46 C. Wartena and m. wibbels at recommendation is proposed by [6 who use non-negative matrix factoriza tion to obtain a weak clustering of tags into topics. Now recommendations are computed by using the probability that a user is interested in a topic and the probability that an item is relevant to that topic. This idea comes very close to the approach for topic diversification that we propose below. However, [ 6use global tag clusters, whereas we apply clustering to the tags of each user profile Moreover, we do not sum up the probabilities for an item over all clusters. 3 Tag based recommendation In the following we will use two basic strategies for tag based recommendation We will show that both strategies can be modified easily to become topic aware and that this leads to improvement of recommendation results in all cases. The first type of algorithm we will consider is item based collaborative filtering. The directly. Therefore we call these algorithms profile based tem and a user profile In all cases the recommendations are based on the tags assigned to the item To be more precise, we will represent each item by a probability distribution over tags. Consider collections of items C=i1,.ik, tags T=ti,.ti) and users= ul,.um Let n(i, t, u) be the number of times a user u assigned tag t to item i, usually 0 or 1. To consider the tags assigned to an item and the ags assigned by a user, respectively, we let n(i,t)=∑n(t,)and (1) n(u,t)=∑n(i,t,u) Furthermore. let nr()=∑n(, ()=∑n(t)an Now we define probability distributions pr(t)and pc(ilz) on respectively the et of tags T and the corpus C that describe how tag occurrences of a given i are distributed over different tags, respectively how the occurrences of a tag z are distributed over different items: Pr(ti)=n(i, t)/nc(i) pc(it)=n(i, t)/nr(t) Finally, for each u E U let Cu be the set of items seen/ bookmarked by u. Note that in many cases a user did not tag all the items he has bookmarked46 C. Wartena and M. Wibbels at recommendation is proposed by [6] who use non-negative matrix factoriza￾tion to obtain a weak clustering of tags into topics. Now recommendations are computed by using the probability that a user is interested in a topic and the probability that an item is relevant to that topic. This idea comes very close to the approach for topic diversification that we propose below. However, [6] use global tag clusters, whereas we apply clustering to the tags of each user profile. Moreover, we do not sum up the probabilities for an item over all clusters. 3 Tag Based Recommendation In the following we will use two basic strategies for tag based recommendation. We will show that both strategies can be modified easily to become topic aware and that this leads to improvement of recommendation results in all cases. The first type of algorithm we will consider is item based collaborative filtering. The second type of algorithms uses the similarity between an item and a user profile directly. Therefore we call these algorithms profile based. In all cases the recommendations are based on the tags assigned to the items. To be more precise, we will represent each item by a probability distribution over tags. Consider collections of items C = {i1,...ik}, tags T = {t1,...tl} and users U = {u1,...um} Let n(i, t, u) be the number of times a user u assigned tag t to item i, usually 0 or 1. To consider the tags assigned to an item and the tags assigned by a user, respectively, we let n(i, t) = u∈U n(i, t, u) and (1) n(u, t) = i∈C n(i, t, u). (2) Furthermore, let nT (t) = i∈C n(i, t), (3) nC(i) = t∈T n(i, t) and (4) nU (u) = t∈T n(u, t). (5) Now we define probability distributions pT (t|i) and pC(i|z) on respectively the set of tags T and the corpus C that describe how tag occurrences of a given item i are distributed over different tags, respectively how the occurrences of a given tag z are distributed over different items: pT (t|i) = n(i, t)/nC(i), (6) pC(i|t) = n(i, t)/nT (t). (7) Finally, for each u ∈ U let Cu be the set of items seen/bookmarked by u. Note that in many cases a user did not tag all the items he has bookmarked.