A novel Knowledge Graph recommendation algorithm based on Graph Convolutional Network

Abstract

Knowledge Graphs (KGs) are widely used in many fields of application, and especially play an essential role in recommendation systems. KGs often need to be complete, missing relationships between users and items, data sparsity, weak associations, and difficulties in knowledge inference, resulting in low credibility of recommendation results. Therefore, we propose a novel Knowledge Graph (KG) recommendation algorithms. Due to the availability of interaction data across numerous events, KGs also exhibit dynamics over time. By taking into account the temporal variable, it is possible to organise well-structured external information to connect users and items, thereby expanding user preferences to a certain extent. The proposed algorithm employs GCNs to encode the heterogeneous graph, which includes user-item interactions and the KG. It addresses the challenge of high-dimensional data by using the inner product of users and items. The algorithm uncovers potential alignment relationships and learns the embedding of user-item and relationships by applying convolutional processing to the graph data's features and performing data fusion, the new algorithm uncovers potential alignment relationships, and learns embedding of user-item and relationships. The experimental results on the Mean Reciprocal Rank (MRR) and Hits@k demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in terms of the credibility and accuracy of recommendation results.

KEYWORDS:

• Graph Convolutional Network
• Knowledge Graph
• embedding dimension
• connection prediction
• credibility

1. Introduction

With the rapid advancement of the Internet and information technology, the world has entered the digital era, leading to exponential growth in data and information generation daily. Filtering out relevant and valuable information that people truly need from this vast sea of data has become increasingly challenging. In recommendation systems, Knowledge Graphs (KGs) contain a wealth of facts and semantic relationships between items. However, their success relies on high-quality KGs, and real-world KGs often suffer from noise and topic-independent connections between users and items. This noise and sparsity can lead to inaccuracies in representing user-item dependencies. To address this problem, Yang et al. (2022) proposed a Knowledge Graph Contrast Learning Framework (KGCL), which reduces KG noise by suppressing noisy information in the KG aggregation process, resulting in more robust item representations with improved knowledge perception. Furthermore, KGCL uses additional supervisory signals during KG enhancement to guide cross-view contrast learning, which helps improve user-item interactions in gradient descent and further reduces noise. Cao et al. (2022) introduced a method called Cross-Modal KG Contrast Learning (CKGC) in 2022. CKGC treats information from descriptive attributes and structural connections as two modes and learns node representations by maximising the consistency between these two views. This approach utilises both descriptive and structural information to provide necessary oversight. In another context, historical bicycle GPS data and track-recorded DL-PBS (Dynamic Bicycle Parking System) systems are used to create graphical representations of bicycle parking facilities. These historical records are organised based on temporal–spatial subsets aligned with municipal administrative divisions and chronological context. Each subset corresponds to bicycle GPS data and administrative regions within specific timeframes (Chen et al., 2021). Information overload has emerged as a significant obstacle, hindering people from retrieving and utilising knowledge. Recommendation systems can effectively mitigate the challenges of information overflow, which mines and identifies user interests and needs by analysing historical user behaviour data. However, due to limited user-item interactions and personalised user behaviour, data sparsity and cold-start problems often occur. As a result, filtering out what users are genuinely interested in from the massive amount of data becomes very difficult.

GCNs have emerged in recent years as an efficient neural network architecture for handling graph-structured data. Traditional convolutional neural network models are limited to processing data with Euclidean structures. They cannot effectively convolve on graph structures by sharing the exact size of the volume nucleus due to the lack of translational invariance in graph nodes (Simon et al., 2023). GCNs address this limitation by considering the graph structure between nodes and the available node attributes. They find a mapping relationship from node attributes to a new space (node embedding), providing an effective solution for graph node embedding (Ghorbani et al., 2019). This allows GCNs to obtain graph features and node representations by using convolutional methods on the node and relational graph structure. Consequently, GCNs have shown remarkable performance in various graph-based applications, including node classification, link prediction, and graph classification (You et al., 2020). For instance, in 2022, Zhu et al. proposed a knowledge representation-driven traffic prediction method based on the spatiotemporal Graph Convolutional Network(GCN), which constructs a traffic prediction KG and utilises the knowledge representation learning method KR-EAR for knowledge representation (Zhu et al., 2022). The comprehensive fusion of nodal characteristics with the topological structure of user attributes and project properties, as discussed by Kang et al. (2023), enables a more in-depth understanding of user information. Similarly, Lin et al. introduced a recommendation method that combines high-order feature interactions and KGs to learn potential user-item associations from graph-structured data (Lin et al., 2022). However, when dealing with large-scale graph-structured data, GCNs encounter many challenges, such as poor model training efficiency and the inability to effectively address the data-dimensional explosion.

To address the challenges of data sparsity, cold-start problem, and exploding data dimensions, we propose a novel solution, which involves merging various auxiliary information (including user-item attributes, social network data, and contextual information) into the recommendation model and performing low-dimensional embeddings. Through training the neural network model, it uncovers the underlying connections between users and items, thereby recommending what users are truly interested in. To tackle the cold-start problem, the structured auxiliary information and semantic knowledge from the KG are fully used, which provides a reliable data foundation and logical basis for the recommendation results. Then, neural network methods, knowledge embedding techniques, and heterogeneous graphs are employed to further analyse and explore the connections between users and their interests. This effectively alleviates the challenges posed by the cold-start problem. To handle data sparsity, we utilise convolutional neural networks to learn structural information, facilitating the fusion of multiple data types. More detailed and accurate measures of the closeness between users and items are obtained by mining potential information associations, thereby mitigating data sparsity. Finally, to address the issue of exploding data dimensions, a transformer that utilises encoding and decoding processes for heterogeneous graph embedding is introduced, effectively resolving the problem of high-dimensional data. In summary, our main contributions are as follows:

1. We introduce a pioneering recommendation model named KG-GCNR, leveraging a transformer-based graph encoder, and devise a decoding technique for entity embedding to tackle high-dimensional data.

2. To enhance recommendation performance and establish robust interpretability, GCNs are employed for extracting insights from graph structures, facilitating the integration of diverse data modalities. Subsequently, we leverage user access probabilities to uncover potential pathways, thereby augmenting the precision of the ultimate recommendation outcomes.

3. Extensive experimentation on two widely employed datasets has empirically substantiated the superior performance of our novel KG-GCNR-EIP (where “EIP” refers to Entity-embedding Inner Product) approach over the top-performing baseline models. Furthermore, a meticulous manual evaluation has ascertained that KG-GCNR consistently delivers more dependable recommendation outcomes than alternative methodologies.

The rests of this paper are organised as follows. Section 2 reviews related works including traditional recommendation algorithms as well as recommendation algorithms based on the combination of KGs and GCNs. Section 3 provides a detailed description of our models and methodologies. In Section 4, we compare experimental results and introduce the details of ablation experiments. Finally, we draw a conclusion in Section 5.

2. Related works

2.1. Traditional recommendation algorithms

Traditional and typical recommendation methods mainly include collaborative filtering and content-based recommendation algorithms. Collaborative filtering relies on users’ historical interactions with items to predict their future behaviour and has proven successful in various applications by selecting valuable content and recommending them to users. However, if users have limited interactions or no interactions with certain items, data sparsity and cold-start problems may occur. In such cases, collaborative filtering algorithms struggle to extract users’ deep needs and interest preferences from sparse interaction data, resulting in significant deviations between recommended content and users’ actual preferences (Wang, Zeng, Chen, Zhao, & Chen, 2022). The principle of Content-based recommendation algorithms is that they learn true interests and preferences from the history of user-item interactions and recommend the similar contents. It can effectively alleviate data sparsity issues to a certain extent. However, in practical applications, content-based recommendation algorithms face challenges in extracting item features, and they only consider items’ characteristics, neglecting users’ behaviours. As a consequence, the recommended results lack diversity.

Due to the limitations of traditional recommendation algorithms and the uncertainty in data representation, researchers have attempted to apply KGs and GCNs to recommendation systems to achieve better results. By using external knowledge, KGs can find additional connection between users and items, and then provide valuable auxiliary information for heterogeneous graphs, improving recommendation performance. By leveraging users’ historical interactions with items, entities can be linked to the KG. Subsequently, entity attributes can be utilised to enhance recommendations. Enhanced recommendations, facilitated by the connection between users and items, have the capacity to explore more comprehensive path information. Introducing KGs into information recommendation systems can represent more semantic relationships, deeply explore user interests, and model user preferences for attributes. In 2022, Wei et al. proposed a Knowledge Graph-based Causal Recommendation framework (KGCR), which achieved user preference learning and used counterfactual reasoning to eliminate biases in similarity calculations (Liu et al., 2022). Recognizing the incompleteness of real-world information, Ines Chami et al. utilised a hyperbolic KG embedding model, combining hyperbolic reflections and rotations to capture hierarchy and logical patterns to predict missing facts (Niu et al., 2022). This approach partially alleviates data sparsity and cold-start problems, improving recommendation effectiveness.

In summary, traditional recommendation algorithms mainly rely on simple user-item interaction data. However, due to singularity of user-item interaction data, these methods face the problem of data sparsity, leading to low recommendation accuracy. Introducing KGs into recommendation algorithms can partially alleviate this issue, but it requires extensive manual work and data preprocessing, which can lead to issues such as increased data dimensions, error propagation, and weak interpretability of recommendation results. To overcome these challenges, a technology solution is designed that combines KGs and GCNs for data feature extraction and processing. This method can result in significant savings in human effort, enhance recommendation accuracy, and alleviate challenges associated with dealing with high-dimensional data.

2.2. Recommendation algorithms based on a combination of KGs and GCNs

The existing research on recommendations for KGs has faced challenges in meeting desired standards, primarily due to the heterogeneous nature of KGs. In response to these limitations, Liu and his colleagues introduced a novel recommendation approach, which involves iterative enhancements to the HGKR model (Liu et al., 2023). The HGKR model aimed to provide a more nuanced representation of recommended KGs by treating the Knowledge Graph as a historical framework. This involved message propagation across both graphical and semantic layers within the neural network and the aggregation of entities within a KG. Additionally, an attention mechanism was developed based on the knowledge perception project filter. This mechanism aimed to capture latent user interests and enhance recommendation effectiveness by leveraging historical user preferences.

To address error propagation issues and weak interpretability in Knowledge Graph-based recommendation systems, a common approach is to integrate GCNs with the KG, which combines user-item interactions and the KG into a heterogeneous graph and utilises GCN technology for computation. In order to capture the information sequences carried by adjacent user-item interactions, Li et al. proposed a Graph Convolutional Network-based Recursive Evolution Network in 2021. They achieved this by recursively modeling the KG sequence learning the evolving representation of users, items, and relationships at each timestamp (Li et al., 2021). In 2022, Zhao et al. introduced an end-to-end ultrasound standard surface detection (USPD) model with a focus on placental data. This model was designed as a multi-task learning system and incorporated a hybrid KG. This approach involved breaking down complex processes into two interconnected tasks: the identification of critical anatomical features and the classification of surfaces (Zhao et al., 2022).

To discover representations of the same object across different KGs, Liu et al. introduced a novel node-level information fusion framework, which involves learning alignment signals between attribute information and names and then achieving strong fusion of structure, attribute, and name information through continuous propagation in multiple neighbourhood contexts, leading to more detailed user-item representations (Koke, 2023). In 2023, Wang et al. introduced the User Interactive Knowledge Recommendation Model (UIKR), which augments user representation and incorporates advanced collaborative signals derived from user interactions into project representation learning. This facilitates the propagation of user preferences within knowledge charts and contributes to acquiring personalised project representations (Wang et al., 2023). To address the problem of sparse KG data, Niu et al. proposed a novel KGC model in 2022 that encodes and decodes feature information. Their model utilises subgraph sampling to extract node structures, introduces channel attention convolution to encode node structure features using GCNs in matrix form, thoroughly mining node feature information, and finally, decodes the high-dimensional structure analysis weight embedding of the encoded matrix to reduce the embedding dimension with minimal performance degradation (Yu et al., 2022). Session-based recommendations employ a spectrum of deep learning models for extracting item pairs, projecting transferable information, predicting the subsequent item of interest grounded in an anonymous behaviour sequence, and constructing user preference models. These models facilitate the timely and efficacious recommendation of potential user interests, fostering product marketing efforts (Wang, Zeng et al., 2022). Wang et al. proposed an MI-KGNN (Multi-dimensional Interaction Knowledge Graph Neural Network) to enhance KG-aware recommendation algorithms. MI-KGNN represents the similarity between users and items through information propagation and aggregation in the KG, effectively capturing and representing structural and semantic information. It addresses issues related to insufficient node interactions or improper node weighting during information propagation (Wang, Wang et al., 2022). These techniques combining GCNs with KGs have been proven effective in enhancing recommendation systems, reducing data sparsity, and improving the interpretability of recommendations. In 2022, Elahi and Halim (2022) introduced a comprehensive recommendation model known as the graph-based synchronous filtration (GACF). This approach falls under the category of communication-based methods and explicitly encodes collaborative signals derived from user-item interaction data. The model utilises cognitive perception through an attention mechanism to systematically integrate entities that share similar relationships with a given entity. Moreover, it assigns varying weights through attention mechanisms to generate personalised recommendations for individual users. In 2023, Chen and his team presented the Knowledge Graph Network, KDL-GCN, as a solution to address the complexities associated with information-rich KGs. This approach simplifies KGs by creating multiple interactive graphs to harness extensive information. Additionally, it involves the development of a deep, lightweight graph network that optimizes the utilization of high-level neighbouring domain information (Chen & Xiao, 2023).

3. Methodology

This section primarily focuses on introducing the recommendation algorithm (model) KG-GCNR. Firstly, we present the key recommendation questions that arise during the recommendation process. Next, we analyse the proposed algorithm and provide a detailed explanation about it. Finally, we describe the training and optimisation process of the KG-GCNR model.

3.1. Problem description

Given a set of users U, items V, and a set of relationships R, the KG is represented by triplets (h, r, t), where h ∈ U and t ∈ V represent users and items, and r ∈ R denotes the corresponding relationship between users and items. Typically, each user-item pair and relationship in a KG is associated with an embedding vector.

To consider the correlations with external factors when predicting user-item interactions, we first construct a KG based on the interaction relationships between users and items. Then, we utilise a KG representation learning model to obtain embeddings for the relevant KGs. Next, to integrate the KG into the main GCN, we combine user-item interaction features with KGs by utilising analogous attributes and relationships. This produces a composite graph, which can be then processed by techniques from GCNs. By iteratively applying graph convolution and aggregating neighbourhood information, we calculate embeddings for users and items. This approach allows the GCN to capture the knowledge structure and semantic relationships between interaction information and attributes and the spatiotemporal features of user-item interactions. The workflow of this model is illustrated in Figure 1.

Figure 1. KG-GCNR workflow diagram.

3.2. Model analysis

In the KG-GCNR model, we calculate the embedding vectors for each user-item pair and relationship in the KG. The user-item interaction information and the KG are fused into a heterogeneous graph, which serves as the input and is fed into the encoder. Potential relationships are extensively explored by considering the user's access probabilities to items and the likelihood of correlations between items. These relationships are then propagated layer by layer outward, with each item updating its representation based on its neighbouring items. The decoding of the encoded heterogeneous graph is achieved by computing the inner product between users and items, which leads to the recommendation objective.

To obtain features for each given user and its neighbouring users, we use weighted sum and aggregator. The neighbouring users are aggregated using the mean function. The sum aggregator combines these representations with a non-linear activation function. Specifically, for a given user, we can initialise their embedding using the original user features that were pre-trained with external knowledge at the initial layer. At higher layers, user embeddings are computed through graph convolution operations.

The calculation for the user’s embedding is as follows: (1) $e_i^{(l+1)}=\theta \left(W_{\mathrm{self}}^{(l)}{e}_i^{(l)}+\sum _{j\in N_i}\frac{1}{|N_i|}{W}^{(l)}{e}_j^{(l)}\right)$(1) where $e_i^{(l+1)}$ and $e_i^{(l)}$ represent the embeddings of user i at the $(l+1)$-th and $(l)$-th layer, respectively. $N_i$ is the user matrix of user i. $W_{\mathrm{self}}^{(l)}$ and $W^{(l)}$are the weight matrices for transforming the user’s onformation and the information of its neighboring users, respectively. After L layers of convolutional operations, there are L representations for a given user. Then, calculate embeddings at each layer by using weighted summation, i.e. a weighted sum from $e_i^{(l)}$ to $e_i^{(L)}$. Let $e_i$ denote the final representation of the user, and its weighted summation of rewordss defined as: (2) $e^i=\sum _{l=0}^L{w}_l{e}_i^{(l)}$(2) where $W_l$ i.e. the weight of the $(l)$-th layer, indicates the importance of the $(l)$-th layer to the final target of the recommendation. The embedding computed at each calculation layer can assist in capturing different semantic information, thereby making the representation more comprehensive and informative (Figure 2).

Figure 2. Some user-item relationships are discarded.

To recommend items for a user, we establish connections by computing the access probability between the user and items and then propagate it outward to other items. This process helps to uncover the potential relationships between users and items. The possible relationships between users and items represent high-order connectivity in the graph and can be extracted to form multiple paths between user-item pairs. Given that high-order connectivity between a given user and candidate items can reflect the potential relationships between the user and other items, we explicitly extract multiple paths for each user-item pair on the heterogeneous graph to obtain representations of the possible relationships between users and items. The calculation of access probability is as follows:

The k-th order access probability for a user is $S_i^k$, the triplet set of users and items is defined by: (3) $S_u^k=\{(h,r,t)\in \text{Gandh}\in {\epsilon }_u^{k-1}\},k=1,2,3,\dots ,$(3) Given a user i and a candidate item j as inputs, the output is the probability of user i accessing candidate item j. User i’s historical records $V_i$represent its potential interests and serve as the starting point for interest propagation on the KG, generating various interest sets $S_i^k(k=1,2,\dots )$. Each candidate item is represented as a d-dimensional vector $V\in R^d$. Given user i's visit history $V_i$ and a triplet $(h_i,r_i,t_i)$ on the first-order interest set, along with the candidate item j, the correlation probability $p_i$ is calculated as follows: (4) $p_i=\text{softmax}(v^T{R}_i{h}_i)=\frac{\exp (v^T{R}_i{h}_i)}{{\sum }_{(h,r,t)\in S_u^1}\exp (v^T{R}_i{h}_i)}$(4) where $R_i\in R^{d\times d}$ is a $d\times d$-dimensional matrix representation of the triplet relations on the first-order interest set, and $h_i\in R^d$ is a d-dimensional vector representation of the user and item in the triple. The correlation probability $p_i$ can be interpreted as the semantic correlation of the candidate item j with the user history $V_i$ with respect to the triple relation $r_i$. Potential interests will then be propagate from user-item $h_i$ to user-item $t_i$ on the first-order interest set, accumulating at the next layer of user-items pair. Therefore, using the relevance probability $p_i$ as weights, we can sum up all user-items’ $p_i$ to obtain the potential interest representation on the first-order interest set: (5) $S_i^1={\sum }_{(h_i,r_i,t_i)}{p}_i{t}_i$(5) where $t_i\in R^d$ is the d-dimensional vector representation of the user and item $t_i$.

For the interest representation $S_i^2$ of the second-order interest set simply replace v in equation (5) with$S_i^1$, keeping the rest unchanged. For higher-order interest sets, it is sufficient to repeat the above iterative process. The vector representation of user i is defined as the accumulation of all interests in each interest set at every layer: (6) $i=S_i^1+S_i^2+\dots +S_i^k$(6) The recommended results should consider the timeliness of item information, giving higher weight to more recent information. Therefore, the time weight for a label is defined as follows: (7) ${\text{W}}_{\text{Time}}^{\text{i}}\text{ = }{\text{e}}^{-\epsilon \ast \frac{{\text{S}}_{\text{new}}{\text{ - S}}_{\text{UT}(\text{x})}^{\text{i}}}{{\text{S}}_{\text{new}}{\text{ - S}}_{\text{UT}(\text{1})}^{\text{i}}}}$(7) where $\epsilon (0\le \epsilon \le 1)$ is the time offset coefficient, the larger $\epsilon$ the greater the time weight, while $\epsilon =0$ means no consideration of time factors. ${\text{S}}_{\text{new}}$ represents the user’s most recent usage time of the label, ${\text{S}}_{\text{UT}(1)}^{\text{i}}$ represents the user’s first usage time of the label, and ${\text{S}}_{\text{UT}(\text{x})}^{\text{i}}$ denotes the time when the user ${\text{u}}_{\text{i}}$ used the tag ${\text{t}}_{\text{i}}$ for the x-th time.

Finally, the user’s vector representation i and the candidate item's vector representation j are combined through an inner product to obtain the predicted probability of the user accessing the candidate item: (8) ${\hat{\mathrm{y}}}_{\text{ij}}=\text{sigmoid}({\text{i}}^{\text{T}}\text{j}){\text{W}}_{\text{Time}}^{\text{i}}$(8) Based on the access probabilities, we can mine the latent relationships between users and items and discover more paths connecting users and items. By analysing these paths, we can gain insights into why certain items are recommended to specific users.

3.3. Decoding

The information above demonstrates the effective representations of users, items, and relationships. The next crucial task is decoding, with the aim of scoring the pre-recommended information in the encoded heterogeneous graph by combining the embeddings present in the target users and items.

EIP is a technique used during the training process to discard relationships with low interaction probabilities between users and items. By doing so, it reduces unnecessary resource consumption and improves the performance of the KG-GCNR model. The EIP method allows the model to focus on the most relevant and significant relationships, leading to more efficient and accurate recommendations.

By giving user i's access history $V_i$, the access probability formula (7) is calculated to choose to lose the relationship between some users and items.

Based on a given triangle (h, r, t), the score is calculated by calculating the amount between the user entity embedded and the item entity Embedded: (9) $\delta (\text{h},\text{r},\text{t})={\text{e}}_{\text{h}}^{\text{T}}{\text{e}}_{\text{t}}$(9)

3.4. Training

In knowledge perception recommendations, recommended data includes user-item interactions and knowledge diagrams, there are associations and constraints between the three groups in the knowledge diagram. In this article, by calculating the probability of access between users and items by interest sets, the quality of the path is measured, thereby cutting out the unrelated path from the noisy diagram with an input of a user i and a candidate item j, output that user i access the item j's probability. The historical record of a user, denoted as $V_i$, signifies their initial interests. It serves as the starting point for interest propagation across the KG, leading to various interest levels represented as $S_i^k(k=1,2,\dots )$. Each embedded candidate is represented as a d-dimensional vector $v\in R^d$. Considering the prevalence of these relationship patterns in user-item interactions and KGs, access probability is the optimal choice for path extraction and module selection.

In the recommended model KG-GCNR, there are interactions between users set to 1, no interactions set to 0. In order to train recommended models, we use binary crossover losses for optimisation. Use the following target functions to optimise and train our models: (10) $\mu =-\frac{1}{|\text{V}|}{\sum }_{\text{t}\in \text{V}}{\text{y}}_{\text{h}}\log {\text{p}}_{\text{t}}+(1-{\text{y}}_{\text{h}})\log (1-{\text{p}}_{\text{t}})$(10) Where $p_t=\sigma (\phi (h,r,t))$ $y_h=\{\begin{array}{ll}1& \mathit{\text{if interact}},\\ 0& \mathrm{otherwise}.\end{array}$In the above equation, $\sigma (\cdot )$ is the logical softmax function and V is the set of all items.

Based on the recommended model KG-GCNR, the reliability of recommended results is assessed by Recall@k, Precision@k and F1. Selected model testing consists of k items with the highest predicted click-through rate. (11) $\begin{array}{rl}& \text{Precision}@\text{k}=\frac{{\text{Q}}_{\text{i}}}{\text{Q}}\end{array}$(11) (12) $\begin{array}{rl}& \text{ Recall}@\text{k}=\frac{{\text{M}}_{\text{i}}}{\text{M}}\end{array}$(12) (13) $\begin{array}{rl}& {\text{F}}_1=\frac{2\ast \mathrm{Precision}@\mathrm{k}\ast \mathrm{Recall}@\text{k}}{\text{Precision}@\text{k}+\text{Recall}@\text{k}}\end{array}$(13)

In this case, M is the total number of related items, $M_i$is the correct number of item predictions in the total amount of items related. Q is the overall number of items predicted candidates, $Q_i$ represents the correct amount of forecasts. The correct number is in all items of prediction, the number of items users are interested in. The higher the likelihood of user engagement with a candidate item, the stronger the user's interest in the recommended item, leading to an increased click-through rate.

4. Experiments and analysis of results

To verify the efficiency and effectivity of the proposed model, we compare it with state-of-the-art models on two widely recognised link prediction benchmarks.

4.1. Experimental setup

4.1.1. Datasets

We conducted experiments on two widely used KG datasets, i.e. FB15k-237 and WN18RR. The detailed descriptions of these datasets are presented in Table 1, including information about user-item interactions and KG relationships. Both datasets are publicly available, and their usage is legitimate and ethical.

Table 1. The notation used in this manuscript.

Notation	Description
KG-GCNR	A recommendation model combining KG and GCN
V	The set of users and items
R	The set of relations
(h,r,t)	The Knowledge Graph triple
$e_i^{(l)}$	The embedding of node i
$e_i$	The final representation of user i
$S_i^k$	The k-level definition of user i
$p_i$	Triples on interest sets are associated with probabilities of post-option items
$O_u^1$	The user’s order 1 interest set
${\hat{y}}_{\mathrm{ij}}$	The access probability of the user accessing the item
$N_i$	N-i is the user matrix of user i
G	G refers to Knowledge Graph
j	candidate item j

FB15k-237 comprises 14,541 users and items, encompassing 237 distinct relationship types. It represents a subset of the larger FB15 K dataset, a subset of the Freebase dataset. The “15k” in the name indicates the presence of 15,000 main entities in the knowledge base, and “237” represents the total number of different relationships. The knowledge base of FB15k-237 is extracted from Freebase and forms a subgraph with selected main entities. FB15k-237 encompasses both forward and reverse relationships, which convey identical semantics but exhibit opposing directionalities. As a result, the number of unique relationships is 237, while considering both forward and backward versions, it becomes 237*2 = 474. Nonetheless, the FB15k-237 dataset omits the reverse relationships found in FB15 K, yielding 237 distinct relationships.

WN18RR is a subset of WordNet and contains 40,943 users and items, with 11 types of relationships. Being a subset of WordNet, WN18RR does not suffer from the issue of information leakage between the training, testing, and validation datasets, making it more challenging compared to the original dataset.

4.1.2. Baselines

We compared our approach against several robust baseline methods and state-of-the-art models spanning various categories. We selected the following models for our analysis: ConvE, QuatE, two Transformers-based models, namely CoKE and HittER, the Neural Network Method in Eurydice Space, TuckER, Hyper, the Quantum Factor Decomposition Model in Euridice Space, MuRP, and ATTH, a model based on the double-curved space approach. We conducted a comprehensive analysis, comparing these different method models to assess their advantages and limitations.

ConvE (Chami et al., 2020) is a multi-layer convolutional neural network model used for link prediction. It utilises 2D convolutions on embedded KGs with multiple layers of non-linear features. ConvE efficiently expresses these features using fewer parameters, making it robust against overfitting caused by batch normalisation and dropout.

MuRP (Balažević et al., 2019c) learns relation-specific parameters by transforming entity embeddings through Mobius matrix-vector multiplication and Mobius addition.

HypER (Balažević et al., 2019a) generates relation-specific convolutional filters and applies them to entity embeddings. Its hypernetwork components allow for information sharing between relation vectors, enabling cross-relation multi-task learning.

ATTH (Sun et al., 2019) combines hyperbolic reflection and attention models to handle complex relation patterns. It learns embeddings with trainable hyperbolic curvature, enabling it to capture the correct geometric shape for each relation and generalise across multiple embedding dimensions.

TuckER (Balažević et al., 2019b) performs multi-task learning across relations by utilising Tucker decomposition on a binary tensor representing KG triplets.

CoKE (Wang et al., 2019) explores two types of graph contexts: edges and paths. Using Transformer encoders, CoKE obtains context-aware representations for entities and relations from given sequences of entities and relations, capturing their contextual semantics.

HittER (Chen et al., 2020) is a hierarchical transformer model consisting of two parts. It extracts features for each entity-relation pair in the local neighbourhood of the source entity, and then aggregates the relationship information from the previous part. It proves effective in learning KG embeddings in complex multi-relational graphs.

R-GCN (Degraeve et al., 2022) generates representations for nodes of interest by repeatedly aggregating their neighbours through parameterised and relation-specific transformations. It can directly handle the highly multi-relational data properties of nodes and edges in real-world KGs.

VR-GCN (Ye et al., 2019) is a vectorised relation GCN that can simultaneously learn graph embeddings for entities and relations in multi-relational networks. It incorporates role distinction and translation characteristics of KGs during the convolution process. The framework uses anchor points for supervision in the objective function, aiming to minimise the distance between anchor points and generate new cross-network triplets to establish bridges between different KGs, thus enhancing alignment performance.

CompGCN (Vashishth et al., 2019) is a novel graph convolution framework that jointly embeds nodes and relations in a relational graph. It utilises various entity-relation combination operations from KG embedding techniques, scaling with the number of relations, and addresses the over-parameterisation problem by sharing relation embeddings across layers using a base decomposition.

4.1.3. Evaluation programme

We use two commonly used standard metrics in recommendation methods to evaluate the performance of our model, i.e. Mean Reciprocal Rank (MRR) and Hits@k. These metrics are based on the ground-truth triplets and calculate the probability relative to the ranking of all triplets. Subsequently, we calculate and rank all the remaining triplets, recording the ranking of the actual triplets. The experiment follows the complete ranking protocol, which involves ranking users and items based on their interactions. MRR is the average reciprocal rank of the true triplets. Hits@k ratio represents the percentage of true triplets ranked below or equal to k.

Based on the principles of click-through rate and Top-k recommendations, we design experiments by recommending the top k candidate items to users. The items that users click on are considered as their interested items, i.e. the correctly recommended items. The evaluation of the proposed model's performance entails the computation of precision, recall, and F1 score.

Access probability refers to the likelihood of recommending an item to a user with a predefined threshold of 0.5. If ${\hat{\mathrm{y}}}_{\text{ij}}$ >  = 0.5, we recommend candidate item j to user i. We employ AUC (Area Under the Curve) and ACC (Accuracy, calculated as the area under the ROC curve) as evaluation metrics to evaluate the access probability.

4.1.4. Implementation details

In the experiments, we mainly encode the heterogeneous graph composed of user-item interactions and KG, and then use the EIP decoding method to achieve good recommendation results. The batch size is set to 1024, with the learning rate being selected from 0.01, 0.001, 0.0001, and 0.00001. We choose the number of GCN layers to be 1, 2, 3, and 4, and select corresponding layer combination coefficients from 1/3, 1/4, and 1/5. The access probability, denoted as y, is calculated by the inner product of users and items. In the GCN path encoder, the embedding dimension is set to 100. The relevance probability of each triplet within a path with candidate items is calculated using the interest set method.

4.2. Analysis of results

To validate the performance of the proposed algorithm, we conducted comparative analyses with various benchmark models. The experimental results are presented in Table 3.

Table 2. Reference data statistics for two datasets.

Datasets	Entities	Relations	Triplets	Train	Valid	Test
FB15k-237	14541	237	544230	272115	17535	3134
WN18RR	40943	11	93003	86538	3034	5000

Table 3. Prediction results of FB 15 k-237 and WN 18 RR link, where d is embedded dimensions, and the best results are represented in gross.

		FB15K-237					WN18RR
	d	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10
ConvE	200	0.325	0.237	0.356	0.501	0.43	0.40	0.44	0.52
MURP	200	0.335	0.243	0.367	0.518	0.481	0.44	0.495	0.566
HypER	200	0.341	0.252	0.376	0.52	0.465	0.436	0.477	0.522
ATTH	500	0.348	0.252	0.384	0.54	0.486	0.443	0.499	0.573
TuckER	200	0.358	0.266	0.394	0.544	0.47	0.444	0.482	0.526
CoKE	256	0.364	0.272	0.400	0.549	0.484	0.450	0.496	0.553
HittER	320	0.373	0.279	0.409	0.558	0.503	0.462	0.516	0.584
R-GCN	100	0.248	0.151	0.264	0.417	-	-	-	-
VR-GCN	100	0.248	0.159	0.272	0.432	-	-	-	-
CompGCN	100	0.355	0.264	0.390	0.535	0.479	0.443	0.494	0.546
EIP	100	0.368	0.278	0.411	0.559	0.505	0.469	0.517	0.588

Note: Bold values significance the numerical values of the experimental results of this study are compared with the maximum values from experiments of other models. They are highlighted in bold for comparison and to emphasize the superiority of this study.

The best results for each baseline correspond to the different embedding dimensions. The results shown in Table 3 are the best results obtained under different dimensions. Some baselines perform well in low dimensions, while others perform well in high dimensions. According to the experimental results in Table 3, the proposed model achieves favourable outcomes in experiments with relatively low embedding dimensions. Comparing to the experimental results of various benchmark models listed, the Conve baseline model exhibits the worst performance in standard metrics. This should be attributed to its limited ability to capture multi-layer nonlinear features using fewer parameters, resulting in limitations in information feature extraction. R-GCN generates node representations of interest through iterative aggregation of parametric, relationship-specific transformations of their neighbouring nodes. However, the constrained node dimensional representation size limits the depth of node characterisation, leading to less-than-ideal experimental results. On the other hand, the HittER model demonstrates the best performance in standard metrics. It is a hierarchical transformer model that consists of two parts: one extracts features for each entity-relation pair in the local neighbourhood of the source entity, and the other aggregates relation information from the output of the previous part. This approach effectively learns KG embeddings in complex multi-relation graphs. Comparing the best-performing baseline model HittER on the FB15K-237 dataset, our model shows improvements of 0.27% in MRR, 0.72% in Hits@1, 0.49% in Hits@3, and 0.18% in Hits@10. Similarly, on the WN18RR dataset, our model exhibited improvements of 0.40% in MRR, 1.52% in Hits@1, 0.20% in Hits@3, and 0.68% in Hits@10. Moreover, on the WN18RR dataset, our model demonstrates significant improvements, achieving 2.85% in MRR, 3.30% in Hits@1, 1.77% in Hits@3, and 5.38% in Hits@10.

Figures 3–5 depict the precision, recall, and F1-score of the recommendation model, respectively. By evaluating the interaction probabilities between users and items, we determine whether a recommendation is correct if the interaction probability is greater than 0.5, indicating user interest in the recommended item. From the figures, it is evident that the proposed model shows superior performance in precision and recall at K = 10. Compared to the baseline, the algorithm demonstrates improvements in precision. At K = 20, the recall and F1-score exhibit the best performance, showcasing improvement compared to the baseline as well.

Figure 3. Comparison of Precision@k of 8 models.

Figure 4. Comparison of Recall@k of 8 models.

Figure 5. Comparison of F1-score of 8 models.

Figure 6 illustrates the comparison of KG models on datasets FB15K-237 and WN18RR. The X-axis represents the names of evaluation metrics, while the Y-axis displays the corresponding values of the evaluation metrics. It is evident that the listed models perform well in various evaluation criteria on the WN18RR dataset, showing overall favourable performance. Additionally, compared to the other three evaluation metrics, all models exhibit strong performance in the Hits@10 metric. In conclusion, the comparison between our model and other models demonstrates that our proposed recommendation algorithm has distinct advantages and performs well on the evaluated datasets.

Figure 6. Data sets FB15K-237 and WN18RR based on kg-related model evaluation criteria comparison.

Figure 7 presents the comparison of R-GCN, VR-GCN, CompGCN models, and our proposed algorithm on the FB15K-237 dataset, as well as the comparison between CompGCN model and our model on the WN18RR dataset. The X-axis represents the names of evaluation metrics, while the Y-axis displays the corresponding values of the evaluation metrics. The blue bars represent the evaluation results of the R-GCN model, the orange bars represent the results of the VR-GCN model, the gray bars represent the results of the CompGCN model, and the yellow bars represent the results of the GCN model. Compared to the other two models, the R-GCN and VR-GCN models exhibit relatively lower performance. However, in contrast, the CompGCN model and our proposed model demonstrate better performance. This comparison highlights the advantages of our proposed recommendation algorithm, which is effective in both the encoding process of the heterogeneous graph and the decoding method for generating recommendations.

Figure 7. FB15K-237 based on GCN model evaluation comparison of indicators.

As depicted in Figure 8, the learning rate emerges as a crucial parameter that significantly impacts recommendation performance. In the figure, the x-axis represents various learning rates, while the y-axis indicates the area under the ROC curve, which serves as an indicator of the model's performance. When the learning rate transitions from 0.0001–0.001, there is a noticeable improvement in both AUC and ACC performance metrics. However, as the learning rate is further increased to 0.01, the performance starts to decline. Consequently, a learning rate of 0.001 is identified as the optimal choice for maximising model performance.

Figure 8. Changes in AUC and ACC performance of models at different learning rates.

As shown in Figure 9, our investigation delved into the influence of GCN layers on model performance, exploring layer values ranging from {1, 2, 3, 4}. The x-axis illustrates the different GCN layers, while the y-axis denotes the performance metrics for both AUC and ACC. Notably, the optimal number of GCN layers emerges as a pivotal factor, with the highest recommended accuracy achieved when aggregating information from user-item interactions through a single-layer neighbourhood representation. This suggests that a one-layer GCN model provides the most effective performance in this context.

Figure 9. Model performance with the trend of changing GCN layers.

4.3. Ablation studies

To evaluate the impact of different factors on model performance, we conducted detailed ablation experiments. These experiments allowed us to systematically analyse how various elements, including interest set propagation layers and decoding methods, affect the overall performance of the model. Our goal was to gain a comprehensive understanding of how these factors contribute to the model's effectiveness in the given context.

4.3.1. Effect of the number of interest set layers

The process of mining the interaction probabilities between a user and its neighbouring users, propagating them layer by layer, and deeply exploring the relationships between users and items, will make the model encounter the challenge of high dimensionality. Increasing the number of propagation layers in the interest set results in more relationships being generated, leading to higher model accuracy. Additionally, the dataset itself contains a substantial number of relationships between users and items, and this number increases with the number of propagation layers. By assigning weights to the interactions between users and items, we can distinguish between different reasoning relationships, effectively capturing more reasonable user interests and providing more accurate recommendations.

The experimental results on the two datasets show that the performance improves with an increase in dimensions. However, with the increase in data volume, the training time also increases accordingly. The experiments conducted at very low dimensions indicate that our proposed model has a considerable advantage in terms of efficiency compared to some baselines. Nevertheless, the recommendation performance does not improve with an increasing number of propagation layers and dimensions, as too many layers and dimensions can lead to over-smoothing and the introduction of noisy information. Therefore, we set appropriate values for the number of propagation layers and dimensions in our experiments to strike a balance between performance and computational efficiency, especially when dealing with large datasets with memory and computational bottlenecks.

4.3.2. Effect of decoding methods

The propose KG-GCNR implicitly utilises the encoded information of users and items in the decoding process. Therefore, the simple EIP (Entity Interaction Probability) method performs quite well and reduces the risk of overfitting, as shown in Table 2. Particularly, the EIP method is highly practical as it does not introduce additional parameters and is convenient to make a decide. The EIP computation method achieves better generalisation and produces improved results with d = 100 (embedding dimension).

Figure 10 illustrates the impact of the user-item and relationship embedding dimensions on the FB15K-237 and WN18RR datasets. We investigated the influence of the parameter embedding dimension d, selecting dimensions from 50, 100, 150, 200, 250, and 300 while keeping other parameters unchanged. It is observed that all metrics on the FB15K-237 and WN18RR datasets achieve the highest performance when the dimension is set to 100, and the performance is lowest when the dimension reaches 300. To take full advantage of the model, we choose 100 as the embedding dimension. Through experiments, we have observed that in the initial stages, increasing the embedding dimension does lead to performance improvement, as more dimensions can encode more useful information. However, as the embedding dimension reaches a certain value, the introduction of noise increases, leading to a decline in performance. This is because excessively high embedding dimensions may introduce redundancy and unnecessary information, thereby disrupting the model's learning and generalisation capabilities. Therefore, increasing the embedding dimension does not always result in continuous performance improvement. A balance needs to be struck to find the optimal embedding dimension.

Figure 10. Effect of embedded dimensions on data sets FB15K-237 and WN18RR.

5. Summary

This paper introduces a novel recommendation model called KG-GCNR, which not only addresses the dimension explosion problem by using EIP, but also improves the accuracy of recommendation results. To enhance the credibility of recommendation results, KG-GCNR calculates the relevance probabilities of triplets in multi-hop paths between user-item dependencies through a progressive propagation mechanism. The user-item interactions and KG are then fused to construct a heterogeneous graph, allowing for a deep exploration of potential relationships between users and items while considering various factors for recommendation. Next, a GCN is employed to encode the heterogeneous graph, effectively handling the high dimensionality caused by the extensive relationships discovered between users and items. Through the decoding process using EIP and extensive experiments on two datasets, the proposed KG-GCNR has been shown that it outperforms baseline models, demonstrating its superior recommendation capabilities.

Acknowledgements

We thank the authors of the cited references for their contributions.

Disclosure statement

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China under Grant (No. 62362016) and by National Social Science Foundation of China under Grant (No. 22BTQ081).