Learning intents behind interactions with high-order graph for session-based intelligent recommendation

2.1 Session-based recommendation

Session-based recommendation is uncertain about the user’s information and can quickly generate personal service information for sites that cannot record the user’s browsing behavior. At present, the session recommendation task has been widely used in many fields, Several studies have gone deeply into the recommendation algorithms, Wang et al. [11] proposed a self-attention method to model sequential relationship that makes possible to discover long-term dependence. Cao et al. [9] took full advantage of the location information and contextual relation in the sequence to model location-aware to enhance recommendation performance. Liu et al. [20] made full use of the long tail effect which improves the diversity of commodity recommendation and produces serendipity. Sheu et al. [21] considered the semantic features and interactive conversational features of news, and proposed a context-aware graph embedding framework to improve the recommendation performance. Jin et al. [22] proposed a multi-behavior model which constructs a unified graph, which is used to represent a variety of behavioral data, which can solve the problem of data scarcity or cold start. Considering that the longer-term preference of a user can improve the recommendations in the current. Beutel et al. [23] came up with an RNN-based method that incorporates auxiliary context information. These positive observations usually exist in the sequential data that express the shifts of interest. These existing methods adopt data enhancement to train data, so as to improve the performance of the model. Yuan et al. [24] combined Sparse kernels and gage-filling for future data interaction to improve the recommendation accuracy.

2.2 Attention mechanisms

Session-based recommendation provides users with the suitable items or personalized service by predicting a user’s interest based on related information about the interactions between items and users, while the user facing the increasing online information explosion problem [1]. Recently, with the rapid development of deep learning technology, attention mechanisms are receiving wide attention as one of the most common deep learning measures, and have shown significant improvement in recommendation system [9]. The advantage of attention mechanisms is that they selectively assign weights to different neighboring nodes according to the importance of different neighborhoods. Quadrana et al. [25] proposed a high-order session-RNN method to model a user’s interests within a session. Later, Li et al. [26] adopted the multi-channel model to construct the transfer relationship between neighbor interactions and target interactions. Li et al. [8] the weighted attention and graph models are used to combine to mine the interest transfer relationship between the users. Most existing sequential recommendation models [4] utilize the self-attention mechanism to capture distant item-to-item transitions in a sequence and have achieved expected performance [27]. Pan et al. [28] take into account the importance of different interactions to integrate the unified vector by the SRIEM model that predicts users’ interest. Lv et al. [29] utilized a multi-head attention mechanism to discover users’ various interests, and fused long-term interests and current interests through gate mechanism to generate a unified expression for users’ interest in dynamic changes. In this work, we exploited high-order attention-aware networks to capture different interactions attention, and present a high-order graph attention-aware neural network for the session-based recommendation. However, in some application domains [30], it seems that it does not generate better recommendations by using repeated item sequence. Compared to previous work, we adopt a session-based graph pooling method, which allows nodes to select the most relevant higher-order information to better aggregate the features of neighborhoods.

Session-based recommendation seeks to calculate output probability of the interactions that users will click according to their previous historical behaviors [31]. For a session sequence, all items are regarded as the nodes of the session graph G _s . G _s  = (V _s , E _s , A _s ), A _s is the adjacency matrix between nodes, E _s is the set of edges and V _s is the set of all unique interactions that m is the length of the session. Each node was embedded into the latent space, where the node vector v s , i ∈ ℝ d represents a d-dimensional feature vector of the i-th node. The interactions is encoded to generated the generation of new vectors in the embedding layer and the embedded layer is represented as follow equation (1): x = embed ( v s , 1 , v s , 2 , … , v s , i , … , v s , m ) ,(1) where embed is the embedding layer, all nodes v_s,m ∈ V _s are updated in the session graphs. Since graph have repeated edges in the session, and two connected nodes are clicked several times, so each edge is normalized. The calculation method is to divide the occurrence of the edge by the outdegree of the starting node of the edge, and the output x _i of the graph neural network layer is calculated as equation (2).

h i t = A s , i : t [ x s , 1 t - 1 , x s , 2 t - 1 , x s , 3 t - 1 , … , x s , i t - 1 , … , x s , m t - 1 ] T H + b t - 1 z s , i t = σ ( W z h i t + W zi x s , i t - 1 ) r s , i t = σ ( W r h i t + W ri x s , i t - 1 ) x ˜ s , i t = tanh ( W h h i t + W hi ( r s , i t ⊙ x s , i t - 1 ) ) x s , i t = ( 1 - z s , i t ) ⊙ x s , i t - 1 + z s , i t ⊙ x ˜ s , i t ,(2)

where A s , i : ∈ ℝ d × 2 n are the two columns of blocks corresponding to the adjacency matrix between nodes. H ∈ ℝ d × 2 d controls the weight, b t - 1 ∈ ℝ d × 2 d is the bias vectors, W z , W r , W h ∈ ℝ 2 d × d , W zi , W ri , W hi ∈ ℝ d × d are the parameter matrices, σ (·) is the logistic sigmoid function, and ⊙ indicates element-wise multiplication. x s , i t represents the final t-th updated state based on candidate state, update gate z _s,i and reset gate r _s,i. x _s,i is the final vectors for the node v_s,i.

In the propagation process, each layer of the graph network can only capture the first-order relationship between nodes. In order to be able to capture higher-order relationships, it is usually captured by stacking multiple layers of GNN networks. As the number of layers deepens, The gradient will be disappeared, and the long-distance dependency cannot be effectively captured. Therefore, we resort to high-order connection mechanism to capture the shift relationship between interactions.

Since adjacent interactions have a strong correlation in the session, the high-order connection layers are introduced to obtain high-order information and generate more important features. The high-order attention-aware network are proposed to select the relatively important neighbors’ nodes to aggregate the embedding of the neighbor nodes in a graph network [27] and capture the users’ main intention.. f s , i = ∑ j , i ∈ N i α ij W ij x s , j ,(3)

α ij = exp ( LeakyRelu ( W att [ x s , i ∥ x s , j ] ) ) ∑ j , i ∈ V exp ( LeakyRelu ( W att [ x s , i ∥ x s , n ] ) ) ,(4) where ∥ means concatenation of two vectors and w ij ∈ ℝ d × d is the parameter. N _i denotes the neighbor set of node i, j ∈N _i , W _att ∈ ℝ 2 d is trainable weights that assign importance to the different neighbors of the item i, respectively.

The graph not only needs to aggregate the node of its neighbors, but also needs to update itself node. The features of nodes are up to itself and its neighbors. We formulate the representation of an item as [32]. o s , i = tanh ( W o [ f s , i ∥ x s , i ] + b o ) ,(5) where W o ∈ ℝ d × 2 d is the transformation weight, b o ∈ ℝ d × 2 d is the bias matrix.

In order to calculate the node’s importance within current session and the candidate, the node’s sequence are modeled to discover the useful information about the users’ primary intent, the feature representation f _s,i in embedding layers as equation (6). F s = ∑ i = 1 n β im o s , i ,(6) To summarize, the attention-aware network can adaptively choose relatively important interactions from the current session to capture the users’ primary intent [27]. β im = p T σ ( W i o s , i + W m x s , m + b )(7) where σ is an activate function, W i ∈ ℝ d × d and W m ∈ ℝ d × d are trainable weights that performs linear mapping across all nodes [8], p , b ∈ ℝ d × d are d-dimensional bias vectors.

The graph high-order layers are served to further propagate and explore the higher-order connectivity information [33], which collect the information propagated from its distant neighborhood among nonadjacent interactions, the distance behavior within item sequences may breakdown the local integrity of the chain structure but can be likely avoided through this high-order connection, which can be formulated as equation (8): E s = softmax ( ( F s q ) ( F s k ) ⊤ d ) ( F s v ) ,(8) where d is the dimension size of the global vector, F _s is the local feature. The values of query,key and value are given to F _s , and transform query and key into the same latent space through non-linear transformation. Consequently, the output features are as follows (9): F s q , F s k , F s v = σ ( F s w q ) , σ ( F s w k ) , F s(9) where σ is an activate function, w _k ,w _q are d × d matrices that represent the corresponding weight matrix.

For the sake of making the best of the feature of each layer, the shortcuts are adopted to prevent information loss that it is more likely to permit additional long-rang information to forward propagation [34]. In order to integrate the concatenated dense representation vector, we adopt a four-layer fully connected layers to aggregate and propagate information and the output vector is represented by equation (10). Q s = MLP ( E s ) + E s(10) where MLP is the connected network.

The hybrid embedding g _s is computed by capturing item-item transitions without regard to their distances and drawing global dependencies, as the follow formula: g s = σ ( W 2 σ ( W 1 [ Q s ∥ F s ] + b 1 ) + b 2 ) ,(11) where σ is an activate function, ∥ denotes the vector concatenation. W 1 ∈ ℝ d × 2 d , W 2 ∈ ℝ d × d are the transformation weight on the first forward neural network layer and second forward neural network layer, respectively. b 1 ∈ ℝ d × 2 d , b 2 ∈ ℝ d × d are the bias vectors.

For a session s, the last-visited item x _s,m of the session is defined as the local preference. The last clicked item. For the embedded nodes, the weighted connection matrices are applied to capture the embedded information of the session, and the output feature of the nodes is used to effectively predict the next item and is computed by the softmax function as equation (12): y ˆ i = softmax ( g s · x s , m ) ,(12) where y ˆ i denotes the clicked probability of item x _i in session s, x _s,m is the last clicked item.

Since the recommended items will appear in the candidate list, the prediction between items is a classification problem, it is required to predict the probability of the clicked items, the cross-entropy loss function is adopted to optimize the loss. To optimize the function, we used the cross-entropy loss function to verify the performance of the model on samples and the loss function demonstrates the gap between the ground-truth and the predicted value. Therefore, the model was trained by minimizing the optimization function, as formula (13):

L ( y ˆ ) = - ∑ i = 1 n y i log ( y ˆ i ) + ( 1 - y i ) log ( 1 - y ˆ i ) + λ ∥ θ ∥ 2 ,(13) where y _i denotes the feature vector of the ground truth node i, λ and θ are the set regularization parameters and the set of all learnable model weights, respectively. The L2 norm is used to avoid overfitting in the process of training the model.

In this paper, we have described the details of our method. To simplify here, we present HOGAN method in Algorithm 1, which is the whole algorithm in our paper.

Algorithm 1 Pseudocode Algorithm of HOGAN.

Input: x_s,m: current session, g _s : global session, d: embedding dimension, α: learning rate, λ: l2-loss weight

Output: optimal model of parameter θ

  repeat

   for v_s,i in V _s do

    obtain user’s current preferences F _s according to Eq.(1)-(5)

    obtain user’s global preferences Q _s according to Eq.(6)-(10)

    compute the final session representation g _s according to Eq.(11)

    compute the prediction y ˆ i according to Eq.(12)

    update θ with gradient descent according to Eq.(13)

   end for

  until convergence

  return θ

4.1 Data sets

To test the effectiveness of our model, our method is conducted on four standard data sets (Yoochoose 2 , Diginetica 3 , Xing 4 , Reddit 5 ) and the performance of different recommendation algorithms are evaluated through a series of comparative experiments.

Yoochoose is a dataset that is from the RecSys competition. It is a collection of sessions clicked by the user. The dataset contains streams collected from e-commerce sites that users click on over six months. To filter out noise data, we filter out interactions repeated appearing less than 5 times and then remove all sessions with fewer than 1 interactions [7].

Similar to the method reported by Xu [7], for a session sequence S ={ v_s,1, v_s,2, …, v_s,m }, we make train dataset and test dataset by generating a series of sequences ({ v_s,1 } , v_s,2) , ({ v_s,1, v_s,2 } , v_s,3) , …). The processed datasets are listed in Table 1.

Due to Yoochoose data set is so large that the training speed is very slow. For the purpose of conducting the experiment more perfectly, we processed the experimental data. The Yoochoose dataset is divided into the yoochoose1_64 dataset. The last-week session is regarded as the test set, with the rest of the session as the training set. The interactions in the training set are removed so they would not appear in the test set, which there will be no duplicate interactions in the train set and test set. The Diginetica and Retailrocket were dealt with by split into the train set and test set, we take the session from the seven days of the dataset as the test set. For the Xing and Reddit, we take the session from the one day of the dataset as the test set. For the purpose of inputting the session sequences in the training model, we split the input session sequences into the sequence sets and the corresponding labels.

We designed the model using pytorch to train our data. Following previous methods [8, 16], the parameters are initialized with a gaussian distribution, and the Adam optimizer is used to optimize the hyper-parameters, where the initial learning rate starts from 0.001 and is set to 0.005 and 0.01, respectively. Moreover, the L2 is set to 10^-5. The batch size and the hidden size are set to 100 and 100, respectively. we use the learning rate decay rate 0.1. The epoch of model iterations is set to 30 and the latent dimensionality of the datasets is set to 100. The experiments are performed on a GeForce GTX Titan1080 GPU to accelerate the model training.

4.3 Baseline methods

To evaluate the performance of the proposed method, we compare the proposed method with other six methods: FPMC, GRU4Rec, HCRNN, NARM SR-GNN and LESSR, respectively, Among them, the proposed method and SR-GNN are based on the graph model. A brief description of the six methods are as follows:

FPMC 6  [18] is a traditional model that combines matrix decomposition with a first-order Markov chain for predict the next item.

4.4 Evaluation methods

Since the recommendation system aims to quickly find the valuable interactions from the massive resource. Despite the capacity and interface show the limited number of interactions, the user’s needs are on the rise. In order to evaluate the performance of each model, we evaluate two widely adopted ranking metrics including MRR and NDCG, and two accuracy metrics including Recall and Precision, which are as follows,

Recall: The main evaluation metric is Recall@ k which statistically tests the probability that the user’s real clicked interactions. Recall selects the part related to the current recommendation by the user from the global item library as the candidate set. The item data finally displayed to the user is a subset of this set. Too few recalls and too little content for users to see are not conducive to more interaction between users and the platform.

4.5 Comparisons of performance

In this statistical test, we select an effect test and fail to choose a parameter test due to the large model parameters generated by the model. The effect test is used to test the performance of the model in a real application. In our study, we compare our method with other algorithms by running against four datasets. Our algorithm outperforms other algorithms for the comparison on four datasets, which validates the importance of high-order attention for the session, as shown in Table 2. Table 2 illustrates the results of HOGAN and baselines. First, we can see that HOGAN outperforms the other methods in MRR@20 and Recall@20. For the baselines, we can know that the neural models generally outperform the traditional methods (e.g, FPMC) in all the datasets as a result of the benefit from deep learning in this field.

In these approaches based on deep learning theory, GRU4Rec makes the most of RNN-like units to model the session as a sequence and combine a current session embedding to form a unified represent to make precise sequence recommendation. Meanwhile, the RNN-based models (HCRNN, GRU4Rec) also achieve excellent results since the sequence models are benefit to capture user’s shift interest. HCRNN performs better than GRU4REC since HCRNN improves the RNN structure with hierarchical context to capture the interest drift. Besides, these methods utilizing the attention mechanism, e.g.,NARM, HCRNN, obtain a great improvement compared with GRU4REC, which shows the capability of the attention mechanism to achieve satisfactory results to learn the dependency with interactions. Especially, LESSR is specifically for the SR problem and obtain perfect results in the experiment. In this experiment, LESSR performs slightly better than SRGNN and HCRNN because graph neural networks have a strong ability to model structured data and the graph attention layer effectively captures long-range dependencies. HOGAN, LESSR and SR-GNN model the session as a graph and apply graph neural network and the attention mechanism. Different from the baseline models mentioned above, HOGAN adopts the high-order attention mechanism to adaptively assign weights to previous interactions, which make good use of higher-order information to capture long-range dependencies between interactions of a session, regardless of the item distances. Furthermore, we propose that the performance is superior to the baselines on the Recall@20 and MRR@20, which in view of the current user’s sequence behavior in the model. As far as we know, our algorithm gets the best performance among all the algorithms on the four datasets.

Table 3 shows the capability of NDCG, and we separately study the performance of NDCG for the recommended top items. As can be seen from the results, 1) As the number of recommended items increases, the performance of NDCG keeps increasing until the value of N reach the twenty, which indicates that the performance of the model is related to the number of recommended items. 2) For the recommended top-n items, the NDCG of different data sets varies significantly, indicating that the recommended performance is related to the length of the session.

We further evaluate our model by the top 20 recommendation results on the four datasets and adopt the Recall@20 and the MRR@20 to show the result. Figure 3 displays the performance of our method and three baselines with a different number of iterations on different data sets. It is clear from results that: (1) Fig. 3(a) and Fig. 3(e) display the experimental results of Yoochose1_64 on both evaluation metric. As we can see, the performances of the four models consistently go up with the number of epochs increasing until the twentieth epoch and have no further improvement. It is the reason that the high-hop layers would make HOGAN easier to precisely capture more detailed information. It also shows that HOGAN is consistently better than the baselines with enough propagation steps and learn the useful features for the task of interest. (2) Fig. 3(b) and Fig. 3(f) show the performances of the Diginetica on both Recall@20 and MRR@20. In the beginning, the effect of our model is better than SRGNN. In the fifteenth epoch, the performances of the four models tend to be stable, and our model is better than SRGNN in all epochs. (3) Fig. 3(c) and Fig. 3(g) show the performances of the Xing on both Recall@20 and MRR@20. In the beginning, the effect of our model is better than SRGNN. In the fifteenth epoch, four models have a closed performance. Their performances have no significant improvement after that. In Recall@20, HOGAN has the best performance in the twentieth epoch and the proposed method is better than SRGNN in all epochs. (4) The results of the Reddit on both Recall@20 and MRR@20 are shown in Fig. 3(d) and Fig. 3(h). From the results, we can see that increasing the number of layers always result in a better performance. In the fifteenth epoch, four models have a closed performance. Their performances have no significant improvement after that. In Recall@20, HOGAN has the best performance in the twentieth epoch and the proposed method is better than LESSR in all epochs.

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Fig. 3

Performance comparison between our method and the baselines.

We conduct ablation experiments by studying different blocks and analysis the effects of different blocks. The Table 4 shows the performance of the ablation experiments. By research the part of the model, we compared the performance of the models. The results are shown in Table 4. We found that the attention-based model is always better than the non-attention model when the number of parameters is small, which shows the effectiveness of the attention mechanism in this task. By adding the model of the attention model, we see that the performance of the fusion method of several models is better than that of a single attention model. From the third and fifth rows of Table 4, we use the self-attention encoding method to show the performance well on the four data sets, indicating that it can capture the dependency of the global addition and solve the dependency problem of the long sequence. At the same time, it can be seen from the second and fourth rows that the addition of GAT can better establish higher-order relationships and can capture features at longer distances. In addition, we can see that the role of each model has played a good effect, which is consistent with the observation results

Figure 4 shows the impact of our method on Recall@20 and MRR@20 on four different datasets with different high-order layers. The left figure displays the Recall@20 when the layer is varying from one to ten, and the performance has not been continuously improved with the high-order layer increases. However, the performance is limited as the high-order layer is increasing. The right figure shows the MRR@20 achieved the best performance when the number of layers is four. Based on the above result, four layers performance is perfect for our algorithm.

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Fig. 4

Performance comparison between different layers over three datasets.

We assessed the model by training speed (time taken for one epoch of training), and all experiments were performed with GTX-1080 Ti GPU. The Fig. 5 shows the training efficiency of the model that the training model converges to the stable performance in the training process. Figure 5 shows the training efficiency of our model and others. For a fair comparison, we are all running on GTX-1080 Ti GPU. We can see that our model requires less time to update one epoch. We can see spends 4.8 seconds on model updates for one epoch which is over 2.4 times faster than Lesser (11.9s/epoch) and 6 times faster than GNN (28.3s/epoch), we also see that our model achieved stable performance within around 200 seconds on the data set Yoochoose1_64 while other models require much longer. Meanwhile, we analyzed our model on reddit dataset, and discover that the time efficiency of our model is better than the efficiency of other baselines.

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Fig. 5

The comparison of time efficiency between our method and the baselines.