M.Y.H. Al-Shamri, K.K. Bharadwaj/ Expert Systems with Applications 35(2008)1386-1399 1391 that the movie has been rated. and zero indicates that the table 4 movie has not been rated yet. Table 2 lists the ratings asso- Comments on genre interestingness measure according to vario ciated with various genres. It is to be noted that the user formulae rating for a specific movie gets associated with all the gen- GIM User Comments res to which the movie belongs. For example, the entry of RGr I Values reflect the actual order of interests user-3 for G4 is 4, 5, and 3(highlighted) where they are cor- 2 Values reflect the actual order of interests responding to movie-5, movie-8, and movie-ll(Table 1) 3 G4 has the highest value as expected. But G3 and Gn have the same value while there is a difference between them respectively, and so on. As discussed earlier, the hybrid fea tures are used as the basis for the genre interestingnes RGF I G] has the highest value as expected. But G4 and G2 hay easure, therefore a user is interested more in G, if it has the same value while there is a difference between them 2 Values reflect the order of interests more high ratings, i.e. good, very good, or excellent. The 3 G4 has the highest value as expected. But GI and G2 have number of hybrid features depends on the number of gen- the same value also. G3 has smaller value than GI and G? res. On this basis, one can infer that user-1, user-2, and while user's interest is more for user-3 are interested more in G3, G1, and G4, respectively Table 2) is because only the number of high rated items is consid- Although some low ratings (r< 3) occur for genres but these can be filtered out at the collaborative stage. Our ered and all high ratings contributed equally in this aim here is to find a compact user model to generate close eighbors for that user. This set of neighbors is used in a are given in Table 4. Obviously, RGR and RGF are appro- collaborative manner to recommend some items. which priate GIM formulae with some weaknesses. To remedy might be liked by the user. Therefore any item with a pre- these weaknesses we introduce in the next subsection a for- dicted rating less than good (3)cannot be recommended to mula that combines both RGR and a modified version of the active user RGF Based on the hybrid features, one can evolve GIM ccording to a suitable formula. To explore the possibility 3.3. The proposed hybrid user model of choosing a formula for GIM, we examined formulae (10) and (11). The first formula, RGR, works well for User preference for a certain item is declared by the rat- user-Iand user-2 but for user-3 it gives Gi and G3 the same ing for that item like good, very good,or excellent.The value(Table 3), whereas they are quite different. G has three good(3)ratings while G3 has very good (4)and excel exact degree of preference is not captured by RGF, because lent(5)ratings. This is because the number of movies for it gives all high ratings the same weight. The following def- inition introduces a modified version of rgf formula each genre is ignored in this formula. The second formula, which tries to reflect the exact preference for items with RGF, works well for user-2 but for user-3 it gives G1, G2 high ratings and G4 the same value, whereas they are quite different Moreover, G3 value is lower than that of Gl, and G,, Definition 1. For a rating-based movie recommender whereas the ratings for G3 are very good and excellent. This system, the modified relative genre frequency (MRGF) of genre G for user ui is defined as Table 2 List of ratings associated with various genres MRGF()=216s)+2×b()+3×5() 3×7F() 3,11,5,4 1.3.5.43.4 5,5,4,35,1,2,2,4,35,1,2,43 As expected, MRGF ( Table 3)overcomes the draw- 1,3,33,4,1, 3 4,5,I4, 5,3 backs of RGF. To develop more accurate Gim, the rela tive genre rating needs to be considered also. Indeed RGR identifies the preferences for genres with some draw- Table 3 backs as discussed before. However. a combined formula Genre interestingness measure according to various formulae of RGR and mRGf will bring out the best in both formu- lae. The following definition gives one possible form of 0.643 0.857 0.500 such a formula 123123 0.773 0.545 0.136 0.474 0.526 0.632 Definition 2. For a rating-based movie recommender 0.200 0.400 0.600 0.400 system, the genre interestingness measure(GIM)of genre 0.286 0.143 Gi for user li is defined as 0.500 0.067 0.333 0.400 2×nf×RGR(i,)×MRGF(,j 0.200 GIM(i,j 0.429 0.286 0.238 0.048 RGR(i,+ MRGF(i, j) 0.167 0.222 0.278 0.333 Here nf is the normalization factor for a given systemthat the movie has been rated, and zero indicates that the movie has not been rated yet. Table 2 lists the ratings asso￾ciated with various genres. It is to be noted that the user rating for a specific movie gets associated with all the gen￾res to which the movie belongs. For example, the entry of user-3 for G4 is 4, 5, and 3 (highlighted) where they are cor￾responding to movie-5, movie-8, and movie-11 (Table 1), respectively, and so on. As discussed earlier, the hybrid fea￾tures are used as the basis for the genre interestingness measure, therefore a user is interested more in Gi if it has more high ratings, i.e. good, very good, or excellent. The number of hybrid features depends on the number of gen￾res. On this basis, one can infer that user-1, user-2, and user-3 are interested more in G3, G1, and G4, respectively (Table 2). Although some low ratings (r < 3) occur for genres but these can be filtered out at the collaborative stage. Our aim here is to find a compact user model to generate close neighbors for that user. This set of neighbors is used in a collaborative manner to recommend some items, which might be liked by the user. Therefore any item with a pre￾dicted rating less than good (3) cannot be recommended to the active user. Based on the hybrid features, one can evolve GIMs according to a suitable formula. To explore the possibility of choosing a formula for GIM, we examined formulae (10) and (11). The first formula, RGR, works well for user-1 and user-2 but for user-3 it gives G1 and G3 the same value (Table 3), whereas they are quite different. G1 has three good (3) ratings while G3 has very good (4) and excel￾lent (5) ratings. This is because the number of movies for each genre is ignored in this formula. The second formula, RGF, works well for user-2 but for user-3 it gives G1, G2 and G4 the same value, whereas they are quite different. Moreover, G3 value is lower than that of G1, and G2, whereas the ratings for G3 are very good and excellent. This is because only the number of high rated items is consid￾ered and all high ratings contributed equally in this formula. Comments on all the GIM formulae for the three users are given in Table 4. Obviously, RGR and RGF are appro￾priate GIM formulae with some weaknesses. To remedy these weaknesses we introduce in the next subsection a for￾mula that combines both RGR and a modified version of RGF. 3.3. The proposed hybrid user model User preference for a certain item is declared by the rat￾ing for that item like good, very good, or excellent. The exact degree of preference is not captured by RGF, because it gives all high ratings the same weight. The following def￾inition introduces a modified version of RGF formula, which tries to reflect the exact preference for items with high ratings. Definition 1. For a rating-based movie recommender system, the modified relative genre frequency (MRGF) of genre Gj for user ui is defined as MRGFði;jÞ ¼ P s2GjSi d3ðri;sÞ þ 2 d4ðri;sÞ þ 3 d5ðri;sÞ 3 TF ðiÞ : ð12Þ As expected, MRGF (Table 3) overcomes the draw￾backs of RGF. To develop more accurate GIM, the rela￾tive genre rating needs to be considered also. Indeed, RGR identifies the preferences for genres with some draw￾backs as discussed before. However, a combined formula of RGR and MRGF will bring out the best in both formu￾lae. The following definition gives one possible form of such a formula. Definition 2. For a rating-based movie recommender system, the genre interestingness measure (GIM) of genre Gj for user ui is defined as GIMði;jÞ ¼ 2 nf RGRði;jÞ MRGFði;jÞ RGRði;jÞ þ MRGFði;jÞ : ð13Þ Here nf is the normalization factor for a given system. Table 2 List of ratings associated with various genres User TF TR G1 G2 G3 G4 1 5 14 1, 3, 1 1, 5, 4 1, 3, 5, 4 3, 4 2 7 22 5, 5, 4, 3 5, 1, 2, 2, 4, 3 5, 1, 2, 4 3 3 6 19 3, 1, 3, 3 3, 4, 1, 3 4, 5, 1 4, 5, 3 Table 3 Genre interestingness measure according to various formulae GIM User G1 G2 G3 G4 RGR 1 0.214 0.643 0.857 0.500 2 0.773 0.545 0.409 0.136 3 0.474 0.526 0.474 0.632 RGF 1 0.200 0.400 0.600 0.400 2 0.571 0.429 0.286 0.143 3 0.500 0.500 0.333 0.500 MRGF 1 0.067 0.333 0.400 0.200 2 0.429 0.286 0.238 0.048 3 0.167 0.222 0.278 0.333 Table 4 Comments on genre interestingness measure according to various formulae GIM User Comments RGR 1 Values reflect the actual order of interests 2 Values reflect the actual order of interests 3 G4 has the highest value as expected. But G3 and G1 have the same value while there is a difference between them RGF 1 G3 has the highest value as expected. But G4 and G2 have the same value while there is a difference between them 2 Values reflect the order of interests 3 G4 has the highest value as expected. But G1 and G2 have the same value also. G3 has smaller value than G1 and G2 while user’s interest is more for G3 M.Y.H. Al-Shamri, K.K. Bharadwaj / Expert Systems with Applications 35 (2008) 1386–1399 1391