s ystems gen erally filter relev ant information by cooperating th e h istory of similar users, the overlap of users’ interests fo r n iche items is very m eaningfu l. I t makes the limited h istorical in formatio n for these nich e items valuable fo r the recom mendation systems to refe r to. In next section, we will detailedly in vestigate how these user s’ online behavior pattern s a ff ect the recommendatio n pro cess. 3. The e ff ect on information filtering In order to r ev eal the e ff ec t of users’ on line behavior patterns o n in formatio n filtering, we in vestigate the rec- ommend ation proc ess on both the r eal ne tworks and th e reshu ffl e d n etworks in which r eal users’ b ehavior patterns are destroied. W e consider four co n ventional recomm endation algo rithms inc luding mass di ff usion (MD), h eat co n- duction (HC), collabor ativ e filterin g (CF), pop ularity-ba sed (PR) methods. W e will stud y how the r ecommend ation perfor mance is in fluenced when we gradually remove users’ real b ehavior p atterns. W e first briefly d escribe these algorithm s. Con sider a system o f N user s and M item s repr esented b y a b ipartite network with adjacency matrix A , where the element a i α = 1 if user i has collected ob ject α , and a i α = 0 o therwise. For a target u ser i , the M D alg orithm starts by assignin g one unit o f r esources to ob jects collected by i , and r edistributes the resource thr ough the user-item network. W e deno te th e vector f as th e initial resou rces on items wher e f α is the resource possessed by object α . T he redistribution is r epresented by e f = W f , where W αβ = 1 k β N X l = 1 a l α a l β k l , (1) is the di ff usion m atrix, with k β = P N i = 1 a i β and k l = P M γ a l γ denoting the degree of ob ject β and user l re spectiv ely [1 2]. T echnically , r ecommen dations for a given user i ar e obtaine d b y settin g th e initial r esource vector f i in acc ordance with the ob jects the user has already co llected, that is, b y setting f i α = a i α . The resulting rec ommend ation list of uncollected objects is then sor ted accor ding to e f i α in d escending order . Phy sically , the di ff usio n is eq uiv alent to a three-step rand om walk starting with k i units of resources o n the target user i . The re commend ation score of a n item 4 0 200 400 600 0 0.2 0.4 0.6 0.8 1 (a) Movielens item degree F 0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 (b) Netflix item degree F 0 500 1000 250 750 0 0.2 0.4 0.6 0.8 1 item degree F (c) Delicious 0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 item degree F (d) Amazon MD HC CF PR Figure 4 : (Color online) The total rec ommendation score F vs it em deg ree in di ff e rent recommend ation systems. The ma ximum F for eac h method has been scaled to 1. is taken to be the amo unt o f r esources o n it after the di ff u sion. The scores f or objects that user i hav e already collected are set to 0. The rec ommend ation list for u ser i is generated by rank ing all h is / her un collected objects in d escending order of their final resources. The HC algorithm works similar to the MD algorithm, the only di ff erence is the di ff usion matrix is calculated as W αβ = 1 k α N X l = 1 a l α a l β k l . (2) Physically , the te mperatur e of an object is consider ed to be th e average tem peratur e of its n earest n eighbo rhood , i.e. its connected users. Th e higher the temperature of an item, the higher its recommen dation sco re [13]. The C F algorithms p rovide recom mendation s based on user o r item similarities. Here, we consider the item-based CF which has b een successfully applied to many online ap plications such as Amazon (on e of the largest online produc t retailers). In the item -based CF metho d, the recommenda tion score o f an item is evaluated based on its similarity with the collected items of the target user . The final recommen dation s core for each item can be written as e f i α = M X β = 1 s αβ a i β . (3) where s αβ is the similarity b etween item α and β [16]. The measur e of similarities used in CF is su bject to definition . Here we simply define the similarity as the number of common neighbo rs in the bip artite networks. The PR algor ithms is very simp le and c ommon ly used in m any websites. In this method , the recomm endation score for each item is proportio nal to its po pularity . Actually , the di ff erence of th ese recom mendation methods has been stu died in de tail in ref . [27]. In order to further understan d these meth ods, we calcula te the total recomme ndation score fo r eac h item as F α = P N i = 1 e f i α . Th e result is shown in fig. 4 . In statistical sense, the MD, CF and PR meth ods assign hig h recomm endation score to th e h igh degree items. In HC m ethod, the items with low degree are g enerally with h igh reco mmend ation s core. Therefo re, the M D, CF a nd PR metho ds ten d to r ecommen d the pop ular items w hile the HC m ethod in clines to recomm end unp opular items. W e then apply all these methods to th e real ne tworks an d th eir reshu ffl ed netw orks to see how u sers’ r eal beha vior patterns a ff e ct the reco mmend ation. Similar to previous work [1 4], to test the recomm endation result we rando mly remove 10% of th e lin ks (the probe set deno ted as E P ). W e then ap ply th e alg orithms to th e r emainder (th e tr aining set denoted as E T ) to produ ce a recomm endation list fo r each user . 5 0 1 2 3 0 0.2 0.4 0.6 (a) Movielens T/L 0 1 2 3 0 0.2 0.4 0.6 (b) Netflix T/L 0 1 2 3 0.2 0.3 0.4 0.5 (c) Delicious T/L 0 1 2 3 0.2 0.3 0.4 0.5 (d) Amazon T/L MD HC CF PR Figure 5: (Color online) The ranking score < RS > of di ff erent recommendati on methods when reshu ffl ing the real networks. T is the reshu ffl ing steps and L is the total links in the networks. In ord er to measure the accuracy of the recommend ation result, we make use of the rank ing scor e index [12]. For a target user , the r ecommen der system will return a ran king list o f all h is uncollected objec ts to h im ac cording to the recom mendation scores. For each hidde n user-object relation ( i.e., the link in pro be set), we measure th e ran k of the ob ject in the reco mmendatio n list of this user . For example, if there are 1 000 u ncollected ob jects fo r u ser i , and o bject α is at 10th place, we say the position of this ob ject is 1 0 / 100 0, denoted by RS i α = 0 . 0 1. A successful recommen dation result is expected to highly recomm end the it ems in the prob e set, and thus leading to small ranking score. A veraging over all th e hid den user-object rela tions, we obtain the mean value of r anking score to evaluate the recommen dation accu racy , namely < R S > = 1 | E P | X i α ∈ E P RS i α , (4) where i α d enotes the p robe link co nnecting user i a nd ob ject α . Clearly , the sm aller the ran king score, th e hig her the algorithm ’ s accuracy , and vice versa. In fig. 5 , we rep ort how the ranking score o f di ff e rent recommend ation meth ods will be influenced when we gradua lly remove real users’ be havior patterns. The results show that the r anking score of PR is hard ly a ff ected by the reshu ffl ing proc ess. It is reason able because the PR me thod doesn’t rely on the d etail bip artite network structure an d giv es th e r ecommen dation scor e for each item simply ac cording to its po pularity . On th e contrar y , the person alized recommen dation su ch as the MD, HC and CF m ethods are influenc ed. Obviously , th e ran king score of HC metho d increases most sign ificantly when we reshu ffl e the n etworks. In fact, the HC method is co nsidered as an e ff ective method to enh ance reco mmendatio n div ersity by mainly p redicting users’ prefe rence for niche item s. Therefo re, the result implies that witho ut the re al correlation b etween users an d items, on ly the inf ormation of d egree is insu ffi cient for the re commend ation systems accurately providin g a di verse recomm endation . Mo re specifically , as we d iscussed in th e p revious section, user s’ inte rests for n iche items highly overlaps in real systems. Hence, the r ecommend ation systems can predict target user’ s poten tial niche items by coo perating the information from his / her similar users. Howe ver , in the reshu ffl ed network s users’ interests f or niche items only slightly overlap, so there is litt le informatio n from the similar users f or the r ecommen dation engin es to refer to. It finally leads to the seriou s incremen t in the ranking score of HC method. As recommendation algorithms w hich tend to recom mend popu lar items, MD and CF m ethods ar e not so sensitive to the resh u ffl ing pro cess as the HC m ethod. In the de nse networks like Movielens and N etflix, the ran king scores of MD an d CF stay alm ost un changed . Howe ver , in th e spa rse n etworks like Delicious an d Am azon, th e r anking scor e of MD and CF metho ds sh ow an obser vable increment. In order to s ee the e ff ect of th e reshu ffl ing process o n the M D 6 10 0 10 1 10 2 0 0.2 0.4 0.6 0.8 1 (a) Movielens item degree 10 0 10 1 10 2 0 0.2 0.4 0.6 0.8 (b) Netflix item degree 10 0 10 1 0 0.2 0.4 0.6 0.8 (c) Delicious item degree 10 0 10 1 10 2 0 0.2 0.4 0.6 0.8 (d) Amazon item degree 10 0 10 1 10 2 0 0.2 0.4 0.6 10 0 10 1 0 0.2 0.4 0.6 10 0 10 1 0 0.5 1 10 0 10 1 10 2 0 0.5 1 real data(MD) reshuffled(MD) real data(CF) reshuffled(CF) Figure 6: (Color online) Dependence of ranking score < RS > on the item de gree. The < RS > is ave raged by the same process in fig.2. The main figures are the result s of MD method while the inserts are the results of CF method. and CF methods in detail, we study the ranking score for each item, namely < R S α > = 1 | E P α | X i α ∈ E P α RS i α , (5) where E P α denotes all the links in the probe set th at co nnect to item α . T hen we can see the r elation between items’ degree and their ran king score, the result is reported in fig. 6. In real networks, th e hot items enjoy a lo w ran king score ( < RS > ≈ 0) while the niche items are with high ranking score (It can b e ev en higher tha n the random recommend ation whose < RS > = 0 . 5). It sug gests that the re commend ation accu racy fo r the ho t items is almo st maximum and cannot be im proved anymore. However , nich e items’ accur acy is quite low and has p lenty of ro om for imp rovement. Therefo re, in ord er to de sign an more e ff ective persona lized recom mendation m ethod th an c urrent ones, it is cru cial to solve the co ld start pro blem [28], i. e. to imp rove the rec ommend ation for niche items. An other interesting fin ding is that o nly the ran king scores fo r unp opular items are a ff e cted by th e resh u ffl ing process while the rank ing score fo r popular items stays almost t he same. Since lots of items are with lo w degree in the sparse networks such as De licious and Amazon, the average ranking sco re increases with the resh u ffl ing process. In the Movielens an d Netflix netw orks where the link s are r elativ ely den se, fewer item s are w ith low degree in these networks. Acco rdingly , the average ranking sco res fo r MD an d CF d o no t incr ease mu ch. Fro m the pra ctical po int of view , if on e want to enhan ce the robustness of the r ecommen der system, the m ost e ff ective way is to preserve th e recomm endation result fo r nic he items since they are s ensitive to r andomn ess. Precious study reveals that hybr id o f the MD and HC me thods can result in significan t improvement in bo th recommen dation accu racy an d item diversity [1 4]. Actually , this hyb rid method is implemen table b ecause the HC method can e ff ectively catch the users’ taste for nich e items. As th e recomm endation accuracy for HC method in th e reshu ffl ed network s is almost th e same as r andom rec ommend ation ( < RS > = 0 . 5), the h ybrid meth od is impossible to b e car ried ou t in the systems where users rando mly choose their items. It me ans th at user s’ be havior p atterns in real systems are essential for solving the di versity-accura cy dilemma of recommen der system s. 4. Conclusion The de velopment for network science has gr eatly improved the function as well as our understanding to many real systems. In recom mendation which is con sidered as a pro mising way to so lve the p roblem of inf ormation overabun- dance, researchers ha ve desig ned the network-b ased inference methods to improve the recommenda tion performan ce. 7 For exam ple, with the help o f som e typical ph ysics dy namics on the bipar tite ne tworks, the mass di ff u sion and heat condu ction algo rithms ha ve been proposed to improve the reco mmendatio n accu racy an d div ersity respecti vely . In this pap er , we investigate the users’ on line b ehavior patterns and related e ff ec t on inform ation filtering. we compare the real bip artite networks with the reshu ffl e d networks in which users’ b ehavior patterns are g radually removed. we find that online users have significan t taste div ersity and their interests fo r nich e item s highly overlap. I n addition, we find that the perfo rmance o f pop ularity-b ased recom mendation me thods don’t rely on the real network structure while th e performance of personalized re commend ation methods is strongly related to it. Detail study o n the personalized m ethods indicates that reco mmenda tion accuracy fo r hot items is almo st maximum and quite r obust to the reshu ffl ing process. On the co ntrary , niche items cannot be accurate ly recommend ed witho ut real users’ be havior proper ties. From the pr actical poin t of v iew , in or der to design a mo re accur ate person alized recomm endation m ethod than current on es, our r esults sug gest that it is crucial to imp rove the recom mendation f or niche item s. If o ne wants to enhance the robustness of the recom mender system, th e most e ff e cti ve way is to pr eserve the reco mmendatio n result for niche items. 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