We assume all the users who tag the items also give rat- delve into it. Their dataset includes three files. One ngs and that all the items which are tagged also receive is rating data which contains users ratings for movies ratings. If some users actually fail to give either ratings another is tagging data which contains movies'tags and or tags, we still can make use of what they input to the the users id who made the tag, and the other is movie recommender system. Even with few entries, the recom overview data which contains the movie's name release mender system still understands what the user wants. year and genre. The user are allowed to give ratings We hold this claim because tags are more informative. and tags to the movies they have seen. The ratings are If the user only put one tag amine"te tegers between 1 to 5. could infer that this is a animation fun. But if this user only give a high rating to the movie Avatar", what We intend to leverage tag analysis to help rating pre- should we infer from this? Which groups of movie does diction. So we need the movies that have both ratings is user like actions. adventures, fantasies or sci-fis? nd tags and the users that give both ratings and tags After taking the intersection of the rating data and tag Most recommender systems use the integral interval data, we get the rating datas subset which contains all 1, Rmaz to represent the users' preference on items the tagged movies. This subset contains 905686 ratings It is necessary to normalize the ratings into the ran from 4001 for 7600 movies. The density of these to 0, 1, because only this interval makes sense for prob- rating data is ability. There are many mapping methods. One of the most widely used mapping function is f(a)=(r 905686 1)/(Rmaz-1). As far as we know, the influence exerted 4001×7600=2.974% on the final recommendation by different mapping func- From this subset, we randomly and independently choose tions is not significantly different 20%, 50%, 80% and 99% of rating data as separate training sets. The remaining rating data are used as So our next step is to make rating predictions based on the testing sets. The experiments are all repeated five the grouping results stated in the last section. The pre- times to reduce errors diction is made according to a neighborhood method. Fij= A+bi+b Toy Examples Because the quality of recommendation is eventually b chero(rhj-bhj)Ih thet( h) reflected in the results of rating prediction accuracy. To obtain a clearer vision about the qualitative quality, we ∑h∈ro(Th-bnh)l (3) present two toy examples in smaller data volume scale Iih First we extract the tags from 6 users. The tag matrix where bi denotes useri's bias for the topic T(i), and b denotes item,'s bias for the topic T(). T(i) and T() denote the topic user is interested in and the topic killer action horror tem, is under, respectively. Each topic is a set which thrill action contains a number of users or items 1墨 anine fantasy anine Plus, we give different weights to the neighbors with Japanese animE different distances. The algorithms weighted variant ic documentary American realistic μ+b+b ∑her(mh-bmy)Sh1lB We set the hyper-parameter topic number as 3 and con- duct LDa analysis to get the probabilistic matrix 2h∈T(i) )(rih-bin)Sp /0.3456790.3456790.308642 0.3641980.3086420.308642 where Ah, 0i and O, denote the row vectors of proba- e=0.306420345679035679 bilities in E. S represents the cosine similarity of the vectors hh and 6 0.3456790.3086420.345679 0.3086420.3456790.345679 EXPERIMENTAL ANALYSIS Dataset Description It is quite obvious that user1 and user2 have the same Movielens Dataset is created by Movielens movie rec- or similar interests. The first column values is the m ommender which aims to provide online movie recom- imum among all three columns for both of him, which endation service [17. Their work is a more involved infers the topic they are most probably interested in is system rather than a particular algorithm, so we do not the first topic. For the same reason, users and useraWe assume all the users who tag the items also give rat￾ings and that all the items which are tagged also receive ratings. If some users actually fail to give either ratings or tags, we still can make use of what they input to the recommender system. Even with few entries, the recom￾mender system still understands what the user wants. We hold this claim because tags are more informative. If the user only put one tag ”amine” to some item, we could infer that this is a animation fun. But if this user only give a high rating to the movie ”Avatar”, what should we infer from this? Which groups of movie does this user like, actions, adventures, fantasies or sci-fis? Most recommender systems use the integral interval [1, Rmax] to represent the users’ preference on items. It is necessary to normalize the ratings into the range to [0, 1], because only this interval makes sense for prob￾ability. There are many mapping methods. One of the most widely used mapping function is f(x) = (x − 1)/(Rmax−1). As far as we know, the influence exerted on the final recommendation by different mapping func￾tions is not significantly different. So our next step is to make rating predictions based on the grouping results stated in the last section. The pre￾diction is made according to a neighborhood method: rˆij = µ + b ∗ i + b ∗ j , b ∗ i = P h∈T(i) (rhj − bhj )I R hj P h∈T(i) I R hj , b ∗ j = P h∈T(j) (rih − bih)I R ih P h∈T(j) I R ih , (3) where b ∗ i denotes useri ’s bias for the topic T(i), and b ∗ j denotes itemj ’s bias for the topic T(j). T(i) and T(j) denote the topic useri is interested in and the topic itemj is under, respectively. Each topic is a set which contains a number of users or items. Plus, we give different weights to the neighbors with different distances. The algorithm’s weighted variant is rˆij = µ + b ∗ i + b ∗ j , b ∗ i = P h∈T(i) (rhj − bhj )ShiI R hj P h∈T(i) ShiI R hj , b ∗ j = P h∈T(j) (rih − bih)Shj I R ih P h∈T(j) Shj I R ih , (4) where θh, θi and θj denote the row vectors of proba￾bilities in Θ. S represents the cosine similarity of the vectors θh and θj . EXPERIMENTAL ANALYSIS Dataset Description Movielens Dataset is created by Movielens movie rec￾ommender which aims to provide online movie recom￾mendation service [17]. Their work is a more involved system rather than a particular algorithm, so we do not delve into it. Their dataset includes three files. One is rating data which contains users’ ratings for movies, another is tagging data which contains movies’ tags and the user’s id who made the tag, and the other is movie overview data which contains the movie’s name, release year and genre. The user are allowed to give ratings and tags to the movies they have seen. The ratings are integers between 1 to 5. We intend to leverage tag analysis to help rating pre￾diction. So we need the movies that have both ratings and tags and the users that give both ratings and tags. After taking the intersection of the rating data and tag data, we get the rating data’s subset which contains all the tagged movies. This subset contains 905686 ratings from 4001 users for 7600 movies. The density of these rating data is 905686 4001 × 7600 = 2.974%. From this subset, we randomly and independently choose 20%, 50%, 80% and 99% of rating data as separate training sets. The remaining rating data are used as the testing sets. The experiments are all repeated five times to reduce errors. Toy Examples Because the quality of recommendation is eventually reflected in the results of rating prediction accuracy. To obtain a clearer vision about the qualitative quality, we present two toy examples in smaller data volume scale. First we extract the tags from 6 users. The tag matrix T U is as follows:   horror killer action horror horror action thrill action f antasy anime f antasy anime anime Japanese anime f antasy documentary 911 terrorist hero historic documentary American realistic   We set the hyper-parameter topic number as 3 and con￾duct LDA analysis to get the probabilistic matrix Θ U =   0.345679 0.345679 0.308642 0.364198 0.308642 0.308642 0.308642 0.345679 0.345679 0.327160 0.345679 0.327160 0.345679 0.308642 0.345679 0.308642 0.345679 0.345679   It is quite obvious that user1 and user2 have the same or similar interests. The first column values is the max￾imum among all three columns for both of him, which infers the topic they are most probably interested in is the first topic. For the same reason, user3 and user4