Arabian Journal for Science and Engineering (2019) 44:2973–2983https://doi.org/10.1007/s13369-018-3358-0

RESEARCH ART ICLE - COMPUTER ENGINEER ING AND COMPUTER SC IENCE

Factored Item Similarity and Bayesian Personalized Ranking forRecommendation with Implicit Feedback

Qinghua Zhao1 · Yihao Zhang1 · Jianfen Ma1 ·Qianqian Duan1

Received: 30 September 2017 / Accepted: 27 May 2018 / Published online: 12 June 2018© King Fahd University of Petroleum &Minerals 2018

AbstractItem recommendations aim to predict a list of items (e.g., items on Amazon website) for each user that he or she might like.In fact, implicit feedback, such as transaction records in e-commerce websites and the “likes” behavior in social networkswebsite (e.g., Facebook), has been received more and more attention in the scenarios of item recommendation. The coreof the recommender system is the ranking algorithm which exploits the implicit feedback and generates the personalizeditem list to meet user’s specific preferences. In most of the previous studies, the pairwise personalized ranking techniquesempirically achieve better performance than thematrix factorization and adaptive k nearest-neighbormethod since the pairwiseranking methods can directly reflect the model user’s ranking preference on items. In most of the recent works, factored itemsimilarity techniques which learn the global item similarity by utilizing two low-dimensional latent factor matrices achievebetter performance than other state-of-art top-N methods with predefined similarity, such as cosine similarity. The individualrelative preference assumption among observed items and unobserved items are critical for the pairwise rankingmethods. As aresponse, this paper proposes a new and improved preference assumption based on the factored item similarity and individualpreference. In addition, a novel recommendation algorithm correspondingly named factored item similarity and BayesianPersonalized Ranking model is designed. The novelty of the algorithm is that it can (1) learn the global item similarity withlatent factor models. (2) utilize effective pairwise ranking methods to deal with the item recommendation problems withimplicit feedback. (3) assign different item weights on explicit feedback and implicit feedback. Empirical results show thatthis model outperforms other state-of-the-art top-N recommendation methods on two public datasets in terms of prec@5 andndcg@5. It can be found that the advantage of FSBPR lies in its ability to exploit implicit feedback and capture global itemsimilarity.

Keywords Recommender systems · Item similarity · Top-N recommendation · Pairwise ranking

1 Introduction

Item recommendation [1,2] has attracted more and moreattention in the industry and academia research since it canovercome the problem of information overloading for Inter-net users. In fact, the recommendation systems embeddedin e-commerce, video stream and social network websites,such as Amazon, YouTube and Facebook, have made sig-nificant contribution in revenue growth, making it moreconvenient in information retrieval for users. The traditionalitem recommendation algorithms are divided into three main

B Qinghua Zhaozhaoqinghua218@163.com

1 College of Information and Computer, Taiyuan Universityof Technology, Taiyuan 030024, Shanxi, China

categories, including content-based recommendation [3–6],collaborative filtering recommendation [6–11] and hybridrecommendation. In the content-based recommendation, therecommender systems utilize contextual information relatedto user profile and item features. Collaborative filtering isdesigned to capture the interests and preferences of neigh-bor users which are similar to those of a particular userand then to recommend items that the user may like. Italso aims to recommend the items similar to the productspurchased by a specific user before, such as the trans-action records that are usually obtained from the historyof the user browser. Furthermore, the recommender sys-tems which utilize both contextual information and userrelationship with items are referred to as hybrid recom-mendations. The content-based recommendations exploitonly a few aspects of context information, and there are

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many other significant aspects contributing to user’s specificpreference.

As for collaborative filtering, cold start problems [12] sig-nificantly reduce the performance since the model cannotcapture the similarities between the new items and otheritems. That is to say, new items will not be recommendedto users with collaborative filtering methods.

The famous Netflix contest recommender algorithms arereferred to as multi class collaborative filtering [13] sincethe datasets utilized in the model consist of 5 class datathat reflect a user’s degree of enjoyment about how muchthe user likes the product. These recommendation prob-lems are called rating predictions and algorithms aim toapproximate the user’s rating on the unobserved items andto minimize the square loss of the corresponding objectivefunction. Matrix factorization [14–20] has proven to be effi-cient in multi class collaborative filtering which predicts userpreferences based on the absolute numerical scores on theobserved items.Koren et al. [14] firstly proposed amatrix fac-torization approach, including varieties of biases (user biasand item bias) for predicting absolute numerical scores onunobserved items for each user. According to their empiri-cal study, the matrix factorization technique can effectivelydealwith data sparseness problems and achieve better recom-mendation results. In addition, a lot of matrix-based methodsaim to exploit not only the numerical ratings but also addi-tional side information, such as social relations [21–25],taxonomy and location information. Ma et al. [23] put for-ward a probabilisticmethod to incorporate social relationshipinformation with explicit feedback in order to improve therecommendations. There are also some work that utilizesthe natural language process to exploit the rich web com-ments on websites (e.g., Yelp) as side information to trainthe matrix-based model. Nonetheless, in real internet webservices, explicit feedbacks are significantly sparse so thatthe recommendation accuracy with pure matrix factoriza-tion method can be reduced. In addition, most real-worlddatasets are implicit feedbacks, such as the e-commercetransaction records in Amazon, the “like” behavior in Face-book, and the “click” behavior in YouTube. There is onlyone class of implicit feedback that is positive record. Theitems that are less preferred by users are unknown withonly implicit feedbacks. For instance, a commerce websiterecords that a user has bought a specific item or chosena tag to search some items. One-class collaborative filter-ing [26,27] is much more studied since most real-worlddatasets are implicit feedbacks without absolute ratings. Asa result, the objective function of item ranking is to maxi-mize the likelihood of preference instead of minimizing theroot-mean-squared error between absolute rating scores andestimated ratings.

To address the recommender problems with implicit feed-back, previous approaches can be summarized into two

respects. The first one adopts a pointwise preference assump-tion which approximates the absolute rating scores andminimizes the pointwise square loss. The second one pro-poses the pairwise preference assumption in which userprefers observed items to unobserved items. Empirically, thepairwise preference method can achieve better recommen-dation accuracy than pointwise recommendation. Pairwisepreference method has been proved to be more effectivewhen compared to thework that proposes the listwise rankingmodel [28]. As a response, a lot of algorithms based on thepairwise ranking assumption have beenproposed.Acommonstrategy in pairwise preference learning is to assume all theunobserved items of lower preference. Bayesian preferenceranking [2] is a seminal pairwise ranking method based onthe aforementioned strategy which samples item pairs duringlearning and applies the stochastic gradient descent methodduring optimization.

Nonetheless, most recommendation algorithms focus ononly one aspect. FISM and SVD++ capture the global itemsimilarity also known as learned similarity. Pairwise rankingmodels, such as BPR, GBPR [33] and WBPR [32], focuson dealing with one-class collaborative filtering situation aswell as utilize implicit feedback information to achieve betterrecommendation accuracy.

This paper puts forward a novel and improved modelwhich combines factored item similarity and pairwise prefer-ence assumption. Furthermore, this studyutilizes the factoreditem similarity methods and pairwise preference methods inthe model and designs a novel algorithm called factored itemsimilarity and Bayesian personalized ranking (FSBPR).

FSBPR inherits the merit of pairwise methods to digestthe uncertain implicit feedback as well as captures the globalitem similarity as a product of the two low-dimensionallatent factor matrices. Extensive empirical studies on twopublic datasets indicate that the proposed algorithm outper-forms other state-of-the-art methods in terms of prec@5 andndcg@5.

Below are the key contributions of the work presented inthis paper:

(1) Presenting a way to convert the factored item similarityinto the bayesian personalized ranking. The model cannot only capture item global similarity but also exploitimplicit feedback information.

(2) In most of the previous BPR-based methods, all theitems are assigned the same weight, which of courseis not the case in reality. This paper utilizes the factoreditem similarity as itemweight. Theweights of items varyand reflect their desirability to a user.

(3) Assigning different item weights on implicit feedbackand focusing on explicit feedback. In more detail, theobserved items with higher average learned similaritywith other observed items can reflect higher desirability

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to a user. There is an insight that in the observed item setspurchased by the user, if item A has the highest averagelearned similarity with other items in the item sets, itemA can be considered as the favorite item to the user.

(4) Analyzing the performance of the model with otherbaselines on different parameters.

The rest of the paper is organized as follows. Some previousclosely related works on the methods dealing with implicitfeedback are introduced in Sect. 2. The preliminaries in per-sonalized recommendation, the notations in this paper andthe limitations of the existing Bayesian personalized rank-ing methods for implicit feedback are presented in Sect. 3.This paper formally proposes the assumption and algorithmin Sect. 4, and then designs extensive experiments to ana-lyze its performance with different parameters in Sect. 5.Finally, conclusion of thework and future outlook are offeredin Sect. 6.

2 RelatedWork

This section introduces some related works on the recom-mender system with implicit feedbacks. Previous relatedworks canbe summarized into twomain categories. (1) Point-wise preference assumption with absolute predicted ratings.(2) Pairwise preference assumption with relative preferenceamong item pairs. Pointwise preference assumption han-dles explicit user preference for rating prediction. The firstlyintroduced approach, proposed by Paterek, is called NSVD[29] and is a factored item similarity model based on thepointwise preference assumption. Item–item similarity canbe captured via two latent factor matrices and consideredas absolute rating score for each specific user. Motivated byNSVD, SVD++ was developed by Koren who combined theidea of traditional neighborhood-based model and latent fac-tor model and was later proved to be more efficient thanNSVD. It has been proved by previous work that better per-formance can be obtained by exploiting explicit feedback,identifying users with similar tastes, and utilizing implicitfeedback which is abundant in recommendation scenarios.Factored item similarity model (FISM) [30] is similar withthe NSVD algorithm. However, unlike NSVD and SVD++,the known rating for a particular user-item pair (rui) is notutilized when the rating for that item is being predicted.Sparse linear methods (SLIM) [31] for top-N recommen-dation methods learn a sparse coefficient matrix for theitem which can be considered as item–item similarity. Fea-ture selection strategy makes the SLIM model reduce theamount of the time required for factoring item–item simi-larity. Weighted matrix factorization (WMF) adopts severalsampling methods for the unobserved items and considersthem as negative feedbacks. Instead of sampling for the

unobserved items, the pure-SVD algorithm exploits all theunobserved items as negative feedback and applies the sin-gular value decomposition theory with negative and positivefeedbacks. There are many approaches based on the non-negative matrix factorization with side information, such asuser review on a specific item and social relations betweenusers who apply the pointwise preference assumption.

Pairwise preference ranking methods exploit user rel-ative preference with the observed and unobserved itempairs. For instance, a user u prefers item i to item j for anobserved user-item pair (u, i) and an unobserved user-itempair (u, j). Bayesian personalized ranking (BPR) first adoptsthe pairwise preference assumption to deal with item recom-mendation with implicit feedback.

Pairwise methods achieve better recommendation accu-racy than pointwise methods. Some previously proposedalgorithms aim to combine BPR with side information, suchas social relationship, temporal information and item-sidetaxonomy. Bayesian personalized ranking for the algorithmof non-uniformly sampled items (WBPR) [32] adopts dif-ferent sampling strategies for the unobserved items. Theseaforementioned methods simply adopt the BPR criterionwhich is individual preference and user preference indepen-dence.Nonetheless, the groupBayesianpersonalized ranking(GBPR) [33] puts forward a new assumption based on grouppreference rather than individual preference and achievesmore recommendation accuracy. GBPR+[34] proposes anassumption over two item sets instead of two items. As amore generic version of the previous conferenceworkGBPR,it becomes equivalent to GBPR, while the item set is a singleitem. MF-BPR [35] proposes the multi-feedback BayesianPersonalized Ranking that exploits different types of feed-back and is built on the insight that different types of feedbackcan reflect different levels of preference. WF-BPR [36] pro-poses a new improved matrix factorization approach wherethe item weights vary and reflect the items’ desirability to auser.

When compared with the aforementioned work, the pro-posed factored item similarity and the Bayesian personalizedranking (FSBPR) is a novel algorithm in dealing withitem recommendation with implicit feedback. In particu-lar, FSBPR inherits the merit of pairwise ranking methodsregarding accuracy and efficiency as well as refines the indi-vidual preference assumption associated with the factoreditem–item similarity.

3 Preliminaries

3.1 Notation

In this paper, rowvectors are represented by lower case lettersand user, and the item latent factor matrices are represented

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by upper case letters. The notation ai defines the ith row of amatrix A. The uppercase letters U and I are utilized to denotethe users set and items set, respectively. That is to say, Uu

denotes a user u and Ii denotes an itemi. This paper discussesthe item recommendation tasks with implicit feedback. Andthis study aims to exploit themodel and to capture the specificuser’s relative preference on the unobserved items.

3.2 Item Similarity

The Top-N recommender systems [37] aim to recommendthe size-N list of the unobserved items for specific users thatthey might like most. Due to its extensive applications inE-commerce websites, they have been studied intensivelyduring the last past few years. There are twomain approachesto deal with the top-N recommender systems which areneighborhood-based collaborative filtering and model-basedmethod. In the first approach, for a specific user, the modelfirst identifies the nearest neighborhood users set and thenrecommends items to those neighborhood users who havepurchased before. The neighborhood-based collaborative fil-tering is also referred to as the memory-based method. Thememory-based methods have to store the full sparse matrixto compute the similarity among items or users and thismakes the models non-scalable. On the other hand, themodel-based methods only have to store the specific model;thus, they are scalable. A common strategy for the memory-based method is that the model identifies a set of similaritems for each of the items that user has bought beforeand then recommends top-N items with highest similarity.The memory-based methods are efficient to generate therecommendation list due to the fact the dataset is signifi-cantly sparse. The item-based nearest neighborhood top-Nrecommendation adopts the mathematical formula similar-ity measurement, such as cosine similarity. The definition ofcosine similarity is as below:

sik = |ui ∩ uk |√|ui | |uk | (1)

where |ui| and |uk| denote the number of users who examine(e.g., purchased, clicked) item i and item k. |ui ∩ uk| denotesthe number of users who examine both item i and item k.Nonetheless, such mathematical measurement has its ownlimitations. The similarity between item i and item k will notbe captured if co-users do not exist (|ui ∩ uk| = ∅). Thus, theneighborhood-based models suffer from low accuracy. Thesecond approach is referred to as the model-based methods,among which the most promising model is the latent factormodel that learns the item–item similarity matrix via the twolow-dimensional matrices. Low-dimensional matrices referto user matrices and item matrices that represent user prefer-ence and item characteristic. Motivated by the latent factor

model, a great number of studies have proposed a factoreditem–item model. The definition of the factored item simi-larity is as below:

fik = ViWTk (2)

The factored similarity between item i and item k can becalculated via the inner product of latent factor Vi for itemi and the latent factor Wk for item k. By formula (2), item ican be connected to any item even if co-users do not exist,which overcomes the limitations of the conventional near-est neighborhood model on item similarity measurement.SVD++ exploits not only the neighborhood-based model butalso the latent factor model to learn item similarity. SVD++model first proves that the neighborhood-basedmodel and thelatent factor model can be smoothly merged, which leads tohigh accuracy. Furthermore, motivated by SVD++, the FISMmodel adopts formula (2) derives a preference prediction ruleas below,

rui = bi + 1√|Iu\ {i}|∑

k∈Iu\{i} fik (3)

where bi is the popularity of item i and |Iu\ {i}| refers to thenumber of items excluding itemiexamined by the specificuser u.

3.3 Bayesian Personalized Ranking

Bayesian personalized ranking (BPR) is the seminal methoddealing with one-class collaborative filtering based on thepairwise preference ranking assumption. A fundamentalassumption in BPR is that the unobserved items are con-sidered less of interest for users. That is, a specific userprefers observed items to unobserved items. This strategyallows BPR to generate a pairwise ranking loss in order todistinguish observed items from other remaining items. Forinstance, a user u prefers item ito item j for an observeduser-item pair (u, i) and unobserved user-item pair (u, j).There are a large number of pairs during the learning pro-cess. Thus, BPR often applies uniform sampling methodswhich randomly select an observed user-item pair (u, i) andan unobserved user-item pair (u, j) as well as utilizes thestochastic gradient descent to minimize the pairwise rankingloss. It is assumed that the pairwise preference of user u isindependent of other user’s preferences. The assumption ofindependence among users is another fundamental assump-tion in the BPR model. For example, the joint likelihood ofthe pairwise preference of two users, including u and k, canbe rewritten as below :

BPR (u, k) = BPR (u)BPR(k). (4)

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Thus, the overall likelihood of BPR can be defined as belowcorrespondingly,

BPR =∏

u∈U BPR (u) (5)

The BPRmodel exploits the relative preferences via low rankuser matrices and low rank item matrices. It is noted that theBPR model fails to capture the global item–item similarity.As discussed previously, the neighborhood-based model andthe latent factormodel can be combined smoothly. In the nextsection, this paper proposes a model based on the factoreditem similarity and the pairwise ranking model.

4 Our Solution

4.1 Inclusion of Factored Item Similarity andIndividual Preference

The neighborhood-based model, such as the neighborhoodcollaborative filtering, and the model-based methods, suchas the latent factor model, can be merged smoothly as afore-mentioned in the SVD++ model. Motivated by the BPRmodel, this paper defines individual preferences through twolow-ranking matrices. And this study tries to combine itemsimilarity knowledge and the latent factor model. Further-more, mathematical similarity measurement, such as cosinesimilarity, fails to capture the similarity between certain itempairs if co-users do not exist. To address this limitation, thispaper exploits the factored item similarity model to capturethe global item similarity. In addition, it can be assumedthat individual preference is associated with item similarity.Specifically, factored item similarity is combined with theindividual preference, such as s′ikUuVT

i . Subsequently, thisstudy further exploits the augmented individual preferenceinto the combined individual preference.Mathematically, thedefinition of the combined individual preference is proposedas below:

pui =(1 − λs + λs

1√|Iu\ {i}| fik)UuV

Ti (6)

where the parameter λs is the leverage weight of combinedindividual preference, parameter fik denotes the factoreditem similarity, parameter UuVT

i refers to the original BPRindividual preference, and parameter pui means the combinedindividual preference. As λs reduces to 0, the pure Bayesianindividual preference can be obtained. When λs becomes 1,the pure augmented preferencemodel can be obtained.Whenλs ∈ (0, 1), a mixed model leveraging individual preferenceand augmented preference associatedwith factored item sim-ilarity can be obtained.

4.2 Recommendation with Pairwise RankingMethod

The goal for the pairwise ranker is to minimize the number ofinversions in ranking, such as cases where the pair of resultsis in the wrong order relative to the ground truth. Pairwiseapproacheswork better in practice than pointwise approachessince the predicting relative order is closer to the nature ofranking than the predicting absolute score. The extensiveempirical study proves that the pairwise ranking methodsoutperform other state-of-the-art methods. The assumptionaims to discriminate the observed items between the unob-served items for each user and to maximize the likelihoodof user preference. Uniform sampling is usually adapted inthe pairwise learning process to reduce the recommendationmodel computation complexity. With the combined individ-ual preference model, the user preference prediction rule onthe observed item i and the unobserved item j can be esti-mated as follows,

rui =(1 − λs + λs

1√|Iu\ {i}|∑

kε|Iu\{i}| fik

)UuV

Ti + bi

(7)

ruj =(1 − λs + λs

1√|Iu|∑

kε|Iu| f jk

)UuV

Tj + bj (8)

where fik denotes factored item similarity among observeditem i and other items purchased by user u; f jk denotes fac-tored item similarity among unobserved item j and otheritems bought by user u; bi and bj denote item bias for item iand item j based on item popularity.

Motivated by the pairwise preference assumption, thispaper integrates the combined individual preference modelwith the Bayesian Personalized Ranking based on the crite-ria in pairwise preference assumption. It is considered thatuser prefer observed item i ∈ Iu to unexamined item j /∈ Iu,where parameter Iu denotes all items purchased by user u.As a response, the algorithm factored item similarity and theBayesian Personalized Ranking (FSBPR) are named in thispaper. Based on the pairwise ranking assumption, the majorobjective function of the model can be obtained as follows:

min∑

u∈U∑

i∈Iu∑

rmj∈I\Iu fuij (9)

fuij = −Inσ(rui − ruj

) + α

2

(||Vi||2 + ∣∣∣∣Vj

∣∣∣∣2 + ||Uu||2

+∑

i’∈Iu||Wi′ ||2F + ||bi||2 + ∣∣∣∣bj

∣∣∣∣2⎞

⎠ (10)

Parameter α refers to the weight of the regularization termutilized to avoid over-fitting. Parameterσ denotes the sigmoidfunction. For simplicity, all the regularization parameters areset to be α in the tentative objective function.

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Fig. 1 The SGD algorithm for FSBPR

4.3 Learning the FSBPR

To learn the ground truth parameters, the stochastic gradientdecent algorithm based on the traditional machine learningoptimization method is adopted to train our model, and thesteps of the SGD framework is described in Fig. 1. FSBPRrandomly samples a (user, observed item) pair and a (user,unobserved item) pair where the sampling strategy is sameas BPR. Subsequently, the gradients of each related modelparameter with the proper learning rate γ can be derived. Thegradients of our model can be calculated as follows:

∇Vi = − σ(ruj − rui

)((1 − λs)Uu

+λs2√

Iu\ {i}∑

i’∈Iu\{i} Wi’UTuVi

)+ αVi (11)

∇Vj = σ(ruj − rui

)((1 − λs)Uu

+λs2√Iu

∑i’∈Iu Wi’U

TuVj

)+ αVj (12)

∇Uu = σ(ruj − rui

) ([(1 − λs) + λs

1√Iu

∑i’∈Iu Wi’Vj

])Vj

+ bj −(1 − λs + λs

1√Iu\ {i}ViW

Ti

)Vi − bi (13)

∇Wi = σ(ruj − rui

)λs

1√IuVjV

Tj Vj + αWi (14)

∇Wi’ = σ(ruj − rui

) (λs

1√IuVjV

Tj Vj

−λs1√

Iu\ {i}ViUuVTi

)+ αWi’ (15)

∇bi = −σ(ruj − rui

) + αbi (16)

∇bj = σ(ruj − rui

) + αbj (17)

The total time complexity is O (Tnd), where T refers to thenumber of iterations, n is the number of sampled users and ddenotes the number of latent features.

5 Empirical Study

5.1 Datasets Description

This study conducts extensive experiments on two publicreal-world datasets, including MovieLens, Netflix moviedatasets. The original Movie Lens dataset contains 71567users, 10681 movies and more than one million observedrecords. The dataset also contains the information regard-ing timestamps. Explicit feedbacks, such as ratings, are alsoavailable and ratings should be removed from the implicitfeedback study. A subset of Netflix datasets which contains5000 users, 5000 items, and 28,274 observed records is taken.In the original datasets, explicit feedbacks are available andthe absolute rating scores from 1 to 5 are given by users.The rating records which ratings is larger than 3 are sampledand they are maintained in the form of (user, item) pair. Thisstudy also classifieds users based on the number of observedrecords and then calculates prediction accuracies in the testdataset of different user groups. This paper only keeps testrecords available for one specific user which is larger than10 and group users in 4 classes, including “11–30”, “31–50”, “51–70” and “> 70”, indicating how many test recordsare observed for a user in that class. The distribution of fourclasses in the test dataset is shown in Fig. 2. Item recommen-dation aims to provide a list of top ranked items rather than thepredicted rating scores. The common evaluation metrics alsoutilized in information retrieval, i.e., PREC@5 are adoptedfor precision and NDCG@5 is adopted for normalized dis-counted gain at location 5 [38]. The mathematical definitionsof PREC@5 and NDCG@5 are presented as follows,

PREC@5 = 1∣∣Ute∣∣

[∑u∈Ute

1

5

∑5

p=1δ(Lu (p) ∈ Iteu

](18)

NDCG@5 = 1∣∣Ute∣∣∑

u∈Ute

⎡

⎣ 1∑min

p=1

(5,

∣∣Iteu∣∣)

1

log (p + 1)

∑5

p=1

2δ

(Lu(p)∈Iute

)

− 1

log (p + 1)

⎤

⎦

(19)

where Lu(p) is the pth item in the personalized recommen-dation list. For instance, Lu(1) means favorite items for useru, and δ(x) is an indicator function with value of 1 if x is trueand 0 otherwise. Ute refers to the set of test users and Iute isthe set of items observed by user u in the test data.

5.2 Experimental Results and Parameter Settings

To study the performance of the novel algorithm, severalstate-of-the-art methods for comparison are chosen. Specif-ically, the baselines are described as below:

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Fig. 2 Distribution of users intwo test datasets

• Bayesian personalized ranking (BPR) is the first modelthat utilizes the pairwise preference assumption to dealwith the implicit feedback recommendation problems,which proves to be efficient in dealing with one-classcollaborative filtering [35].

• WBPR is adapted version of the Bayesian personalizedranking that applies the non-uniform sampling strategyof negative test items into account.

• FISM is the seminal algorithm based on the learned sim-ilarity.

• The group personalized ranking (GBPR) refines the cri-terion in the BPR which adopts the group preferenceinstead of individual preference.

Normalized discounted cumulative gain (NDCG) as afore-mentioned by formula (17) measures the accuracy of a rec-ommender algorithm based on the graded relevance ofthe recommended items. The precision (PREC) as aforemen-tioned by formula (16) is proportion of recommendationswhich are good recommendations. This section mainly ana-lyzes the empirical result with respect to PREC@5. In Fig. 3,to determine the optimal learning rate γ for the model, therate γ is chosen between 0.01 and 0.1 and a factorizationdimension of d=20 is utilized. As presented in Fig. 3, whenγ increases from 0.01 to 0.05, PREC@5 increases corre-spondingly. When γ increases from 0.06 to 0.1, PREC@5decreases and it can be inferred that the system is over-fittingwhile γ is larger than 0.05. The convergence of stochasticgradient descent with testing dataset with different epochs ispresented in Fig. 4. To find the optimal number of iterations,the number of iterations is chosen between 100 and 1000.It can be seen that 500 is the best value of iterations for themodel.

5.2.1 Comparison with Other Methods

The main empirical results are illustrated in Table 1 on tworanking-orientedmetrics, includingPREC@5andNDCG@5.Among all the experimental comparisons, the best perfor-mance is emphasized in bold font and a learning rate ofγ = 0.04 is utilized. For all the methods, the tradeoff param-eters are the same as α = 0.01 to reduce computationcomplexity. For WBPR, this study samples the unobserveditems by popularity with the usage of a non-uniformly strat-egy. For GBPR, the number of users in a group is set to 5. Asindicated byTable 1, the following conclusions can be drawn:(1) The proposed FSBPR model outperforms other state-of-the-art methods in terms of PREC@5 and NDCG@5 and isproved to be accurate in recommendation performance in allcases. The dimensions are set at 10, 15, 20, 25 and empiricalstudies show that the model can achieve better performancethan other baselines which demonstrate the assumption thatindividual preference is associated with item similarity. Themodel has the merit of combining item similarity knowledgeand the Bayesian personalized ranking preference assump-tion to achieve better performance; (2) The models basedon factored item similarity (e.g., FSBPR) via two low rankmatrices are better than those models without item similarityknowledge. It shows that item similarity information is veryhelpful in improving the performance of the traditional rec-ommendation algorithms.We choose factored item similarityinstead of predefined similarity, such as cosine similaritysince factored item similarity can capture the global itemcorrelations even if co-users do not exist; (3) in most of thepreviouswork based on theBayesian pairwise ranking, all theitems are assigned with the same weight, which of course isnot the case in reality. The model utilizes the factored item–

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Fig. 3 Recommendationperformance with varyinglearning rates

Fig. 4 Recommendationperformance with differentnumber of iterations

item similarity as item weights and high item weight canreflect high desirability to a user. (4) Furthermore, the modelapplies the popular pairwise rankingmethods, aiming tomin-imize the number of inversions in the ranking where the pairof results are in the wrong order relative to the ground truth.Combining factor item similarity with the pairwise rankingmodel is indeed more effective than the simple BPR-basedmodel.

5.2.2 Effect of the Observed Items Size

This part studies how the observed items size for each useraffects the model performance of different algorithms. It

is noted that the ranking-oriented evaluation metrics areNDCG@5 and PREC@5, and this paper only keeps recordswith the observed items larger than 10 in test dataset andthen classifies the remaining records into four classes, includ-ing 11–30,30–50,50–70, and > 70, to describe how manyobserved items are available for a user. As indicated inFigs. 5, 6, given different user groups in test datasets, theFSBPR model outperforms other models on both datasets inall cases. As presented in Fig. 5, the FSBPR model whichadopts factored item similarity can significantly improvetheir performance in terms of NDCG@5. As the number ofobserved items increase, the performances of all the mod-els improve and the proposed FSBRP can achieve the best

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Table 1 Comparison with otheralgorithms on differentdimensions

Dataset Dimension Metrics BPR WBPR FISM GBPR GBPR+ FSBPR

MovieLens 10 PREC@5 0.2101 0.2220 0.2263 0.2280 0.2316 0.2649

NDCG@5 0.2198 0.2283 0.2316 0.2479 0.2537 0.2868

15 PREC@5 0.2197 0.2267 0.2330 0.2331 0.2439 0.2668

NDCG@5 0.2214 0.2357 0.2362 0.2398 0.2441 0.2872

20 PREC@5 0.2208 0.2186 0.2301 0.2343 0.2422 0.2728

NDCG@5 0.2373 0.2165 0.2422 0.2476 0.2551 0.2917

25 PREC@5 0.2229 0.2046 0.2278 0.2352 0.2432 0.2749

NDCG@5 0.2384 0.2020 0.2393 0.2382 0.2446 0.2925

Netflix 10 PREC@5 0.1303 0.1320 0.1322 0.1324 0.1444 0.1610

NDCG@5 0.1400 0.1420 0.1469 0.1463 0.1561 0.1665

15 PREC@5 0.1368 0.1370 0.1375 0.1378 0.1561 0.1620

NDCG@5 0.1439 0.1445 0.1452 0.1488 0.1427 0.1672

20 PREC@5 0.1379 0.1397 0.1407 0.1410 0.1516 0.1626

NDCG@5 0.1464 0.1471 0.1487 0.1506 0.1643 0.1692

25 PREC@5 0.1395 0.1413 0.1429 0.1463 0.1573 0.1643

NDCG@5 0.1473 0.1486 0.1512 0.1522 0.1721 0.1723

Fig. 5 Recommendation performance on Movielens dataset in termsof NDCG@5 on different user group

performance. As shown in Figs. 6, 7 and 8, the BPR-basedmodels tends to converge when items size is larger than70, while FSBPR still improves performance significantly,which shows the effectiveness and general applicability ofthe model proposed in this study.

6 Conclusion

This paper discusses the neighborhood-based collaborativefiltering and the model-based methods. Motivated by theFISM and BPR models, this paper first applies factoreditem similarity to augment individual preference as rela-

Fig. 6 Recommendation performance on Netflix dataset in terms ofNDCG@5 on different user group

tive preference in the model. Subsequently, pairwise rankingassumption is taken and the objective function is designed.Furthermore, a novel model called FSBPR is put forward todealwith one-class collaborativefiltering and to combine fac-tored item similarity and individual preference assumptionproposed by the BPR model. The FSBPR model can cap-ture the global item correlations even if co-users do not existand directly optimize the ranking order. Hence, the FSBPRmodel can achieve better performance than other state-of-the-art methods, showing great effectiveness on two publicreal-world datasets.

Future work will focus on how to exploit item-side infor-mation and integrate them with the BPR-based models.Item-side information, such as user review, temporal infor-

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Fig. 7 Recommendation performance on Movielens dataset in termsof PREC@5 on different user group

Fig. 8 Recommendation performance on Netflix dataset in terms ofPREC@5 on different user group

mation and location information, is proved to be very helpfulin improving recommendation performance. Furthermore, itis deployed into a cloud computing environment.

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