Preference Function Learning over Numeric and Multi-valued Categorical Attributes

Transcription

1 Preference Functon Learnng over Numerc and Mult-valued Categorcal Attrbutes Lucas Marn 1, Antono Moreno and Davd Isern Abstract. 1 One of the most challengng goals of recommender systems s to nfer the preferences of users through the observaton of ther actons. Those preferences are essental to obtan a satsfactory accuracy n the recommendatons. Preference learnng s especally dffcult when attrbutes of dfferent knds (numerc or lngustc) ntervene n the problem, and even more when they take multple possble values. Ths paper presents an approach to learn user preferences over numerc and mult-valued lngustc attrbutes through the analyss of the user selectons. The learnng algorthm has been tested wth real data on restaurants, showng a very good performance. 1 Introducton Nowadays t s practcally unconcevable to select our summer holday destnaton or to choose whch flm to see n the cnema ths weekend wthout consultng specalzed sources of nformaton n whch, n some way or another, our preferences can be specfed to ad the system to recommend us the best choces. That s because we lve n an era where there are so many data easly avalable that t s mpossble to manually flter every pece of nformaton and evaluate t accurately. Recommender Systems (RS) have been desgned to do ths tme-consumng task for us and, by feedng them wth nformaton about our nterests, they are capable enough to tell us the best alternatves for us n a personalzed way. A RS stores the preferences of the user about the values of some crtera and uses ths nformaton to rate and sort a corpus of alternatves. The management of the preferences, the accuracy of the recommendatons, and how these nterests evolve over tme are three of the most challengng tasks of these type of systems [8]. Concernng the frst goal, RSs may obtan feedback from a user mplctly, explctly or combnng both approaches. Ths paper dscusses an unsupervsed way to nfer the user nterests, whch observes the user nteracton and does not requre any explct nformaton from hm [4]. The crtera used to descrbe the alternatves may have dfferent natures. Some works propose the use of ontologes to represent concepts wthn a herarchy [2,9]. Other researchers use fuzzy logc technques to deal wth lngustc crtera [1,10], and many approaches only consder numercal crtera [5]. Ths paper consders the use of lngustc and numercal data, whch permt a hgh degree of expressvty and can be appled n a wde range of domans. The basc dea s to use the preferences to sort a set of alternatves, show ths ordered lst to the user, and observe hs fnal selecton. Wth ths nformaton, the preference learnng algorthm s able to modfy the user profle so that t captures better the user preferences and the next recommendaton s more accurate. The rest of the paper s organzed as follows. Secton 2 ncludes a bref explanaton of the related work the authors conducted n the area of preference learnng over lngustc and numerc attrbutes, explanng how the nterests of users over certan attrbutes or crtera are managed and learned. Secton 3 explans a new approach to manage categorcal attrbutes when they can take multple lngustc values n a sngle alternatve. Secton 4 descrbes how a more expressve functon whch defnes the behavour of the preference over numerc attrbutes can be automatcally learned. In Secton 5 the case study where our approach has been tested (restaurant recommendaton) s explaned, descrbng the data set used and the results obtaned. Fnally, Secton 6 gves the man conclusons of the paper and dentfes some lnes of future research. 2 Preference learnng over categorcal and numercal attrbutes When we face a decson problem n whch we requre the ad of a RS to help us make a choce, all of the possble alternatves to sad problem are defned, n most of the cases, by the same attrbutes. In ths work we focus only on categorcal and numerc attrbutes. The followng subsectons explan how preferences over the two dfferent knds of attrbutes are expressed, how alternatves are evaluated and ranked, and how the user nterests are learned and adapted from hs selectons. 2.1 Attrbutes and management of preferences In a recent work ([7]) we proposed to represent the level of nterest over categorcal attrbutes by usng a lngustc scale n whch preference labels are defned as fuzzy sets representng values of preference such as Very Low, Low, Medum, Hgh or Very Hgh (see Fgure 1). 1 Department of Computer Scence and Mathematcs, Unverstat Rovra Vrgl, Tarragona, Catalona (Span). Emal addresses: lucas.marn@urv.cat, antono.moreno@urv.cat, davd.sern@urv.cat.

2 Fgure 1. Example of a lngustc preference set For the case of numerc attrbutes, we assumed that each user has a preference functon for each attrbute. Ths functon has a trangular shape (see ) and s defned as x v pa ( x) 1 pref where p a (x) s the preference of the value x of the attrbute a, and s the wdth of the functon, whch we consdered to be 10% of the attrbute doman. Fgure 2. Basc numerc preference functon 2.2 Alternatves evaluaton When evaluatng an alternatve, the objectve s to aggregate all of the values of all of the attrbutes nto a sngle value. Snce we have two knds of attrbutes, a converson to the same doman s made. In our approach, we chose to translate the numercal preferences to lngustc ones. The translaton s done by, frst, calculatng the value of preference of a certan numerc attrbute value by usng Eq. (1). Then that value s mapped to the fuzzy lngustc labels doman and matched wth the label wth a hgher value n that pont. When all the attrbutes have been assgned a value of preference usng the same fuzzy lngustc scale, all the terms are aggregated usng the ULOWA aggregaton operator [3]. The fnal result of ths aggregaton s the value of preference assgned to the whole alternatve, used to rank the alternatves. 2.3 Preference learnng When the ranked alternatves are presented to the user, two thngs can happen: (a) the user selects the frst ranked alternatve or (b) the user selects any other alternatve. The frst case means that the recommendaton process has worked accurately, snce the system gave the frst place to the selected alternatve. However, n the second case, there were other alternatves (whch we call over ranked) that were consdered by the system as better than the one the user fnally selected. Thus, that s probably ndcatng that the (1) nformaton that we have n the user profle s not accurate enough and should be modfed. In a nut shell, the man ntuton behnd the user profle change algorthm s that we should ncrease the preference on the attrbute values present n the selected alternatve and decrease the preference on the attrbute values appearng n the over ranked alternatves. The nformaton requred to nfer ths reasonng s extracted from what s called relevance feedback. In ths case, t conssts n the over ranked alternatves and the selected one. Numercal and categorcal attrbutes are managed n dfferent ways, as descrbed n the followng subsectons Lngustc preference adaptaton The man dea s to fnd attrbute values repeated among the over ranked alternatves that do not appear on the selecton, whch wll be the canddates for havng hs preference decreased. Smlarly, the preference of the attrbute values that appear on the selecton and do not appear often on the over ranked alternatves s lkely to be ncreased. The nterested reader may fnd a more detaled explanaton of the process of adaptaton of lngustc preferences n [7]. The profle adaptaton s conducted by two processes. The frst one called on-lne adaptaton s executed every tme the user asks the system for a recommendaton, and t evaluates the nformaton that can be extracted from the current ranked set of alternatves. The man goals of ths stage are to decrease the preference of the attrbute values that are causng non-desred alternatves to be gven hgh scores and to ncrease the preference of the attrbute values that are mportant for the user but are not well judged on the bass of the current user profle. For each recommendaton made by the system, two sources of nformaton are evaluated: the selected alternatve, whch s the choce made by the user, and the alternatves that were ranked above t. Values extracted from the over-ranked alternatves haver ther level of preference decreased whereas the ones extracted from the user s fnal selecton that do not appear n the set of over-ranked alternatves have ther preference ncreased. The second one called off-lne adaptaton s trggered after the recommender system has been used a certan number of tmes. It consders the nformaton gven by the hstory of the prevous rankngs of alternatves and the selectons made by the user n each case, but consders that nformaton separately. When the system faces cases n whch the number of over ranked alternatves s not large enough for relable characterstcs to be extracted, t stores the small number of over ranked alternatves n a temporary buffer. After several teratons n whch the number of over ranked alternatves has been nsuffcent for evaluaton, the system wll have recorded enough alternatves to start evaluatng them. When there are enough saved over-ranked alternatves, the values n ther attrbutes wll be analysed and ther preference decreased. Moreover, user selectons are also stored, and after a certan number of choces have been made, they are evaluated wth the objectve to ncrease the preference of the most repeated attrbute values, snce ther repeated selecton ndcates that the user s really nterested n them.

3 2.3.2 Numerc preference learnng The numerc adaptaton of the user profle presented n [6] s nspred by Coulomb s Law: the magntude of the electrostatcs force of nteracton between two pont charges s drectly proportonal to the scalar multplcaton of the magntudes of charges and nversely proportonal to the square of the dstances between them. The man dea s to consder the value stored n the profle (current preference) as a charge wth the same polarty as the values of the same crteron on the over ranked alternatves, and wth opposte polarty to the value of that crteron n the selected alternatve. Thus, the value of the profle s pushed away by the values n the over ranked alternatves and pulled back by the value n the selected alternatve. Two stages have been consdered n the adaptaton algorthm. The frst one, called on-lne adaptaton process, s performed each tme the user asks for a recommendaton. The other stage, called off-lne process, s performed after a certan amount of nteractons wth the user. Fgure 3. Attracton and repulson forces For the on-lne stage, the nformaton avalable n each teraton s the user selecton and the set of over ranked alternatves. In order to calculate the change of the value of preference n the user profle for each crteron t s necessary to study the attracton force done by the selected alternatve and the repulson forces done by the over ranked ones n each crteron, as represented n the example n Fgure 3, n whch the j-th value of the fve over ranked alternatves o 0, o 1, o 2, o 3, and o 4 causes a repulson force F o j, and the value for the same crteron of the selected alternatve, s j, causes an attracton force F s j. Both forces are appled on the j-th value of the profle, P j. The attracton force F s done by the selected alternatve for each attrbute j s defned as 1 sj P j s j f s j P j F ( P, s, j, ) s s j Pj j P j 0 f s j Pj In ths equaton, j s the range of the crteron j, s j s the value of the crteron j n the selected alternatve and P j s the value of the same crteron n the stored profle P. The parameter α adjusts the strength of the force n order to have a balanced adaptaton process. The repulson force exerted by the over ranked alternatves for each crteron j s defned as a generalzaton of Eq.(2) as follows: o 1 no F P, o,..., o, j, no 1 Pj oj 1 P P j o j j oj Fnally, both forces are summed up and the resultng force s calculated. The technques desgned for the on-lne stage fal at detectng user trends over tme snce they only have nformaton of a sngle selecton. The off-lne adaptaton process gathers nformaton from several user nteractons. Ths technque allows consderng changes n the profle that have a hgher relablty than those (2) (3) proposed by the on-lne adaptaton process, because they are supported by a larger set of data. The off-lne adaptaton process can be trggered n two ways: the frst one evaluates the user choces, whle the second one analyses the over ranked alternatves dscarded by the user n several teratons. The possblty of runnng the off-lne process (n any of ts two possble forms) s checked after each recommendaton. In the frst case, the system has collected some alternatves selected by the user n several recommendaton steps, and t calculates the attracton forces (F s ) exerted by each of the stored selected alternatves over the values stored n the profle, usng an adaptaton of Eq. (2), that has as nputs the profle P, the past selectons {s 1,,s rs }, the crteron to evaluate j, and the strength-adjustng parameter α.: ' 1 s rs F P, s,..., s, j, The second knd of off-lne adaptaton process evaluates the set of over ranked alternatves that have been collected through several teratons and whch were not used n the on-lne adaptaton process (because t dd not have enough over ranked alternatves n a sngle teraton). When the stored over ranked alternatves reach a certan number, the off-lne adaptaton process calculates the repulson forces over the profle values exerted by those alternatves (F o ), whch are calculated usng Eq.(3). 3 Mult-valued lngustc attrbutes rs 1 sj Pj 1 s s j P j j Pj As explaned n Secton 2, n our prevous work we consdered categorcal attrbutes that could take only one lngustc value (For example, a cty could have a sngle value n the Clmate attrbute). However, there are cases n whch t s nterestng to consder multple values. One example of that stuaton could be the attrbute Types of food n a restaurant: a restaurant can have the values { Asan, Seafood, Vegetaran } whle another can have only Italan food. Extendng our model so that t can manage lsts of categorcal values mples addressng two ssues: how to represent and calculate the user preferences over the attrbute takng nto account all of the values and how to adapt dynamcally those preferences. 3.1 Preference value on mult-valued attrbutes When there s an attrbute wth multple values a procedure should be defned to decde whch sngle lngustc preference represents better the whole set of lngustc values. Gong back to the restaurant example, f a user has a Hgh preference over Asan food restaurants and a Low preference over Rce dshes, we can argue that the preference we could assgn to the Type of food attrbute n a restaurant wth both values should be Medum (an average of the two knds). If another restaurant only offers Asan food then ts preference should be Hgh, so ths restaurant would have a hgher rankng than the frst one. The ratonale of ths procedure s that t seems more adequate to reward the alternatves that are more focused n the aspects the user really lkes. Ths example represents an average preference aggregaton polcy, however, other polces can also be consdered dependng on the attrbute defnton. (4)

4 3.2 Preference learnng on mult-valued categorcal attrbutes The lngustc algorthm used to adapt categorcal preferences explaned n Secton 2 needs some mprovements to be able to manage lsts of values. When sngle-valued attrbutes were consdered, the user selecton ponted drectly towards the value the user lked for that attrbute. Now, however, we cannot be sure whch one/s of the values lsted n the attrbute s/are the one/s of nterest for the user. That s the reason why t has been necessary to desgn a relevance functon whch ndcates how relevant s a value found among the over ranked alternatves or n the selected alternatve. Relevance s measured n a [0,1] scale, wth 1 meanng maxmum relevance. To calculate how relevant a term t of the attrbute j s among the over ranked alternatves we use ths expresson (the relevance value s 0 f t does not appear n the over ranked alternatves): nt o 1 1 Rj () t (5) no 1 nv j Here, no represents the number of over ranked alternatves, nt the number of over ranked alternatves where t appears, and nv j the number of values that appear for the attrbute j n the alternatve. In ths equaton we consder that every lngustc term that appears n the over ranked alternatves has a relevance whch s nversely proportonal to the number of other values for the same attrbute that appear among the entre set of over ranked alternatves. To calculate the relevance of a term n the selecton we use: 1 s 1 nl (6) Rj () t 2 nv j tv Here nv j represents the number of values that appear for the attrbute j n the selecton, nl the total number of lngustc attrbutes, and tv the total number of lngustc values that appear n the selecton. The relevance of a term n the selecton s the mean between the mportance of the term among the values that appear wth t n the same attrbute and the mportance of each lngustc term that appears n the selecton compared wth the number of lngustc attrbutes. Fnally, after calculatng both partal relevances for all the terms, the overall relevance R j (t) s calculated as: s o R ( ) ( ) ( ) (7) j t Rj t Rj t In concluson, consderng a threshold γ to avod makng changes n the profle wth low relevance, t can be deduced that: If R j (t)>γ, the preference over term t for the attrbute j needs to be ncreased (moved to the next term). If R j (t)<γ, the preference over term t for the attrbute j needs to be decreased (moved to the prevous term). 4 Learnng preference functons for numerc attrbutes Although the numerc preference learnng approach descrbed n Secton 2 provded an adequate way of learnng the deal value of preference over a numerc attrbute, t was unable to learn all of the parameters that model the preference functon such as the slope or the wdth, whch were fxed. The new learnng method presented n ths secton reles on hstorc data about the user selectons to approxmate the preference functon of the numerc attrbutes to the most adequate one. Wth ths approach, we have a new defnton of the functon of preference whch now has 5 parameters (left and rght slope, left and rght wdth, and value of preference) nstead of just the value of preference: ml x vpref 1 f ( x vpref ) l pa ( x) 1 f ( x vpref ) mr x vpref 1 f ( x vpref ) r In ths expresson p a (x) s the preference of the value x of the attrbute a, m l and m r are the functon slope values (for the left and rght sdes of the trangle, respectvely) and l and r are the parameters whch defne the wdth of the functon (also for the left and rght sdes of the trangle, respectvely). An example of graphcal representaton of a preference functon can be seen n Fgure 4, where the left slope s a value under 1, the rght slope s a value over 1, and the left wdth s greater than the rght one. Fgure 4. Numerc preference functon wth 5 parameters The whole process of adaptng the numerc preference functon s depcted n Fgure 5. functon PREF-FUNC-ADAPTATION( V(v 0,,v n ), //hstorc of values of past selectons v pref, //value of maxmum preference v mn, //mnmum numerc value v max, //maxmum numerc value t, //trust nterval s //probablty dstrbuton samplng) begn B=getBestValues(V, v pref, t); PD=calculateProbabltyDstrbuton(B, v mn, v mn, s); {left,rght}=calculatedelta(pd); m{left,rght}=calculatebestslope(pd, v pref, ); PreferenceFuncton=(, m, v pref ); return PreferenceFuncton; end; Fgure 5. Preference functon learnng algorthm The frst step conssts n obtanng the more relable values from the hstorc set of selectons. Ths s done by extractng a percentage of the values closer to the value of preference (trust nterval), normally of 90%. Wth that we avod consderng outler values. Then a probablty dstrbuton functon, represented wth a hstogram, s calculated wth those best values. The sample or (8)

5 dscretzaton step s a parameter, normally around 1% of the doman range. Delta values are then calculated by observng the wdth of the probablty dstrbuton. For example, f the frst value dfferent to 0 n the hstogram s 3 and the last s 56, and the value of hgher preference (v pref ) s 34, l would be 31 and r would be 22. Afterwards, the algorthm generates preference functons wth dfferent combnatons of values for the slope values (m) (n the range from 0 to 4 n steps of 0.2), and compares the dstance between each preference functon and the probablty dstrbuton. The functon wth the lower dstance shows the chosen slope. Fnally, the new preference functon s bult wth the new delta and slope values. 5 Case study: restaurant recommendaton In order to test our new approach to mult-valued attrbute evaluaton and numerc preference functon learnng, we have used data of the restaurants n Barcelona to mplement a RS wth the ablty to learn the users nterests from ther selectons. In the frst part of ths secton a descrpton of the data s gven. Then, a basc explanaton of the whole recommender and learnng algorthm s gven, as well as the preferences setup. Fnally, the results of the evaluaton are provded. 5.1 Barcelona restaurants data The data used n ths problem has been collected from the BcnRestaurantes web page 2. The data set contans nformaton about 3000 restaurants of Barcelona evaluated by 5 attrbutes: 3 categorcal ( Type of food - 15 values, Atmosphere - 14 values, Specal characterstcs 12 values) and 2 numercal ( Average prce, Dstance to cty center ). One example of regster n the data fle s Fonda España; Natonal, Season cusne, Tradtonal; Classc, For famles; Round tables, In a hotel, Wth vdeo; 45; 0.979, beng Fonda España the restaurant name, Natonal, Season cusne and Tradtonal the types of food served, Classc and For famles the restaurant atmosphere, Round tables and In a hotel other mportant restaurant characterstcs, 45 the average menu prce, and km the dstance to the cty centre. 5.2 Recommendaton and adaptaton The set of 3000 restaurants has been dvded n blocks of 15 alternatves that are ranked ndependently, whch gves out a total of 200 dfferent recommendatons. An deal profle was manually defned and three ntal profles were created randomly. The goal s to learn the deal profle startng from these three dfferent ponts. In ths evaluaton the preferences over the categorcal attrbutes are represented wth a lngustc label term set of 7 values, whch are Very Low, Low, Almost Low, Medum, Almost Hgh, Hgh and Very Hgh. The whole process (for each of the three profles, repeated 200 tmes) conssts n: 1. Rankng a set of 15 alternatves accordng the current (ntally random) profle. 2. Smulate the selecton of the user by choosng the alternatve that fts better the deal profle. 3. Extract relevance feedback from the selecton (over ranked alternatves and the selecton tself). 4. Decde whch changes need to be made to the current profle and apply them. Some nformaton about the whole process s stored after each teraton, ncludng the poston of the selected alternatve, the dstance between the deal and current profles, and the preferences over lngustc and numerc values. 5.3 Results evaluaton In order to evaluate the results of the new learnng technques, a dstance functon has been defned to calculate how dfferent the profle we are learnng s to an deal profle whch represents the exact preferences of the user. The frst step s to calculate the dstance for each attrbute, takng nto account f t s numerc or categorcal. The dstance between numerc attrbutes s calculated as c d( n, c, ) 1 p ( ) (9) n vpref n where n s the numercal attrbute, c s the current profle (the one c beng learned), s the deal profle, and pn ( v pref n) s the value of preference of the v pref value for the attrbute n n usng the preference functon of the same attrbute n the profle c. A dstance 0 means that the v pref values n both profles are equal. The equaton to calculate the dstance between categorcal attrbutes s card () l 1 CoG( pl ( vk )) CoG( pl ( vk )) d( l, c, ) card ( l) CoG( s ) CoG( s ) (10) where l s the categorcal attrbute, card(l) s the cardnalty of the attrbute l (.e., the number of dfferent lngustc values t can c take), CoG( pl ( vk)) and CoG( pl( vk)) are the x-coordnate of the centres of gravty of the fuzzy lngustc labels assocated to the value of preference of v k n the profles c and, respectvely, and CoG( smn ) and CoG( s max ) are the centres of gravty of the mnmum and maxmum labels of the doman, respectvely. Fnally, the dstance between two profles s calculated as na k1 1 D( c, ) d( k, c, ) na k 1 (11) where na s the total number of attrbutes. Durng the three tests (one for each ntal random profle) the dstance between the adaptng and the deal profle has been calculated n each teraton. Fgure 6 (contnuous lne) shows the average of the three dstances. It can be seen that the ntal average dstance between the deal and the adaptng profles s around After 200 teratons t reaches a dstance around 0.1. Although 200 teratons may seem a large number, t can also be observed that wth only 50 teratons a very acceptable result of 0.2 s obtaned. To see to what extent the new approach to learn the numerc preference functon explaned n Secton 4 has mproved the result of our prevous work (commented n Secton 2), Fgure 6 also compares the results wth and wthout (dashed lne) that functonalty. It can be seen how the mprovement has been notceable (dstance mprovement of about 0.07). c mn max 2 Last access May 30th, 2012.

6 The second contrbuton, whch s learnng the numerc preference functon, allows shapng a more expressve and personalsed representaton of user preferences over each numerc attrbute, defnng a preference functon wth 5 parameters. Ths addtonal expressvty helped to mprove the profle learnng process by reducng the learnng error around 7%. As a future work, two nterestng lnes can be consdered. As ponted out n Secton 3, an aggregaton polcy can be consdered n the aggregaton of the preferences n a sngle attrbute, other than the use of the common average polcy. Research can be made n ths area n order to learn the aggregaton polcy that fts more the user nterests. Another nterestng lne to consder s to ncorporate nformaton about the numerc preference functon n the dstance measure used to evaluate the algorthm snce, currently, just the value of preference s beng consdered. Fgure 6. Average dstance between current and deal profle To wrap up the results evaluaton, Fgure 7 shows n what poston the user selecton s beng ranked by the RS on each of the teratons n the frst test (the three gve smlar results). Ths fgure shows the results n a more ntutve way. Notce that the system s accurate f the selected alternatve s n the frst postons of the 15- tems lst n each teraton. Many factors can nterfere n the process and make the learnng of the exact deal profle a very hard task, but f the user selecton appears n the frst postons, we can consder that the learnng process s workng properly. As t can be observed n Fg.7, after about 50 teratons, the selected alternatve s among the frst three ones n 95% of the cases (and the frst one n around 70% of the cases). Fgure 7. Poston of the selected alternatve n each teraton (test 1) 6 Conclusons and future work Two man contrbutons wth respect to our prevous work have been presented n ths paper. The frst one conssts n managng mult-valued categorcal attrbutes n the alternatves of a RS, allowng. more expressvty n ther representaton. The system consders a sngle preference for each possble value and aggregates them to fnd out the preference over the whole attrbute. The consderaton of mult-valued attrbutes s mandatory when workng wth alternatves such as the ones presented n ths paper (e.g. Type(s) of Food n a restaurant alternatve). ACKNOWLEDGEMENTS Ths work has been supported by the Unverstat Rovra Vrgl (a pre-doctoral grant of L. Marn) and the Spansh Mnstry of Scence and Innovaton (DAMASK project, Data mnng algorthms wth semantc knowledge, TIN ) and the Spansh Government (Plan E, Spansh Economy and Employment Stmulaton Plan). REFERENCES [1] G. Castellano, C. Castello, D. Dell'Agnello, A. M. Fanell, C. Mencar, M. A. Torsello, Learnng Fuzzy User Profles for Resource Recommendaton, Internatonal Journal of Uncertanty, Fuzzness and Knowledge-Based Systems 18 (4) (2010), [2] I. Garca, L. Sebasta, E. Onanda, On the desgn of ndvdual and group recommender systems for toursm, Expert Systems wth Applcatons 38 (6) (2011), [3] D. Isern, L. Marn, A. Valls, A. Moreno, The Unbalanced Lngustc Ordered Weghted Averagng Operator, n: IEEE Internatonal Conference on Fuzzy Systems, FUZZ-IEEE 2010, IEEE Computer Socety, Barcelona, Catalona, 2010, [4] G. Jawaheer, M. Szomszor, P. Kostkova, Comparson of Implct and Explct Feedback from an Onlne Musc Recommendaton Servce, n: 1st Internatonal Workshop on Informaton Heterogenety and Fuson n Recommender Systems, ACM Press, Chcago, US, 2010, [5] T. Joachms, F. Radlnsk, Search Engnes that Learn from Implct Feedback, Computer 40 (8) (2007), [6] L. Marn, D. Isern, A. Moreno, Dynamc adaptaton of numercal attrbutes n a user profle, Internatonal Journal of Innovatve Computng Informaton and Control (2012). [7] L. Marn, D. Isern, A. Moreno, A. Valls, On-lne dynamc adaptaton of fuzzy preferences, Informaton Scences do: /j.ns (2012). [8] M. Montaner, B. López, J. L. de La Rosa, A taxonomy of recommender agents on the nternet, Artfcal Intellgence Revew 19 (4) (2003), [9] A. Moreno, A. Valls, D. Isern, L. Marn, J. Borràs, SgTur/E- Destnaton: Ontology-based personalzed recommendaton of Toursm and Lesure Actvtes, Engneerng Applcatons of Artfcal Intellgence do: /j.engappa (2012). [10] C. Porcel, A. G. López-Herrera, E. Herrera-Vedma, A recommender system for research resources based on fuzzy lngustc modelng, Expert Systems wth Applcatons 36 (3, Part 1) (2009),