\section{Related Work} One of the main sources of information exploited by tag recommendation methods are co-occurrence patterns computed over a history of tag assignments. In particular, co-occurrences are used to expand an initial set of tags associated with the object that is target of the recommendation \cite{belem_sigir2011,wu_www09,sigur2008ftr,menezes2010}. To that end, existing solutions often exploit association rules, i.e., implications of the form $X \rightarrow y$, where the antecedent $X$ is a set of tags, and $y$ is a candidate tag for recommendation, restricting the rules by a confidence threshold. Such methods have been called as {\it associative tag recommenders}. %One such method is proposed by \cite{heymann_sigir08}, although the authors do not provide a ranking of the recommended tags. \cite{sigur2008ftr}, on the contrary, exploit metrics of tag co-occurrence (e.g., confidence), aggregating them over all tags in the initial set to produce a final ranking of candidate tags. Some of the considered metrics, related to tag frequency, try to capture the ``relevance" of each candidate. Another associative recommender is LATRE - Lazy Associative Tag Recommendation \cite{menezes2010}, which computes association rules in an on-demand manner, allowing an efficient generation of more complex and potentially better rules, and producing superior results in comparison with the best method in \cite{sigur2008ftr}. One example is LATRE - Lazy Associative Tag Recommendation \cite{menezes2010}, which computes association rules in an on-demand manner, allowing an efficient generation of more complex and potentially better rules. %, and producing superior results in comparison with the best method in \cite{sigur2008ftr}. %Due to efficiency issues, most of these strategies usually compute co-occurrences between only two tags (i.e., $X$ contains only one tag), thus possibly missing important co-occurrence relationships. To address this problem, \citep{menezes2010} propose LATRE - Lazy Associative Tag Recommendation, which computes association rules in an on-demand manner, allowing an efficient generation of more complex and potentially better rules, and producing superior results in comparison with the best method in \cite{sigur2008ftr}. A few other efforts do not exploit tags previously assigned to the target object, focusing, rather, on other textual features \cite{lipczak11,jian_rsdc09}. For example, \cite{lipczak11} extract terms from other textual features (e.g., title) of the target object, expanding them with association rules, and sorting the extracted terms by their usage as tags in a training set. %They also exploit a metric related to the target user history of tag assignments to provide personalized recommendations. \cite{jian_rsdc09}, in turn, use the traditional $TF$ $\times$ $IDF$ metric to extract and rank the most important terms from the object's textual content. % \cite{lu_ijcai09}, as well as \cite{zhang2009tag}, propagate tags between objects with similar textual content. In \cite{belem_sigir2011}, we extend LATRE and the best method proposed in \cite{sigur2008ftr} to exploit not only co-occurrence patterns among tags previously assigned to the target object, but also the contents of multiple textual features associated with it, and various metrics of relevance. Our comparison of the proposed strategies against various state-of-the-art baselines, including the original associative methods and a method that exploits only other textual features \cite{lipczak11} showed that our solutions outperform the previous techniques. %Another effort adopt multilabel text classification techniques in which each tag represents a possible label to be assigned to an object, and terms extracted from textual features are used directly as attributes for the classifier \cite{katakis_2008}. %These previous methods address the %object-centered % tag recommendation problem by exploiting a combination of (i) co-occurrence patterns among previously assigned tags, (ii) multiple textual features, and (iii) metrics of relevance. However, to our knowledge, none of them jointly exploits all three dimensions of the problem. In contrast, %in \cite{belem_sigir2011}, we investigate the benefits of combining these three dimensions to perform tag recommendation by designing new heuristics and L2R based methods for object-centered recommendation. Our evaluation, comparing the proposed strategies against various state-of-the-art baselines in three different datasets, showed that our solutions outperform the previous techniques. These findings motivated the present study, which greatly extends our prior work \cite{belem_sigir2011} by % exploiting various other L2R strategies which produced signficantly better results when compared to the previous methods. %also addressing the problem of personalized tag recommendation, by using one more dataset to evaluate our methods (the Bibsonomy dataset), and by comparing different tag co-occurrence patterns for personalized recommendation. % and evaluating all methods in a scenario with no pre-assigned tags. %proposing new metrics of relevance and several new recommendation strategies (including L2R based strategies), evaluating them on more recently collected and larger datasets, comparing them against more baselines, and reaching significantly better results. % proposed a heuristic strategy called $Sum^{+}TS$ , an extension of the best method proposed in \cite{sigur2008ftr} ( $Sum^{+}$), which does combine all three approaches. In particular, we used the $TS$ metric \cite{SS} that, based on the contents of multiple textual features, tries to capture how accurately a candidate tag describes the target object. Our preliminary results were significantly superior to those of the previous $Sum^{+}$ method. We here greatly extend that work by exploiting not only $TS$ but also another new metric of descriptive power. Moreover, in addition to $Sum^{+}TS$, we also propose 3 other heuristics as well as 3 learning-to-rank strategies. % \cite{belem_cikm2010} jointly exploit co-occurrences with previously assigned tags, terms extracted from other textual features and one metric that captures the descriptive power of a term for tag recommendation purposes. The solution presented by the authors is a simple heuristic function that associates a score to a candidate tag. In comparison, we here exploit other relevance metrics, particularly for the descriptive power, and we propose not only new heuristics but also learning to rank strategies. In addition to tag co-occurrence and textual features, other dimensions, such as image content \cite{wu_www09,lin_cikm2012}, video content \cite{siersdorfer_2011} and graph clustering \cite{song_2011}, have also been exploited for tag recommendation. A recent work \cite{yin_wsdm2013} addresses not only the problem of recommending tags, but also of predicting different kinds of relationships (such as relations between users and comments), exploiting a generalized latent factor model and Bayesian inference. The authors found that connecting comments and tags within the same model allows mutual reinforcement and improves predictive accuracy. However, it is not possible to compare this method with our strategies because comments are absent in our datasets. Moreover, even if present in a collection, they are usually noisy and tend to be absent in a large fraction of the objects \cite{IPM_flavio}. In another direction, in \cite{belem_ecir2013}, we extend our previous methods \cite{belem_sigir2011} to consider not only relevance, but also novelty and diversity as important aspects in recommender systems. Similarly, other studies tackle the problem of producing {\it personalized recommendations}, often exploiting the history of tag assignments of all users of the application or of a specific (target) user \cite{pairwise2010,lipczak11}. %, feng_kdd2012}. Our current focus is on recommending tags that are relevant to a target object. We plan to address personalized recommendations in the future. %Other studies address the problem of {\it personalized recommendation}, often exploiting the history of tag assignments of all users of the application, or of a specific (target) user. Collaborative filtering and {\it FolkRank} \cite{jaschke07}, as well as PITF - Pairwise Interactions Tensor Factorization \cite{pairwise2010} - and the graph-based ranking proposed in \cite{sigir09_guan} fall into this category. %Some studies focus on exploiting tag co-occurrences in these histories of tag assignments \cite{sigur2010, garg2008}. \cite{sigur2010} extend the strategy proposed in \cite{sigur2008ftr} to include personalization, exploiting tag co-occurrences in different contexts: (1) the whole data collection, (2) the objects of a specific user, (3) the social contacts of the user, and (4) the groups in which the target user is included. %Social network relationships are used in object recommendation \cite{ma_social_trust}. %Lipczak \textit{et al}. \cite{lipczak09} include a metric related to the target user's history to provide personalized recommendations. %On another direction, Chirita \textit{et al.} \cite{chirita_www2007} did not exploit the history of tag assignments using, rather, textual data present in webpages and in the target user's Desktop. %Feng and Wang \cite{feng_kdd2012} model the folksonomy as a heterogeneous graph containing tags, users and objects as nodes, and employ an optimization strategy, OptRank, to learn the weights of the edges that connect these nodes. Yin \textit{et al}. \cite{yin2011temporal} consider the temporal aspect of tagging systems, i.e., the variation of user interests over time. %However, these two recent studies still focuses only on the folksonomy, disregarding the use of textual features. %Personalized tag recommendation is a different variation of the problem that we plan to treat in the future. %In common, none of these previously proposed personalized tag recommendation methods jointly exploits all three dimensions of the problem identified and exploited by us, that is, tag co-occurrence, multiple textual features and metrics of tag relevance (including the user-related UF metric for personalization). Moreover, our experimental results indicate that our simple extension of object-centered recommendation strategies to include personalization can significantly outperform state-of-the-art personalized tag recommendation methods. % Collaborative filtering, which is based on suggesting items according to the interests of similar users, and \textit{FolkRank}, an adaptation of {\it PageRank} to the user context, fall into this category \cite{jaschke07}. Another personalized recommendation method is PITF - Pairwise Interactions Tensor Factorization \cite{pairwise2010}. PITF factorizes the tensor representing tag assignment events into matrices that model the interactions among users, objects and tags. A Bayesian personalized rank criterion is employed to learn the model. %For instance, Guan \textit{et al}. \cite{sigir09_guan} provide personalized recommendations from a bipartite graph composed of users, documents and tags. % and Konstas \textit{et al}. \cite{konstas} exploit friendship relationships for improving traditional item recommendation methods based only on content. %Other efforts exploit user links in social networks \cite{sigir09_guan, konstas, ma_social_trust}. Guan \textit{et al}. \cite{sigir09_guan} provide personalized recommendations from a bipartite graph composed of users, documents and tags. Konstas \textit{et al}. \cite{konstas} exploit friendship relationships among LastFM users for improving traditional object recommendation methods based only on content. . We are aware of only a few prior efforts to apply learning-to-rank (L2R) techniques to recommend tags. One such effort is our prior investigation \cite{belem_sigir2011}, where both RankSVM and Genetic Programming were used to recommend tags, producing some gains over state-of-the-art (unsupervised) methods. Although such gains are somewhat limited, the flexibility and the easiness at which the solutions can be extended, for example to include as attributes metrics that capture new aspects of the problem (e.g., personalization, novelty), makes L2R a very attractive technique. Two other related efforts are those by \cite{cao_2009} and \cite{wu_www09}, which exploit RankSVM and RankBoost as L2R techniques, respectively, but do not compare them against alternative L2R methods. Moreover, \cite{wu_www09} consider only metrics related to tag co-occurrences and image content, and do not exploit textual features, whereas \cite{cao_2009} consider only metrics related to tag frequency, disregarding tag co-occurrence metrics. Instead, we here exploit a much richer set of metrics. Furthermore, these prior efforts focus only on the effectiveness of the L2R based tag recommenders. We here analyze not only their effectiveness but also their efficiency with respect to the time required to produce a recommendation for a target object. % Moreover, previous work do not compare the effectiveness and efficiency of different L2R methods in the tag recommendation context, as we do here. The effectiveness of L2R has been studied in other domains, particularly document and image retrieval \cite{gomes_2013,faria_mir2010}. \cite{gomes_2013} compare 13 L2R techniques for document ranking using various datasets of the LETOR benchmark. They found that: (i) in most datasets the results of all analyzed methods are statistically tied with each other and with an unsupervised strategy that uses the best individual attribute in isolation, and (ii) for the other datasets, there is not a clear winner method. In contrast, in the context of image ranking, \cite{faria_mir2010} show that all studied L2R methods outperform the unsupervised technique (i.e., ranking by attribute values in isolation), and that two L2R methods, one based on association rules and the other based on Genetic Programming, are clear winners. To the best of our knowledge, no previous work has studied issues related to the effectiveness \textit{and} the efficiency of L2R methods for tag recommendation. %Figueiredo \textit{et al.} \cite{IC, cikm} evaluated the quality of different textual features across four Web 2.0 applications, with respect to usage, amount of content, descriptive and discriminative power as well as classification performance. They found that title is the most descriptive feature, followed by tags, although tags are superior for classification tasks. %Finally, we are aware of only one previous effort to apply learning-to-rank algorithms to the tag recommendation problem. Cao \textit{et al}. \cite{cao_2009} apply the RankSVM strategy to recommend tags. However, unlike us, they exploit only metrics related to tag frequency, and no tag co-occurrence metrics. %Thus, to our knowledge, we are the first to exploit the GP framework in the tag recommendation context. %There is a strong theoretical background behind Machine learning algorithms such as \textit{Support Vector Machines} and Genetic Programming %\cite{XX}, and little of those methods has been exploited in the tag recommendation scenery. Cao \textit{et al}. \cite{cao_2009} apply a RankSVM %strategy to recommend tags, but they exploit only relevance metrics related to the frequency of a tag in the collection and in the target object, and %no tag co-occurrence metrics are employed. Furthermore, we are the first to exploit a GP framework for tag recommendation, obtaining results that outperform traditional SVM ranking strategies. %A related body of previous work focuses on {\it characterizing} tagging systems, thus producing useful knowledge for the design of tag recommendation systems \cite{lipczak_2010, rader_2008, li_www2008, IC, cikm}. For example, Lipczak and Milios \cite{lipczak_2010} found that the title and the personal tagging history of a user are the main factors that impact tagging decisions, whereas Rader and Wash \cite{rader_2008} showed that personal organization has a stronger impact on tagging decisions than social influences. In another direction, Figueiredo \textit{et al.} \cite{IC, cikm, IPM_flavio} proposed several metrics to assess the quality of different textual features commonly associated with objects in Web 2.0 applications. They found that the title is the textual feature with the best capacity of {\it describing} the object's content, followed by tags. Similarly, Li \textit{et. al}. \cite{li_www2008} found that user-generated tags are consistent with the web textual content they are associated with, and that they capture the user's interests. In a very recent work, Zhang \textit{et al.} \cite{zhang_wsdm2012} study geo-spatial and temporal relationships between tags, but only apply them for clustering and visualization of tags, not for recommending tags. % Leveraging tagging for neighborhood-aware probabilistic matrix factorization % Collaborative Filtering(CF) is a popular way to build recommender systems and has been successfully employed in many applications. Generally, two kinds of approaches to CF, the local neighborhood methods and the global matrix factorization models, have been widely studied. Though some previous researches target on combining the complementary advantages of both approaches, the performance is still limited due to the extreme sparsity of the rating data. Therefore, it is necessary to consider more information for better reflecting user preference and item content. To that end, in this paper, by leveraging the extra tagging data, we propose a novel unified two-stage recommendation framework, named Neighborhood-aware Probabilistic Matrix Factorization(NHPMF). Specifically, we first use the tagging data to select neighbors of each user and each item, then add unique Gaussian distributions on each user's(item's) latent feature vector in the matrix factorization to ensure similar users(items) will have similar latent features}. Since the proposed method can effectively explores the external data source(i.e., tagging data) in a unified probabilistic model, it leads to more accurate recommendations. Extensive experimental results on two real world datasets demonstrate that our NHPMF model outperforms the state-of-the-art methods.