Personalized recommendation by matrix co-factorization with tags and time information

Accepted Manuscript

Personalized Recommendation by Matrix Co-Factorization with Tags and Time Information Ling Luo, Haoran Xie, Yanghui Rao, Fu Lee Wang PII: DOI: Reference:

S0957-4174(18)30723-1 https://doi.org/10.1016/j.eswa.2018.11.003 ESWA 12302

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Expert Systems With Applications

Received date: Revised date: Accepted date:

18 May 2018 2 November 2018 3 November 2018

Please cite this article as: Ling Luo, Haoran Xie, Yanghui Rao, Fu Lee Wang, Personalized Recommendation by Matrix Co-Factorization with Tags and Time Information, Expert Systems With Applications (2018), doi: https://doi.org/10.1016/j.eswa.2018.11.003

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Personalized Recommendation by Matrix Co-Factorization with Tags and Time Information Ling Luoa , Haoran Xieb,∗, Yanghui Raoa , Fu Lee Wangc a School

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of Data and Computer Science, Sun Yat-sen University, Guangzhou, China b Department of Mathematics and Information Technology, The Education University of Hong Kong, Hong Kong c School of Science and Technology, The Open University of Hong Kong, Hong Kong

Abstract

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Personalized recommendation systems have solved the information overload problem caused by large volumes of Web data effectively. However, most existing recommendation algorithms are weak in handling the problem of rating data sparsity that characterizes most recommender systems and results in deteriorated recommendation accuracy. The results in the KDDCUP and Netflix competition have proven that the matrix factorization algorithm achieves better performance than other recommendation algorithms when the rating data is scarce. However, the highly sparse rating matrix will cause the overfitting problem in matrix factorization. Although regularization can relieve the issue of overfitting to some extent, it is still a significant challenge to train an effective model for recommender systems when the data is highly sparse. Therefore, this paper proposes a co-SVD model to enrich the single data source and mitigate the overfitting problem in matrix factorization. The user preferences are enriched not only by rating data but also the tag data; subsequently, the relevance between tags and item features are explored. Furthermore, according to the assumption that user preferences will change with time, we optimize the preference and relevance by adding the temporal influence. Based on the MovieLens benchmark datasets, the experimental results indicate that the proposed co-SVD method is more effective than other baselines. Matrix co-factorization provides an effective method to the solve data sparsity problem with additional information. The method can be used to address this problem in various expert and intelligent systems such as recommendation advertisements, e-commerce sites, and social media platforms, all of which require a relatively large amount of input data from users.

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Keywords: Personalized Recommendation, Matrix Factorization, Data Sparsity, Tags, Temporal Factor

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Corresponding author. Tel.: +852 29488545 Email addresses: [email protected] (Ling Luo), [email protected] (Haoran Xie), [email protected] (Yanghui Rao), [email protected] (Fu Lee Wang)

Preprint submitted to Expert Systems with Applications

November 3, 2018

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1. Introduction

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With the continuous growth of Web resources, users can access a large volume of information from the Web. However, the rapid expansion of Internet information has also led to the problem of information overload. Personalized recommender systems are feasible solutions to solve such problems. They first identify user preferences by analyzing historical user behavior, and subsequently assist users to obtain and access resources according to the identified user preferences (Adomavicius & Tuzhilin, 2005, 2001). Because accurate recommendations enable users to locate desirable items quickly, studies on recommendation techniques have become significant in recent years. With in-depth research on recommendation algorithms, several techniques such as collaborative filtering (CF) (Su & Khoshgoftaar, 2009; Bao et al., 2012), matrix factorization (MF) (Pacula, 2009), naive Bayes (Park et al., 2007), Clustering (DuBois et al., 2009; Shinde & Kulkarni, 2012; Kim & Ahn, 2008), association rules mining (Huang et al., 2008), and deep learning (Christakou et al., 2007) have been applied to personalized recommendations. Among these models, CF is currently the most mature and widely adopted recommendation algorithm (Goldberg et al., 1992; Schafer et al., 2007). However, with the increasing complexity of system structure and the increasing number of users, CF techniques have encountered a series of challenges, including cold start (Bobadilla et al., 2013), data sparsity (Ricci et al., 2015), and changes in user interest (Inuzuka et al., 2016). In particular, the data sparsity problem has affected the recommended quality significantly. Generally, collaborative filtering recommendation algorithms can be divided into two categories: memory-based collaborative filtering and model-based collaborative filtering. Memory-based collaborative filtering algorithms exploit user rating data to compute the similarity between users or items, and subsequently predict the ratings of the target user to an item based on the similarity. The performance of these algorithms will be poor if the training data are sparse. Meanwhile, MF is a model-based collaborative filtering algorithm. MF can achieve better accuracy in prediction than memory-based collaborative filtering by exploring the implicit characteristics of the users and items. However, MF also suffers from the overfitting problem that deteriorates recommendation accuracy when the rating matrix is extremely sparse. Although regularization can relieve the issue of overfitting to some extent, it is still a significant challenge to train an effective model for recommender systems when the rating data are highly sparse. User-generated tags imply their preferences that can be exploited as a supplement of rating to alleviate the sparsity problem. Researchers (Liang et al., 2010; De Gemmis et al., 2008; Hsu, 2013; Han et al., 2010) reported that tags are important information sources that can reflect user interests by treating tags as a potential relationship among users and items. However, the methods above primarily separate ratings and tags as independent data sources by following the assumption that a user is likely to be interested in an item if he/she annotates a tag on it. However, the assumption may not always be rational. It is possible that users may also tag items that they do not like. In this case, the rating data reflect the true preferences of the users, as shown in the following Example 1. Example 1: Figure1 illustrates the behavioral records of user A on a movie website. According to the assumption that users will assign high ratings on their favorite movies and low ratings on movies with negative impressions, three observations can be obtained by analyzing the behavioral records. 2

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Figure 1: Behavioral records of user A on a movie website

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Observation 1: User A annotates both his/her favorite movies and low-rating movies with tags. Observation 2: User A prefers action movies to science fiction movies, as he/she has watched action movies frequently recently even if he/she assigns the same high ratings to these two categories. Observation 3: User A has different views on “Movie 1” at different stages; therefore, the individual preferences and opinions of user A has changed over time. Motivated by the idea of Observation 1, Liu et al. (2012) and Du et al. (2016) perceived that a misinterpretation of user preferences that are derived only from tags will occur. They integrated tagging and rating sources to infer user preferences. Du et al. (2016) proposed a multilevel user profiling model by integrating tags and ratings. Liu et al. (2012) inferred user preferences by proposing a concept termed “tag rating” to indicate the user preferences for the preferred and disliked tags. However, some limitations still exist in the two methods above. First, the frequency of using a tag, an important indicator to reflect user preferences according to Observation 2, is neglected by these methods. Next, according to Observation 3 and some studies (Inuzuka et al., 2016; Yin et al., 2015) about the change in user preference, the effects of time for the prediction of user preferences is ignored by these methods. To address these limitations and establish an effective recommendation model, a co-singular-value decomposition (SVD) model is proposed herein. The co-SVD model follows the idea of a user’s tag preference by integrating the tag’s rating, frequency, and novelty. The tag’s rating is defined by the observation that the tag reflects some of the user’s concerned attributes among all attributes of an item, and the rating conveys their true intentions of using the tag; the tag’s frequency refers to the number of times that a particular user uses the tag to annotate the items; the tag’s novelty is defined to measure the effects of time on the tag preference. Furthermore, according to the tag’s weight (Sen et al., 2009) and novelty for an item, the model identifies the relevance among the tags and items. Two matrices: user-tag preference matrix and tag-item relevance matrix, are defined according to the user’s tag preference, and the relevance among tags and items, 3

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respectively. Finally, the model factorizes the three matrices (user-item rating matrix, user-tag preference matrix, and tag-item relevance matrix) collaboratively to handle the overfitting problem with the tagging and temporal information sources. The primary contributions of this article are listed as follows:

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1. We define the tag’s novelty to measure the impact of time on a user’s preference analysis. To the best of our knowledge, this is the first study that uses the idea of a user’s tag preference by integrating the tag’s rating, frequency, and novelty. 2. We not only consider the rating matrix between users and items, but also define the user-tag preference (tag-item relevance) matrices by identifying the relationships among users and tags (tags and items), which is a novel framework compared to the extant studies. 3. To tackle the overfitting problem caused by the sparse rating data, we propose a matrix co-factorization method (co-SVD) by further exploiting tagging and temporal information sources. 4. The proposed co-SVD model is not a data-demanding method. With the sparse data source of user tags and ratings, the co-SVD model can improve the recommendation accuracy significantly.

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As an information filtering method, personalized recommendation addresses the problem of information overload in many expert systems. The proposed co-SVD includes tags as an additional data source to ratings and subsequently co-factorizes both sources in the matrix form to improve the accuracy of personalized recommendation in the context of sparse data. The idea of matrix co-factorization provides an effective method to the solve data sparsity problem with additional information. The method can be used to address this problem in various expert and intelligent systems such as recommendation advertisements, e-commerce sites, and social media platforms, all of which require a relatively large amount input data from users. Furthermore, co-SVD can be used in data-oriented systems such as the low-dimensional visualizations of data space and neighborhood selection. The remaining sections of this article are organized as follows. Chapter 2 provides a brief overview of the primary techniques and current status of personalized recommender systems. In Chapter 3, we specify the proposed co-SVD model with a detailed introduction of each step. Experiments on the MovieLens datasets are conducted to evaluate the performance of the co-SVD model; this is described in Chapter 4. Chapter 5 summarizes the primary research findings, innovations, limitations, and future research plans of this study.

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2. Related work In this section, we briefly review some related studies pertaining to data sparsity in recommender systems. The tags posted by users on recommender systems are supposed to be highly dependent on their interests, and can be exploited as an important data source with ratings to build more accurate and specific user profiles. Wang et al. (2010) found similar users based on the hypothesis that similar users exhibit similar tagging history, and combined the traditional rating-based neighbor CF with the tag-based neighbor CF to provide recommendations. De Gemmis et al. (2008) considered tag data as an additional source, 4

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and captured user preferences from both item descriptions and tag data. Gedikli & Jannach (2013) argued that tag preferences should be considered in the context of items, and proposed a scheme to exploit context-specific tag preferences in the recommendation process. Zhang et al. (2010) introduced tag information by constructing a tripartite model to simulate the links between users, resources, and tags, and subsequently provided recommendations according to the tripartite model. Further, a weighted hybrid tag recommender system was proposed using blended multiple recommender components on the complementary dimensions (Gemmell et al., 2010). In another study (Said et al., 2012), each tag was assigned a value obtained from averaging the ratings provided by the user to movies tagged with that particular tag, and such a tag value improved the predictive accuracy by personalizing the tags. These methods assumed that all tags aim to express the users’ favorite features of the items. However, users may also tag items that they do not like. In this case, separating tags from ratings can confuse a user’s intentions of tagging, thus resulting in a prediction error. Liu et al. (2012) and Du et al. (2016) perceived that a misinterpretation of user preferences that are derived only from tags will occur. They integrated tagging and rating sources to infer user preferences. Du et al. (2016) proposed a multilevel user profiling model by integrating tags and ratings. Liu et al. (2012) inferred user preferences by proposing a concept termed “tag rating” to indicate user preferences for preferred and disliked tags. However, memory-based methods cannot adapt easily to large-scale datasets. In other words, they are time consuming when searching for candidate neighbors in a large user space, while model-based approaches can be scaled up readily to large datasets and predict ratings more efficiently. In addition, model-based approaches can achieve higher accuracy by alleviating the issue of data sparsity than memory-based approaches (Koren et al., 2009). MF, a model-based method, decomposes the user-item rating matrix into two lowrank user-feature and item-feature matrices, and subsequently predicts ratings by the inner products of user-specific and item-specific latent feature vectors. The SVD algorithm proposed by (Funk, 2006) first initialized two low rank matrices to express the features of the users and items, and subsequently optimized the feature matrices using stochastic gradient descent such that it resembles the original rating matrix and can predict the unknown ratings. Koren combined the domain-based approach and the matrix factorization to obtain the SVD++ model (Koren, 2008). Salakhutdinov and Mnih described the problem of MF in terms of probability, and proposed a probabilistic matrix decomposition model (Mnih & Salakhutdinov, 2008). However, these MF approaches (Koren, 2008; Mnih & Salakhutdinov, 2008) fail to extract sufficient feature information of users and items owing to the high sparsity of the rating data. Based on Koren’s SVD++ (Koren, 2008), Enrich et al. (2013) proposed another SVD++ algorithm that combined tag information to study the impact of tag data on rating prediction. Bao et al. (2012) proposed a collaborative filtering model based on probabilistic matrix factorization to predict a user’s interests to items by utilizing both tag and rating information simultaneously. These methods combine the tag and rating information to alleviate the overfitting problem in matrix decomposition, and have improved the prediction accuracy effectively. However, these methods still exhibit limitations in the prediction of user preferences owing to the insufficient analysis of tag information and neglect of the changes in user interest. A recent study conducted by Wang & He (2016) on TV program recommendations has used the temporal information regarding TV viewing for group recommendations. However, this temporal information is different from that in 5

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tagging behaviors. Therefore, this study focuses on how to further exploit and integrate the additional tagging and temporal data sources to better understand a user’s tag preferences, and provide accurate recommendations. 3. The co-SVD model

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The proposed co-SVD model is divided into three steps. The first step is to obtain the user’s tag preference based on the ratings, tags, and temporal information. The second step aims to estimate the relevance between tags and items based on a tag’s frequency and temporal effect. The last step is to predict the ratings using the co-SVD model. The diagram of the model structure is shown in Fig. 2.

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Figure 2: Personalized recommendation by matrix co-factorization with tags and time information

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3.1. Tag preference Users typically exhibit their own preferences through their behaviors. In recommender systems that support both user rating and tagging, tags can indicate the preferred or disliked features among all features of the items. Meanwhile, the ratings reflect how much the user is interested in an item, without distinguishing the features a user liked and disliked. Hence, we integrate these two information sources as indicated in Example 2. Example 2 : User B loves science fiction movies. He/She scores 5 for the two movies Ice Age and Soldier Joe that exhibits sci-fi properties, and tags the two films with “science fiction.” However, user B does not like thrillers. He/She scores Silent Hill and The 6

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Exorcist with 2 and 1, respectively, and tags the two movies with “Thrillers.” Species is a science fiction movie with slight terror. He/she tags Species with “science fiction” and “Thriller.” User B does not like the horror aspect in Species, but he/she assigns 3 points owing to his/her appreciation of science fiction elements. Therefore, we can explore more information behind the multiple ratings of the item through tags, thus allowing us to better understand the user preferences and provide more accurate recommendations. In reference to previous research studies (Liu et al., 2012; Gedikli & Jannach, 2013; Sen et al., 2009; Gedikli & Jannach, 2010; Zhang et al., 2014), user preferences are optimized according to the following assumptions. Assumption 1: In general, if a user marks more high-rating items with a special tag, he/she is more interested in the features expressed by the tag of the item, and exhibits a higher preference for this tag. Based on the Assumption 1, we define the likeability of user u for tag t by the t tag’s rating and t tag’s frequency of the user u: P w(i, t)×(ru,i −ru ) +λ ×fu,t ×(rf u,t −ru ) , (1) rlu,t = ru + i∈ItP i∈It w(i, t) where w(i, t) was proposed by a previous study (Sen et al., 2009) to calculate the tag’s weight in the item based on the rationale that the tag that was marked more frequently on the item should possess a larger weight. number of times tag t was applied to item i . overall number of tags applied to item i

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w(i, t) =

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ru is the average rating of user u, ru,i is the rating of user u to item i, It is the set of items containing the tag t, and λ is a hyperparameter to adjust the impact of the tag’s frequency on the likeability. fu,t is defined as Eq.(3): fu,t =

times of user u uses tag t , overall times user u uses tags

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fu,t indicates the tag’s frequency of user u using tag t, and rf u,t is the average rating of the user to the set It . Assumption 2: User’s preference changes over time. Based on Assumption 2, we consider that the user’s tag preference will change over time, and the effects of time should be considered in the calculation of the user’s tag preferences. To measure the influence of time on the user’s tag preferences, this study uses an adaptive exponential forgetting function(Zhang et al., 2014) to define a user’s tag novelty: nlu,t = exp(−α × times(u, t)) ,

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where nlu,t indicates the novelty of tag t to user u, α is a hyperparameter used to adjust the descent speed of novelty, and times(u, t) returns a non-negative integer expressing the tag’s ranking. Tags are ranked according to the temporal information that the last time tag t was used by the user u. For example, t1 , t2 and t3 are different tags, the ranking of tag t1 that is used most recently by the user u is times(u, t1 ) = 0, the ranking 7

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of tag t2 that is used before t1 by user u is times(u, t2 ) = 1, the ranking of tag t3 that is used before t2 by user u is times(u, t3 ) = 2. The more the user uses the tag t, the smaller ranking the t will be, and the more novel the tag t is to the user u. Formally, the tag preference of user u to tag t is defined based on the likeability and the novelty of the tag:

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Pu,t = rlu,t + β ×nlu,t P w(i, t)×(ru,i −ru ) +λ×fu,t ×(rf u,t −ru )+β ×nlu,t , = ru + i∈ItP i∈It w(i, t)

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where λ and β are both hyperparameters, λ is the weight of the tag frequency on the user’s tag preference, and β indicates the effect of tag novelty on the user’s tag preference.

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3.2. Relevance between tag and item Assumption 3: The more times a tag is marked on an item, the more the tag can express the item. Based on Assumption 3, we consider that the relevance between tag t and item i is related to the tag’s weight of the item, which is defined in Eq.(2). In addition, the relevance between tags and items is changed over time, the idea of which is illustrated by Example 3. Example 3 : A user used the tag “fast CPU” to label the latest computer a year ago. With the development of CPU techniques, more computers with faster CPUs were produced. The “fast CPU” computer has reduced to a “slow CPU” computer today. The recent tag “slow CPU” annotated to this computer can better reflect the feature of the item. Therefore, we define the tag novelty for an item as nli,t to express the effect of time on the relevance between the tag and item, and calculates it similarly as the novelty of the tag for the user. nli,t = exp(−α × times(i, t)) ,

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We define the relevance between tags and items in Eq.(7): Fi,t = w(i, t) + γ × nli,t ,

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where γ is a hyperparameter to adjust the effect of time on the relevance between tags and items.

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3.3. Co-SVD model Koren’s RSVD model considers the user/item biases and user/item-specific vectors on the rating prediction. bu,i = u + bu + bi + Vi T Uu , R

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where bu and bi represent the rating bias of user u and item i, respectively, u is the global average rating, Uu is the specific vector of user u, and Vi is the specific vector of item i. Koren et al. (2009) has shown that integrating user/item biases can improve the predictive accuracy. However, we have already stressed the overfitting problem for 8

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considering only ratings in MF, and its potential to integrate other supplementary information in MF to solve the problem. Hence, consistent with the definitions of the previous section, we first construct the user-tag preference matrix P by the definition of a user’s tag preference in section 3.1, in which each element Pu,t indicates the tag preference of user u to tag t. We subsequently construct the tag-item relevance matrix F based on the definition of Fi,t in section 3.2, and each element Fi,t in matrix F indicates the relevance between tag t and item i. Finally, we build the co-SVD model on top of the RSVD. In the co-SVD model, we exploit both the tagging and rating information. The user’s preference for tags, the relevance between items and tags, and the rating of users to items are all applied to the matrix decomposition. By exploring the preference in matrix P, the relevance in matrix F, and the rating in matrix R collectively, the missing ratings in R can be predicted more accurately than applying the rating-based RSVD method. On the top of the basic SVD model, we further consider the user/item/tag biases and user/item/tag-specific vectors on the rating/preference/relevance prediction as follows.

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Figure 3: The co-SVD model

bu,i = ur + bu + bi + Vi T Uu R Pbu,t = up + bu + bt + Zt T Uu Fbi,t = uf + bi + bt + Zt T Vi ,

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where bu and bi represent the rating bias of user u and item i; bt represents the preference bias of tag t; ur , up and uf are the global average ratings, global average preference, and 9

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n m 1 XX R bui )2 SSE = I (Rui − R 2 u=1 i=1 ui

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global average relevance, respectively; Uu is the specific vector of user u; Vi is the specific vector of item i; Zt is the specific vector of tag t. By considering the user-item rating, user-tag preference, and item-tag relevance, the objective function to be minimized is given as follows:

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m w 2 λF X X F + Iit (Fit − Fbit ) 2 i=1 t=1 X 2 X λR X 2 2 2 2 2 |bi | + |bt | + ||U ||F + ||V ||F + ||Z||F ) , + ( |bu | + 2 u t i

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2 bui , Pbut , and where λP ; λF and λR are supper parameters; || · ||F is the Frobenius norm; R Fbit are the predicted rating, predicted preference and predicted reference, respectively, which are defined in Eq.(9). To obtain a local minimization of the objective function given by Eq.(10) above, we perform the following gradient descents on bu , bi , bt , Uu , Vi , and Zt across all the users, items, and tags in a training dataset.

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∂SSE bui ) − λP (Put − Pbut ) + λR bu = −(Rui − R ∂bu ∂SSE bui ) − λF (Fit − Fbit ) + λR bi = −(Rui − R ∂bi ∂SSE = −λP (Put − Pbut ) − λF (Fit − Fbit ) + λR bt ∂bt m w X X ∂SSE R P b =− Iui (Rui − Rui )Vi − λP Iut (Put − Pbut )Zt + λR Uu ∂Uu t=1 i=1

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n w X X ∂SSE R F bui )Uu − λF =− Iui (Rui − R Iit (Fit − Fbit )Zt + λR Vi ∂Vi u=1 t=1

n m X X ∂SSE P F = −λP Iut (Put − Pbut )Uu − λF Iit (Fit − Fbit )Vi + λR Zt ∂Zt u=1 i=1

3.4. Comparisons

As a model-based CF, co-SVD learns the implicit characteristics of the users and items from the data directly, and subsequently obtains the unknown ratings through user-implicit vectors and item-implicit vectors. Instead of relying heavily on the similarity metrics used in other memory-based CF models that are typically invalid for sparse data, the co-SVD can relieve this issue by including the additional data sources in the 10

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computational process. However, the co-SVD exhibits the problem of poor explanation in the implicit vector, which occurs in most MF models (Rastegarpanah et al., 2017). Meanwhile, co-SVD can be considered as a generalization of the classical SVD. Rather than considering the user-item relationships in SVD only, co-SVD explores the relationships among the user, item, and tag. In other words, co-SVD extends the binary relation to a tripartite relation. In the co-SVD model, the user profiles and item profiles are established from both the ratings and tags, thereby mitigating the negative effects of sparse ratings on the recommended accuracy effectively. However, the computational cost of co-SVD becomes higher owing to the exploration of ternary relations. 4. Evaluation

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We conducted some experiments to verify the effectiveness of the proposed co-SVD method in two real datasets. We first describe the datasets and metrics used in the experiments, and subsequently explain the parameter selection processes. Further, we compared our co-SVD model with the item-specific tag preference method (Gedikli & Jannach, 2013), Koren’s RSVD model (Koren et al., 2009), TriFac model (Bao et al., 2012), and BPTF model (Xiong et al., 2010) . 4.1. Data set

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We adopt the MovieLens datasets (http://grouplens.org/datasets/) in the experiments as the datasets contain the complete information of the tags, ratings, and time stamps. To demonstrate the efficiency of our proposed approach, we performed experiments on two benchmark datasets. The smaller dataset 1 contains 100, 004 rating records and 1, 296 tag records of 671 users for 164, 979 movies, while the larger dataset 2 contains 10, 000, 054 rating records and 95, 580 tag records of 71, 567 users for 71, 552 movies. Each user rates at least 20 movies and the value of the rating is in the range of 0.5 to 5. A higher rating indicates the user’s higher preference on the movie in these two datasets. We name the smaller dataset as the “Small MovieLens dataset” and the larger dataset as the “10M MovieLens dataset.” Because of issues in the discontinuous user id and movie id, and invalid tags in the raw dataset, we pre-processed the dataset before the experiment. The pre-processing includes the following two aspects: (i) reorder the user id and movie id by mapping the id to a lower range as much as possible, which will not distort the original dataset; and (ii) filter tags by deleting the tags that appear less than five times and attaching the attributes of the item as the tag information. After the pre-processing steps above, the Small MovieLens dataset retains 100, 004 rating records and 1, 056 tag records of 671 users for 9, 125 movies, and the 10M MovieLens dataset retains 10, 000, 054 rating records and 92, 809 tag records of 71, 552 users for 10, 681 movies. Table 1 and Table 2 show the details of the two post-processed datasets.

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http://files.grouplens.org/datasets/movielens/ml-latest-small-README.html http://files.grouplens.org/datasets/movielens/ml-10m-README.html

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Table 1: Details of the Small MovieLens dataset

Value 671 9125 1056 100004 1.63e−2 1.72e−4

Attribute users] movies] tags] ratings] sparsity(ratings) sparsity(tags)

Value 71552 10681 91450 10000054 1.31e−2 1.20e−4

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Attribute users] movies] tags] ratings] sparsity(ratings) sparsity(tags)

Table 2: Details of the 10M MovieLens dataset

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4.2. Performance metrics To evaluate an individual item prediction, we used two widely used metrics: the mean absolute error (MAE) and the root mean square error (RMSE). The MAE is defined as the average absolute difference between the predicted ratings and the actual user ratings [11]. The MAE is formally defined as follows. P ˆu,i | u,i∈T |ru,i − r . (12) M AE = |T |

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The RMSE is another typical metric for the evaluation of recommender systems. Because the errors are squared before they are averaged, RMSE metrics are more sensitive to large-error predictions when compared to MAE metrics. Formally, RMSE metrics are defined as follows: sP 2 ˆu,i | u,i∈T |ru,i − r RM SE = , (13) |T |

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where T indicates the test set; u and i indicate the user and item in the test set, respectively. ru,i is the specified rating of user u to item i, and ru,i is the prediction provided by a recommender system. If the MAE and RMSE scores are low, it suggests that the recommender system can predict a user’s ratings with high accuracy. In general, the RMSE score achieved by a recommender system is always greater than or equal to the MAE score. The greater the difference between the MAE score and RMSE score achieved by a system, the larger the variance of the individual errors produced by the system. Precision and recall have been used widely as the metrics to evaluate recommendation quality. To measure the performance of co-SVD in terms of precision and recall, we conducted experiments to examine the global precision and global recall. However, these two measures are often conflicting (Herlocker et al., 2004). We used a combination of the two, named the F1 metric, to evaluate the recommendation quality as well. As the MovieLens datasets do not contain binary classification preference information, we used 3.5 as the threshold that was typically adopted in other research studies (Adomavicius et al., 2007), and split the ratings into a binary scale by treating ratings greater than or equal to 3.5 (i.e., ratings 3.5, 4.0, 4.5 and 5.0) as “high rating” and ratings less than 3.5 (i.e., ratings 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0) as “non-high rating.” Let ph and th represent the set of predicted “high rating” movies and the set of true “high rating” movies, respectively. Three metrics: precision, recall, and F1, are formally defined as the following: |ph ∩ th| P recision = (14) |ph| 12

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Recall =

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2 ∗ Recall ∗ P recision Recall + P recision

4.3. Impact of parameters

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F1 =

|ph ∩ th| |th|

Table 3 shows eight hyperparameters involved in the co-SVD model. To select suitable values for these parameters, we randomly divided the MovieLens dataset into training, validation, and test sets. Seventy percent of the dataset was assigned to the training set, 20 Table 3: Parameters of the model

α

β γ

λP λF λR D

rlu,t =

w(i,t)×(ru,i−r u ) i∈IP t i∈It w(i,t)

(4) (6)

+λ ×fu,t ×(rf u,t −r u ) (1)

Put = rlu,t + β × nlu,t

(5)

Fi,t = w(i, t) + γ × nli,t (7) Pn Pn 2 R 1 d SSE = 2 I (Rui − Rui ) u=1 Pwi=1P ui 2 λP P n d + 2 t=1 Iut (Put − Put ) Pu=1 2 λ m Pw F c + 2F Iit (Fit − F it ) i=1 t=1 P P λ P + 2R( u |bu |2 + i |bi |2 + t |bt |2 +||U ||2F +||V ||2F +||Z||2F ) (10) −−

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Relevant Formulas nlu,t = exp(−α × times(u, t)) nl = exp(−α × times(i, t)) P i,t

Parameter Effects Adjust the drop rate of the tag novelty for user or for item Adjust the influence of tag frequency on users’ tag preference Adjusting the influence of tag novelty on users’ tag preference Adjust the influence of tag novelty on the relevance of tags and items

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Regularization weights in objective function.

Dimensions of feature space.

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For the proposed co-SVD model, determining the hyperparameter values is important. We set different parameter values to verify the model on the validation set. Figure 4 shows the impact of the parameters on the model. The parameter α simulates the change rate of the user interests, and is expressed as the drop rate of the tag novelty. To approach the change speed of the real user interests, we set the range of α from 0 to 0.01. In Fig. 4(a), the differences are not obvious with the values of α, and the MAE and RMSE exhibit the lowest values when α = 0.006. λ and β are the weights of the tag’s frequency and tag’s novelty in the users’ tag preference, respectively. Fig. 4(b) and 4(c) show that the model exhibits the lowest MAE/RMSE when λ = 1.7 and β = 0.05. These experiments regarding parameters λ and β show the importance of adopting the tag frequency and novelty in the tag preference. γ is the weight of the tag novelty in item-tag relevance, and it expresses the impact of time on item features, which is illustrated in Example 3. Fig 4(d) shows that the most suitable value of γ is 0.05. λP and λF are the weights of the objective function. They are responsible for adjusting the impact of the predicted preference accuracy and predicted relevance accuracy of the model. If λP = λF = 0 in the objective function, the defined user-item preference matrix and item-tag relevance matrix are not relevant in the model, and the model is degraded to the RSVD model as baseline 1. In Fig 4(e) and 4(f), we obtain the best results when λP = 0.001 and λF = 1.5. The results demonstrate the effectiveness of the tagging data source in alleviating the overfitting problem. We further revise the co-SVD model using regularization to enhance the generalization ability. λR 13

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0.7900 0.7895

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0.7885 0.004 0.006 Value of parameter alpha

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Impact of parameter beta MAE RMSE

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MAE value for validation

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0.004 0.006 Value of parameter lambdaP

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Impact of parameter lambdaF MAE RMSE

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0.6050 1.0

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1.4 1.6 Value of parameter lambdaF

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(f) Impact of parameter λF

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0.02 0.03 Value of parameter lambdaR

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(g) Impact of parameter λR Figure 4: The effects of hyper paremeters

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Impact of parameter lambdaR

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Impact of parameter lambdaP

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(c) Impact of parameter β

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MAE RMSE

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MAE value for validation

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0.04 0.06 Value of parameter beta

1.4 1.6 Value of parameter lambda

Impact of parameter gamma

0.610

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(b) Impact of parameter λ

0.609

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is the weight of the regularization in the objective function, which achieves the best performance at 0.035. Therefore, based on the experimental results on the validation set, we set the parameters of the model as shown in Table 4. Table 4: Values of model parameters

α 0.006

λ 1.7

β 0.05

γ 0.05

4.4. Baseline methods

λP 0.001

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To compare the performance of the co-SVD model with some baseline methods, two model-based and one memory-based personalized recommendation baselines were chosen. Baseline 1: Koren’s RSVD model (Koren et al., 2009), which is based on a classic model, predicts ratings by both user/item bias and user/item implicit features, and has shown that integrating user/item bias can well improve predictive accuracy. Baseline 2: TriFac model (Bao et al., 2012), proposed by Bao et al., is based on the PMF model and represents tags, users, and items in the same latent feature space to explore both tag information and rating information in an integrated manner. Baseline 3: Item-specific tag preference method (Gedikli & Jannach, 2013) proposed a new scheme to infer and exploit context-specific tag preferences with the argument that tag preferences should be considered in the context of an item. Baseline 4: BPTF model (Xiong et al., 2010) is a factor-based algorithm with a special constraint on the time dimension. It considers time by introducing additional factors for time, and these additional factors represent the population-level preference of latent features at each particular time. To better demonstrate the effect of the experiments, we selected the most suitable values for the parameters of the baselines. The “learning rate” and “regulation weights” in Koren’s RSVD model were set as 0.01 and 0.05, respectively. For the TriFac model, we set 70% of the dataset as the training set for model training, and 20% as the validation set to select the suitable values of the model parameters. Finally, we obtained the parameter as follows: λP = 0.1, λQ = 4, λU = λV = λT = 0.1 to achieve the lowest RMSE for the TriFac model. For the BPTF model, the parameters used for the priors are the same as those in the original paper, and the maximum number of iterations is set to 150. 4.5. Experimental results

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For the two datasets, we conducted 10 experiments for each different factor number D (D indicates the dimensions of the feature space). The average results of the MAE and RMSE metrics are shown in Table 5 and Table 6, respectively. The performances of precision, recall, and F1 of these methods are shown in Table 7 and Table 8. To prove the validity of the experimental results, we conducted a significance test and list the test results in Table 9. The results indicate that all p values are less than 0.05, thereby demonstrating the high reliability of the experimental results.

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Table 5: MAE and RMSE performance on Small MovieLens dataset

TriFac RSVD BPTF Co-SVD Item-specific

MAE D=30 0.6771 0.6735 0.6764 0.6731 0.7394

D=20 0.6771 0.6738 0.6775 0.6731

D=40 0.6763 0.6724 0.6734 0.6721

D=20 0.8860 0.8820 0.8831 0.8818

RMSE D=30 0.8861 0.8823 0.8810 0.8818 0.9591

D=40 0.8846 0.8805 0.8808 0.8804

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Table 6: MAE and RMSE performance on 10M MovieLens dataset

TriFac RSVD BPTF Co-SVD Item-specific

MAE D=30 0.6097 0.6075 0.6143 0.6061 0.6937

D=20 0.6103 0.6092 0.6139 0.6076

D=40 0.6085 0.6063 0.6141 0.6054

D=20 0.7930 0.7922 0.7994 0.7917

RMSE D=30 0.7908 0.7899 0.8001 0.7899 0.9052

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D=40 0.7899 0.7899 0.7998 0.7890

Table 7: Precision, recall, and F1 performance on Small MovieLens dataset

Precision D=30 0.8457 0.8466 0.7949 0.8473 0.7451

D=40 0.8496 0.8507 0.7970 0.8504

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D=20 0.8420 0.8408 0.7938 0.8410

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D=20 0.7776 0.7776 0.7042 0.7781

Recall D=30 0.7812 0.7844 0.7083 0.7848 0.7324

D=40 0.7857 0.7871 0.7071 0.7899

D=20 0.8085 0.8080 0.7463 0.8083

F1 D=30 0.8122 0.8143 0.7491 0.8149 0.7387

D=40 0.8164 0.8176 0.7494 0.8190

F1 D=30 0.7837 0.8027 0.7765 0.8050 0.7258

D=40 0.7893 0.8052 0.7764 0.8078

Table 8: Precision, recall and F1 performance on 10M MovieLens dataset

D=20 0.8367 0.8342 0.8002 0.8264

Precision D=30 0.8423 0.8387 0.8003 0.8301 0.7325

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Dataset

MAE RMSE Precision Recall F1

D=20 6.03 × 10−4 9.11 × 10−3 3.89 × 10−2 8.34 × 10−4 8.96 × 10−3

D=40 0.8472 0.8414 0.7999 0.8331

D=20 0.7267 0.7651 0.7546 0.7778

Recall D=30 0.7327 0.7696 0.7542 0.7813 0.7194

D=40 0.7388 0.7720 0.7542 0.7840

D=20 0.7778 0.7982 0.7768 0.8014

Table 9: The p value in significance test

small D=30 5.83 × 10−4 1.85 × 10−3 7.14 × 10−3 1.47 × 10−2 1.07 × 10−4

D=40 7.57 × 10−5 4.89 × 10−3 3.90 × 10−2 1.18 × 10−3 5.52 × 10−2 16

D=20 3.98 × 10−8 1.31 × 10−4 3.60 × 10−3 2.08 × 10−3 3.09 × 10−4

10M D=30 2.05 × 10−10 3.81 × 10−4 1.53 × 10−5 2.03 × 10−6 5.62 × 10−5

D=40 6.98 × 10−10 1.50 × 10−4 9.77 × 10−4 7.79 × 10−3 1.76 × 10−2

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4.6. Discussions

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As shown in Table 5 and Table 6, all model-based methods outperform the memorybased method (i.e., item-specific tag preference model) in terms of prediction performance. This suggests that nearest-neighbor-based collaborative filtering algorithms are impressionable to data sparsity, as the neighborhood formation process is hindered by the insufficient training data. Meanwhile, MF-based prediction algorithms can overcome the sparsity problem by exploiting the latent relationships. The results verify the superiority of model-based methods in handling data sparsity. Furthermore, the co-SVD performs better than the RSVD model. The reason is that co-SVD exploits multiple relationships and additional data sources, while RSVD uses only the rating matrix decomposition. Although both the BPTF model and co-SVD model consider time, the rating prediction performance of the co-SVD model is better than that of the BPTF. One possible explanation is that the BPTF model fits the rating matrix by a three-way tensor decomposition, which may aggravate the sparsity problem and reduce the accuracy on rating prediction. In addition, the co-SVD outperforms the TriFac model, although the TriFac model also represents tags, users, and items in the same latent feature space to explore both tag and rating information in an integrated manner. A possible explanation is that the coSVD model exploits more in the various relationships among tags, users, and items than TriFac as introduced in Section 3. The experimental results indicate that the proposed co-SVD outperforms other methods in terms of rating prediction. The results in Table 7 and Table 8 indicate that all model-based methods also outperform the memory-based method (i.e., item-specific tag preference model) in terms of precision and recall. The co-SVD model performs the best in the recall metric and exhibits a slightly lower precision on both the small and 10M MovieLens datasets. The result reflects that the co-SVD can offer comprehensive recommendation results by exploiting additional information sources and various relationships. Although the precision of co-SVD has been sacrificed slightly, it is at the similar level as those of other modelbased methods. The overall performance can be measured by F1, which is a harmonic metric of precision and recall. The co-SVD model exhibits the best F1 score than other models, thus verifying that the overall recommendation quality of the co-SVD is the best. Significance test is a method to detect whether the significant difference emerged between two different variables. In general, if the value from the significance test is less than the value of the significance level, i.e., 0.05, we consider that the difference between the variables is significant. The significance test results shown in Table 9 indicate that the experimental results of the co-SVD model are significantly better than those of other baseline models.

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5. Conclusions and future works Because users use tags to express their focus points and feelings of items, we believe that tag data is an important information source that reflects a user’s interests. To mitigate the negative effects of sparse rating data on the recommended accuracy, tags were used as another link to users and items to identify a user’s tag preferences. The changes in a user’s interests were considered in the proposed co-SVD model using temporal information. By exploring the relations among the users, tags, and items, we factorized three matrices collaboratively. The overfitting problem caused by sparse rating 17

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data could be relieved in the co-factorization owing to the integration of temporal and tagging data. The experimental results on the MovieLens datasets indicated that our co-SVD model was more effective than the baselines, and could improve the accuracy of recommendations. For future work, we will continue our research in the following five directions: (1) We will exploit the various data sources and integrate them into co-SVD to establish a more powerful recommendation model. In addition to the ratings and tags, the reviews from users, content information such as attributes of users or products, and implicit user feedbacks are available in the current web 3.0. (2) Deep learning (LeCun et al., 2015) has been acknowledged as an effective technology with promising performance in many domain-specific applications. We will examine whether matrix decomposition can be adopted in a deep-learning framework for recommendations. (3) As mentioned in Section 3.4, the computational cost of the co-SVD model is relatively high. Clustering can be adopted to reduce the computational cost of co-SVD, as clustering CF algorithms are more efficient by making recommendations within small clusters rather than the whole dataset. (4) To improve the accessibility, efficiency, and ease-of-use of the co-SVD, a cloud-based platform with parallel computing for this model can be built. (5) The core idea of co-SVD is to provide an extensive framework for the integration of additional data sources to address the data sparsity issue, which is highly practical for user-dataintensive applications such as recommendation advertisements, e-commerce sites, and social media platforms in expert and intelligent systems.

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The work described herein was fully supported by the Innovation and Technology Fund (Project No. GHP/022/17GD) from the Innovation and Technology Commission of the Government of the Hong Kong Special Administrative Region, the Funding Support to Early Career Scheme Proposal (RG 23/2017-2018R), the Individual Research Scheme of the Dean’s Research Fund 2017-2018 (FLASS/DRF/IRS-8) and the Internal Research Grant (RG 92/2017-2018R) of The Education University of Hong Kong, a grant from the Research Grants Council of Hong Kong Special Administrative Region, China (UGC/FDS11/E06/14), and the Science and Technology Planning Project of Guangdong Province (No. 2017B050506004). References

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