Enhanced Sub-graph Reconstruction Graph Neural Network for Recommendation

ABSTRACT

Personalized recommendation can recommend items of interest to different users and is widely used in the real world. Among them, graph collaborative filtering is a method of personalized recommendation. It can enrich the connection between users and items on the basis of collaborative filtering, to learn the embedded representation of nodes more accurately. Since graph collaborative filtering is based on bipartite graphs, few exciting graph collaborative methods consider the relationships between users (or items), the message between homogeneous nodes are diluted or ignored. Predicting and constructing the relationship between users (or items) has become a challenging. To solve this problem, we propose an enhanced sub-graph reconstruction graph neural network for recommendation (SRCF), using a heterogeneous graph neural network based encoder-decoder learn potential relationships between users (or items), and reconstruct sub-graphs based on those relationships. In the proposed model, the information of user and item sub-graphs is merged with the network of graph collaborative filtering, which enhances effective information transfer between homogeneous nodes, thereby improving the model performance. We have selected a number of data sets of different scenarios and different scales to comprehensively evaluate the performance of the model, and the experimental results confirmed the superiority of our model.

Introduction

In this era of information explosion, personalized recommendation plays an extremely important role. It recommends items that different users may like by learning the embedded representation of users and items. This recommendation method is widely used in all walks of life. Such as: movie recommendation (A and Hunt 2015), news recommendation (Zheng et al. 2018), media recommendation (Guy et al. 2010), health-care recommendation (Forouzandeh et al. 2024; Rostami et al. 2024; Srivani, Murugappan, and Mala 2023), personalized education recommendation (Atalla et al. 2023), recommendations based on energy conservation and emission reduction (Himeur et al. 2021; Sardianos et al. 2020), smart home recommendations (Dudekula et al. 2023), etc. The key point of building a personalized recommendation method is to model the relationship between users and items. Collaborative filtering (CF) is a widely applied recommendation method (Su and Khoshgoftaar 2009). In the application scenario of collaborative filtering, users and items are naturally divided into a bipartite graph structure due to the connection between them, and the graph neural network can improve the performance of the traditional collaborative filtering model by learning the network structure (Wang et al. 2019, 2020). This is because the graph neural network can obtain the CF signals in the graph structure by learning the high-order connections between users and items, and reduce the impact of data sparsity on the model. For example, NGCF (Wang et al. 2019) learns the high-order relationship between users and items through graph aggregation layers, and aggregates the learned information to obtain the embedded representation of nodes. LightGCN (He et al. 2020) simplifies GCN (Kipf and Welling 2016a) by removing feature transformation and nonlinear activation, and also learns user and item representation through this improved graph neural network.

In the existing research, most of the methods are deeply studying the interactive relationship between users and items, but ignore the relationship between users (or items) (He et al. 2020; Sun et al. 2022; Wang et al. 2019). The information transfer process in these methods is shown in Figure 1. From the figure, we can see that when we need to get the embedded representation of a user node u1, the information of other “associated” user nodes needs to be aggregated to an item node first, and then aggregated by multiple item nodes to calculate the final embedding of the user. Assume there is a high correlation between u4 and u1. In the traditional graph collaborative filtering method, if u4 wants to pass information to u1, it must first pass through i2 and mix with i1. There is a large portion of important information that gets diluted, which leads to the loss of information. However, how to predict and model such node relationships has become a challenge.

Figure 1. Message passing process.

In order to solve this problem, and inspired by the learnability of node relationships in Graph Neural Networks (GNN) (Zhao et al. 2021), we hope to mine the implicit association hidden in the initial user-item relationship graph structure, reconstruct this part of the relationship into a sub-graph, so the information aggregated in the sub-graph can enrich the CF signal in the user-item interaction graph. To achieve this idea, there are several difficulties to be solved: (1) How to learn the initial interaction structure; (2) How to reflect the importance of edges on the reconstructed graph; (3) How to maintain the connectivity of the reconstructed sub-graph. so we propose our model: Enhanced Sub-graph Reconstruction Graph Neural Network for Recommendation (SRCF). Firstly, we propose a graph encoder to learn the structure of the user-item interaction graph, calculate the possibility that there may be edges between users, digging out the potential behavior relationship between users. To ensure the connectivity of the graph structure, we select edges with high probability for each user (or item) according to the learned possibility, then convert possibility scores into weights through normalized calculations, finally construct a weighted user sub-graph and a weighted item sub-graph, this process is shown in the Figure 2, and detailed in the Figure 3. Secondly, we need to aggregate the information in the user sub-graph and the item sub-graph with the CF signal in the user-item interaction graph. In this step, SRCF design a weighted-GNN method to obtain the high order aggregate representation of each node in the user (or item) sub-graph, and merges it with the node representation in the user–item interaction graph to obtain a vector representation of the user (or item). Finally, we perform iterative optimization through BPRLoss. Our significant contributions are highlighted as follows:

Figure 2. Reconstruction of sub-graphs.

Figure 3. An overview of the SRCF model. (a) shows the detailed process of the sub-graph reconstruction module, and (b) shows the learning process of the node embedding representation learning module.

• We propose a GNN-based encoder to learn the interaction of users and items, mine potential relationships between users (or items), and reconstruct weighted user sub-graphs and weighted item sub-graphs through these potential relationships. So that our model can accurately learn the transfer of information between homogeneous nodes.

• We take advantage of the feature that GNN can aggregate high-order connected relationships, thus obtain high-order relationship representations between users (or items) from weighted user sub-graph and weighted item sub-graph, combine these representations with CF signals in the user-item interaction graphs. We take advantage of the feature that GNN can aggregate high-order connected relationships, thus obtain high-order relationship representations between users (or items) from weighted user sub-graph and weighted item sub-graph, combine these representations with CF signals in the user-item interaction graphs. Compared with traditional graph collaborative filtering models, we dig out more useful information from the dataset and use that information to fully and accurately represent users and items.

• We conduct experiments on multiple datasets of different scenarios and scales, and the experimental results show that our model is effective.

Related Work

This section including two parts: (1) Graph Neural Network, (2) Graph-based Collaborative Filtering.

Graph Neural Network (GNN)

Since CNN has made great achievements in the field of image processing, many researchers have also applied the idea of convolution to the graph structure, forming a graph convolutional neural network. Homogeneous graph convolutional models can be broadly classified into two categories. The first is in the spectral domain, where Bruna et al. (2013) first proposed a graph convolution method based on the graph Laplacian transform. Defferrard, Bresson, and Vandergheynst (2016) applied k-order Chebyshev polynomials and improved performance based on them, and Kipf and Welling (2016a) adopted local first-order approximation to design a graph model called graph convolutional network, which also achieved good performance. The second is a spatial approach, GAT Veličković et al. (2017) applies the attention mechanism to learn the influence coefficient, that is, the weight between different nodes, so as to aggregate the nodes. GraphSAGE (Hamilton, Ying, and Leskovec 2017) samples neighbor nodes to aggregate objects. In recent years of research, graph neural network methods have been applied to many scenarios, such as: social recommendation (Fan et al. 2019; Wu et al. 2019), bio-informatics (Wang et al. 2021; Yan, Hamilton, and Blanchette 2020), traffic forecast (Cui et al. 2019; Li et al. 2017). Collaborative filtering recommendation based on graph neural network is also a hot research direction.

Graph-Based Collaborative Filtering

Methods based on graph neural networks have also been applied in the field of recommendation. Because the interaction graph between users and items in the collaborative filtering method is a natural bipartite graph, method based on graph neural network can enhance the information transfer between users and items, meanwhile graph-based method can effectively solve the sparsity of data (Wang et al. 2019), many researchers have begun to try the collaborative filtering method based on the graph neural network. We can divide these methods into two categories: (1) The first category methods obtain node embeddings by deep learning the relationship between users and items. NGCF (Wang et al. 2019) uses graph neural network to capture high-order information in graph structure as a supplement to traditional collaborative filtering signals. DGCF (Wang et al. 2020) models each user-item interaction to obtain a disentangled representation for efficiently extracting intent-related information. Dynamic-GCF (Li et al. 2020) captures the collaborative relationship directly acting on users and items through dynamic graphs. EGLN (Yang et al. 2021) let the augmented graph learning module and the node embedding module learn iteratively from each other without any feature input. However, none of these methods take into account whether there is a relationship between users (or items). (2) The second category of methods considers the relationship between users (or items). Multi-GCCF (Sun et al. 2019) expand the feature information of nodes through node similarity calculation, and iterate through graph neural network, DMGCF (Tang et al. 2021) update node features through dynamic graph structure, calculate similar nodes, and use graph convolutional network for aggregation. MCCF (Wang, Wang et al. 2020) enrich the learning of node embeddings by calculate the relationships between user nodes to predict potential user purchase motivations. RESCHet (Forouzandeh et al. 2023) present a new method for Recommendation Based on Embedding Spectral Clustering in Heterogeneous Networks. Compared to our method, the relationships these model constructed cannot adequately express the process of information transfer between homogeneous nodes.

Preliminaries

User-Item Bipartite Graph

In the GNN-based recommendation method, we will construct a user-item bipartite graph with user’s historical rating on the item. This graph is denoted as G = (U, I, R, E), where U represents the set of users. I denotes the set of items. R represents user’s historical ratings for items, it represents the possible weights in the graph structure. E is the edge set corresponding to the user’s rating of the item, the edge set directly corresponds to the connectivity in the graph.

Our Model

In this section, we will introduce our model SRCF. Firstly we will overview the various parts of our model and their functions, and then we will detail each part. The model structure of SRCF is shown in the Figure 3.

SRCF Overview

Our model SRCF consists of three modules, namely (1) user and item sub-graph reconstruction module, (2) GNN-based node embedding learning module, and (3) Graph score prediction module.

User and item sub-graph reconstruction module. SRCF learns the relationship between users and items through the structure of the user-item interaction graph, predicts the relationship between users (or items), and reconstructs the user sub-graph and item sub-graph based on the predicted results. The structure of these two sub-graphs will be connected with nodes that have high correlation or similarity, so as to strengthen the information transfer between them.

GNN-based node embedding learning module. Based on the method of graph neural network, SRCF learns the embedded representation of users and items through the three graph network structures of user sub-graph, item sub-graph and user-item bipartite graph, which complements the traditional collaborative filtering method. The internal information transfer of users (or items) enriches the process of embedding information learning.

Graph score prediction module. Our model SRCF performs dot calculation between user and item representations. The final prediction score is obtained from the calculation results.

User and Item Embedding Initialization

According to the practice of mainstream recommendation models (Cao et al. 2019; He et al. 2017; Rendle et al. 2012), we obtain the initial embedding through random initialization, we use a vector e_u ∈ R^d to represent a user u, use a vector e_i ∈ R^d describe an item i, R^d is the dimension of the embedded vector, and the vector dimensions of users and items are the same, thus constructing a feature embedding lookup table:

(1) $\mathit{E}=\left[e_{\mathit{u}1},\cdots ,e_{\mathit{uN}},e_{\mathit{i}1},\cdots ,e_{\mathit{iM}}\right]$(1)

where N and M denotes the dimensions of user node and item node.

User and Item Sub-Graph Reconstruction

We believe that in the user-item bipartite graph, there is also an important potential information transfer between users (or items) with high relevance, but the traditional graph collaborative filtering model cannot capture and learn this partial information. We hope that this information can be transmitted through the relationship constructed by structure learning. According to the work of (Zhao et al. 2021), it is proved that the graph neural network based on structure unsupervised learning can mine the implicit link of the graph structure, thereby enhancing the learning effect of the graph neural network. So we set up an encoder and decoder based on VGAE (Kipf and Welling 2016a) and LightGCN (He et al. 2020) to learn the structure of the user-item interaction graph, and predict the possibility of edge relationships between different nodes. The specific content of the encoder and decoder is shown in the formula:

• encoder

(2) $\begin{array}{c}{e}_u^{(k+1)}=\sum _{i\in N_u}\frac{1}{\sqrt{\left|{\mathrm{N}}_u\right|}\sqrt{\left|{\mathrm{N}}_i\right|}}{e}_i^{(k)}\\ e_i^{(k+1)}=\sum _{\mathit{u}\in {\mathrm{N}}_i}\frac{1}{\sqrt{\left|{\mathrm{N}}_i\right|}\sqrt{\left|{\mathrm{N}}_u\right|}}{e}_u^{(k)}\end{array}$(2)

• decoder

(3) $\begin{array}{c}Re\mathit{latio}{n}_{\mathit{uiuj}}=\mathit{\sigma }(e_{\mathit{ui}}{w}_u{e}_{uj}^T)\\ Re\mathit{latio}{n}_{i_x{i}_y}=\mathit{\sigma }(e_{\mathit{ix}}{w}_i{e}_{iy}^T)\end{array}$(3)

where $e_u^{(k+1)}$denotes the embedding of user u at layer $\mathrm{k}+1$, $\mathit{N}$ represents the degree of user u, $\mathit{Relatio}{n}_{\mathit{uiuj}}$ is the link probability score.

After we have obtained the user-user matrix $\mathit{Relatio}{n}_u$and item-item matrix $\mathit{Relatio}{n}_i$ based on Formula.3, we connect the unlink nodes with higher scores, and the construction of the sub-graph follows the conditions: (1) To reconstruct the connectivity of sub-graphs, we ensure that each node has an edge to connect it; (2) There will be no repeated edges in the reconstructed sub-graph; (3) The probability scores between nodes will become the weights of the edges in the sub-graph. The error situation of reconstructing the sub-graph is shown in the Figure 4.

Figure 4. Wrong example of sub-graph refactoring.

After reconstructing the sub-graph, we will normalize the weight of the sub-graph. The purpose of this is to retain the degree of association we have learned. We think that the nodes with higher degree of association needs to conveye more information, and the normalized formula is shown in formula:

(4) ${\beta }_{\mathit{ij}}\leftarrow \frac{{\mathit{\alpha }}_{\mathit{ij}}}{{\sum }_{\mathit{j}\in \mathrm{N}(i)}{\alpha }_{\mathit{ij}}}$(4)

where $\mathrm{N}(\mathit{i})$ is the set of neighbors of node $\mathit{i}$, ${\beta }_{\mathit{ij}}$ is the weight between node $\mathit{i}$ and $\mathit{j}$, ${\alpha }_{\mathit{ij}}$ is the probability score learned by our method.

GNN-Based Node Embedding Learning

After we reconstruct the sub-graph of user and item nodes, we get $g_{\mathit{user}}$ and $g_{\mathit{item}}$, we will use the method based on graph neural network to collect the multi-level information transfer in the two sub-graphs and user-item interaction graph $g_u$.

User-Item Message Propagation

In the user-item information transfer, our model SRCF, like the traditional recommendation model, uses a graph neural network-based method to obtain the collaborative filtering signal (CF) in the graph structure. We believe that the user-item bipartite graph belongs to heterogeneous qualitative graph structure, so we use learnable transition matrices for different types of nodes on the basis of the traditional method (He et al. 2020; Wang et al. 2019). The formula of transition is:

(5) $\begin{array}{c}\mathit{f}{ }_u^{\prime }=\mathit{\sigma }(W_u\cdot f_n+b_u)\\ \mathit{f}{ }_i^{\prime }=\mathit{\sigma }(W_i\cdot f_n+b_i)\end{array}$(5)

where $\mathit{f}$ denotes the feature of node, $\mathit{W}$ is a learnable transition matrices.

Then we need to employ the graph convolution neural network to learn the embedded representation of users and items:

(6) ${\mathrm{F}}^{\left(\mathrm{k}\right)}=\mathrm{LeakyReLU}\left(\left(\mathcal{L}+\mathrm{I}\right){\mathrm{F}}^{\left(\mathrm{K}-1\right)}{\mathrm{W}}_1^{\left(\mathrm{k}\right)}+\mathcal{L}{\mathrm{F}}^{\left(\mathrm{k}-1\right)}\odot {\mathrm{F}}^{\left(\mathrm{K}-1\right)}{\mathrm{W}}_2^{\left(\mathrm{k}\right)}\right)$(6)

where $F^{\left(\mathit{k}\right)}$ is the node feature matrix calculated at layer $\mathit{k}$,$\mathit{L}$ denotes the Laplacian matrix, ⊙represents the element-wise product, $\mathrm{W}$ is a trainable matrix.

(7) $\mathcal{L}={\mathrm{D}}^{-\frac{1}{2}}\mathrm{A}{\mathrm{D}}^{-\frac{1}{2}}\mathrm{and}\mathrm{A}=\left[\begin{array}{cc}0& \mathrm{R}\\ {\mathrm{R}}^{\mathrm{T}}& 0\end{array}\right]\mathit{\hspace{0.17em}}$(7)

where $\mathit{D}$ represents the degree matrix.

User-User Message Propagation

For user nodes, in addition to the CF signal in the user-item interaction graph, we will also learn the information transfer between user nodes with high correlations from the user sub-graph. Our approach allows the model to learn the relationship shown in Figure 1. This homogeneous relationship contains a large amount of associated information. And learning methods based on graph neural networks allow us to simultaneously learn high-level information about nodes in each graph. From a practical point of view, this approach can be understood as: for user node $u_1$, user $u_2$ and $u_1$ have a high correlation, than we can recommend the items which is interested in $u_2$ to $u_1$, directly aggregate the information of $u_2$ to $u_1$. The user-user message propagation process can be summarized as:

(8) $h_u^k=\mathit{\sigma }\left(W_u\mathit{AGG}\left(h_u^{k-1},h_{N\left(u\right)}^{k-1}\right)+b_u\right)$(8)

where $h_u^k$ is the node feature matrix at the k-th layer, $W^u$ denotes the learnable matrix corresponding to the user type node, AGG represents the aggregated function. The detailed formula of AGG is:

(9) $\mathrm{AGG}\left({\mathrm{h}}_{\mathrm{u}}^{\mathrm{k}-1},{\mathrm{h}}_{\mathrm{N}\left(\mathrm{u}\right)}^{\mathrm{k}-1}\right)=\frac{{\mathrm{h}}_{\mathrm{u}}^{\mathrm{k}-1}+{\sum }_{\mathrm{j}\in \mathrm{N}\left(\mathrm{u}\right)}{\mathit{\alpha }}_{\mathrm{uj}}{\mathrm{h}}_{\mathrm{j}}^{\mathrm{k}-1}}{1+\left|\mathrm{N}\left(\mathrm{u}\right)\right|}$(9)

where $h_u^{k-1}$ denotes node feature matrix of node $\mathrm{u}$ at the (k-1)-th layer, $h_{N\left(u\right)}^{k-1}$ denotes the representation of the neighbors of node u under the (k-1)-th layer, $\mathrm{N}\left(\mathrm{u}\right)$ is the degree of node u, ${\alpha }_{\mathit{uj}}$ is the weight between node u and j calculated in subgraph reconstruction, which is also learnable. The complete formula for user-user information transfer is:

(10) ${\mathrm{h}}_{\mathrm{u}}^{\mathrm{k}}=\mathit{\sigma }\left({\mathrm{W}}_{\mathrm{u}}\frac{{\mathrm{h}}_{\mathrm{u}}^{\mathrm{k}-1}+\sum _{\mathrm{jeN}\left(\mathrm{u}\right)}{\mathit{\alpha }}_{\mathrm{uj}}{\mathrm{h}}_{\mathrm{j}}^{\mathrm{k}-1}}{1+\left|\mathrm{N}\left(\mathrm{u}\right)\right|}+{\mathrm{b}}_{\mathrm{u}}\right)$(10)

Item-Item Embedding Propagation

For item nodes, there is also important information transmission between high relationship items. We need to let this information be transmitted directly instead of being diluted in the user-item interaction graph, so we use the weighted sub-graphs for information aggregation. Our approach also has practical significance. Information transmission between item nodes with a high degree of correlation can be understood as: $i_1$ and $i_2$ have a high degree of correlation, and we can directly transfer the user node information around $i_1$ to $i_2$, because if a user likes a certain item, there is a high

probability that he also likes items similar to this item. The formula for item-item information transfer is:

(11) $h_i^k=\mathit{\sigma }(W_i\frac{h_i^{(k-1)}+\sum { }_{\mathit{j}\in \mathit{N}(\mathit{i})}{\alpha }_{\mathit{ij}}{h}_j^{(k-1)}}{(1+|\mathit{N}(\mathit{i})|)}+b_i)$(11)

Graph Score Prediction

Embedding Aggregate

After we get the embedded representations of users and items from $g_{\mathit{user}}$, $g_{\mathit{item}}$ and $g_{\mathit{ui}}$, we need to integrate them to predict the user’s rating for the user. Our approach is to concat the user representation in the user sub-graph with the user-item interaction graph becomes a complete representation of the user, as same as the item representation:

(12) $\begin{array}{c}{e}_u^{\ast }=e_u^{\left(u\right)}\parallel |e_u^{\left(ui\right)}\\ e_i^{\ast }=e_i^{\left(i\right)}\parallel e_i^{\left(ui\right)}\end{array}$(12)

where $e_u^{\ast }$ the final embedding representation of the user u, $e_u^{\left(u\right)}$ is the user embedding learned in the user sub-graph,$e_u^{\left(ui\right)}$is the user embedding learned in the user-item interaction graph,$\parallel$denotes the concat calculation.

Score Prediction

After we have obtained the embedding representations of users and items, refer to the operation of the classic recommendation model (He et al. 2020; Wang et al. 2019), we need to obtain the prediction scores of each user for items by way of inner product: way of inner product:

(13) ${\hat{y}}_{\mathit{SRCF}}\left(\mathit{u},\mathit{i}\right)=e_u^{\ast T}{\mathrm{e}}_{\mathrm{i}}^{\ast }$(13)

Optimization

To obtain optimal model parameters, we use the BPR loss[19], which is extensively used in recommend method (Chen et al. 2017; Koren, Rendle, and Bell 2022; Zhang et al. 2019). BPR assumes that existing interactions reflect user preferences and assigns higher predictive values to existing interactions than nonexistent interactions. The formula for BPR is:

(14) $\mathit{Loss}=\sum { }_{\left(\mathit{u},\mathit{i},\mathit{i}\right)}-\mathit{In\sigma }\left({\hat{\mathrm{y}}}_{\mathit{ui}}-{\hat{y}}_{\mathit{uj}}\right)$(14)

where $\left(\mathit{u},\mathit{i}.\mathit{j}\right)$ represents a triplet, $\mathit{u}$and $\mathit{i}$ are related nodes, and $\mathit{u}$ and $\mathit{j}$ are unrelated nodes, ${\hat{y}}_{\mathit{ui}}$ denotes the product of user $\mathit{u}$ and item $\mathit{i}$.$\mathit{\sigma }$ is the sigmod function,

Experiments

We test our model on multiple real-world datasets and answering the following questions:

• Q1 Compared with other recommendation models, does our model SRCF have an advantage in performance?

• Q2 Does the reconstruction of sub-graphs have a substantial effect in our model?

• Q3 In the training of the model, will the settings of some hyper-parameters affect the effect of the model?

Datasets

In order to evaluate the effect of our model SRCF, we select four public datasets in the real-world, namely: ML-100k, ML-1 M (Harper and Konstan 2015), Yelp, Gowalla (Cho, Myers, and Leskovec 2011), the detail of the datasets are shown in the Table 1. These datasets are different in scene, scale, and sparsity, and we can use the results on these datasets to fully measure the effect of the model. For each dataset, we divide 80% into a train set, 10% into a valid set, and the remaining 10% into a test set during training.

Table 1. The detail of various datasets.

Dataset	Users	Items I	Interactions	Density
ML-100k	943	1682	100,000	0.06305
ML-1M	6040	3629	836,478	0.03816
Yelp	45,478	30,709	1,777,765	0.00127
Gowalla	29,859	40,989	1,027,464	0.00084
Agri	12,386	16,942	1,268,737	0.00046

Baseline

We select seven recently proposed classical model models for comparison, so as to comprehensively evaluate the level of our model SRCF. Compared with our model, although these benchmark models have very good recommendation effects in their respective fields, they cannot learn the direct information transfer between homogeneous nodes in the bipartite graph, which is also their biggest flaw.

• BPRMF (Rendle et al. 2012) It is the first time to optimize the model through BPR loss, the most classic BPR model.

• NeuMF (He et al. 2017) It applies a multi-layer perceptron to learn the interaction relationship between nodes, so as to learn the embedding representation of users and items.

• NGCF (Wang et al. 2019) It firstly uses a GNN-based method to understand the high-order relationship between users and items, thereby improve the effect of collaborative filtering.

• MCCF (Sun et al. 2019) It learns the relationship between potential users and items in the user item bipartite graph based on the attention mechanism.

• DGCF (Wang et al. 2019) It obtains more accurate representation through separate learning of users and items, and improve the efficiency of model recommendation.

• LightGCN (He et al. 2020) It simplifies GCN (Kipf and Welling 2016a) by removing feature transformation and nonlinear activation.

• SGAT (Sun et al. 2022) It uses a sequential attention algorithm to obtain node representations.

• simGCL (Sun et al. 2022) Based on comparative learning and the introduction of directional random noise into the data, simGCL represents another recently proposed recommendation model in the domain of graph neural networks.

• RocSE (Sun et al. 2022) RocSE is a graph neural network based on adversarial learning, and the robustness of the model can be significantly improved by adversarial perturbation

Evaluation Metrics

In order to comprehensively test the effect of our model, we apply two evaluation metrics widely used in recommendation systems, namely RECALL@N and NDCG@N, and the values of N are 10, 20 and 50.

Personalized Recommendation (Q1)

The experimental results of personalized recommendation are shown in the Table 2. The data of our model is marked in bold. According to the data in the table, we can analyze: (1) LightGCN is the best model among most models except our model, followed by DGCF and NGCF which are two classic graph collaborative filtering models. (2) In most datasets, our model SRCF is better than all the comparison models. We believe that the reason why our model is superior to other models is that in addition to the user item bipartite graph, our model also learns the information of user sub graph and project sub graph, so that we can calculate the embedded representation of nodes more accurately. The functional analysis of each module in our model will be given in the ablation study section.

Table 2. Experimental results of personalized recommendation.

			BPRMF	NeuMF	NGCF	MCCF	DGCF	LightGCN	SGAT	simGCL	RocSE	SRCF
ML-100K	Recall@	10	0.2693	0.2479	0.2753	0.2731	0.2756	0.2814	0.2741	0.2876	0.2847	0.2913
		20	0.3961	0.3777	0.3979	0.3962	0.3983	0.4029	0.3999	0.4101	0.3988	0.4116
		50	0.6205	0.6016	0.6231	0.6217	0.6227	0.6334	0.6297	0.6427	0.6401	0.6437
	NDCGa	10	0.4461	0.4237	0.4494	0.4452	0.4507	0.4634	0.4546	0.4759	0.4713	0.4784
		20	0.4608	0.4419	0.4633	0.4586	0.4657	0.4763	0.4709	0.4827	0.4803	0.4858
		50	0.4608	0.4869	0.5115	0.5086	0.5113	0.5274	0.5263	0.5306	0.5297	0.5314
ML-1 M	Recall@	10	0.1796	0.1647	0.1855	0.1799	0.1861	0.1869	0.1804	0.1927	0.1876	0.1901
		20	0.2708	0.2493	0.2739	0.2721	0.2741	0.2813	0.2726	0.2837	0.2814	0.2846
		50	0.4314	0.4106	0.4347	0.4298	0.4356	0.4423	0.4365	0.4424	0.4397	0.4489
	NDCG@	10	0.2471	0.2309	0.2533	0.2512	0.2530	0.2511	0.2497	0.2553	0.2539	0.2562
		20	0.2564	0.2388	0.2615	0.2603	0.2614	0.2615	0.2603	0.2627	0.2624	0.2629
		50	0.3019	0.2872	0.3061	0.3029	0.3065	0.3072	0.3064	0.3092	0.3053	0.3107
Yelp	Recall@	10	0.0655	0.0542	0.0647	0.0633	0.0710	0.0725	0.0696	0.0787	0.0743	0.0803
		20	0.1022	0.0874	0.1028	0.1017	0.1132	0.1147	0.1098	0.1164	0.1143	0.1186
		50	0.1853	0.1644	0.1864	0.1853	0.1926	0.1998	0.1907	0.2032	0.1989	0.2065
	NDCG@	10	0.0455	0.0362	0.0446	0.0450	0.0502	0.0517	0.0477	0.0521	0.0502	0.0538
		20	0.0563	0.0471	0.0571	0.0582	0.0629	0.0641	0.0611	0.0639	0.0627	0.0648
		50	0.0788	0.0699	0.0801	0.0813	0.0851	0.0877	0.0812	0.0854	0.0846	0.0862
Agri	Recall@	10	0.8124	0.7996	0.8339	0.8407	0.8444	0.8532	0.8429	0.8359	0.8342	0.8671
		20	0.8272	0.8107	0.8405	0.8433	0.8473	0.8674	0.8537	0.8562	0.8437	0.8864
	NDCG@	10	0.8296	0.8139	0.8682	0.8762	0.8821	0.8863	0.8762	0.8739	0.8621	0.8911
		20	0.8338	0.8274	0.8774	0.8836	0.8979	0.9076	0.8993	0.8961	0.8703	0.9134
Gowalla	Recall@	10	0.1147	0.1022	0.1185	0.1109	0.1239	0.1267	0.1221	0.1317	0.1299	0.1339
		20	0.1687	0.1548	0.1766	0.1651	0.1829	0.1921	0.1802	0.1945	0.1914	0.1976
	NDCG@	10	0.0826	0.0726	0.08604	0.0787	0.0825	0.0831	0.0833	0.0879	0.0842	0.0891
		20	0.1001	0.0876	0.1021	0.0933	0.1034	0.1108	0.1067	0.1157	0.1132	0.1179

Ablation Study (Q2)

In this chapter, we will analyze the role of each module in our model through experiments. We will divide SRCF into three models, namely SRCF-, SRCF-user and SRCF-item:

• SRCF- : Remove user and item sub-graph reconstruction modules.

• SRCF-user : Remove user sub-graph reconstruction modules.

• SRCF-item : Remove item sub-graph reconstruction modules.

Like the personalized recommendation experiments, we use Movielens-1 M, Yelp and Gowalla as test datasets., the evaluation Matrix are Recall@10 and NDCG@10.

Table 3 shows the experimental results of our model after removing each module. From the table, we can analyze and get: (1) SRCF has the best effect, that is to say, the best effect can be achieved only after the modules are combined together. The effect of SRCF-user is ranked second, and the worst is SRCF- with two sub-graph reconstruction modules removed. (2) We believe that the reason for such experimental results is that there is important information transfer between homogeneous nodes, the data in the table also confirms that there is effective information transmission in both the user sub-graph and the item sub-graph, which is particularly important for the task of recommendation.

Table 3. Ablation Study.

	M1-lM		Yelp		Gowalla
	Recall@10	NDCG@10	Recall@10	NDCG@10	Recall@10	NDCG@10
SRCF-	0.1831	0.2492	0.0658	0.0444	0.1198	0.0854
SRCF-user	0.1877	0.2571	0.0782	0.0526	0.1296	0.0881
SRCF-item	0.1846	0.2543	0.0736	0.04570.0861	0.1263	0.0861
SRCF	0.1901	0.2652	0.0803	0.0538	0.1339	0.0891

Hyper-Parameters Sensitivity (Q3)

In this section, we will tune different hyper-parameters for experimental analysis and observe whether different hyper-parameters will change the performance of the model.

Figure 5 shows the influence of different aggregation layers on the experimental results of the model. It should be noted that our aggregation layers are uniform for the three graph structures. From the experimental data, we can find that the effect of the model is the best when the number of aggregation layers is 2, and the effect is the worst when the number of aggregation layers is 1. Due to the characteristics of the graph neural network, when the number of aggregation layers is 2–3, it will aggregate to most of the surrounding high-order Figure 6. Effects of Different Aggregation Layers of Graph Neural Network associated nodes, thus showing the best performance, and when the number of layers is too large, the graph neural network will be lead to over-fitting due to the aggregation of too much content. Because of this property, our method can not only learn high-order relations in user-item interaction graphs, but also learn high-order relations in user sub-graphs and item sub-graphs, which is the strength of our model.

Figure 5. Effects of different aggregation layers of GNN-based methods.

Figure 6. Effects of different aggregation layers of graph neural network.

Figure 6 shows the impact of different embedding dimensions on the model results. The left picture changes the dimension of the node features, and the right picture changes the hidden layer dimension of the graph neural network. From the figure, we can see that when the dimension is 64, the effect of the model reaches the highest value, and too few or too many dimensions will lead to a decline in the experimental results. We analyze that too few dimensions cannot allow the model to learn sufficiently accurate information, and when the dimension is too large, the model will learn too much information which cause over-fitting.

As shown in the Figure 7, the influence of the number of edges of each node in sub-graph reconstruction on the effect of the model is shown. To consider the difference of data sets, we conducted experiments in three data sets. From the data in the table, we can get: (1) In the M1-1 M, the effect of the model is the best when the edge of the node is 4, while in Yelp and Gowalla, the effect is the best when the edge is 5. Both too few edges and too many edges will lead to a decrease in the effect of the model. (2) In sub-graph reconstruction, each node needs to have 4 or more edges, but too many edges will lead to a decline in the effect of the model. We think that different data set structures will have different requirements for the size of the sub-graph. In M1- 1 m, the average connection of users to items is higher than Gowalla and Yelp, which also makes it unnecessary to have too many edges in the sub-graph to transfer information. But what is certain is that no matter which dataset, after adding the sub-graph, our model can obtain better performance.

Figure 7. Effects of the number of edges reconstructed by the model.

Conclusions

In this paper, we have proposed an Enhanced Sub-graph Reconstruction Graph Nerual Network for Recommendation, we construct a graph encoder on the basis of structural learning to mine the information transfer between homogeneous nodes hidden in user-item interaction graphs, construct these relationships into a weighted user sub-graph and a weighted item sub-graph, which enhances the information transfer be tween nodes, and finally we merge the information on the sub graph with the CF signal on the user-item interaction graph, get the final node embedding. Through a large number of experiments, it is confirmed that our method is effective, and the construction of sub-graphs can improve the effect of the model. Compared with the traditional method, our method can obtain the information transfer between homogeneous nodes with high correlation, which can effectively improve the effect of our model recommendation. It can also be seen from our experimental results that removing any one of the two subgraphs will affect the effect of the model, which also illustrates the importance and effectiveness of the subgraph from another aspect. In the future, inspired by (Areeb et al. 2023; Himeur et al. 2022, 2022) and (Caro-Martínez, Jiménez-Díaz, and Recio-Garcia 2023; Markchom, Liang, and Ferryman 2023; Sardianos et al. 2021),we will carry out two aspects of work in the follow-up work: 1. Research on privacy protection, security and filter bubbles, and combine them with the algorithm of the recommendation system. 2. Research can explain the role of sex in recommendation systems. In addition, we hope to add more node attributes in the next work, so as to achieve more accurate relationship prediction.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data that support the findings of this study are available in the public domain:

ML-100k, https://grouplens.org/datasets/movielens/100k

ML-1 M, https://grouplens.org/datasets/movielens/1m

Yelp, https://www.yelp.com/dataset/download

Gowalla, https://snap.stanford.edu/data/loc-gowalla

Additional information

Funding

This study was supported by Key R&D Projects in Zhejiang Province [2022C02009, 2022C02044, 2021C03138]. Scientific Research Project of Zhejiang Province [No. LGG22F020010, LGG21A010001].