ARTICLE IN PRESS H.-F. Wang C-T. Wu/ Computers 8 Operations Research I(m)Il 7 tem-group. For the former, the similarity measures would refer to where sim(U, U) is the similarity measure between the target ow 2 in Fig 3. For the latter that refers to arrow 1 in Fig 3. the user-group U and the other user-group Ut.Therefore, the relative purchase frequency in the binary basket analysis has been similarity measures indicated in the Appendix a could be adopted as the prediction of purchase priority [10 computed as shown in Appendix B, in which the similarity measure is more appropriate. w S(UI mmary of the proposed CeCF items in P: s(U) is the total number of market baskets for U. purchase probability measure as Eq. (5), which is a convex Therefore, the probability measure of"out-of-clique"purchase combination of two distinct probability measures from in-clique n be presented effects of Eq. (2)and out-of-clique effects of Eq. (4). The Pout-o-aique=K2> sim(U,U)x wi (4) classification of the target user into in-clique users as out-of-clique users, the proposed probability measure where sim(U, U), which refers to arrow 2, is the similarity function provides different insight from that of conventional CF measure between the target user-group u and other user-group ethod U K2 is a zing factor to ensure the absolute values of As for the probability measure of in-clique users, we adopt the probability sum to unity. Therefore, the probability measure of a traditional CF method, whereas for the measure of out-of-clique target user up purchasing item Pa would be represented a sers, we propose an alternative similarity function by incorpo ting the items not purchased simultaneously by each pair of compared users to find the similarity among user-groups. Prug, Po)=p=0.(K1 2 sim(up. ue)x Cuy. Pe Then the proposed probability measure is predicted by the purchase and non-purchase behaviors of the users, which could be expected to provide more information in expounding the users. Therefore, to facilitate flexible applications, under +(1-0) (5) the proposed CECE, we have two schemes in the recommendation method, namely, CECF-C and CECF-NC. C and NC represent where the probability measure Prupd-Pg) is replaced by a" for the choice of similarity functions applied in computing the simplicity: and 0 is an adjustable weight on the in-clique probab similarities among user-groups. C is based on the Com measure The way of the probability measure in Eq (5)would tem set. whereas Nc is based on Non-Common item set. it is worthy to discuss the hybrid of C and NC in measuring similarities us into the consideration on how to select similarity functions that the CF performance depends on the choice of similarity currently since the adjustment of weights would make the measures. Conventionally, the similarity function for market basket module more complex for analysis. Note that measuring simila- data is based on the Jaccard coefficient [10, 22, 36]as rities between in-clique users still apply the concept of common S(up)ns(ur) item set since their basket sizes are much smaller. In Table 3 S(up)US(ufe)I S(up )l+IS(uf)I-S(up)ns(ufe)I we list all recommendation schemes that would be compared in Section 4 where S(up) is the item set purchased by user up: S(upi)nS(ufe)is the common item set purchased by user up and fre, sun/os(r) 3.3. The analytical model and recommendation procedures is the item set purchased by user up or uft. However, as indicated In this section would discuss the analytical m [36], the Jaccard coefficient missed the information that two proposed by Wang and Wu [51] as well as the operat users do not choose the same items simultaneously. The non procedures of the proposed module mmon item set would affect the similarity measure between influence of non-common item set into consideration. Therefore. 3.3.1. The analytical model with two marketing strategies: maximal on the grounds of effects caused by non-common item set profit strategy and win-win strategy After the offline operations, three databases were constructed measure between two users based on the similarity function namely item-group database defined by Pi=(Pa(ak)d'=1,22 considering nor item set as D', i=1,2,. I]: user-group database defined by U=(up(og) f=1,2,., Fij=1, 2,.JI; their relations constructed by CECF sim(p, pr)= sup)n S(uy )I () of Eqs. (4 -(6),and (8). When a user is online, we could identify S(up)US(uf) a user s eleven ces through the corresponding information retrieved from the databases the retrieved data as well as the S()represents the non-purchased item set and the comple- users requests(desired satisfaction level and budget limit)are et of S(). Consequently, Eq (7)preserves the information of that are not commonly purchased by two compared users. However, the similarity measure of the non-common item set is not very appropriate in a large-scale database. The reason is Table 3 nat the value of this indicator would be probably close to one Recommendation schemes. hen comparing two users(see Appendix A). As a consequence. we suggest that they are compared on the grounds of group Schemes Function of user similarity tion of user-group similarity In-clique effects purchase behavior, which is given as -of-clique eff (U,U) lU-, S(U)-(S(U)US(U") Common item set lUi-1S(U)-(S(U)nS(UT) CECF-NC Non-common item se 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. 2010.03.011ARTICLE IN PRESS item-group. For the former, the similarity measures would refer to arrow 2 in Fig. 3. For the latter that refers to arrow 1 in Fig. 3, the relative purchase frequency in the binary basket analysis has been adopted as the prediction of purchase priority [10]: wj i ¼ CðUj ,Pi Þ SðUj Þ , ð3Þ where CðPi ,Uj Þ is the relative frequency that users in Uj purchase items in Pi ; S(Uj ) is the total number of market baskets for Uj . Therefore, the probability measure of ‘‘out-of-clique’’ purchase can be presented as Pout-of-clique rðufj ,pdi Þ ¼ k2 X taj simðUj ,UtÞ wt i , ð4Þ where simðUj ,UtÞ, which refers to arrow 2, is the similarity measure between the target user-group Uj and other user-group Ut; k2 is a normalizing factor to ensure the absolute values of probability sum to unity. Therefore, the probability measure of a target user ufj purchasing item pdi would be represented as Prðufj ,pdi Þ ¼ @ ufj pdi ¼ y  k1 X uf t AUj simðufj ,uf t Þ Cuf t ,pdi zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ in-clique þ ð1yÞ  k2 X taj simðUj ,UtÞ wt i zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ out-of-clique , ð5Þ where the probability measure Prðufj ,pdi Þ is replaced by @ ufj pdi for simplicity; and y is an adjustable weight on the in-clique probability measure. The way of the probability measure in Eq. (5) would lead us into the consideration on how to select similarity functions. Note that the CF performance depends on the choice of similarity measures. Conventionally, the similarity function for market basket data is based on the Jaccard coefficient [10,22,36] as simðufj ,uf t Þ ¼ jSðufjÞ \ Sðuf t Þj jSðufjÞ [ Sðuf t Þj ¼ jSðufjÞ \ Sðuf t Þj jSðufjÞjþjSðuf t ÞjjSðufjÞ \ Sðuf t Þj , ð6Þ where SðufjÞ is the item set purchased by user ufj; SðufjÞ \ Sðuf t Þ is the common item set purchased by user ufj and uf t ; SðufjÞ [ Sðuf t Þ is the item set purchased by user ufj or uf t . However, as indicated in [36], the Jaccard coefficient missed the information that two users do not choose the same items simultaneously. The non￾common item set would affect the similarity measure between two objects; as a result, the similarity function shall take the influence of non-common item set into consideration. Therefore, on the grounds of effects caused by non-common item set between users’ purchase histories, we propose the similarity measure between two users based on the similarity function considering non-common item set as simðufj ,uf t Þ ¼ jSðufjÞ \ Sðuf t Þj jSðufjÞ [ Sðuf t Þj , ð7Þ where SðÞ represents the non-purchased item set and the comple￾ment set of SðÞ. Consequently, Eq. (7) preserves the information of items that are not commonly purchased by two compared users. However, the similarity measure of the non-common item set is not very appropriate in a large-scale database. The reason is that the value of this indicator would be probably close to one when comparing two users (see Appendix A). As a consequence, we suggest that they are compared on the grounds of group purchase behavior, which is given as simðUj ,UtÞ ¼ j SJ j ¼ 1 SðUj ÞðSðUj Þ [ SðUtÞÞj j SJ j ¼ 1 SðUj ÞðSðUj Þ \ SðUtÞÞj , ð8Þ where simðUj ,UtÞ is the similarity measure between the target user-group Uj and the other user-group Ut. Therefore, the similarity measures indicated in the Appendix A could be computed as shown in Appendix B, in which the similarity measure is more appropriate. 3.2.1. Summary of the proposed CECF In this section, we have proposed the CECF containing users’ purchase probability measure as Eq. (5), which is a convex combination of two distinct probability measures from in-clique effects of Eq. (2) and out-of-clique effects of Eq. (4). The classification of the target user into in-clique users as well as out-of-clique users, the proposed probability measure function provides different insight from that of conventional CF method. As for the probability measure of in-clique users, we adopt the traditional CF method, whereas for the measure of out-of-clique users, we propose an alternative similarity function by incorpor￾ating the items not purchased simultaneously by each pair of compared users to find the similarity among user-groups. Then the proposed probability measure is predicted by the purchase and non-purchase behaviors of the users, which could be expected to provide more information in expounding the users. Therefore, to facilitate flexible applications, under the proposed CECF, we have two schemes in the recommendation method, namely, CECF-C and CECF-NC. C and NC represent the choice of similarity functions applied in computing the similarities among user-groups. C is based on the Common item set, whereas NC is based on Non-Common item set. It is worthy to discuss the hybrid of C and NC in measuring similarities among user-groups. We would not focus on a hybrid approach currently since the adjustment of weights would make the module more complex for analysis. Note that measuring simila￾rities between in-clique users still apply the concept of common item set since their basket sizes are much smaller. In Table 3, we list all recommendation schemes that would be compared in Section 4. 3.3. The analytical model and recommendation procedures In this section, we would discuss the analytical model proposed by Wang and Wu [51] as well as the operation procedures of the proposed module. 3.3.1. The analytical model with two marketing strategies: maximal profit strategy and win–win strategy After the offline operations, three databases were constructed, namely item-group database defined by Pi ¼ fpdiðakÞjdi ¼ 1i ,2i , ... , Di ,i ¼ 1,2, ... ,Ig; user-group database defined by Uj ¼ fufjðogÞj fj ¼ 1j ,2j , ... ,Fj ,j ¼ 1,2, ... ,Jg; their relations constructed by CECF of Eqs. (4)–(6), and (8). When a user is online, we could identify a user’s preferences through the corresponding information retrieved from the databases. The retrieved data as well as the user’s requests (desired satisfaction level and budget limit) are Table 3 Recommendation schemes. Schemes Function of user similarity Function of user-group similarity In-clique effects Out-of-clique effects CF Common item set – CECF-C Common item set Common item set CECF-NC Common item set Non-common item set H.-F. Wang, C.-T. Wu / Computers & Operations Research ] (]]]]) ]]]–]]] 7 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