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 be214 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