Accepted 2 December 2012Available online 28 December 2012
(PMF), and a ranking-oriented CF approach, i.e., list-wise learning-to-rank with matrix fac-
ividual items rstas rating-orientedatings, but[14,15,27
To illustrate the difference between rating- and ranking-oriented CF, we consider two specic toy examples. Texample involves the ratings of a user on items i and j. We assume that the user has rated item i with a 4 and itema 3; these are the reference values that we use to judge the quality of the predictions of the recommender system. If tworecommendation approaches give rating predictions of (3,4), and (5,2) on items (i; j), the rating prediction error, e.g.,
0020-0255/$ - see front matter 2012 Elsevier Inc. All rights reserved.
Corresponding author. Address: HB.11.070, Mekelweg 4, 2628CD Delft, Netherlands. Tel.: +31 152785812; fax: +31 152781843.E-mail address: email@example.com (Y. Shi).
Information Sciences 229 (2013) 2939
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Information Scienceshttp://dx.doi.org/10.1016/j.ins.2012.12.002order to generate recommendation lists for users. Under one approach, the system predicts ratings for indand then generates the ranked recommendation list. We refer to this type of CF-based recommendation[7,12,22]. Under the other approach, the system predicts rank scores, that are not necessarily related to rused directly to generate the recommendation list. We refer to this type of approach as ranking-orientedrather,30,31].he rstj withRecommender systems attract research attention because they are able to connect users directly with consumable items,supporting them in handling the unprecedentedly large amounts of content, e.g., movies, music and books currently avail-able online by providing personalized recommendations [1,6]. Collaborative ltering (CF) is widely acknowledged as one ofthe most successful recommender techniques. Compared to content-based approaches, CF enjoys the advantage of beingcontent-agnostic. In other words, it can recommend items without the additional computational expense or copyright issuesinvolved with processing items directly. One of two different types of approaches can be taken by a recommender system inMatrix factorizationRankingRecommender systemsUnied recommendation model
1. Introductiontorization (ListRank). The URM benets from the rating-oriented perspective and the rank-ing-oriented perspective by sharing common latent features of users and items in PMF andListRank. We present an efcient learning algorithm to solve the optimization problem forURM. The computational complexity of the algorithm is shown to be scalable, i.e., to be lin-ear with the number of observed ratings in a given user-item rating matrix. The experi-mental evaluation is conducted on three public datasets with different scales, allowingvalidation of the scalability of the proposed URM. Our experiments show the proposedURM signicantly outperforms other state-of-the-art recommendation approaches acrossdifferent datasets and different conditions of user proles. We also demonstrate that theprimary contribution to improve recommendation performance is contributed by theranking-oriented component, while the rating-oriented component is responsible for asignicant enhancement.
2012 Elsevier Inc. All rights reserved.Unifying rating-oriented and ranking-oriented collaborativeltering for improved recommendation
Yue Shi , Martha Larson, Alan HanjalicMultimedia Information Retrieval Lab, Department of Intelligent Systems, Delft University of Technology, Netherlands
a r t i c l e i n f o
Article history:Received 23 February 2012Received in revised form 1 November 2012
a b s t r a c t
We propose a novel unied recommendation model, URM, which combines a rating-oriented collaborative ltering (CF) approach, i.e., probabilistic matrix factorization
journal homepage: www.elsevier .com/locate / ins
(NDCG) evaluation metric [14,15,30,31]. As discussed in more detail in Section 4.2, NDCG simultaneously takes into account
30 Y. Shi et al. / Information Sciences 229 (2013) 2939both the rank ordering of a list as well as the graded relevance, i.e., the magnitude of the scores of the items in the list. Some-what unexpectedly, although recommender system research is increasingly taking both rank and rating prediction into ac-count for evaluation, up until this point, no concerted research effort has been devoted to developing algorithms thatproduce recommendation lists that simultaneously optimize both rank and ratings of the recommended items. The contri-bution of this paper is to combine the two types of recommendation, ranking-oriented and rating-oriented, in order to arriveat a system that generates recommendations that are more completely suited to satisfy user needs.
We accomplish the goal of generating recommendations optimized not only for ranking, but also for rating by proposing anovel unied recommendation model (URM) that enhances ranking-oriented recommendation using a rating-oriented ap-proach. The model combines probabilistic matrix factorization (PMF) , i.e., rating-oriented CF, and ListRank , i.e.,ranking-oriented CF, by exploiting common latent features shared by both PMF and ListRank. In fact, by incorporatingPMF we enable ListRank to benet from rating predictions, which contributes another basis for generating the recommen-dation list. We demonstrate experimentally that the URM achieves signicant improvement of recommendation perfor-mance over the state-of-the-art CF approaches on various data sets. Furthermore, we analyze and empiricallydemonstrate that URM maintains linear complexity with the number of observed ratings in the given user-item matrix,which means that it can scale up with the increasing amount of data.
The approach presented in this paper builds on and expands the basic nding of the effectiveness of list-wise learning-to-rank, demonstrated in , where we rst introduced ListRank, a ranking-oriented matrix factorization approach. Theexpansions that are presented here extend along two dimensions. First, we combine the advantages of ranking-orientedand rating-oriented recommendation by combining ListRank with a rating-oriented component, resulting in URM, a new rec-ommendation model. Second, we conduct experimental evaluations on multiple datasets of various scales to validate theusefulness of the proposed URM approach, and demonstrate its specic contributions to the state of the art.
The remainder of the paper is structured as follows. In the next section, we summarize related work and position our ap-proach with respect to it. Then, we present the URM and validate it experimentally. Finally, we sum up the key aspects ofURM and address possible directions for future work.
2. Related work
Our work builds on the foundation of the large body of work that has been carried out on CF. CF approaches are generallyconsidered to fall into one of two categories, i.e., memory-based CF and model-based CF [1,6]. In general, memory-based CFuses similarities between users (user-based CF) or similarities between items (item-based CF) to make recommendations.User-based CF [7,21] recommends items to a user on the basis of how well similar users like those items. Item-based CF[5,13,23] recommends items to a user based on the similarity between the users favored items and the items to be recom-mended. Recently, various studies have been devoted to the modication and enhancement of memory-based CF, e.g., tospecically improve user-based CF [26,33], to specically improve item-based CF , and to combine user-based CF anditem-based CF [16,29]. Although substantial improvements have been achieved, memory-based CF approaches still sufferfrom high computational complexity, i.e., computing similarities among the typically enormous number of users or itemsin recommender system applications is expensive.
In comparison, model-based CF approaches rst t prediction models based on training data and then use the model topredict users preferences on items. These models include latent semantic models , mixture models [11,28] and fuzzy lin-guistic models [17,19]. Matrix factorization (MF) [12,22] has been recognized as one of the most successful model-based CFapproaches, due to its superior accuracy and scalability. Generally, MF models learn low-rank representations (latent fea-tures) of users and items from the observed ratings in the user-item matrix, which are further used to predict unobservedmeasured by mean absolute error or root mean square error  will be the same for both approaches. However, only theranking-oriented perspective identies the second approach as faithfully reecting the users relatively higher preferencefor item i over item j. This example should not lead to the conclusion that working with absolute ratings is detrimentalto recommendation performance. Quite to the contrary, successful recommender systems do use a rating-oriented approachto generate recommendation lists for users, e.g., MovieLens  and Netix . Our second example illustrates the useful-ness of absolute ratings in capturing users preference strength. If user u and v have ratings (5,3) and (4,3) on items (i; j), useru is more explicit about his preference for item i over item j than user v. This information holds the potential to help resolvepossible ambiguities in generating a ranked item list for the user u. Further, predicted ratings can provide the user with addi-tional information used to inform the decision of whether or not view, purchase or download the item. Taken together, theseexamples serve to motivate our standpoint that ranking-oriented approaches have high potential and that combining rating-oriented and ranking-oriented approaches holds promise for designing more successful recommendation algorithms.
Another source of motivation derives from the recent recommender system literature, which demonstrates a growingawareness that under ranking-oriented recommendation, the ability of the system to predict ratings is also important. Thisawareness is based on the insight that although users nd it important to receive a high quality ranked list from the recom-mender system, the list will be less useful or less acceptable to the user if the ratings assigned by the system to the items failto approximate those that the user would have assigned. The increasing emphasis on providing the user with both a highquality ranked list and accurate ratings is reected in the recent adoption of the Normalized Discounted Cumulative Gain
ratings. MF can also be formulated from a probabilistic perspective, i.e., PMF , which models the conditional probabilityof latent features given the observed ratings, and factors for complexity regularization encoding prior information on userand item ratings. In this paper, we adopt PMF as the rating-oriented CF component of our proposed URM.
Compared to the large volume of research on rating-oriented CF, the research on ranking-oriented CF is limited. The rstmature ranking-oriented CF approach is CoRank [30,31], which introduces structured ranking losses and various otherextensions to MF. Further studies mainly focus on exploiting pair-wise preference between items for users, e.g., EigenRank, probabilistic latent preference analysis  and Bayesian personalized ranking . Although empirical study hasshown the great value of pair-wise comparisons other than individual ratings for representing users preferences , allthese existing pair-wise approaches [14,15,20] require deriving pair-wise training examples from individual ratings, thus,in general all suffer from high computational complexity of pair-wise comparisons, which scale quadratically to the numberof rated items in a given data collection. In contrast, ListRank  is designed to incorporate a list-wise learning-to-rank con-
Y. Shi et al. / Information Sciences 229 (2013) 2939 31In this section, we rst briey present the basic formulation of PMF and ListRank. Then, we combine PMF and ListRank bymeans of the URM and, nally, we present an efcient learning algorithm for solving the optimization problem in the URMand analyze the complexity of the algorithm.
3.1. PMF: matrix factorization for rating
If we denote by R a user-item rating matrix consisting ofM users ratings on N items, PMF  seeks to represent the ma-trix R by two low-rank matrices, U and V. A d-dimensional set of latent features is used to represent both users (in U) anditems (in V). Note that we use Ui to denote a d-dimensional column feature vector of user i;Vj to denote a d-dimensionalcolumn feature vector of item j, and Rij to denote the user is rating on item j. Usually, the rating scale is different fromone dataset (application scenario) to another. To achieve generality, the ratings are normalized to the range from [0,1].The objective of PMF is now to t each rating Rij with the corresponding inner product U
Ti Vj, which can be formulated as
U;V arg minU;V
Iij Rij gUTi Vj 2
Uk k2F kV2
Vk k2F( )
Here, Iij is an indicator function that is equal to 1 when Rij > 0, and 0 otherwise. The parameters kU and kV are regularizationcoefcients used to reduce over-tting, while kUkF and kVkF are the Frobenius norms of the matrices U and V. For simplicity,we set kU kV k. The gx is a logistic function serving to bound the range of UTi Vj to be also in the range [0, 1], i.e.,gx 1=1 ex. The inputoutput diagram of PMF is illustrated in Fig. 1.
3.2. ListRank: matrix factorization for ranking
In order to model the users preference from her ranked list of rated items, we need to transform the users ratings ondifferent items to ranking scores, which are required to maintain two properties. First, for a given user, the ranking score
(a) PMF (b) ListRankFig. 1. The inputoutput diagrams of PMF and ListRank.ed approach as the basis of our unied recommendation model (URM) and deploy rating-oriented PMF to expand it.
ed recommendation modelcept with MF, which is characterized by a low complexity, i.e., complexity is linear with the number of the observed ratingsin a given user-item rating matrix. Preliminary experiments  also show ListRank to be competitive for recommendationin comparison to other state-of-the-art approaches, represented by CoRank. One of the latest contributions on exploitingother learning-to-rank methods for CF  shares the same motivation of ListRank, and also envisioned the potential oflist-wise approach for CF, which is represented by ListRank. The established performance and value of ListRank makes ita natural choice as our ranking-oriented approach, to be extended within the proposed URM.
Our work in this paper unies a rating-oriented CF, i.e., PMF and a ranking-oriented CF, i.e., ListRank in terms of the samelatent features shared by PMF and ListRank. In view of the comparison of ranking-oriented and rating-oriented CF in the pre-vious section...