the fusion of collaborative and content-based models. The ming over all latent variables z. authors of 2 present a multi-dimensional technique which incorporates contextual information for an optimized recom- P(imU)=>P(imIzk)P(Khun) mender training. The fusion of co-occurrence relationships ong multiple types of objects is also proposed in [15 For the annotation-based scenario we assume the same hid- tent semantic analysis(LSA)algorithm that outperforms den topics as origin of the item tag co-occurrence observa- standard LSA in a variety of domains, such as collaborative tions given by IT. Analog to(1), the conditional probability filtering or text categorization. A more general overview of tween tags and items can be written as: recommender systems is given in 3, 6 P(im(tn)=>P(iml=k)P(=kltn Probabilistic latent semantic analysis(PLSA) has beer shown to improve the quality of collaborative filtering base recommenders 9 by assuming an underlying lower dimen- Following the procedure in 5, we can now combine both sional latent topic model. Similar to our approach, the au models based on the common factor P(imlzk)by maximizing thors of 5 consider the problem of document clustering and the log-likelihood function extend the Plsa algorithm to combine content-based and lyperlink-based similarities into a unified model. Model ft ∑f(m,u)ogP(nln) ion using PLSA was also successfully applied to the dis- overy of navigational patterns on the Web[12, in music recommendation combining multiple similarity measures 4 and for the cross-domain knowledge transfer [17] +(1-a)2/(im, tn)log P(imIt),(3) Until recently, research on recommender systems and folk where a is a predefined weight for the influence of each two- onomies mainly focused on tag recommendation [ 8, 11, 13 The authors of [14 enrich a collaborative movie recom mender by incorporating tags that were assigned to each Using the Expectation-Maximization(EM)algorithm 5 we movie in external folksonomies. Finally, [1 proposes to hen perform maximum likelihood parameter estimation for smooth tag item distributions based on usage patterns in the aspect model. During the expectation(E)step we first order to improve resource retrieval. calculate the posterior probabilitic The remainder of this paper is structured as follows. In P(z:Jul, in P(im zk)P(zUn) section 2 we extend the PlsA model to a recommendation P(imMun model which unifies annotations and usage patterns. We then present our experimental settings and the results ob- P(Enltn, im)=P(im Ek)P(=*ltm) P(imIt) tained from our experiments in sections 3 and 4 and summa- rize our conclusions and ideas for future directions in section and then re-estimate parameters in the maximization (M) step as follows: P(2ku)∝∑f(u,im)P(kuy,tn) 2. MODEL FUSION USING PLSA According to 10, a folksonomy can be described as a tri- P(ekIn)o>/(n, im)P(ekIn, im partite graph whose vertex set is partitioned into three dis- int sets of users U=ul,,u, tags T=(ti, .. tn) and p(im|zk)∝a∑f(u,imn)P(zku,in) ms I=i1,.,im. We simplify this model to two bi partite models where the collaborative filtering model IU is built from the item user co-occurrence counts f(i, u) and the +(1-a)>/(tn, im)P(ExItn, im)(6) annotation-based model it derives from the co-occurrence counts between items and tags f(i, t). In the case of social Based on the iterative computation of the above E and M bookmarking IU becomes a binary matrix ((i, u)E(0, 1), steps, the EM algorithm monotonically increases the likeli- as users can bookmark a given web resource only once hood of the combined model on the observed data. Using Given our model, we want to recommend the most inter- the a parameter, our new model can be easily reduced to a esting new items from I to a user u given the user's item collaborative filtering or annotation-based model by setting history. a to 1.0 or 0.0 respectively The aspect model of PLSA associates the co-occurrence of We can now recommend items to a user un weighted by the observations with a hidden topic variable Z=[21,.., 2k). probability P(imMun)from equation(1)2. For items already In the context of borative filtering an observation corre bookmarked by the user in the training data we set this sponds to the bookmarking of an item by a user and all ob- weight to 0, thus they are appended to the end of the rec- servations are given by the co-occurrence matrix IU. Users ommended item list and items are assumed independent given the topic variable Z. Applying the aspect model, the probability that an item It is also ole to recommend items with respect to a was bookmarked by a given user can be computed by su given tag tn based on equation(2)the fusion of collaborative and content-based models. The authors of [2] present a multi-dimensional technique which incorporates contextual information for an optimized recom￾mender training. The fusion of co-occurrence relationships among multiple types of objects is also proposed in [15], where the authors present a multi-type extension of the la￾tent semantic analysis (LSA) algorithm that outperforms standard LSA in a variety of domains, such as collaborative filtering or text categorization. A more general overview of recommender systems is given in [3, 6]. Probabilistic latent semantic analysis (PLSA) has been shown to improve the quality of collaborative filtering based recommenders [9] by assuming an underlying lower dimen￾sional latent topic model. Similar to our approach, the au￾thors of [5] consider the problem of document clustering and extend the PLSA algorithm to combine content-based and hyperlink-based similarities into a unified model. Model fu￾sion using PLSA was also successfully applied to the dis￾covery of navigational patterns on the Web [12], in music recommendation combining multiple similarity measures [4] and for the cross-domain knowledge transfer [17]. Until recently, research on recommender systems and folk￾sonomies mainly focused on tag recommendation [8, 11, 13]. The authors of [14] enrich a collaborative movie recom￾mender by incorporating tags that were assigned to each movie in external folksonomies. Finally, [1] proposes to smooth tag item distributions based on usage patterns in order to improve resource retrieval. The remainder of this paper is structured as follows. In section 2 we extend the PLSA model to a recommendation model which unifies annotations and usage patterns. We then present our experimental settings and the results ob￾tained from our experiments in sections 3 and 4 and summa￾rize our conclusions and ideas for future directions in section 5. 2. MODEL FUSION USING PLSA According to [10], a folksonomy can be described as a tri￾partite graph whose vertex set is partitioned into three dis￾joint sets of users U = {u1, ..., ul}, tags T = {t1, ..., tn} and items I = {i1, ..., im}. We simplify this model to two bi￾partite models where the collaborative filtering model IU is built from the item user co-occurrence counts f(i, u) and the annotation-based model IT derives from the co-occurrence counts between items and tags f(i, t). In the case of social bookmarking IU becomes a binary matrix (f(i, u) ∈ {0, 1}), as users can bookmark a given web resource only once. Given our model, we want to recommend the most inter￾esting new items from I to a user ul given the user’s item history. The aspect model of PLSA associates the co-occurrence of observations with a hidden topic variable Z = {z1, . . . , zk}. In the context of collaborative filtering an observation corre￾sponds to the bookmarking of an item by a user and all ob￾servations are given by the co-occurrence matrix IU. Users and items are assumed independent given the topic variable Z. Applying the aspect model, the probability that an item was bookmarked by a given user can be computed by sum￾ming over all latent variables Z: P(im|ul) = X k P(im|zk)P(zk|ul), (1) For the annotation-based scenario we assume the same hid￾den topics as origin of the item tag co-occurrence observa￾tions given by IT. Analog to (1), the conditional probability between tags and items can be written as: P(im|tn) = X k P(im|zk)P(zk|tn). (2) Following the procedure in [5], we can now combine both models based on the common factor P(im|zk) by maximizing the log-likelihood function L = X m " α X l f(im, ul) log P(im|ul) +(1 − α) X n f(im, tn) log P(im|tn) # , (3) where α is a predefined weight for the influence of each two￾mode model. Using the Expectation-Maximization (EM) algorithm [5] we then perform maximum likelihood parameter estimation for the aspect model. During the expectation (E) step we first calculate the posterior probabilities: P(zk|ul, im) = P(im|zk)P(zk|ul) P(im|ul) P(zk|tn, im) = P(im|zk)P(zk|tn) P(im|tn) , and then re-estimate parameters in the maximization (M) step as follows: P(zk|ul) ∝ X m f(ul, im)P(zk|ul, im) (4) P(zk|tn) ∝ X m f(tn, im)P(zk|tn, im) (5) p(im|zk) ∝ α X l f(ul, im)P(zk|ul, im) +(1 − α) X n f(tn, im)P(zk|tn, im) (6) Based on the iterative computation of the above E and M steps, the EM algorithm monotonically increases the likeli￾hood of the combined model on the observed data. Using the α parameter, our new model can be easily reduced to a collaborative filtering or annotation-based model by setting α to 1.0 or 0.0 respectively. We can now recommend items to a user ul weighted by the probability P(im|ul) from equation (1)2 . For items already bookmarked by the user in the training data we set this weight to 0, thus they are appended to the end of the rec￾ommended item list. 2 It is also possible to recommend items with respect to a given tag tn based on equation (2)