Feature Factorization for top-n Recommendation: from item rating to features relevance

Abstract

In the last decade, collaborative ltering approaches have shown their e ectiveness in computing accurate recommendations starting from the user-item matrix. Unfortunately, due to their inner nature, collaborative algorithms work very well with dense matrices but show their limits when they deal with sparse ones. In these cases, encoding user preferences only by means of past ratings may lead to unsatisfactory recommendations. In this paper we propose to exploit past user ratings to evaluate the relevance of every single feature within each pro le thus moving from a user-item to a userfeature matrix. We then use matrix factorization techniques to compute recommendations. The evaluation has been performed on two datasets referring to di erent domains (music and books) and experimental results show that the proposed method outperforms the matrix factorization approach performed in the user-item space in terms of accuracy of results.

INTRODUCTION

Recent years have seen the ourishing of many and diverse recommendation techniques based on the collaborative information encoded in the user-rating matrix. Factorization techniques working in such matrix have proven their e ectiveness in improving the performance of recommendation engines and are implemented in many industrial and commercial systems [ 1, 14 ]. State-of-art algorithms can capture complex non-linear or latent factors-based relationships between users and items and this results more e ective in all those scenarios where several users partially overlap their ratings or, in other words, the user-rating matrix is less sparse. In order to overcome the limits of pure collaborative approaches, hybrid ones [ 4 ] have been proposed that encode also side information about the items, typically content-based. Hybrid recommender systems have widely proved to improve performances in terms of accuracy and diversity of results[ 15, 18, 25, 29 ]. Whenever available, descriptions of the items can be used as a valuable source of information to augment the knowledge injected in and exploited by the system to compute the recommendation list of items. In this direction, an interesting class of recommender systems is the so called semantics-aware [ 8 ] where the information describing items goes beyond text and keywords and is represented by categorical/ontological data. SA approaches make use of ontologies or encyclopedic sources to encode and exploit domain-speci c knowledge and in the last years many approaches have been proposed [ 2, 17, 19 ]. More recently, thanks to the Linking Open Data initiative, many structured data have become freely available to represent the content of items in di erent knowledge domains and then feed recommendation engines [ 9 ].

As a general remark, we can say that most of the recommendation algorithms available in the literature focus on computing the relevance of a set of items with reference to the user pro le. Recommendation algorithms are designed around the computation of a relevance score to an item by evaluating its similarity with reference to other items. Features composing the description of an item, whatever the source, are not considered per se in the recommendation process but are usually exploited to evaluate the similarity between items or users. We believe that more attention should be paid to modeling the recommendation problem with a focus on recommending features rather then items. Expanding an item in its features brings with it some interesting side e ects. On the one hand, all features may represent relations that, e.g., latent factor models are not able to look at. On the other hand, features give us a new set of explicit connections between items to be exploited with collaborative ltering algorithms. Finally, recommending items via feature recommendation may lead to an easier generation of explanation for the recommended list of items. Unfortunately, moving from items to features is not that straight as in a forest of many features, most of them may result not relevant to a user. Moreover, once we design an algorithm able to compute a recommendation list of features, we have to go back to the items space, as the ultimate goal of a recommender systems is to suggest items to a user.

In this paper we present FF (for Features Factorization), a top-N recommendation algorithm relying on user’s feature preferences and collaborative ltering information in the features space. The main goal of FF is to compute an ordered list of features preferred by the user and, starting from such list, to reassemble the relevance values of each returned feature to produce a top-N list of items to recommend. All the side information adopted by FF is retrieved from DBpedia, the cornerstone dataset of the Linked Data cloud. For each item in the user pro le we retrieve its features by querying DBpedia thus having them as a set of entities. This avoids all problems related to synonymy and polysemy which usually occur when dealing with keyword-based features. By combining the popularity of a feature in the user pro le and the ratings assigned to items it is part of, for each user we compute a pair containing the relevance of the feature and its inferred rating. The resulting matrix in the user-feature space is then manipulated via factorization techniques to compute, for each user, a ranked list of features which is in turn post-processed to produce the nal list of recommendations. Experimental evaluations of FF on two datasets related to the domains of books and music show its e ectiveness in terms of accuracy of results in very sparse settings.

The remainder of the paper is structured as follows. In the next section we report some related work on LOD-based and featurebased approaches to recommendation. We continue in Section 3 by introducing and describing FF. Experimental evaluations are presented in Section 4 while in Section 5 we present and discuss the corresponding results. Conclusion and future works close the paper. 2

RELATED WORK

Several works have tried to build recommender systems by exploiting Linked Open Data (LOD) as side information for representing users or items, in addition to the user preferences usually collected through user ratings. Such approaches usually rely on DBpedia, the nucleus which acts as a hub for most of the knowledge in the socalled LOD cloud. In the following we review the recent literature on both LOD-based recommender systems and approaches which leverage the relevance of single features in the user pro le.

LOD-based RS. A detailed review of recommender systems leveraging Linked Open Data is presented in [ 8 ]. Properties gathered from DBpedia may be used for di erent tasks, i.e. to produce cross-domain recommendations [ 10 ], to build a multirelational graph for a graph-based recommender [ 27 ], or to generate e ective natural-language recommendation explanations [ 22 ]. On the other hand, DBpedia properties may be used in di erent ways: 1) to de ne semantic similarity measures for providing more accurate recommendations [ 18, 23, 30 ]; 2) to deal with problems as the limited content analysis or cold-start, e.g. by introducing new relevant features to improve item representations [ 3, 33 ], or to cope with the increasing data sparsity [ 21 ]; 3) to improve the overall accuracy of a recommender [ 20, 29 ], or to provide a good balance between different recommendation objectives, such as accuracy and diversity [ 15, 21, 28 ].

Feature-based RS. Several works attempt to analyze the user purchasing behavior based on item features. In [ 35 ], products are represented using vectors of features, and a customer pro le module computes the level of interest of the customer in product features as the ratio of features among the products purchased, and the product quantity purchased by that customer. Similarly, in [ 12 ] a feature-based recommender system for domains without enough historical data to e ectively measure user or item similarities is presented. The authors build the system based on the idea that users who bought items with speci c features also buy items with the same or similar features. A similar approach is proposed in [ 26 ], in which e ective strategies to incorporate item features for top-N recommender systems are developed. In graph-based recommender systems, an interesting work was proposed in [ 13 ], in which recommendations are produced inferring user preferences, evaluating item-preferences and attribute-preferences. The paper points out the importance of the feature evaluation and a method is proposed, which exploits explicit feature ratings, named attributes. Recently, an interesting approach called Feature Preferences Matrix Factorization (FPMF) has been proposed in [ 24 ]. FPMF incorporates user feature preferences in a matrix factorization to predict user likes. It is worth to note that none of the previous mentioned approaches rely on features coming from the Linked Open Data cloud. 3 3.1

PROPOSED APPROACH

Motivation

This work aims at investigating the role of feature rating and relevance in the item rating process. The main intuition behind FF is that items can be handled as a collection of features on which the recommendation process is then performed. Hence, when users rate an item, they are actually expressing their preference over the whole collection. The item rating action can be then summarized as the non trivial attempt to choose an overall rate for the entire set. If we want to discover the contribution of each single feature in the evaluation, rst of all, we need to unpack each item in its composing features. Then, by combining the overall popularity of each feature in the user pro le (feature relevance) and the rating assigned to items containing that feature we may estimate the implicit rating the user is giving to that speci c feature. In the evaluation of a movie, the user implicitly evaluates the director, the actors, the producer, the country in which the movie is set. Each feature has its own rating and a relevance degree, hence a recommender system should consider these factors.

The second observation we based our work on, is that the relevance of an item in the user pro le cannot be entirely encoded in its rating as the single rating represents a degree of liking about the speci c item. The relevance of the item within a collection is not explicitly encoded anywhere with reference to the user’s view. Our assumption is that such item-relevance naturally in uences feature-relevances and vice-versa.

In our model the user pro le is not just a set of hitem; ratingi pairs but it contains information about the relevance of each feature composing the rated items and its estimated rating hf eature; relevance; ratingi. In the following we will see principled methods to estimate both the user-feature rating and the user-feature relevance. Then, we focus the recommendation problem on the features composing the user pro le. FF exploits a collaborative ltering step to get approximated information about the missing features in the users-features matrix and nally it combines the predicted ratings and relevance for each feature available in each item to compute a personalized ranked list of items. 3.2

Data Model

For a better understanding of the data we use to reshape the user pro le as user-feature matrices, we rst introduce the multidimensional graph we used to build them. As we can see from Figure 1 the user pro le is built by considering information coming from both the user-item matrix and from DBpedia as external knowledge source. The graph-based nature of this latter one is exploited to identify features used to represent items. The knowledge encoded in Linked Data is represented as RDF labeled oriented graphs and the corresponding data model is based on the notion of triple hsubject ; predicate; object i where predicate represents the relation connecting the two entities subject and object . With reference to Figure 1, we have that each item in the catalog represents the subject of a triple hi; p; ei 2 DBpedia. In order to catch the di erent knowledge encoded in the use of the same entity as object in triples with diverse predicates, in our model, we consider the chain predicate object , (corresponding to property entity, pe path in the knowledge graph) as a feature associated to the item i which in turn represents the subject of the corresponding triple.

Each item in the user pro le is associated with a relevance function we denote with ρui ( ). Its value represents an estimation of how important is a particular item to the user u. Analogously, we have a value associated to each feature in the pro le computed via the function ρuf ( ) computing the relevance of the feature f (represented by the pair of property and entity pe) in the user pro le. Actually, each feature is associated also with a rating ruf ( ) which is inferred by considering the rating of all the items containing f . By considering the data associated to the user pro le as described in the previous section we can move from a rating matrix connecting user and items to a user-feature matrix where each value is represented by the pair hρuf ( ); ruf ( )i. In other words, we may consider two user-feature matrices: the one P containing relevance values ρuf ( ), the other R including the inferred ratings ruf ( ).

In FF, the relevance of a feature pe is computed as its probability of belonging to the set Iu representing the items already rated by a user u. More formally we have: ρuf (pe ) =

Pi 2Iu jfhi; p; ei j hi; p; ei 2 DBpediagj jIu j

The idea behind this computation is quite straight: the more a feature is connected to the items in the user pro le , the higher its relevance for the user.

Once we have computed the relevance of all the features in the user pro le, we can move to the computation of the relevance for the items i 2 Iu . This can be computed as the normalized summation of the relevance for all the features it is composed by. In formulas, we have ρui (i ) =

Phi;p;ei2DBpedia ρuf (pe )

jfhi; p; ei j hi; p; ei 2 DBpediagj Given a feature pe, the computation of the feature rating ruf (pe ) exploits both the rating and the relevance of each item i 2 Iu containing pe.

ruf (pe ) =

Phi;p;ei2DBpedia rui ρui (i )

Phi;p;ei2DBpedia ρui (i )

(1) 3.4

top-N Recommendation The pro les we built contain only the features the user met before, but usually the number of those features is dramatically smaller than the overall number of features and this results in P and R being very sparse. In order to complete the information they contain, we compute, via Biased Matrix Factorization, the missing values ρˆuf (pe ) for P and rˆuf (pe ) for R. We run matrix factorization independently on P and R. Biased Matrix Factorization is a matrix factorization model that minimizes RMSE using stochastic gradient descent [ 16 ]. It computes user’s and item’s biases to improve the estimation of the predicted value. Biased Matrix Factorization represents a state-of-the-art algorithm in rating prediction task. ρˆuf (pe ) and rˆuf (pe ) represent the predicted relevance and the predicted rating for all those features not belonging to any of the items in Iu . As the resulting matrices contain both content-based and collaborative informations (due to the matrix factorization), we refer to them as hybrid pro le.

With the hybrid pro le we can estimate a ranked list for all the remaining items within the collection. In fact, the ranking of an item in the list is computed by considering the rating of the features belonging to the item and their relevance.

3.4.1 Post-filtering. In order to improve the results of the nal recommendation process, we propose a post- ltering step aimed at reducing the number of features considered while computing the nal rank. The proposes ltering springs from the following observations: Not all the features items are relevant in the computation of the ranking for an item. All those features whose rating results low just introduce noise in the nal values we compute.

Feature ranking and relevance values evaluated via pure content-based approaches, i.e., before the matrix factorization, have a di erent in uence if compared with the collaborative ones representing latent factors computed after the matrix factorization.

In order to lower the number of features involved in the computation and produce recommendations based only on the best ratings of the estimated features, we propose a lter that operates separately on directly estimated features (content-based) and estimated features coming from collaborative computation. We then introduce two thresholds α and β that act as lters on the feature rating values respectively in the content-based and in the collaborative cases. Hence, Equation (2) is slightly modi ed in

EXPERIMENTAL EVALUATION

In this section the experimental evaluation settings and the metrics used to evaluate the proposed algorithm are presented. We evaluated the algorithms in terms of ranking accuracy for top-N recommendations. The evaluation has been carried out on two datasets, LibraryThing and Last.fm belonging respectively to the domains of books and music. In order to remove the popularity bias from the evaluation results we removed the 1% most popular items [ 7 ]. Moreover we removed users with a number of ratings smaller than ve as we want to evaluate the algorithms in a non cold start setting. The LibraryThing dataset contains 7,564 users, 39,515 items and 797,299 ratings. The minimum, mean and maximum number of ratings for user in the dataset are 20, 63, 3,018, respectively. Last.fm contains 1,892 users, 17,632 items and 92,834 ratings. In LibraryThing, ratings are distributed over a 1-10 scale. In Last.fm the rating is the number of times a song has been played, hence that number has been rescaled for each user in a 1-10 scale. Table 1 shows some statistics of the datasets subsets considering only the items mapped to DBpedia (using publicly available mappings [ 29 ]) after the pre-processing step. In case a mapping does not exist, a simple placeholder feature is used, that inherits the corresponding item values in terms of rating and relevance.

Table 1 also reports the sparsity values both for users-items and users-features matrices.

To evaluate FF we use the all unrated items [ 34 ] evaluation protocol, in which the ability to choose the correct set of items to propose to the users is favorite despite of the local ranking ability (rated testitems evaluation protocol). In all unrated items the recommendation list is produced using as candidate list the Cartesian product between users and item minus the items the user experimented in the training set. The evaluation has been conducted using a hold-out 80-20 splitting, in which 20% of the ratings are retained as test set.

LibraryThing user-item space user-feature space

Last.fm user-item space user-feature space # users 1,866 # users 1,866 # items 8,502 # features 274,523 # ratings 39,557 # ratings 4,989,281 sparsity (%)

99.7157 sparsity (%) 99.11226 sparsity (%) 99.75066 sparsity (%) 99.02603

We evaluated the accuracy of our approach by computing Precision (P @N ), Recall (R@N ) and nDCG (nDCG@N ). Besides, as test-set could contain non-relevant documents, i.e. a low rated item we set a simple threshold in the 1 to 10 rating scale thus considering as relevant only the items that fall above it.

Baselines. In the experimental evaluation we compared FF with the popularity baseline (PopRank) and, as we rely on matrix factorization, the well known matrix factorization algorithm BPRMF [ 32 ] both in its pure collaborative version and in the hybrid one considering side information BPRMF+SI. We included also PopRank as it is acknowledged that popularity ranking can show good performance and it is an important baseline to compare against [ 7 ]. In order to produce recommendation lists from these well-known algorithms we used their MyMediaLite1 implementation [ 11 ]. As for the selection of α and β parameters needed in Equation (3), in these experiments we kept a conservative approach and set respectively α to the mean μ of the rated items and β to the mean μ plus the standard deviation σ . Clearly, these values are not the optimal ones and the performances could be improved by a cross-validation setting of these parameters. 5

EXPERIMENTAL RESULTS

10 recommendation list and relevance threshold of 7/10.

CONCLUSION

In this paper we presented FF, a novel algorithm that bases on feature recommendation as an intermediate step for computing top-N items recommendation lists. The main idea behind FF is that feature relevance in a user pro le plays a key role in the selection and rating of an item in a collection. Based on this observation we developed an algorithm that shifts the recommendation problem from a useritem space to a user-feature one. In this new space we introduced the explicit notion of feature relevance and feature rating and combined them with well known factorization techniques to perform a Features Factorization aimed at predicting a rating and a relevance for each feature unknown to the user. We compared FF with well known factorization techniques (both pure collaborative and hybrid with side information) on two datasets in the domains of books and music. In both datasets FF results the best algorithm in terms of recommending accurate items. This can be considered as a strong clue to con rm our intuition that recommending items via feature ranking is a feasible way to develop content-aware recommendation engines. As future work, we are investigating the behavior of FF with respect to novelty and diversity of results. We are also interested in exploring the behavior of FF approach with di erent collaborative ltering algorithms, other than factorization techniques in the item-feature space and in particular with Factorization Machines [ 31 ]. Moreover, since we collected content-based data from Linked Open Data datasets, an analysis on the in uence of such datasets on the recommendation results is also in progress. Another aspect we are willing to deepen is related to results explanation. Indeed, very interestingly, item recommendation via feature ranking paves the way to new proposals for explanation services.

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