Multi-Task Feature Learning for Knowledge Graph Enhanced Recommendation

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.

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1. Introduction

Recommender systems (RS) aims to address the information explosion and meet users personalized interests. One of the most popular recommendation techniques is collaborative filtering (CF) (Koren et al., 2009), which utilizes users’ historical interactions and makes recommendations based on their common preferences. However, CF-based methods usually suffer from the sparsity of user-item interactions and the cold start problem. Therefore, researchers propose using side information in recommender systems, including social networks (Jamali and Ester, 2010), attributes (Wang et al., 2018b), and multimedia (e.g., texts (Wang et al., 2015), images (Zhang et al., 2016)). Knowledge graphs (KGs) are one type of side information for RS, which usually contain fruitful facts and connections about items. Recently, researchers have proposed several academic and commercial KGs, such as NELL111http://rtw.ml.cmu.edu/rtw/, DBpedia222http://wiki.dbpedia.org/, Google Knowledge Graph333https://developers.google.com/knowledge-graph/ and Microsoft Satori444https://searchengineland.com/library/bing/bing-satori. Due to its high dimensionality and heterogeneity, a KG is usually pre-processed by knowledge graph embedding (KGE) methods (Wang et al., 2018a)

, which embeds entities and relations into low-dimensional vector spaces while preserving its inherent structure.

Existing KG-aware methods

Inspired by the success of applying KG in a wide variety of tasks, researchers have recently tried to utilize KG to improve the performance of recommender systems (Yu et al., 2014; Zhao et al., 2017; Wang et al., 2018d; Wang et al., 2018c; Zhang et al., 2016). Personalized Entity Recommendation (PER) (Yu et al., 2014) and Factorization Machine with Group lasso (FMG) (Zhao et al., 2017) treat KG as a heterogeneous information network, and extract meta-path/meta-graph based latent features to represent the connectivity between users and items along different types of relation paths/graphs. It should be noted that PER and FMG rely heavily on manually designed meta-paths/meta-graphs, which limits its application in generic recommendation scenarios. Deep Knowledge-aware Network (DKN) (Wang et al., 2018d) designs a CNN framework to combine entity embeddings with word embeddings for news recommendation. However, the entity embeddings are required in advance of using DKN, causing DKN to lack an end-to-end way of training. Another concern about DKN is that it can hardly incorporate side information other than texts. RippleNet (Wang et al., 2018c) is a memory-network-like model that propagates users’ potential preferences in the KG and explores their hierarchical interests. But the importance of relations is weakly characterized in RippleNet, because the embedding matrix of a relation can hardly be trained to capture the sense of importance in the quadratic form ( and are embedding vectors of two entities). Collaborative Knowledge base Embedding (CKE) (Zhang et al., 2016) combines CF with structural knowledge, textual knowledge, and visual knowledge in a unified framework. However, the KGE module in CKE (i.e., TransR (Lin et al., 2015)) is more suitable for in-graph applications (such as KG completion and link prediction) rather than recommendation. In addition, the CF module and the KGE module are loosely coupled in CKE under a Bayesian framework, making the supervision from KG less obvious for recommender systems.

The proposed approach

To address the limitations of previous work, we propose MKR, a multi-task learning (MTL) approach for knowledge graph enhanced recommendation. MKR is a generic, end-to-end deep recommendation framework, which aims to utilize KGE task to assist recommendation task555KGE task can also benefit from recommendation task empirically as shown in the experiments section.. Note that the two tasks are not mutually independent, but are highly correlated since an item in RS may associate with one or more entities in KG. Therefore, an item and its corresponding entity are likely to have a similar proximity structure in RS and KG, and share similar features in low-level and non-task-specific latent feature spaces (Long et al., 2017). We will further validate the similarity in the experiments section. To model the shared features between items and entities, we design a crosscompress unit in MKR. The crosscompress unit explicitly models high-order interactions between item and entity features, and automatically control the cross knowledge transfer for both tasks. Through crosscompress units, representations of items and entities can complement each other, assisting both tasks in avoiding fitting noises and improving generalization. The whole framework can be trained by alternately optimizing the two tasks with different frequencies, which endows MKR with high flexibility and adaptability in real recommendation scenarios.

We probe the expressive capability of MKR and show, through theoretical analysis, that the crosscompress unit is capable of approximating sufficiently high order feature interactions between items and entities. We also show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning, including factorization machines (Rendle, 2010, 2012), deepcross network (Wang et al., 2017a), and cross-stitch network (Misra et al., 2016). Empirically, we evaluate our method in four recommendation scenarios, i.e., movie, book, music, and news recommendations. The results demonstrate that MKR achieves substantial gains over state-of-the-art baselines in both click-through rate (CTR) prediction (e.g., improvements on average for movies) and top- recommendation (e.g., improvements on average for books). MKR can also maintain a decent performance in sparse scenarios.

Contribution

It is worth noticing that the problem studied in this paper can also be modelled as cross-domain recommendation (Tang et al., 2012) or transfer learning (Pan et al., 2010)

, since we care more about the performance of recommendation task. However, the key observation is that though cross-domain recommendation and transfer learning have single objective for the target domain, their loss functions still contain constraint terms for measuring data distribution in the source domain or similarity between two domains. In our proposed MKR, the KGE task serves as the constraint term

explicitly to provide regularization for recommender systems. We would like to emphasize that the major contribution of this paper is exactly modeling the problem as multi-task learning: We go a step further than cross-domain recommendation and transfer learning by finding that the inter-task similarity is helpful to not only recommender systems but also knowledge graph embedding, as shown in theoretical analysis and experiment results.

2. Our Approach

In this section, we first formulate the knowledge graph enhanced recommendation problem, then introduce the framework of MKR and present the design of the crosscompress unit, recommendation module and KGE module in detail. We lastly discuss the learning algorithm for MKR.

(a) Framework of MKR
(b) Crosscompress unit
Figure 1. (a) The framework of MKR. The left and right part illustrate the recommendation module and the KGE module, respectively, which are bridged by the crosscompress units. (b) Illustration of a crosscompress unit. The crosscompress unit generates a cross feature matrix from item and entity vectors by cross operation, and outputs their vectors for the next layer by compress operation.

2.1. Problem Formulation

We formulate the knowledge graph enhanced recommendation problem in this paper as follows. In a typical recommendation scenario, we have a set of users and a set of items . The user-item interaction matrix is defined according to users’ implicit feedback, where indicates that user engaged with item , such as behaviors of clicking, watching, browsing, or purchasing; otherwise . Additionally, we also have access to a knowledge graph , which is comprised of entity-relation-entity triples . Here , , and denote the head, relation, and tail of a knowledge triple, respectively. For example, the triple (Quentin Tarantino, film.director.film, Pulp Fiction) states the fact that Quentin Tarantino directs the film Pulp Fiction. In many recommendation scenarios, an item may associate with one or more entities in . For example, in movie recommendation, the item ”Pulp Fiction” is linked with its namesake in a KG, while in news recommendation, news with the title ”Trump pledges aid to Silicon Valley during tech meeting” is linked with entities ”Donald Trump” and ”Silicon Valley” in a KG.

Given the user-item interaction matrix as well as the knowledge graph , we aim to predict whether user has potential interest in item with which he has had no interaction before. Our goal is to learn a prediction function , where

denotes the probability that user

will engage with item , and is the model parameters of function .

2.2. Framework

The framework of MKR is illustrated in Figure 0(a). MKR consists of three main components: recommendation module, KGE module, and cross

compress units. (1) The recommendation module on the left takes a user and an item as input, and uses a multi-layer perceptron (MLP) and cross

compress units to extract short and dense features for the user and the item, respectively. The extracted features are then fed into another MLP together to output the predicted probability. (2) Similar to the left part, the KGE module in the right part also uses multiple layers to extract features from the head and relation of a knowledge triple, and outputs the representation of the predicted tail under the supervision of a score function and the real tail. (3) The recommendation module and the KGE module are bridged by specially designed crosscompress units. The proposed unit can automatically learn high-order feature interactions of items in recommender systems and entities in the KG.

2.3. Crosscompress Unit

To model feature interactions between items and entities, we design a crosscompress unit in MKR framework. As shown in Figure 0(b), for item and one of its associated entities , we first construct pairwise interactions of their latent feature and from layer :

(1)

where is the cross feature matrix of layer , and is the dimension of hidden layers. This is called the cross operation, since each possible feature interaction between item and its associated entity is modeled explicitly in the cross feature matrix. We then output the feature vectors of items and entities for the next layer by projecting the cross feature matrix into their latent representation spaces:

(2)

where and

are trainable weight and bias vectors. This is called the

compress operation, since the weight vectors project the cross feature matrix from space back to the feature spaces . Note that in Eq. (2), the cross feature matrix is compressed along both horizontal and vertical directions (by operating on and ) for the sake of symmetry, but we will provide more insights of the design in Section 3.2. For simplicity, the crosscompress unit is denoted as:

(3)

and we use a suffix or to distinguish its two outputs in the following of this paper. Through crosscompress units, MKR can adaptively adjust the weights of knowledge transfer and learn the relevance between the two tasks.

It should be noted that crosscompress units should only exist in low-level layers of MKR, as shown in Figure 0(a). This is because: (1) In deep architectures, features usually transform from general to specific along the network, and feature transferability drops significantly in higher layers with increasing task dissimilarity (Yosinski et al., 2014). Therefore, sharing high-level layers risks to possible negative transfer, especially for the heterogeneous tasks in MKR. (2) In high-level layers of MKR, item features are mixed with user features, and entity features are mixed with relation features. The mixed features are not suitable for sharing since they have no explicit association.

2.4. Recommendation Module

The input of the recommendation module in MKR consists of two raw feature vectors and that describe user and item , respectively. and can be customized as one-hot ID (He et al., 2017), attributes (Wang et al., 2018b), bag-of-words (Wang et al., 2015), or their combinations, based on the application scenario. Given user ’s raw feature vector , we use an -layer MLP to extract his latent condensed feature666We use the exponent notation in Eq. (4) and following equations in the rest of this paper for simplicity, but note that the parameters of layers are actually different.:

(4)

where

is a fully-connected neural network layer

777Exploring a more elaborate design of layers in the recommendation module is an important direction of future work. with weight , bias

, and nonlinear activation function

. For item , we use crosscompress units to extract its feature:

(5)

where is the set of associated entities of item .

After having user ’s latent feature and item ’s latent feature , we combine the two pathways by a predicting function , for example, inner product or an -layer MLP. The final predicted probability of user engaging item is:

(6)

2.5. Knowledge Graph Embedding Module

Knowledge graph embedding is to embed entities and relations into continuous vector spaces while preserving their structure. Recently, researchers have proposed a great many KGE methods, including translational distance models (Bordes et al., 2013; Lin et al., 2015) and semantic matching models (Nickel et al., 2016; Liu et al., 2017). In MKR, we propose a deep semantic matching architecture for KGE module. Similar to the recommendation module, for a given knowledge triple , we first utilize multiple crosscompress units and nonlinear layers to process the raw feature vectors of head and relation (including ID (Lin et al., 2015), types (Xie et al., 2016), textual description (Wang et al., 2014), etc.), respectively. Their latent features are then concatenated together, followed by a -layer MLP for predicting tail :

(7)

where is the set of associated items of entity , and is the predicted vector of tail . Finally, the score of the triple is calculated using a score (similarity) function :

(8)

where is the real feature vector of . In this paper, we use the normalized inner product as the choice of score function (Misra et al., 2016)

, but other forms of (dis)similarity metrics can also be applied here such as Kullback–Leibler divergence.

2.6. Learning Algorithm

The complete loss function of MKR is as follows:

(9)

In Eq. (9), the first term measures loss in the recommendation module, where and traverse the set of users and the items, respectively, and is the cross-entropy function. The second term calculates the loss in the KGE module, in which we aim to increase the score for all true triples while reducing the score for all false triples. The last item is the regularization term for preventing over-fitting, and are the balancing parameters.888 can be seen as the ratio of two learning rates for the two tasks.

Note that the loss function in Eq. (9) traverses all possible user-item pairs and knowledge triples. To make computation more efficient, following (Mikolov et al., 2013), we use a negative sampling strategy during training.

1:Interaction matrix , knowledge graph
2:Prediction function
3:Initialize all parameters
4:for number of training iteration do
5: // recommendation task
6:   for  steps do
7:      Sample minibatch of positive and negative interactions from ;
8:      Sample for each item in the minibatch;
9:      Update parameters of by gradient descent on Eq. (1)-(6), (9);
10:   end for
11: // knowledge graph embedding task
12:   Sample minibatch of true and false triples from ;
13:   Sample for each head in the minibatch;
14:   Update parameters of by gradient descent on Eq. (1)-(3), (7)-(9);
15:end for
Algorithm 1 Multi-Task Training for MKR

The learning algorithm of MKR is presented in Algorithm 1, in which a training epoch consists of two stages: recommendation task (line 3-7) and KGE task (line 8-10). In each iteration, we repeat training on recommendation task for

times ( is a hyper-parameter and normally ) before training on KGE task once in each epoch, since we are more focused on improving recommendation performance. We will discuss the choice of in the experiments section.

3. Theoretical Analysis

In this section, we prove that crosscompress units have sufficient capability of polynomial approximation. We also show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning.

3.1. Polynomial Approximation

According to the Weierstrass approximation theorem (Rudin et al., 1964), any function under certain smoothness assumption can be approximated by a polynomial to an arbitrary accuracy. Therefore, we examine the ability of high-order interaction approximation of the crosscompress unit. We show that crosscompress units can model the order of item-entity feature interaction up to exponential degree:

Theorem 1 ().

Denote the input of item and entity in MKR network as and , respectively. Then the cross terms about and in and (the L1-norm of and ) with maximal degree is , where , for , , and ().

In recommender systems, is also called combinatorial feature, as it measures the interactions of multiple original features. Theorem 1 states that crosscompress units can automatically model the combinatorial features of items and entities for sufficiently high order, which demonstrates the superior approximation capacity of MKR as compared with existing work such as WideDeep (Cheng et al., 2016), factorization machines (Rendle, 2010, 2012) and DCN (Wang et al., 2017a). The proof of Theorem 1 is provided in the Appendix. Note that Theorem 1 gives a theoretical view of the polynomial approximation ability of the crosscompress unit rather than providing guarantees on its actual performance. We will empirically evaluate the crosscompress unit in the experiments section.

3.2. Unified View of Representative Methods

In the following we provide a unified view of several representative models in recommender systems and multi-task learning, by showing that they are restricted versions of or theoretically related to MKR. This justifies the design of crosscompress unit and conceptually explains its strong empirical performance as compared to baselines.

3.2.1. Factorization machines

Factorization machines (Rendle, 2010, 2012)

are a generic method for recommender systems. Given an input feature vector, FMs model all interactions between variables in the input vector using factorized parameters, thus being able to estimate interactions in problems with huge sparsity such as recommender systems. The model equation for a 2-degree factorization machine is defined as

(10)

where is the -th unit of input vector , is weight scalar, is weight vector, and is dot product of two vectors. We show that the essence of FM is conceptually similar to an 1-layer crosscompress unit:

Proposition 0 ().

The L1-norm of and can be written as the following form:

(11)

where is the sum of two scalars.

It is interesting to notice that, instead of factorizing the weight parameter of into the dot product of two vectors as in FM, the weight of term is factorized into the sum of two scalars in crosscompress unit to reduce the number of parameters and increase robustness of the model.

3.2.2. DeepCross Network

DCN (Wang et al., 2017a) learns explicit and high-order cross features by introducing the layers:

(12)

where , , and are representation, weight, and bias of the -th layer. We demonstrate the link between DCN and MKR by the following proposition:

Proposition 0 ().

In the formula of in Eq. (2), if we restrict in the first term to satisfy and restrict in the second term to be (and impose similar restrictions on ), the crosscompress unit is then conceptually equivalent to DCN layer in the sense of multi-task learning:

(13)

It can be proven that the polynomial approximation ability of the above DCN-equivalent version (i.e., the maximal degree of cross terms in and ) is , which is weaker than original crosscompress units with approximation ability.

3.2.3. Cross-stitch Networks

Cross-stitch networks (Misra et al., 2016) is a multi-task learning model in convolutional networks, in which the designed cross-stitch unit can learn a combination of shared and task-specific representations between two tasks. Specifically, given two activation maps and from layer for both the tasks, cross-stitch networks learn linear combinations and of both the input activations and feed these combinations as input to the next layers’ filters. The formula at location in the activation map is

(14)

where ’s are trainable transfer weights of representations between task A and task B. We show that the cross-stitch unit in Eq. (14) is a simplified version of our crosscompress unit by the following proposition:

Proposition 0 ().

If we omit all biases in Eq. (2), the crosscompress unit can be written as

(15)

The transfer matrix in Eq. (15) serves as the cross-stitch unit in Eq. (14). Like cross-stitch networks, MKR network can decide to make certain layers task specific by setting () or () to zero, or choose a more shared representation by assigning a higher value to them. But the transfer matrix is more fine-grained in crosscompress unit, because the transfer weights are replaced from scalars to dot products of two vectors. It is rather interesting to notice that Eq. (15) can also be regarded as an attention mechanism (Bahdanau et al., 2015), as the computation of transfer weights involves the feature vectors and themselves.

4. Experiments

In this section, we evaluate the performance of MKR in four real-world recommendation scenarios: movie, book, music, and news999The source code is available at https://github.com/hwwang55/MKR..

Dataset # users # items # interactions # KG triples Hyper-parameters
MovieLens-1M 6,036 2,347 753,772 20,195 , , ,
Book-Crossing 17,860 14,910 139,746 19,793 , , ,
Last.FM 1,872 3,846 42,346 15,518 = 2, , ,
Bing-News 141,487 535,145 1,025,192 1,545,217 , , ,
Table 1. Basic statistics and hyper-parameter settings for the four datasets.

4.1. Datasets

We utilize the following four datasets in our experiments:

Since MovieLens-1M, Book-Crossing, and Last.FM are explicit feedback data (Last.FM provides the listening count as weight for each user-item interaction), we transform them into implicit feedback where each entry is marked with 1 indicating that the user has rated the item positively, and sample an unwatched set marked as 0 for each user. The threshold of positive rating is 4 for MovieLens-1M, while no threshold is set for Book-Crossing and Last.FM due to their sparsity.

We use Microsoft Satori to construct the KG for each dataset. We first select a subset of triples from the whole KG with a confidence level greater than 0.9. For MovieLens-1M and Book-Crossing, we additionally select a subset of triples from the sub-KG whose relation name contains ”film” or ”book” respectively to further reduce KG size.

Given the sub-KGs, for MovieLens-1M, Book-Crossing, and Last.FM, we collect IDs of all valid movies, books, or musicians by matching their names with tail of triples (head, film.film.name, tail), (head, book.book.title, tail), or (head, type.object.name, tail), respectively. For simplicity, items with no matched or multiple matched entities are excluded. We then match the IDs with the head and tail of all KG triples and select all well-matched triples from the sub-KG. The constructing process is similar for Bing-News except that: (1) we use entity linking tools to extract entities in news titles; (2) we do not impose restrictions on the names of relations since the entities in news titles are not within one particular domain. The basic statistics of the four datasets are presented in Table 1. Note that the number of users, items, and interactions are smaller than original datasets since we filtered out items with no corresponding entity in the KG.

4.2. Baselines

We compare our proposed MKR with the following baselines. Unless otherwise specified, the hyper-parameter settings of baselines are the same as reported in their original papers or as default in their codes.

  • PER (Yu et al., 2014) treats the KG as heterogeneous information networks and extracts meta-path based features to represent the connectivity between users and items. In this paper, we use manually designed user-item-attribute-item paths as features, i.e., ”user-movie-director-movie”, ”user-movie-genre-movie”, and ”user-movie-star-movie” for MovieLens-20M; ”user-book-author-book” and ”user-book-genre-book” for Book-Crossing; ”user-musician-genre-musician”, ”user-musician-country-musician”, and ”user-musician-age-musician” (age is discretized) for Last.FM. Note that PER cannot be applied to news recommendation because it’s hard to pre-define meta-paths for entities in news.

  • CKE (Zhang et al., 2016) combines CF with structural, textual, and visual knowledge in a unified framework for recommendation. We implement CKE as CF plus structural knowledge module in this paper. The dimension of user and item embeddings for the four datasets are set as 64, 128, 32, 64, respectively. The dimension of entity embeddings is .

  • DKN (Wang et al., 2018d) treats entity embedding and word embedding as multiple channels and combines them together in CNN for CTR prediction. In this paper, we use movie/book names and news titles as textual input for DKN. The dimension of word embedding and entity embedding is 64, and the number of filters is 128 for each window size 1, 2, 3.

  • RippleNet (Wang et al., 2018c) is a memory-network-like approach that propagates users’ preferences on the knowledge graph for recommendation. The hyper-parameter settings for Last.FM are , , , , .

  • LibFM (Rendle, 2012) is a widely used feature-based factorization model. We concatenate the raw features of users and items as well as the corresponding averaged entity embeddings learned from TransR (Lin et al., 2015) as input for LibFM. The dimension is {1, 1, 8} and the number of training epochs is 50. The dimension of TransR is 32.

  • WideDeep (Cheng et al., 2016) is a deep recommendation model combining a (wide) linear channel with a (deep) nonlinear channel. The input for WideDeep is the same as in LibFM. The dimension of user, item, and entity is 64, and we use a two-layer deep channel with dimension of 100 and 50 as well as a wide channel.

(a) RS to KG
(b) KG to RS
Figure 2. The correlation between the number of common neighbors of an item pair in KG and their number of common raters in RS.
Model MovieLens-1M Book-Crossing Last.FM Bing-News
PER 0.710 (-22.6%) 0.664 (-21.2%) 0.623 (-15.1%) 0.588 (-16.7%) 0.633 (-20.6%) 0.596 (-20.7%) - -
CKE 0.801 (-12.6%) 0.742 (-12.0%) 0.671 (-8.6%) 0.633 (-10.3%) 0.744 (-6.6%) 0.673 (-10.5%) 0.553 (-19.7%) 0.516 (-20.0%)
DKN 0.655 (-28.6%) 0.589 (-30.1%) 0.622 (-15.3%) 0.598 (-15.3%) 0.602 (-24.5%) 0.581 (-22.7%) 0.667 (-3.2%) 0.610 (-5.4%)
RippleNet 0.920 (+0.3%) 0.842 (-0.1%) 0.729 (-0.7%) 0.662 (-6.2%) 0.768 (-3.6%) 0.691 (-8.1%) 0.678 (-1.6%) 0.630 (-2.3%)
LibFM 0.892 (-2.7%) 0.812 (-3.7%) 0.685 (-6.7%) 0.640 (-9.3%) 0.777 (-2.5%) 0.709 (-5.7%) 0.640 (-7.1%) 0.591 (-8.4%)
WideDeep 0.898 (-2.1%) 0.820 (-2.7%) 0.712 (-3.0%) 0.624 (-11.6%) 0.756 (-5.1%) 0.688 (-8.5%) 0.651 (-5.5%) 0.597 (-7.4%)
MKR 0.917 0.843 0.734 0.704 0.797 0.752 0.689 0.645
MKR-1L - - - - 0.795 (-0.3%) 0.749 (-0.4%) 0.680 (-1.3%) 0.631 (-2.2%)
MKR-DCN 0.883 (-3.7%) 0.802 (-4.9%) 0.705 (-4.3%) 0.676 (-4.2%) 0.778 (-2.4%) 0.730 (-2.9%) 0.671 (-2.6%) 0.614 (-4.8%)
MKR-stitch 0.905 (-1.3%) 0.830 (-1.5%) 0.721 (-2.2%) 0.682 (-3.4%) 0.772 (-3.1%) 0.725 (-3.6%) 0.674 (-2.2%) 0.621 (-3.7%)
Table 2. The results of and in CTR prediction.

4.3. Experiments setup

In MKR, we set the number of high-level layers , as inner product, and for all three datasets, and other hyper-parameter are given in Table 1. The settings of hyper-parameters are determined by optimizing on a validation set. For each dataset, the ratio of training, validation, and test set is . Each experiment is repeated times, and the average performance is reported. We evaluate our method in two experiment scenarios: (1) In click-through rate (CTR) prediction, we apply the trained model to each piece of interactions in the test set and output the predicted click probability. We use and to evaluate the performance of CTR prediction. (2) In top- recommendation, we use the trained model to select items with highest predicted click probability for each user in the test set, and choose and to evaluate the recommended sets.

(a) MovieLens-1M
(b) Book-Crossing
(c) Last.FM
(d) Bing-News
Figure 3. The results of in top- recommendation.
(a) MovieLens-1M
(b) Book-Crossing
(c) Last.FM
(d) Bing-News
Figure 4. The results of in top- recommendation.

4.4. Empirical study

We conduct an empirical study to investigate the correlation of items in RS and their corresponding entities in KG. Specifically, we aim to reveal how the number of common neighbors of an item pair in KG changes with their number of common raters in RS. To this end, we first randomly sample 1 million item pairs from MovieLens-1M. We then classify each pair into 5 categories based on the number of their common raters in RS, and count their average number of common neighbors in KG for each category. The result is presented in Figure

1(a), which clearly shows that if two items have more common raters in RS, they are likely to share more common neighbors in KG. Figure 1(b) shows the positive correlation from an opposite direction. The above findings empirically demonstrate that items share the similar structure of proximity in KG and RS, thus the cross knowledge transfer of items benefits both recommendation and KGE tasks in MKR.

4.5. Results

4.5.1. Comparison with baselines

The results of all methods in CTR prediction and top- recommendation are presented in Table 2 and Figure 3, 4, respectively. We have the following observations:

  • PER performs poor on movie, book, and music recommendation because the user-defined meta-paths can hardly be optimal in reality. Moreover, PER cannot be applied to news recommendation.

  • CKE performs better in movie, book, and music recommendation than news. This may be because MovieLens-1M, Book-Crossing, and Last.FM are much denser than Bing-News, which is more favorable for the collaborative filtering part in CKE.

  • DKN performs best in news recommendation compared with other baselines, but performs worst in other scenarios. This is because movie, book, and musician names are too short and ambiguous to provide useful information.

  • RippleNet performs best among all baselines, and even outperforms MKR on MovieLens-1M. This demonstrates that RippleNet can precisely capture user interests, especially in the case where user-item interactions are dense. However, RippleNet is more sensitive to the density of datasets, as it performs worse than MKR in Book-Crossing, Last.FM, and Bing-News. We will further study their performance in sparse scenarios in Section 4.5.3.

  • In general, our MKR performs best among all methods on the four datasets. Specifically, MKR achieves average gains of , , , and in movie, book, music, and news recommendation, respectively, which demonstrates the efficacy of the multi-task learning framework in MKR. Note that the top- metrics are much lower for Bing-News because the number of news is significantly larger than movies, books, and musicians.

Model
PER 0.598 0.607 0.621 0.638 0.647 0.662 0.675 0.688 0.697 0.710
CKE 0.674 0.692 0.705 0.716 0.739 0.754 0.768 0.775 0.797 0.801
DKN 0.579 0.582 0.589 0.601 0.612 0.620 0.631 0.638 0.646 0.655
RippleNet 0.843 0.851 0.859 0.862 0.870 0.878 0.890 0.901 0.912 0.920
LibFM 0.801 0.810 0.816 0.829 0.837 0.850 0.864 0.875 0.886 0.892
WideDeep 0.788 0.802 0.809 0.815 0.821 0.840 0.858 0.876 0.884 0.898
MKR 0.868 0.874 0.881 0.882 0.889 0.897 0.903 0.908 0.913 0.917
Table 3. Results of on MovieLens-1M in CTR prediction with different ratios of training set .

4.5.2. Comparison with MKR variants

We further compare MKR with its three variants to demonstrate the efficacy of crosscompress unit:

  • MKR-1L is MKR with one layer of crosscompress unit, which corresponds to FM model according to Proposition 2. Note that MKR-1L is actually MKR in the experiments for MovieLens-1M.

  • MKR-DCN is a variant of MKR based on Eq. (13), which corresponds to DCN model.

  • MKR-stitch is another variant of MKR corresponding to the cross-stitch network, in which the transfer weights in Eq. (15) are replaced by four trainable scalars.

From Table 2 we observe that MKR outperforms MKR-1L and MKR-DCN, which shows that modeling high-order interactions between item and entity features is helpful for maintaining decent performance. MKR also achieves better scores than MKR-stitch. This validates the efficacy of fine-grained control on knowledge transfer in MKR compared with the simple cross-stitch units.

(a) KG size
(b) Training frequency
(c) Dimension of embeddings
Figure 5. Parameter sensitivity of MKR on Bing-News w.r.t. (a) the size of the knowledge graph; (b) training frequency of the RS module ; and (c) dimension of embeddings .
dataset KGE KGE + RS
MovieLens-1M 0.319 0.302
Book-Crossing 0.596 0.558
Last.FM 0.480 0.471
Bing-News 0.488 0.459
Table 4. The results of on the KGE module for the three datasets. ”KGE” means only KGE module is trained, while ”KGE + RS” means KGE module and RS module are trained together.

4.5.3. Results in sparse scenarios

One major goal of using knowledge graph in MKR is to alleviate the sparsity and the cold start problem of recommender systems. To investigate the efficacy of the KGE module in sparse scenarios, we vary the ratio of training set of MovieLens-1M from to (while the validation and test set are kept fixed), and report the results of in CTR prediction for all methods. The results are shown in Table 3. We observe that the performance of all methods deteriorates with the reduce of the training set. When , the score decreases by , , , , , for PER, CKE, DKN, RippleNet, LibFM, and WideDeep, respectively, compared with the case when full training set is used (). In contrast, the score of MKR only decreases by , which demonstrates that MKR can still maintain a decent performance even when the user-item interaction is sparse. We also notice that MKR performs better than RippleNet in sparse scenarios, which is accordance with our observation in Section 4.5.1 that RippleNet is more sensitive to the density of user-item interactions.

4.5.4. Results on KGE side

Although the goal of MKR is to utilize KG to assist with recommendation, it is still interesting to investigate whether the RS task benefits the KGE task, since the principle of multi-task learning is to leverage shared information to help improve the performance of all tasks (Zhang and Yang, 2017). We present the result of (rooted mean square error) between predicted and real vectors of tails in the KGE task in Table 4. Fortunately, we find that the existence of RS module can indeed reduce the prediction error by . The results show that the crosscompress units are able to learn general and shared features that mutually benefit both sides of MKR.

4.6. Parameter Sensitivity

4.6.1. Impact of KG size

We vary the size of KG to further investigate the efficacy of usage of KG. The results of on Bing-News are plotted in Figure 4(a). Specifically, the and is enhanced by and with the KG ratio increasing from to in three scenarios, respectively. This is because the Bing-News dataset is extremely sparse, making the effect of KG usage rather obvious.

4.6.2. Impact of RS training frequency

We investigate the influence of parameters in MKR by varying from 1 to 10, while keeping other parameters fixed. The results are presented in Figure 4(b). We observe that MKR achieves the best performance when . This is because a high training frequency of the KGE module will mislead the objective function of MKR, while too small of a training frequency of KGE cannot make full use of the transferred knowledge from the KG.

4.6.3. Impact of embedding dimension

We also show how the dimension of users, items, and entities affects the performance of MKR in Figure 4(c). We find that the performance is initially improved with the increase of dimension, because more bits in embedding layer can encode more useful information. However, the performance drops when the dimension further increases, as too large number of dimensions may introduce noises which mislead the subsequent prediction.

5. Related Work

5.1. Knowledge Graph Embedding

The KGE module in MKR connects to a large body of work in KGE methods. KGE is used to embed entities and relations in a knowledge into low-dimensional vector spaces while still preserving the structural information (Wang et al., 2017b). KGE methods can be classified into the following two categories: (1) Translational distance models exploit distance-based scoring functions when learning representations of entities and relations, such as TransE (Bordes et al., 2013), TransH (Wang et al., 2014), and TransR (Lin et al., 2015); (2) Semantic matching models measure plausibility of knowledge triples by matching latent semantics of entities and relations, such as RESCAL (Nickel et al., 2011), ANALOGY (Nickel et al., 2016), and HolE (Liu et al., 2017). Recently, researchers also propose incorporating auxiliary information, such as entity types (Xie et al., 2016), logic rules (Rocktäschel et al., 2015), and textual descriptions (Zhong et al., 2015) to assist KGE. The above KGE methods can also be incorporated into MKR as the implementation of the KGE module, but note that the crosscompress unit in MKR needs to be redesigned accordingly. Exploring other designs of KGE module as well as the corresponding bridging unit is also an important direction of future work.

5.2. Multi-Task Learning

Multi-task learning is a learning paradigm in machine learning and its aim is to leverage useful information contained in multiple related tasks to help improve the generalization performance of all the tasks

(Zhang and Yang, 2017). All of the learning tasks are assumed to be related to each other, and it is found that learning these tasks jointly can lead to performance improvement compared with learning them individually. In general, MTL algorithms can be classified into several categories, including feature learning approach (Zhang et al., 2015; Wang et al., 2017a), low-rank approach (Han and Zhang, 2016; McDonald et al., 2014), task clustering approach (Zhou and Zhao, 2016), task relation learning approach (Lee et al., 2016), and decomposition approach (Han and Zhang, 2015). For example, the cross-stitch network (Zhang et al., 2015) determines the inputs of hidden layers in different tasks by a knowledge transfer matrix; Zhou et. al (Zhou and Zhao, 2016) aims to cluster tasks by identifying representative tasks which are a subset of the given tasks, i.e., if task is selected by task as a representative task, then it is expected that model parameters for are similar to those of

. MTL can also be combined with other learning paradigms to improve the performance of learning tasks further, including semi-supervised learning, active learning, unsupervised learning,and reinforcement learning.

Our work can be seen as an asymmetric multi-task learning framework (Xue et al., 2007; Zhang and Yeung, 2012, 2014), in which we aim to utilize the connection between RS and KG to help improve their performance, and the two tasks are trained with different frequencies.

5.3. Deep Recommender Systems

Recently, deep learning has been revolutionizing recommender systems and achieves better performance in many recommendation scenarios. Roughly speaking, deep recommender systems can be classified into two categories: (1) Using deep neural networks to process the raw features of users or items

(Wang et al., 2015, 2018b; Zhang et al., 2016; Wang et al., 2017c; Guo et al., 2017); For example, Collaborative Deep Learning (Wang et al., 2015)

designs autoencoders to extract short and dense features from textual input and feeds the features into a collaborative filtering module; DeepFM

(Guo et al., 2017) combines factorization machines for recommendation and deep learning for feature learning in a neural network architecture. (2) Using deep neural networks to model the interaction among users and items (Huang et al., 2013; Cheng et al., 2016; Covington et al., 2016; He et al., 2017). For example, Neural Collaborative Filtering (He et al., 2017) replaces the inner product with a neural architecture to model the user-item interaction. The major difference between these methods and ours is that MKR deploys a multi-task learning framework that utilizes the knowledge from a KG to assist recommendation.

6. Conclusions and Future Work

This paper proposes MKR, a multi-task learning approach for knowledge graph enhanced recommendation. MKR is a deep and end-to-end framework that consists of two parts: the recommendation module and the KGE module. Both modules adopt multiple nonlinear layers to extract latent features from inputs and fit the complicated interactions of user-item and head-relation pairs. Since the two tasks are not independent but connected by items and entities, we design a crosscompress unit in MKR to associate the two tasks, which can automatically learn high-order interactions of item and entity features and transfer knowledge between the two tasks. We conduct extensive experiments in four recommendation scenarios. The results demonstrate the significant superiority of MKR over strong baselines and the efficacy of the usage of KG.

For future work, we plan to investigate other types of neural networks (such as CNN) in MKR framework. We will also incorporate other KGE methods as the implementation of KGE module in MKR by redesigning the crosscompress unit.

Appendix

A    Proof of Theorem 1

Proof.

We prove the theorem by induction:

Base case: When ,

Therefore, we have

It is clear that the cross terms about and with maximal degree is , so we have , and for . The proof for is similar.

Induction step: Suppose and hold for the maximal-degree term and in and . Since and , without loss of generosity, we assume that and exist in and , respectively. Then for , we have

Obviously, the maximal-degree term in is the cross term in . Since we have and for both and , the degree of cross term therefore satisfies and . The proof for is similar. ∎

B    Proof of Proposition 2

Proof.

In the proof of Theorem 1 in Appendix A, we have shown that

It is easy to see that , , and . The proof is similar for . ∎

We omit the proofs for Proposition 3 and Proposition 4 as they are straightforward.

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