ARTICLE IN PRESS H.-F. Wang, C-T. Wu/ Computers 8 Operations Research i(Im)Il-l hresholds of a3 as denoted by (a1, 2\(o3 Thus, the classification 3. 2. Derivation of relations among users and items--CECF rules will provide exclusive groups so that one item belongs to only one group. Properties of each item-group could be also easily In the proposed offline database, the framework of bipartite prices of items in the market basket are defined as embedded in the framework are regarded as clique effects of as c=[cld=1,2 , i=1, 2,..., n where sa and ca represent effects result mainly from the grouping of users. Users ique 1, 2,..., ] possible profits are defined the purchase probability measured for get user. The the corresponding price and profit of Pd. Therefore, for the items same clique with the target user(the so-called neighbors in CE database, it will be stored by each item-group with its items and could provide collaborative information to measure purchase specified properties probability. However, users in different cliques may also provide collaborative information to the target user to a certain degree. In his respect, we propose the following concept to measure the 3. 1.2. User-groups with their profile purchase probability of the target user with respect to a predicted Denote a user as u with fEN. Let U=(U(Og)U E N) be a set of Item users labeled by the demographic features og E(o1, 02 Pruser, item)=0.Pruse, item, +(1-0). Pruser, item. (1) g,..., ODG). To facilitate analysis--providing solutions for the new user"problem and exploiting clique effects, the users are where the probability Pruser, item, is a convex combination of two classified into mutually exclusive user-groups and assumed to distinct probabilities: one is the purchase probability predicted by behave similarly as the DF method suggests. The user-groups are collaboration of users in the same clique(the neighbors)with the formed by the following rules: assume each demographic feature target user, and the other is predicted by collaboration of users in Og could be divided/categorized into vg intervals/categories the different cliques. The composition of the proposed probability denoted by a", and then we define u:U→o21×o2…xob measure is illustrated in Fig 3. ve have u={u(og)og∈og,g=1,2,…,j=1,2,…J.Then Let us refer to Fig. 3. First, note that arrows 3 and 4 jointly each user-group could be represented as U=fup(og)I represent the"in-clique"purchase probability measure used by 卩=1,2,,F=12.,,|U=F U U=U. For convention al fh. hine commont concept of the 1 i method with instance, we define the demographic features to be gender pincligue=K, 2 sim(up p)x Cupe-Pa (o1)and age (o): @1 is categorized into vi=2 categories as male and female: @2 is divided into v2=4 intervals (O.20).(20, 30). 130.40. 140, co). Then we define the user- where Pinda ,'ing t to ensure the absolute values of probability u is the probability that target user up purchases groups as Up: U-01 x o2 and eight user-groups yield as U,j=1,2,,8. sum to unity; sim(up, ur), which refers to arrow 4, is the similarity Relations between the target user ug and the neighbors uft; and G which refers to arrow 3, is the binary choice whether a user uft purchases pa or not. It is noteworthy that for the similarity measure between the target user up and the neighbors ufr, as specified in Eg. (2), the neighbors are chosen from the user-group to which the target user belongs: this is in compliance with the structure of our proposed Rs, which assumes that users in the same demographic group would tend to behave similarly. Second for the probability measure of"out-of-clique"based on the concept of Cf, two factors should be considered: (1) the similarity between the target user-group and other user-groups as Fig. 2. Framework of relations among user-groups and item-groups. well as(2)other user-groups purchase priorities on the predicted Purchase prority among user-groups and sim(U, U binary choice whether a ure between the target Fig 3. Various probability measurements of the target user on the predicted item. Please cite this article H-F, Wu C-T. A strategy-oriented operation module for recommender systems in E-com Computers and Operations Research(2010). doi: 10. 1016/j. cor. 2010.03.011ARTICLE IN PRESS thresholds of a3 as denoted by fa1,a2g\fa3g. Thus, the classification rules will provide exclusive groups so that one item belongs to only one group. Properties of each item-group could be also easily and clearly identified by observing attribute labels. The selling prices of items in the market basket are defined as s ¼ ½sdi jdi ¼ 1i ,2i , ... ,Di ,i ¼ 1,2, ... ,I; possible profits are defined as c ¼ ½cdi jdi ¼ 1i ,2i , ... ,Di ,i ¼ 1,2, ... ,I where sdi and cdi represent the corresponding price and profit of pdi . Therefore, for the items database, it will be stored by each item-group with its items and specified properties. 3.1.2. User-groups with their profiles Denote a user as uf with fAN. Let U ¼ fufðog Þjf ANg be a set of users labeled by the demographic features og Afo1,o2, ... ,og, ... ,oGg. To facilitate analysis—providing solutions for the ‘‘new user’’ problem and exploiting clique effects, the users are classified into mutually exclusive user-groups and assumed to behave similarly as the DF method suggests. The user-groups are formed by the following rules: assume each demographic feature og could be divided/categorized into ng intervals/categories denoted by ong g , and then we define Uj : U-on1 1 on2 2  onG G , we have Uj ¼ fufðogÞjog Aong g , g ¼ 1,2, ... ,G,j ¼ 1,2, ... ,Jg. Then each user-group could be represented as Uj ¼ fufjðogÞj fj ¼ 1j ,2j , ... , Fj ,j ¼ 1,2, ... ,Jg, jUj j ¼ Fj and thus S J i ¼ 1 Uj ¼ U. For instance, we define the demographic features to be gender (o1) and age (o2); o1 is categorized into n1 ¼ 2 categories as male and female; o2 is divided into n2 ¼ 4 intervals as (0, 20], [20,30], [30,40], [40, N). Then we define the user￾groups as Uj : U-o2 1 o4 2 and eight user-groups yield as Uj ,j ¼ 1,2, ... ,8. 3.2. Derivation of relations among users and items—CECF In the proposed offline database, the framework of bipartite grouping connects users and items (Fig. 2). The relations embedded in the framework are regarded as clique effects of the purchase probability measured for a target user. The clique effects result mainly from the grouping of users. Users in the same clique with the target user (the so-called neighbors in CF) could provide collaborative information to measure purchase probability. However, users in different cliques may also provide collaborative information to the target user to a certain degree. In this respect, we propose the following concept to measure the purchase probability of the target user with respect to a predicted item as Prðuser, itemÞ ¼ y  Pin-clique rðuser, itemÞ þ ð1yÞ  Pout-of-clique rðuser, itemÞ , ð1Þ where the probability Prðuser, itemÞ is a convex combination of two distinct probabilities: one is the purchase probability predicted by collaboration of users in the same clique (the neighbors) with the target user, and the other is predicted by collaboration of users in the different cliques. The composition of the proposed probability measure is illustrated in Fig. 3. Let us refer to Fig. 3. First, note that arrows 3 and 4 jointly represent the ‘‘in-clique’’ purchase probability measure used by conventional CF. The common concept of the CF method with adaptation to the binary market basket data [6,35] is presented as Pin-clique rðufj ,pdi Þ ¼ k1 X uf t AUj simðufj ,uf t Þ Cuf t ,pdi , ð2Þ where Pin-clique rðufj ,pdi Þ is the probability that target user ufj purchases item pdi by using a collaboration of neighbors’ preferences; k1 is a normalizing factor to ensure the absolute values of probability sum to unity; simðufj ,uf t Þ, which refers to arrow 4, is the similarity between the target user ufj and the neighbors uf t ; and Cuf t ,pdi , which refers to arrow 3, is the binary choice whether a user uf t purchases pdi or not. It is noteworthy that for the similarity measure between the target user ufj and the neighbors uf t , as specified in Eq. (2), the neighbors are chosen from the user-group to which the target user belongs; this is in compliance with the structure of our proposed RS, which assumes that users in the same demographic group would tend to behave similarly. Second, for the probability measure of ‘‘out-of-clique’’ based on the concept of CF, two factors should be considered: (1) the similarity between the target user-group and other user-groups as well as (2) other user-groups’ purchase priorities on the predicted U1 U2 P1 P P 2 U Relations User￾Groups Item￾Groups J I Fig. 2. Framework of relations among user-groups and item-groups. : j wi ( user, item ) out-of-clique arrow 1 arrow 2 Purchase priority among user-groups and item-groups. Neighbor Neighbor Uj U1 Uj Pi Target user Predicted item Similarity measures among user-groups. Similarity measure between the target user and his/her neighbor. The binary choice whether a user purchases the item or not. arrow 3 arrow 4 r P in-clique r( user, item ) P C ( , ): f f sim u u , : u p ( , ): j sim U Uτ Fig. 3. Various probability measurements of the target user on the predicted item. 6 H.-F. Wang, C.-T. Wu / Computers & Operations Research ] (]]]]) ]]]–]]] Please cite this article as: Wang H-F, Wu C-T. A strategy-oriented operation module for recommender systems in E-commerce. Computers and Operations Research (2010), doi:10.1016/j.cor.2010.03.011