Unified Embedding Model over Heterogeneous Information Network for Personalized Recommendation

1 Introduction

Recommender system has became an essential part in various internet services as it can help people to tackle the problem of information overload and find useful information with less time. Recently, heterogeneous information network (HIN) based recommendation models attract much attention due to its advantage of modeling complex information [Yu et al., 2013; Shi et al., 2017]. Most HIN based recommendation models use meta-paths [Sun et al., 2011] to mine the semantic relations between users and items. As different metapaths can capture different semantics [Jiang et al., 2018;

∗Corresponding author

Liu et al., 2019] and result in different recommendation lists [Shi et al., 2015], information extracted from different metapaths should be fused properly.

To extract and fuse information from different meta-paths, most of existing methods follow a two-step process. First, they explore and extract information from HINs along each meta-path independently. Secondly, information from different meta-paths are fused and then incorporated in a recommendation model. To extract information under a given metapath, existing methods always use PathSim [Sun et al., 2011] or its variants to measure the semantic relations between users and items [Shi et al., 2015; Han et al., 2018]. However, these methods rely on explicit path reachability, and may fail when path connections are sparse or noisy [Shi et al., 2019]. To fuse information from meta-paths, most methods [Yu et al., 2013; Shi et al., 2016] try to learn a weight vector for meta-paths. However, they always assume the weights on meta-paths are the same for all users without consideration of users' personalized preferences on meta-paths. Recently, [Shi et al., 2019] proposed to learn a separate weight vector on meta-paths for every user. However, this method introduces too many parameters to be learned.

Compared with traditional recommendation model like matrix factorization [Koren et al., 2009], HIN based methods have achieved performance improvement to some extent. However, there still exist two problems for these models. First, they separately model users and items under each meta-path, which assumes users' and items' representations are mutual independent under different meta-paths. This kind of information extraction could be misled and contains some errors, since connections along one meta-path may be sparse or noisy [Shi et al., 2019]. Second, the two-step framework may lead to useful information for recommendation lost irreversibly in the first step. They only aim to model structural features of HINs for information extraction during the first step, then some information which is useful for recommendation but less important for modeling HIN structural features will loss. Moreover, we cannot get the lost information back in the second step, i.e. the information loss is irreversible.

To address the first problem, we assume there exist some common characteristics under different meta-paths for each user or item, and these characteristics can be modeled by latent vectors, i.e. embeddings. Inspired by the translation based model [Bordes et al., 2013] in the knowledge graphs, we embed users and items into one unified latent space, instead of learning a embedding space for users and items independently based on each meta-path. We use data from all meta-paths to learn the unified user and item embeddings, i.e. utilizing the interrelation between meta-paths to alleviate the problems of data sparsity and noises on one meta-path. Following this method even if there is little information about a user based on some meta-paths, information from other metapath is available, which helps to prevent under-fitting or overfitting.

To address the second problem, we combine the two steps (i.e. information extraction and recommendation) into an end-to-end training model to avoid useful information lost in initial phases. Simultaneously optimizing the objectives of both steps can help to distinguish and keep the information useful for recommendation.

In addition, we assume different users have different preferences on meta-paths. Besides users' and items' embeddings, we also learn embeddings of meta-paths themselves, which can reflect characteristics of meta-paths. Based on users' and meta-paths' embeddings, we utilize an attention mechanism [Bahdanau et al., 2015] to measure the preferences of users on meta-paths.

By integrating the above mechanisms, this work presents a HIN based unified embedding model for recommendation, called HueRec. The basic idea for the proposed approach is shown in Fig. 1.

The main contributions of this work can be summarized as follow:

1. Based on meta-paths, we propose an end-to-end information exploring and exploiting framework over heterogeneous information network for top-n recommenda-

tion.

1. We propose a joint learning method to get unified embeddings of users and items from different meta-paths, so information is fused to some extent in the information extraction step.
2. Based on users' and meta-paths' embeddings, the framework can effectively measure users' preferences on meta-paths using an attention mechanism.
3. We conduct extensive experiments on three real-world datasets, which demonstrate the effectiveness of proposed method.

2 Preliminary

2.1 Heterogeneous Information Network

HIN is a kind of information network involving multipletyped objects and multiple-typed links, which is defined as follows:

Definition 1 Heterogeneous Information Network [Sun et al., 2011]. A HIN is a directed graph G = (V, E) with an entity type mapping function φ : V → A and a link type mapping function ϕ : E → R. A and R denote the sets of predefined entity and link types, where |A| + |R| > 2.

Due to the complexity of HINs, we use meta-paths to describe the semantic relations between two nodes.

Definition 2 Meta-path [Sun et al., 2011]. A meta-path p is defined on a network schema TG = (A,R) and is denoted as a path in the form of A1 R1 --→ A2 R2 --→ · · · Rl -→ Al+1 (abbreviated as A1A2 · · · Al+1), which describes a composite relation R = R1 ◦R2 ◦ · · · ◦Rl between object A1 and Al+1, where ◦ denotes the composition operator on relations.

In recommender systems, we only concern users' interests on items. So only meta-paths from USER to ITEM are selected in this paper. To measure connections between users to items based on meta-paths, commuting matrix can be used.

Definition 3 Commuting Matrix [Sun et al., 2011]. Given a network G = (V, E) and its network schema TG, a commuting matrix Cp for a meta-path p = (A1A2 . . .Al) is defined as Cp = WA1A2 WA2A3 . . .WAl-1Al , where WAiAj is the adjacency matrix between type Ai and type Aj . Ci,j,p represents the number of paths instances between object xi ∈ A1 and object yj ∈ Al under meta path p.

2.2 ProblemDefinition

In this paper, we try to solve the personalized recommendation problem based on HINs. We focus on the common scenario with implicit feedback (e.g. clicks, purchases). Compared with explicit feedback data, implicit feedback data is more widespread and easier to be collected [Liu et al., 2018]. With n users U = {u1, · · · , un} and m items I = {i1, · · · , im}, we define implicit user feedback matrix R ∈ Rn×m as follows,

Given a heterogeneous information network G with user feedback matrix R, we aim to recommend a ranked list of items for each user ui according to users' preferences on items.

3 The ProposedModel

3.1 Model Overview

In this section, we present the proposed HIN based unified embedding model for recommendation, called HueRec. The overall framework of this model is shown in Fig.1. We assume there exist common characteristics of users and items under different meta-paths, and use data from all metapaths to learn unified users' and items' representations (Section3.2), as shown in Fig. 1(b). We assume users have different preferences on meta-paths and try to learn this kind of preferences to make better personalized recommendation (Section3.3), as shown in Fig. 1(c). In addition, we propose an end-to-end training method for parameter learning to avoid useful information for recommendation lost during separated information extraction phase (Section3.4).

3.2 Embedding of HIN Information

We regard meta-paths between USER and ITEM as contexts for user-item interactions and assume they contain useful information for the predictions of user-item interactions [Hu et al., 2018]. However, the original commuting matrices of these meta-paths may be sparse or noisy. To extract useful information for user and item modeling, we propose to learn the embedding representations of all users, items and metapaths simultaneously. Therefore, we can use the interrelation information between meta-paths to alleviate the problems of data sparsity and noises on individual meta-paths.

To measure the effectiveness of the embedding representations based on all l meta-paths P = {p1, · · · , pl}, we define a loss function for each user-item pair (u, i) as follows,

where LossHIN u,i,p and wp denote the loss and the corresponding weight of the p-th meta-path, respectively. We assume meta-paths have different importances for recommendation and use weights wp to control the importances. However, the importance of each meta-path for recommendation is unknown during exploring HINs, we remain it to be defined in Section3.3.

The LossHIN u,i,p in Eq. 2 represents the loss function of HIN information extraction under the p-th meta-path. We define it based on the sigmoid cross entropy,

where σ is the sigmoid function. cu,i,p denotes the number of path instances between user u and item i under metapath p, and ̂cu,i,p denotes the corresponding estimated value. average(Cp,u) denotes the average of non-zero values in the u-th row of the meta-path commuting matrix Cp.

We assume the path counts cu,i,p are determine by some latent factors of users, items and meta-paths. Therefore, the key for the estimation is to determine the latent representations. Different from previous methods which assume users and items have different latent representations under different meta-paths, we regard meta-paths as contexts and assume there exist unified latent representations for users and items under different meta-paths. Let eUu ∈ Rd , eIi ∈ Rd , and ePp ∈ Rd denote the latent representations of user u, item i and path p, respectively, where d is the dimension of the latent space. We estimate the path count cu,i,p as follows,

where eUu,q is the q-th bit of the user latent vector eUu and so on.

As a result, the unified embeddings of users and items are shared in all LossHIN u,i,p . For each meta-path p, the HIN information based on p can be extracted into the unified embeddings by minimizing its loss function LossHIN u,i,p . Therefore, by minimizing the aggregated loss function in Equation 2, we can learn common characteristics of users and items on all meta-paths.

3.3 Personalized Preferences onMeta-paths

We assume users' preferences on meta-paths are different. So we need to personalize the weights on meta-paths, and then use them to predict users' interests on items. We utilize an attention mechanism to measure users' personalized preferences on meta-paths. As the data may be sparse for individual users, it may be difficult to directly learn the personalized weights for some users individually. To solve this problem, we propose to integrate data of different users and learns the global weights for meta-paths. So the preference of a user on a meta-path consists of two parts: a global weight and a personalized weight.

We use the weighted sum of scores to predict the interest of a user u on an item i:

where wu,p denotes personal preference of a user u on a metapath p, wGlobal p denotes the global weights on meta-paths, and ̂cu,i,p denotes the estimated score w.r.t. meta-path p as given in Eq. 4. The global weights wGlobal p will be useful for users with little records, whose personalized weight wu,p may be unprecise. Since wGlobal p shows global importance of the meta-path p, it can be used as the weight of p in the HIN information extraction, i.e. wp in Eq. 2. We suppose that for any meta-path, its contribution to information extraction and recommendation should be non-negative and the sum of all weights should be equal to 1. To this end, we define the global weight vector on meta-paths wGlobal = (wGlobal 1 ; · · · ;wGlobal l ) as follow:

where vGlobal ∈ Rl are parameters to be learned.

If we directly take the personalized weights wu,p as parameters to be learned, there will be |U| × |P| parameters to learn. However, training samples are usually insufficient for the weight learning. Following the idea in Section3.2, we assume the personalized weights are determined by some latent factors of users and meta-paths. So we can measure users' preferences on meta-paths with their embedding representations using an attention mechanism. Since users are entities and meta-paths are relations, their embeddings eU , eP should be in different latent spaces [Fu et al., 2017]. Therefore, we need to transform their embeddings into a same space, then take the dot product of transformed embeddings as the measure of users' preferences on meta-paths, then we define personal weight vector wu = (wu,1; · · · ; wu,l) as follow:

whereEP = (eP1 , · · · , ePl ) is the embeddingmatrix of metapaths, and Mua,Mua ∈ Rd×d are the matrices for transforming users and meta-paths into the same attention space, respectively.

The HueRec model generates a recommendation list based on the predictions of users' interests on items. To measure the effectiveness of the preference learning on meta-paths and recommendation results, we define a loss function as follows.

where ru,i represents the implicit feedback of user u to item i. By minimizing the loss function in the Eq. 8, users' preferences on meta-paths can be learned. Embeddings of users, items and meta-paths can also be trained based on implicit feedback data.

3.4 Parameters Learning

To learn the parameters of the proposed model, we design an end-to-end training architecture, which is shown in the Fig. 2. The total objective is to minimize the following loss function:

(9)

where λ1 is the trade-off coefficient to control the importance of the LossHIN . We apply L2 regularization on all parameters Θ to prevent the possible over-fitting and λ2 is the regularization coefficient.

As the final loss function in Equation 9 is differentiable, we adopt gradient descent based algorithms to optimize it. In this paper, we appeal to Adaptive Moment Estimation (Adam) [Kingma and Ba, 2015] to minimize the total loss. It is worth noting that the global weights on meta-paths wG p are only determined by the recommendation loss LossRec . As a result, we exclude the gradient from the LossHIN when calculating the gradient of wG p .

Training all pairs in the Cartesian product of U ×I for full gradient in each update step is not feasible. So we sample X in U × I with equal number of positive samples and negative samples. Then the computational complexity for one iteration training is O(l · d2 · |X|) since Eq. 7 costs O(l · d2 ) training time. Here we implement the HueRec model using the python library of TensorFlow 1 .

4 Experiments

In this section, we first introduce the experimental datasets, evaluation metrics and experimental settings. Then we evaluate the effectiveness of HueRec compared with several stateof-the-art recommendation methods.

1 https://www.tensorflow.org/

4.1 Experimental Setup

Datasets

Three real-world data sets with the rich heterogeneous information is used as experimental data, including Yelp 2 , MovieLens 3 and Douban Movie 4 . The Yelp dataset records users' ratings on local businesses and contains users' social relations and businesses' attribute information. The MovieLens dataset contains users' ratings on movies and some attribute information of movies. The Douban Movie dataset contains user attributes and movie attributes besides users' ratings. Detailed descriptions of the three datasets are shown in Table 1.

We select all meta-paths within three steps , since long meta-paths are likely to introduce more noise than useful information [Sun et al., 2011].

Evaluation Methodology and Metrics

Since we focus on implicit feedback, we adopt the same processing as in [Yu et al., 2014] to treat a rating record as a implicit (positive) feedback if the rating score exists.

Three-fold cross-validation is adopted to better evaluate the performances of different algorithms. The entire implicit feedback records of each dataset are randomly split into three roughly equally sized subsets. Each time, we use two-thirds of feedback records as the training set, the rest one-third as the testing set. The process is repeated three times with each of the three subsets used exactly once as the testing data. Experimental results are recorded as the average of the three runs.

For evaluation metrics, we adopt four widely used evaluation metrics for top-N recommendation [Wang and Blei, 2011; Van den Oord et al., 2013; Hu et al., 2018], including Precision at top k (Prec@k), Recall at top k (Recall@k), Mean Average Precision at top k (MAP@k) and Normalized Discounted Cumulative Gain at top k (NDCG@k). The former two are used to test model's ability of distinguishing items of users' interest, while the latter two focus on the position of preferred items in the ranked list.

2 https://www.yelp.com/dataset challenge

3 https://grouplens.org/datasets/movielens/

4 http://movie.douban.com

Baselines

We compare our model with these following methods:

-MF [Koren et al., 2009]: Matrix factorization (MF) is a commonly used model-based collaborative filtering method.

-BPR [Rendle et al., 2009]: Bayesian Personalized Ranking (BPR) is a typical pairwise learning method to rank for personalized recommendation based on implicit feedback.

-FM [Rendle, 2010]: Factorization machine (FM) models all interactions between each pair of features to estimate the target.

-HeteRec [Yu et al., 2014]: HeteRec is a meta-path similarity based recommendation method. It first apply non-negative matrix factorization on each meta-path, then weighted ensemble all meta-path predicted scores.

-FMGrank [Zhao et al., 2017]: FMG is a state-of-the-art HIN based recommendation model, which adopts a two-stage extraction (MF for HIN) and exploitation (FM for recommendation) process. We modify its optimization objective as pairwise ranking loss as in BPR for top-N recommendation.

-HueRecnoAtt: It is our model without attention mechanism as personalized meta-path weights.

-HueRecnoUni: It is a variant of our model in which we don't embed user and item into a shared latent space. It means we factorize meta-path connection matrix into a user embedding matrix and an item embedding matrix separately based on each meta-path.

4.2 Model Comparison

Experimental Design

We first randomly initialize model parameters with truncated Gaussian distribution with mean value 0 and standard deviation 0.02, then adopt Adaptive Moment Estimation (Adam) optimizer and L2 regularization coefficient λ2 as 0.0001 for all models' optimization for a fair comparison. We set the dimension of embeddings to 64 for all models if needed. For our model, the coefficient λ2 for HIN exploration part is set to 1. For baseline models, we tune their parameters based on authors' implementation if they exist, otherwise we tune to their best.

Experimental Results

Table 2 shows the performances of HueRec and baseline algorithms on different datasets with different evaluation metrics. The major findings from the experimental results are summarized as follows:

(1) Our HueRec model performs consistently better than all baselines on the three datasets according to different evaluation metrics. The results indicate the effectiveness of HueRec to extract HIN information and make top-N recommendation.

(2) Among side-information aware models, FM performs well on the Yelp dataset but fails on MovieLens and Douban Movie datasets. This may be due to the excessive attribute features in the latter two datasets. For example, MovieLens

.

has 10k movies while over 20k actors, which imports too much noise. While HIN based methods (HeteRec, FMG, HueRec) performs more stably on the latter two datasets, because they only focus on attribute sharing relations instead of what these attributes exactly are. This demonstrates the advantage of HIN based models.

(3) As a two step model, HeteRec and FMG perform poorly on the Yelp dataset. This may be caused by the sparsity of the Yelp dataset. Some errors may occur in the information extraction step, which may mislead the following recommendation model.

(4) Our complete model HueRec performs consistently better than the two variants HueRecnoAtt and HueRecnoUni.

This confirms that it is essential to embed users and items into a unified latent space based on all meta-paths, and to personalize the weights on meta-paths.

4.3 Hyper-Parameter Study

The weight of HIN exploration part λ1 is an important parameter for the proposed model HueRec. It determines the relative importance of information extracted from HINs for user and item modeling. When λ1 is large, we model users and items mainly based on structural features of HINs. Otherwise, we model users and items mainly based on historical behaviors. Fig. 3 shows the performances of HueRec with different λ1. When the weight is small (less than 10 for Yelp or 1 for MovieLens and Douban Movies), performances become better as the increasing of the weight. It indicates that extracting information from HIN is helpful to recommendation. When the weight continues to increase, performances become worse, which means not only useful information but also some noises have been extracted. To make a better trade-off for the model, we suggest to set the HIN exploration weight as 1.

5 Conclusion

In this paper, we propose an HIN based unified embedding model for recommendation,i.e. HueRec. We design a method to learn unified embeddings, which can extract and fuse information from different meta-paths. We use an attention mechanism to combine predicted scores of different meta-paths. Furtherly, we conduct information extraction and recommendation simultaneously to alleviate information loss. Extensive experiments on three real datasets demonstrated the effectiveness of HueRec.

As future work, we would like to design a more sophisticated model, in place of the weighted linear sum in the recommendation part, to further improve the recommendation performance.

Acknowledgements

This work was partially sponsored by National Natural Science Foundation of China (Grant No. 61672062), National 863 Program of China (Grant No. 2015AA016009) and Delta Innovation Research Program.