《电子商务 E-business》阅读文献：Managing uncertainty in group recommending processes

User Model User-Adap Inter(2009)19: 207-242 DOI10.1007/s11257-008-9061-1 ORIGINAL PAPER Managing uncertainty in group recommending Luis M. de Campos. Juan M. Fernandez.Luna Juan F Huete. Miguel A Rueda- Morales Received: 25 February 2008/ Accepted in revised form 26 October 2008/ Published online: 21 November 2008 O Springer Science+Business Media B V. 2008 Abstract While the problem of building recommender systems has attracted con siderable attention in recent years, most recommender systems are designed for rec- ommending items to individuals. The aim of this paper is to automatically recommend a ranked list of new items to a group of users. We will investigate the value of using Bayesian networks to represent the different uncertainties involved in a group rec ommending process, i.e. those uncertainties related to mechanisms that govern the interactions between group members and the processes leading to the final choice or recommendation. We will also show how the most common aggregation strategies might be encoded using a Bayesian network formalism. The proposed model can be considered as a collaborative Bayesian network-based group recommender systen where group ratings are computed from the past voting patterns of other users with Probabilistic hical models L M. de Campos.J M. Fernandez-Luna.J F Huete(). M. A. Rueda-Moral Department of Computer Science and Artificial Intelligence, University of Granada, 8071 Granada, Spain e-mail: Ici(@desai.ugres e-mail: jmfluna@desai. ugres M. A. Rueda- Morales e-mail: mrueda (@desai. ugres

User Model User-Adap Inter (2009) 19:207–242 DOI 10.1007/s11257-008-9061-1 ORIGINAL PAPER Managing uncertainty in group recommending processes Luis M. de Campos · Juan M. Fernández-Luna · Juan F. Huete · Miguel A. Rueda-Morales Received: 25 February 2008 / Accepted in revised form : 26 October 2008 / Published online: 21 November 2008 © Springer Science+Business Media B.V. 2008 Abstract While the problem of building recommender systems has attracted con￾siderable attention in recent years, most recommender systems are designed for rec￾ommending items to individuals. The aim of this paper is to automatically recommend a ranked list of new items to a group of users. We will investigate the value of using Bayesian networks to represent the different uncertainties involved in a group rec￾ommending process, i.e. those uncertainties related to mechanisms that govern the interactions between group members and the processes leading to the final choice or recommendation. We will also show how the most common aggregation strategies might be encoded using a Bayesian network formalism. The proposed model can be considered as a collaborative Bayesian network-based group recommender system, where group ratings are computed from the past voting patterns of other users with similar tastes. Keywords Group recommending · Management of uncertainty · Probabilistic graphical models L. M. de Campos · J. M. Fernández-Luna · J. F. Huete (B) · M. A. Rueda-Morales Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain e-mail: jhg@decsai.ugr.es L. M. de Campos e-mail: lci@decsai.ugr.es J. M. Fernández-Luna e-mail: jmfluna@decsai.ugr.es M. A. Rueda-Morales e-mail: mrueda@decsai.ugr.es 123

L. M. de Campos et al. 1 Introduction Recommender systems (RS) provide specific suggestions about items(or actions) within a given domain which may be considered of interest to the user(Resnick and Varian 1997). Depending on the information used when recommending, traditional RS are mainly classified into content and collaborative-based RS, although hybrid approaches do exist. The first type recommends a product by considering its content similarity with those products in which the user has previously expressed an interest. The second alternative attempts to identify groups of people with similar tastes to the user and to recommend items that they have liked Most RS are designed for individual use, i.e. there is an active user who receives recommendations about certain products once they have logged on to the system In this paper, we will focus on the related problem of group recommending(Gr) here the objective is to obtain recommendations for groups of people(Jameson and Smyth 2007). This kind of Rs is appropriate for domains where a group of people participate in a single activity such as watching a movie or going on vacation and also in situations where a single person must make a decision on behalf of the group. In one way or another, GR involves merging different individual preferences. In these situations, it is natural that one of the most important issues is the search for an aggregation mechanism to obtain recommendations for the group. According to Pennock and Wellman(2005)". there is nothing close to a single well-accepted normative basis for group beliefs, group preferences or group decision making. and many aggregation strategies can therefore be found in literature for group decisions (Masthoff 2004; Masthoff and Gatt 2006; Yu et al. 2006; Jameson and Smyth 2007) It is typically assumed that member preferences are given using a rating domain (let us say from 5*, really like, to 1*, really hate). An aggregation strategy is then used to determine the group rating. For example, let us consider a group with three individuals, John, Ann and Mary, where John rates a product 5, Ann rates it 2, and Mary rates it 5". Following an average aggregation criterion, we could then say that the group duct is 4 As in the previous example, the methods proposed in GR literature(see Jameson and Smyth 2007 for a review) do not deal with uncertainty. They assume that the inputs of the aggregation functions (i.e. user preferences)are precise and use a merging strat egy to compute precise outputs. This assumption is not necessarily true, especially if we consider that the user's preferences are normally determined by means of auto matic mechanisms In these cases, a probability distribution over the candidate ratings might be used to express user likelihoods. For example, Table I shows the probability distributions representing the preferences of three users(A, B, and C). In this case Table 1 User ratings for a given User

208 L. M. de Campos et al. 1 Introduction Recommender systems (RS) provide specific suggestions about items (or actions) within a given domain which may be considered of interest to the user (Resnick and Varian 1997). Depending on the information used when recommending, traditional RS are mainly classified into content and collaborative-based RS, although hybrid approaches do exist. The first type recommends a product by considering its content similarity with those products in which the user has previously expressed an interest. The second alternative attempts to identify groups of people with similar tastes to the user and to recommend items that they have liked. Most RS are designed for individual use, i.e. there is an active user who receives recommendations about certain products once they have logged on to the system. In this paper, we will focus on the related problem of group recommending (GR), where the objective is to obtain recommendations for groups of people (Jameson and Smyth 2007). This kind of RS is appropriate for domains where a group of people participate in a single activity such as watching a movie or going on vacation and also in situations where a single person must make a decision on behalf of the group. In one way or another, GR involves merging different individual preferences. In these situations, it is natural that one of the most important issues is the search for an aggregation mechanism to obtain recommendations for the group. According to Pennock and Wellman (2005) “... there is nothing close to a single well-accepted normative basis for group beliefs, group preferences or group decision making.”, and many aggregation strategies can therefore be found in literature for group decisions (Masthoff 2004; Masthoff and Gatt 2006; Yu et al. 2006; Jameson and Smyth 2007). It is typically assumed that member preferences are given using a rating domain (let us say from 5∗, really like, to 1∗, really hate). An aggregation strategy is then used to determine the group rating. For example, let us consider a group with three individuals, John, Ann and Mary, where John rates a product 5∗, Ann rates it 2∗, and Mary rates it 5∗. Following an average aggregation criterion, we could then say that the group rating for this product is 4∗. As in the previous example, the methods proposed in GR literature (see Jameson and Smyth 2007 for a review) do not deal with uncertainty. They assume that the inputs of the aggregation functions (i.e. user preferences) are precise and use a merging strat￾egy to compute precise outputs. This assumption is not necessarily true, especially if we consider that the user’s preferences are normally determined by means of auto￾matic mechanisms. In these cases, a probability distribution over the candidate ratings might be used to express user likelihoods. For example, Table 1 shows the probability distributions representing the preferences of three users (A, B, and C). In this case, Table 1 User ratings for a given item User 1* 2* 3* 4* 5* A 0.2 0.2 0.2 0.19 0.21 B 0 000.1 0.9 C 0.49 0 0 0 0.51 123

Uncertainty in group recommending lthough 5" might be considered the most probable rating, we will not have the same confidence about every situation. Surprisingly, little attention has been paid in GR literature to the problem of man aging uncertainty although it has been well established in the general group decision framework(see Clemen and winkler 1999: Genest and Zidek 1986 for a review ) In his paper, therefore, we will focus on this particular problem. We maintain that two different sources of uncertainty can be found in group recommending processes: the uncertainty shown when user preferences are set, i.e. the user's personal opinion about an item or feature; and the uncertainty which is inherent to the merging process The purpose of this paper is to investigate the value of using Bayesian networks (BN) to represent how different individuals in a group interact in order to make a final choice or recommendation. In our approach, the BN formalism is used to represent both the interactions between group members and the processes leading to the final choice or recommendation We will show how common decision rules in literature could be managed by adequately designing canonical models with the BN language, thereby shedding new light on the combination processes. Discussion about subjects such as how the groups are formed, how long they have existed, relationships between group members, how the group might interact to reach a consensus, etc are beyond the scope of this paper. We shall assume that all the individuals use the same set of labels to express their preferences for an item, and that these preferences are represented by means of a probability distribution(probably estimated from a data set) We consider BNs appropriate because they combine a qualitative representation of the problem through an explicit representation of the dependence relationships between items, users and groups, with a quantitative representation by means of a set of probability distributions to measure the strength of these relationships. Throughout the process, we must consider the computational aspects of the RS, where the sparse ness of the data and the fact that the ranking should be computed in real time represent two challenges. The second section of this paper briefly examines group recommender systems nd related work. Section 3 presents the proposed BN-based model which enables the interaction between individuals to be represented. Section 4 examines how to represent the strength of the individuals'interactions (i.e. conditional probability distributions) and Sect. 5 discusses how inference is performed in order to make recommendations to the group. Section 6 examines the experimental framework. Section 7 discusses e experimental results obtained when considering uncertainty in individual ratings and in Sect. 8 we study those situations where the process behind the group rating is also uncertain. Finally, our conclusions and comments regarding further research are discussed in Sect. 9 2 Classification of group recommender systems and related work Although GR is quite a new research topic, many papers on this problem have already been published. The specific objectives of recommender systems in the research pub- lished so far are determined by the characteristics of the domain for which the system has been developed. These characteristics significantly affect the choice of design and

Uncertainty in group recommending 209 although 5∗ might be considered the most probable rating, we will not have the same confidence about every situation. Surprisingly, little attention has been paid in GR literature to the problem of man￾aging uncertainty although it has been well established in the general group decision framework (see Clemen and Winkler 1999; Genest and Zidek 1986 for a review). In this paper, therefore, we will focus on this particular problem. We maintain that two different sources of uncertainty can be found in group recommending processes: the uncertainty shown when user preferences are set, i.e. the user’s personal opinion about an item or feature; and the uncertainty which is inherent to the merging process. The purpose of this paper is to investigate the value of using Bayesian networks (BN) to represent how different individuals in a group interact in order to make a final choice or recommendation. In our approach, the BN formalism is used to represent both the interactions between group members and the processes leading to the final choice or recommendation. We will show how common decision rules in literature could be managed by adequately designing canonical models with the BN language, thereby shedding new light on the combination processes. Discussion about subjects such as how the groups are formed, how long they have existed, relationships between group members, how the group might interact to reach a consensus, etc. are beyond the scope of this paper. We shall assume that all the individuals use the same set of labels to express their preferences for an item, and that these preferences are represented by means of a probability distribution (probably estimated from a data set). We consider BNs appropriate because they combine a qualitative representation of the problem through an explicit representation of the dependence relationships between items, users and groups, with a quantitative representation by means of a set of probability distributions to measure the strength of these relationships. Throughout the process, we must consider the computational aspects of the RS, where the sparse￾ness of the data and the fact that the ranking should be computed in real time represent two challenges. The second section of this paper briefly examines group recommender systems and related work. Section 3 presents the proposed BN-based model which enables the interaction between individuals to be represented. Section 4 examines how to represent the strength of the individuals’ interactions (i.e. conditional probability distributions) and Sect. 5 discusses how inference is performed in order to make recommendations to the group. Section 6 examines the experimental framework. Section 7 discusses the experimental results obtained when considering uncertainty in individual ratings and in Sect. 8 we study those situations where the process behind the group rating is also uncertain. Finally, our conclusions and comments regarding further research are discussed in Sect. 9. 2 Classification of group recommender systems and related work Although GR is quite a new research topic, many papers on this problem have already been published. The specific objectives of recommender systems in the research pub￾lished so far are determined by the characteristics of the domain for which the system has been developed. These characteristics significantly affect the choice of design and 123

L. M. de Campos et al. RECOMM STRATEGIES A. Prof INFORMATION SOURCE Fig. 1 Classification of Group Recommending Systems each publication therefore focuses on a specific issue( from how to acquire information about group preferences or how the system generates and explains the recommenda- tions to studying the mechanism used to reach a consensus (Jameson and Smyth 2007)). As a result, relating the different approaches is a difficult task. In this section, we will present a new classification taxonomy for group recom ending systems. This classification is based on three independent components of primary importance in the design of a group recommending system and not on the particular techniques used to solve each problem: the information source, the aggre gation criterion used to make the recommendations, and the user's interaction with the system Figure I shows a graphical representation of the proposed classification Source of information: This classification criterion, which has been borrowed from classical RS literature(Adomavicius and Tuzhilin 2005), distinguishes betweer content-based(CB)and collaborative filtering(CF). In the first case, the recom- mended items are those which are similar to the ones that individuals have found interesting in the past. As a result, it is necessary to analyze the content's features recommending. The second alternative considers that the recommendations for a target product have been obtained by considering how people with similar tastes rated a product in the past. These systems are based on the idea that people will agree in future evalua- tions if they have also agreed in their past evaluations. The information sources are therefore the preference ratings given by similar users A new category can obviously be obtained if we consider hybrid approaches that combine both(collaborative and content-based) methods Recommendation strategies: Once we have the information to hand, the strategy used for aggregating this infor mation is a central point in group recommending, and generally in any group deci sion process. In this case, two different approaches can be distinguished. The first I Without loss of generality, we have decided not toinclude thi ory in our taxonomy since, to the best of our knowledge, no study has tried to combine both techniques

210 L. M. de Campos et al. USER active passive INFORMATION SOURCE content collaborative A. Rec. A. Prof. RECOMM. STRATEGIES Fig. 1 Classification of Group Recommending Systems each publication therefore focuses on a specific issue (from how to acquire information about group preferences or how the system generates and explains the recommenda￾tions to studying the mechanism used to reach a consensus (Jameson and Smyth 2007)). As a result, relating the different approaches is a difficult task. In this section, we will present a new classification taxonomy for group recom￾mending systems. This classification is based on three independent components of primary importance in the design of a group recommending system and not on the particular techniques used to solve each problem: the information source, the aggre￾gation criterion used to make the recommendations, and the user’s interaction with the system. Figure 1 shows a graphical representation of the proposed classification. – Source of information: This classification criterion, which has been borrowed from classical RS literature (Adomavicius and Tuzhilin 2005), distinguishes between content-based (CB) and collaborative filtering (CF). In the first case, the recom￾mended items are those which are similar to the ones that individuals have found interesting in the past. As a result, it is necessary to analyze the content’s features for recommending. The second alternative considers that the recommendations for a target product have been obtained by considering how people with similar tastes rated a product in the past. These systems are based on the idea that people will agree in future evalua￾tions if they have also agreed in their past evaluations. The information sources are therefore the preference ratings given by similar users. A new category can obviously be obtained if we consider hybrid approaches that combine both (collaborative and content-based) methods.1 – Recommendation strategies: Once we have the information to hand, the strategy used for aggregating this infor￾mation is a central point in group recommending, and generally in any group deci￾sion process. In this case, two different approaches can be distinguished. The first 1 Without loss of generality, we have decided not to include this category in our taxonomy since, to the best of our knowledge, no study has tried to combine both techniques in the group recommending framework. 123

approach, aggregating recommendations(Ar), is a two-step strategy, where an indi- vidual recommendation is first obtained for each group member, and then a common recommendation is obtained by merging these individual recommendations. In the second approach, aggregating profiles(AP), the objective is to obtain a common profile by representing group preferences. This can be done explicitly, where the ndividuals use a common group account to give their preferences, or implicitly by means of an aggregation mechanism for the different individuals' profiles or Individual interactions Finally, a group recommending system can also be categorized by considering the way in which the users interact with the system. The individuals can be dichoto- mized into passive members(PM)and active members(AM). Focusing on the active embers, the final purpose is to reach a consensus between the group members and like many decision support system approaches, it is necessary for the users to eval- uate the system recommendations. In contrast, when the members are passive, the final purpose is only to provide a recommendation to the group, as might be the case when using an RS in a marketing campaign. In this situation, the individuals do not interact with the system in order to evaluate the proposed recommendations Since we use three non-overlapping criteria for classification purposes, a given GrS can be classified using three labels, one for each category. For instance, a GRS can be classified as CB-+AP+PM if the group profile is obtained by combining the infor mation about the content of the items which have been previously evaluated by each user. This profile will be used to send the final recommendations to the group 2.1 Related work Once the taxonomy has been presented, we will then go on to classify previously published GR systems CB+AP+PM: most published GRSs might be included in this category. For exam ple, let us consider MusicFX (McCarthy and Anagnost 2000). Given a database of member preferences for musical genres(each user rates each of the 91 genres on a five-point scale), the group profile is computed by summing the squared individual preferences. Using a weighted random selection operator, the next music station to be played is then selected. No interaction with the system is possible except by changing user preferences The inputs in the case of group modeling(Masthoff 2004)are user preferences(rat- ings)for a series of programs, and in this paper we study the performance of several aggregation strategies. The article(Yu et al. 2006) presents various TV program recommendations for multiple viewers by merging individual user preferences on eatures(e.g. genre, actor, etc. )to construct a group profile. The aim of the aggrega tion strategy is to minimize the total distance in such a way that the merged profile s close to most user preferences, thereby satisfying most of the group. CB+AP+AM: The Travel Decision Forum (Jameson 2004)was developed to help a group of users agree on the desired attributes of a vacation. This system allows

Uncertainty in group recommending 211 approach, aggregating recommendations(AR), is a two-step strategy, where an indi￾vidual recommendation is first obtained for each group member, and then a common recommendation is obtained by merging these individual recommendations. In the second approach, aggregating profiles (AP), the objective is to obtain a common profile by representing group preferences. This can be done explicitly, where the individuals use a common group account to give their preferences, or implicitly, by means of an aggregation mechanism for the different individuals’ profiles or preferences. – Individual interactions Finally, a group recommending system can also be categorized by considering the way in which the users interact with the system. The individuals can be dichoto￾mized into passive members(PM) and active members(AM). Focusing on the active members, the final purpose is to reach a consensus between the group members and, like many decision support system approaches, it is necessary for the users to eval￾uate the system recommendations. In contrast, when the members are passive, the final purpose is only to provide a recommendation to the group, as might be the case when using an RS in a marketing campaign. In this situation, the individuals do not interact with the system in order to evaluate the proposed recommendations. Since we use three non-overlapping criteria for classification purposes, a given GRS can be classified using three labels, one for each category. For instance, a GRS can be classified as CB+AP+PM if the group profile is obtained by combining the infor￾mation about the content of the items which have been previously evaluated by each user. This profile will be used to send the final recommendations to the group. 2.1 Related work Once the taxonomy has been presented, we will then go on to classify previously published GR systems. – CB+AP+PM: most published GRSs might be included in this category. For exam￾ple, let us consider MusicFX (McCarthy and Anagnost 2000). Given a database of member preferences for musical genres (each user rates each of the 91 genres on a five-point scale), the group profile is computed by summing the squared individual preferences. Using a weighted random selection operator, the next music station to be played is then selected. No interaction with the system is possible except by changing user preferences. The inputs in the case of group modeling (Masthoff 2004) are user preferences (rat￾ings) for a series of programs, and in this paper we study the performance of several aggregation strategies. The article (Yu et al. 2006) presents various TV program recommendations for multiple viewers by merging individual user preferences on features (e.g. genre, actor, etc.) to construct a group profile. The aim of the aggrega￾tion strategy is to minimize the total distance in such a way that the merged profile is close to most user preferences, thereby satisfying most of the group. – CB+AP+AM: The Travel Decision Forum (Jameson 2004) was developed to help a group of users agree on the desired attributes of a vacation. This system allows 123

L. M. de Campos et al. group members to collaboratively specify their preferences and to reach an agree ment about an overall solution. In this case, a group profile is obtained through the nteraction of the members, taking into account the systems current recommenda tion which is obtained by aggregating individual preferences for each dimension In the article(Kudenko et al. 2003), a system is presented to help a group of users reach a joint decision based on individual user preferences CB+AR+PM: Intrigue(Ardissono et al. 2003)recommends tourist attractions for heterogeneous groups that include homogeneous subgroups where the members have similar preferences. In this system, the users record their preferences for a series of tourist attractions, and recommendations(obtained using a fuzzy AND) are then merged using a weighted scheme where each weight represents the rele vance of the corresponding subgroup(for instance, a subgroup could be particularly influential since it represents a large portion of the group) explains their recommendations, it has no means of interacting with the user CF+AR+PM: Polylens(O'Connor et al. 2001), an extension of MovieLens(Her locker et al. 2004), recommends movies to groups of users. This system uses a nearest neighbor-based algorithm to find the individuals with the most similar tastes to those of each group member and to obtain recommendations for every user. The voting preferences of these individuals are then merged according to the principle of least misery(minimum criterion). Under the same classification( Chen et al 2008)uses genetic algorithms to learn the group rating for an item that best fits the existing ratings for the item given by the individuals and the subgroups. The idea is that it is possible to learn how the user interacts from the known group ratings The proposed algorithm therefore recommends items based on the group's previous ratings for similar items. 2.1.1 The role of uncertainty As far as the authors are aware, the role of uncertainty in group recommending pro- cesses has not been considered. Nevertheless, many papers have been published which tackle this problem when recommendations are made to individual users(Zuker man and Albrecht 2001; Albrecht and Zukerman 2007). Focusing on probabilistic approaches, those relating to the one presented in this paper include content-based RSs(Mooney and Roy 2000: de Campos et al. 2005), collaborative filterin (Breese et al. 1998; Schiaffino and Amandi 2000: Butz 2002; Lekakos and 2007: Miyahara and Pazzani 2000: Heckerman et al. 2001)and hybrid methods(Pope- scu et al. 2001: de Campos et al. 2006). In terms of the group's process, the treatment of uncertainty is, however, a well known problem in other disciplines and so in this section we will review those papers which focus on the combination of probabilistic information from a purely approach(see Clemen and winkler 1999: Genest and Zidek 1986). In general, we might consider these methods as analytical models operating on the individual prob ability distributions to produce a single"combined"probability distribution. These approaches can generally be further distinguished into axiomatic approaches(by con- sidering a set of assumptions that the combination criteria might satisfy) and Bayesian approaches

212 L. M. de Campos et al. group members to collaboratively specify their preferences and to reach an agree￾ment about an overall solution. In this case, a group profile is obtained through the interaction of the members, taking into account the system’s current recommenda￾tion which is obtained by aggregating individual preferences for each dimension. In the article (Kudenko et al. 2003), a system is presented to help a group of users reach a joint decision based on individual user preferences. – CB+AR+PM: Intrigue (Ardissono et al. 2003) recommends tourist attractions for heterogeneous groups that include homogeneous subgroups where the members have similar preferences. In this system, the users record their preferences for a series of tourist attractions, and recommendations (obtained using a fuzzy AND) are then merged using a weighted scheme where each weight represents the rele￾vance of the corresponding subgroup (for instance, a subgroup could be particularly influential since it represents a large portion of the group). Although the system explains their recommendations, it has no means of interacting with the user. – CF+AR+PM: Polylens (O’Connor et al. 2001), an extension of MovieLens (Her￾locker et al. 2004), recommends movies to groups of users. This system uses a nearest neighbor-based algorithm to find the individuals with the most similar tastes to those of each group member and to obtain recommendations for every user. The voting preferences of these individuals are then merged according to the principle of least misery (minimum criterion). Under the same classification, (Chen et al. 2008) uses genetic algorithms to learn the group rating for an item that best fits the existing ratings for the item given by the individuals and the subgroups. The idea is that it is possible to learn how the user interacts from the known group ratings. The proposed algorithm therefore recommends items based on the group’s previous ratings for similar items. 2.1.1 The role of uncertainty As far as the authors are aware, the role of uncertainty in group recommending pro￾cesses has not been considered. Nevertheless, many papers have been published which tackle this problem when recommendations are made to individual users (Zuker￾man and Albrecht 2001; Albrecht and Zukerman 2007). Focusing on probabilistic approaches, those relating to the one presented in this paper include content-based RSs (Mooney and Roy 2000; de Campos et al. 2005), collaborative filtering RSs (Breese et al. 1998; Schiaffino and Amandi 2000; Butz 2002; Lekakos and Giaglis 2007; Miyahara and Pazzani 2000; Heckerman et al. 2001) and hybrid methods (Pope￾scu et al. 2001; de Campos et al. 2006). In terms of the group’s process, the treatment of uncertainty is, however, a well￾known problem in other disciplines and so in this section we will review those papers which focus on the combination of probabilistic information from a purely statistical approach (see Clemen and Winkler 1999; Genest and Zidek 1986). In general, we might consider these methods as analytical models operating on the individual prob￾ability distributions to produce a single “combined” probability distribution. These approaches can generally be further distinguished into axiomatic approaches (by con￾sidering a set of assumptions that the combination criteria might satisfy) and Bayesian approaches: 123

Uncertainty in group recommending Axiomatic approach: the following common functions deal with belief aggregation: (i)Linear Opinion Pool where the group probability, Pr(G), is obtained as the weighted arithmetic average over the individual probabilities, Pr(vi),i= 1,……,n,i.e.Pr(G)=∑=1UPr(V), with wi being the weights totaling one () Logarithmic Opinion Pool(weighted geometric average)defined as Pr(G) IIs Pr(viu, with a being a normalization constant and the weights wi (called expert weights) are typically restricted to total one. If the weights are equal to 1/n, then the combined distribution is proportional to the geometric Bayesian Approach( Genest and Zidek 1986; Clemen and Winkler 1999): this has been used to combine expert information by taking into account the so-called Naive Bayes assumption. In our context, in order to obtain efficient combinations, indi- vidual opinions are assumed to be conditionally independent given the group vote 3 Modeling group decision networks The purpose of this paper is to develop a general methodology based on the Bayes ian network(BN) formalism for modeling those uncertainties that appear in both the interactions between group members and the processes leading to the final choice or recommendation. For example, let us imagine that we want to advise a group of tourists to visit a particular monument or not. In such a situation, we should assume hat the individuals in the group are unfamiliar with the monument (or item to be recommended). Each group member might speculate about their possible preference for visiting this monument and this is necessarily uncertain. Nevertheless, the group recommendations must be obtained by aggregating these preferences Individual preferences can be computed by considering two alternatives: the first considers content information(such as a description of the monument, location, etc. nd the second considers how people with similar tastes rated this monument in the ast(for instance, dislike or like). This is the approach followed in this paper where the similarity between users will be computed by considering how common items have been rated. Following the classification presented in Sect. 2, our GRS can therefore be categorized as CF+AR+PM As a collaborative approach, our model will inherit most of the disadvantages of classical collaborative filtering approaches. For example, the system cannot draw any inferences about items for which it has not yet gathered sufficient information,i.e.we also have the First-Rater problem. Similarly, we also inherit the Cold-Start problem it is difficult to recommend items to new users who have not submitted any ratings. Without any information about the user, the system is unable to guess user preferences and generate recommendations until a few items have been rated. For our information sources, we will consider a database of ratings r(which is usually extremely sparse) to store user ratings for the observed items. For example Table 2 shows the ratings given by each user Ui for an item /j using the values I dislike and 2=like(the value '-represents the fact that the user has not seen the item

Uncertainty in group recommending 213 – Axiomatic approach: the following common functions deal with belief aggregation: (i) Linear Opinion Pool where the group probability, Pr(G), is obtained as the weighted arithmetic average over the individual probabilities, Pr(Vi),i = 1,..., n, i.e. Pr(G) =
n i=1 wi Pr(Vi), with wi being the weights totaling one. (ii) Logarithmic Opinion Pool (weighted geometric average) defined as Pr(G) = α n i=1 Pr(Vi)wi , with α being a normalization constant and the weights wi (called expert weights) are typically restricted to total one. If the weights are equal to 1/n, then the combined distribution is proportional to the geometric average. – Bayesian Approach (Genest and Zidek 1986; Clemen and Winkler 1999): this has been used to combine expert information by taking into account the so-called Naive Bayes assumption. In our context, in order to obtain efficient combinations, indi￾vidual opinions are assumed to be conditionally independent given the group vote. 3 Modeling group decision networks The purpose of this paper is to develop a general methodology based on the Bayes￾ian network (BN) formalism for modeling those uncertainties that appear in both the interactions between group members and the processes leading to the final choice or recommendation. For example, let us imagine that we want to advise a group of tourists to visit a particular monument or not. In such a situation, we should assume that the individuals in the group are unfamiliar with the monument (or item to be recommended). Each group member might speculate about their possible preference for visiting this monument and this is necessarily uncertain. Nevertheless, the group recommendations must be obtained by aggregating these preferences. Individual preferences can be computed by considering two alternatives: the first considers content information (such as a description of the monument, location, etc.) and the second considers how people with similar tastes rated this monument in the past (for instance, dislike or like). This is the approach followed in this paper where the similarity between users will be computed by considering how common items have been rated. Following the classification presented in Sect. 2, our GRS can therefore be categorized as CF+AR+PM. As a collaborative approach, our model will inherit most of the disadvantages of classical collaborative filtering approaches. For example, the system cannot draw any inferences about items for which it has not yet gathered sufficient information, i.e. we also have the First-Rater problem. Similarly, we also inherit the Cold-Start problem since it is difficult to recommend items to new users who have not submitted any ratings. Without any information about the user, the system is unable to guess user preferences and generate recommendations until a few items have been rated. For our information sources, we will consider a database of ratings R (which is usually extremely sparse) to store user ratings for the observed items. For example, Table 2 shows the ratings given by each user Ui for an item Ij using the values 1 = dislike and 2 = like (the value − represents the fact that the user has not seen the item). 123

214 L. M. de Campos et al. Table 2 database of user h2b456 12222 1-1-22 22211 山12 U1222 In order to achieve this objective, our aim is to build a bn where two compo- nents might be considered. The first, described in Sect. 3. 1 relates to the collaborative component of the recommender system. Both the topology of this component and the probability values will be learned from a set of past user ratings, and this will be used to compute a probability distribution representing the preferences of each group member for a given item. The second component will be used to merge these preferences in order to reach the final group opinion. This component is modeled using a Bn with a fixed structure given the group members, and the weights will be computed based on he ratings provided by the group members(see Sect. 3.2) 3. 1 BN-based collaborative component In this section, we will briefly describe this component(those readers interested in further details can consult(de Campos et al. 2008)). Our objective is to model how each user should rate an item. In order to represent relationships between users, we shall include a node, Ui, for each user in the system. We use l to denote the set of user nodes, i.e.u=(U1,., Un. The user variable Ui will therefore represent the probability distribution associated to its rating pattern. For instance, using the data in Table 2, each node will store two probability values representing the probability of U; liking(Pr(Ui= 2))or disliking(Pr(Ui= 1)an item. In order to facilitate the presence of dependence relationships between individuals in the model(to avoid a possibly complex network topology ) we propose that a new set of nodes y be included to denote collaborative ratings. There is one collaborative node for each user in the system, i.e. V=(V1, V2,..., Vn). These nodes will represent a probability distribution over ratings, and they will therefore take their values in the same domain as l 3.1.1 Learning stage Given an active user, the parent set of the variable Va in the graph, Pa(va), will be learnt from the database of votes, R. This set will contain those user variables, Ubel where Ua and Ub are most similar in taste, i. e the best neighbors for the active user Given a similarity measure, the set Pa(va)can therefore be obtained by using a thresh old or by only considering the first p variables in the ranking(see Fig. 2). It should be

214 L. M. de Campos et al. Table 2 Database of user ratings U0 U1 U2 U3 U4 U5 I1 112211 I2 1–2–22 I3 112112 I4 2–1–12 I5 221111 I6 22–222 I7 2–––12 In order to achieve this objective, our aim is to build a BN where two compo￾nents might be considered. The first, described in Sect. 3.1 relates to the collaborative component of the recommender system. Both the topology of this component and the probability values will be learned from a set of past user ratings, and this will be used to compute a probability distribution representing the preferences of each group member for a given item. The second component will be used to merge these preferences in order to reach the final group opinion. This component is modeled using a BN with a fixed structure given the group members, and the weights will be computed based on the ratings provided by the group members (see Sect. 3.2). 3.1 BN-based collaborative component In this section, we will briefly describe this component (those readers interested in further details can consult (de Campos et al. 2008)). Our objective is to model how each user should rate an item. In order to represent relationships between users, we shall include a node, Ui , for each user in the system. We use U to denote the set of user nodes, i.e. U = {U1,..., Un}. The user variable Ui will therefore represent the probability distribution associated to its rating pattern. For instance, using the data in Table 2, each node will store two probability values representing the probability of Ui liking (Pr(Ui = 2)) or disliking (Pr(Ui = 1)) an item. In order to facilitate the presence of dependence relationships between individuals in the model (to avoid a possibly complex network topology), we propose that a new set of nodes V be included to denote collaborative ratings. There is one collaborative node for each user in the system, i.e. V = {V1, V2,..., Vn}. These nodes will represent a probability distribution over ratings, and they will therefore take their values in the same domain as U. 3.1.1 Learning stage Given an active user, the parent set of the variable Va in the graph, Pa(Va), will be learnt from the database of votes, R. This set will contain those user variables, Ub ∈ U, where Ua and Ub are most similar in taste, i.e. the best neighbors for the active user. Given a similarity measure, the set Pa(Va) can therefore be obtained by using a thresh￾old or by only considering the first p variables in the ranking (see Fig. 2). It should be 123

Fig 2 Collaborative Recommending Sy sten 1)(v2)(3)(V4 noted that we do not include the links between Ui->Vi, Vi, since we are modeling a collaborative rating scheme where(assuming that the item being recommended ha not been observed by the active user)the predicted rating will only depend on those ratings given by its neighbors The similarity measure proposed in this paper is a combination of two different, but complementary, criteria: vote correlation between common items and the overlap sim(Ua, Ub)=abs (PCC(Ua, Ub))x D(Ua, Ub) The first criterion, which is normally used as the basis for calculating the weights in different collaborative systems, attempts to capture those similar users, i.e. those with the highest absolute value of pearsons correlation coefficient defined as PCC(Ua, Ub)= (ra. j-Fa)(rb, j-Fb) 7b)2 where the summations overj are over those items for which users Ua and Ub have recorded votes and Ta is the mean vote for user Ua. It should be noted that PCC ranges from +1 to-1: +l means that there is a perfect positive linear relationship between users;-I means that there is a perfect negative linear relationship: a correlation of 0 means that there is no relationship. Therefore, when there are no common items in Ua and Ub voting records, then PCC(Ua, Ub)=0 by default. In our approach, by using the absolute value of PCC, abs (PCC), we consider that both positively(those with similar ratings) and negatively correlated users(those with opposite tastes)might help- to predict an active user's final rating The second criterion tries to penalize those highly correlated neighbors which are based on very few co-rated items, which have proved to be bad predictors(Herlocker et al. 1999). We might therefore take into account the number of items that both a and Ub rated simultaneously, i. e. their overlap degree. In particular, we consider that the quality of Ub as the parent of variable Ua is directly related with the probability of a user Ua rating an item which has been also rated by Ub. This criterion can be defined by the following expression 2 For instance. if whenever Ub rates as like Ua rates with dislike, then knowing that U, had rated item with like provides information about Uas possible rating

Uncertainty in group recommending 215 Fig. 2 Collaborative Recommending System Topology U2 V0 V1 V2 V3 V4 V5 U0 U1 U3 U4 U5 noted that we do not include the links between Ui −→ Vi, ∀i, since we are modeling a collaborative rating scheme where (assuming that the item being recommended has not been observed by the active user) the predicted rating will only depend on those ratings given by its neighbors. The similarity measure proposed in this paper is a combination of two different, but complementary, criteria: vote correlation between common items and the overlap degree, i.e. sim(Ua, Ub) = abs(PCC(Ua, Ub)) × D(Ua, Ub) (1) The first criterion, which is normally used as the basis for calculating the weights in different collaborative systems, attempts to capture those similar users, i.e. those with the highest absolute value of Pearson’s correlation coefficient defined as PCC(Ua, Ub) =
j(ra,j − r a)(rb,j − r b)
j(ra,j − r a)2
j(rb,j − r b)2 (2) where the summations over j are over those items for which users Ua and Ub have recorded votes and r a is the mean vote for user Ua. It should be noted that PCC ranges from +1 to −1: +1 means that there is a perfect positive linear relationship between users; −1 means that there is a perfect negative linear relationship; a correlation of 0 means that there is no relationship. Therefore, when there are no common items in Ua and Ub voting records, then PCC(Ua, Ub) = 0 by default. In our approach, by using the absolute value of PCC, abs(PCC), we consider that both positively (those with similar ratings) and negatively correlated users (those with opposite tastes) might help2 to predict an active user’s final rating. The second criterion tries to penalize those highly correlated neighbors which are based on very few co-rated items, which have proved to be bad predictors (Herlocker et al. 1999). We might therefore take into account the number of items that both Ua and Ub rated simultaneously, i.e. their overlap degree. In particular, we consider that the quality of Ub as the parent of variable Ua is directly related with the probability of a user Ua rating an item which has been also rated by Ub. This criterion can be defined by the following expression: 2 For instance, if whenever Ub rates as like Ua rates with dislike, then knowing that Ub had rated an item with like provides information about Ua’s possible rating. 123

216 L. M. de Campos et al. D(Ua, Ub) JI(Ub) where I(U) is the set of items rated by user U in the data set. It should be noted that we are not considering the particular votes, merely whether the users rated an item or 3.2 Modeling the group component As mentioned previously, since groups are usually created by their members, we shall not consider how groups are formed or how they are managed. We shall therefore assume that we know the composition of the groups, and our problem is to study how this information can be represented in the Bn and also how to predict ratings for We propose to identify a group G as a new node in the BN. Since the recommen- dations are made by considering the preferences of its members, we propose that the parents(Pa(G))of the group node(G)will be the set of nodes in V representing its individuals. In this case, we are modeling that the predictions of the grou ill depend on the collaborative predictions obtained for each of its members. Figure 3 illustrates a group Ga with three members: V1, V2, and V3. We use dashed lines to epresent user-group relations since we assume that the composition of the group is known In this paper, we will focus on how different aggregation strategies can be repre sented in our BN-based model. In order to maintain generality (so that the proposed aggregation mechanisms can be applied in more general situations ) we will use the following independence assumption: given that we know the opinion(ratings)of all the group members, group opinion does not change(it is independent)if the state of any other variable in system Xi is known, i.e. I(G, XiIPa(g)), vxi Pa(Gi. It is important to remember that in certain domains this restriction might be very restric tive. For example, it might also be possible to consider other factors that would affect the group rating such as the context. Nevertheless, the study of how to include these factors in the model is beyond the scope of this paper. 3 For example, it might be used to combine multiple classifiers(Kittler et al. 1998; Abellan and Masegosa 2007)where the new cases will be classified by considering all the results obtained by each classifier

216 L. M. de Campos et al. Fig. 3 Modeling groups Ga U0 U1 U2 U3 U4 U5 V1 V2 V3 V4 V5 D(Ua, Ub) = |I(Ua) ∩ I(Ub)| |I(Ub)| . where I(U) is the set of items rated by user U in the data set. It should be noted that we are not considering the particular votes, merely whether the users rated an item or not. 3.2 Modeling the group component As mentioned previously, since groups are usually created by their members, we shall not consider how groups are formed or how they are managed. We shall therefore assume that we know the composition of the groups, and our problem is to study how this information can be represented in the BN and also how to predict ratings for groups. We propose to identify a group G as a new node in the BN. Since the recommen￾dations are made by considering the preferences of its members, we propose that the parents (Pa(G)) of the group node (G) will be the set of nodes in V representing its individuals. In this case, we are modeling that the predictions of the group’s ratings will depend on the collaborative predictions obtained for each of its members. Figure 3 illustrates a group Ga with three members: V1, V2, and V3. We use dashed lines to represent user-group relations since we assume that the composition of the group is known. In this paper, we will focus on how different aggregation strategies can be repre￾sented in our BN-based model. In order to maintain generality (so that the proposed aggregation mechanisms can be applied in more general situations3), we will use the following independence assumption: given that we know the opinion (ratings) of all the group members, group opinion does not change (it is independent) if the state of any other variable in system Xi is known, i.e. I(G, Xi|Pa(G)), ∀Xi ∈/ Pa(Gi). It is important to remember that in certain domains this restriction might be very restric￾tive. For example, it might also be possible to consider other factors that would affect the group rating such as the context. Nevertheless, the study of how to include these factors in the model is beyond the scope of this paper. 3 For example, it might be used to combine multiple classifiers (Kittler et al. 1998; Abellán and Masegosa 2007) where the new cases will be classified by considering all the results obtained by each classifier. 123