CGRS: Collaborative Knowledge Propagation Graph Attention Network for Recipes Recommendation

In the age of big data, recipe recommendation is of great significance. It can recommend recipes in line with the user's eating habits in massive data. Compared with other recommendation tasks, recipe recommendation is influenced by multiple aspects and requires fine-grained learning to obtain entity representations. Therefore, the traditional recommendation method cannot meet people's requirements. In this paper, we propose the Collaborative Knowledge Propagation Graph Attention Network for Recipes Recommendation (CGRS). This method designs collaborative information propagation to make full use of user interaction and recipe attribute information to meet the needs of multiple influencing factors. Use the graph attention feature learning network to obtain the high-order feature information of the entity to meet the demand for fine-grained representation. Specifically, the method first obtains the multi-hop triplet sets of users and recipes through a collaborative message propagation strategy. Then utilises a graph attention feature learning layer to learn the topological proximity structure features of the triplet sets. Obtain high-level semantic information of entities by superimposing network layers. Design an attention aggregator at the prediction layer to refine the embedding representation of entities. Finally predict the user-recipe interaction probability. Experimental results prove the advancement and effectiveness of CGRS.

Keywords: Recipe recommendation; attention neural network; collaborative knowledge propagation; attention feature learning network; recipe knowledge graph

With the continuous advancement of technology, more and more smart products are pouring into people's lives, and people's lives are becoming more and more convenient. However, the information generated by these smart products is too large for people, and people cannot fully understand it. It is inevitable that people are faced with the problem of an information explosion. Therefore, it is necessary to come up with a solution for the dilemma of how to use these data to improve people's lives. The recommendation system is to recommend a set of items that meet user preferences for users in massive data, which can well solve the problem of information overload (Shafqat & Byun, [26]; Wang et al., [38]). Therefore, an efficient and credible personalised recommendation system is needed by all major platforms. In this way, the recommendation system came into being. Nowadays, recommendation systems have almost become an indispensable part of various platforms, such as e-commerce platforms, short video websites, and social networking sites. Food platforms are no exception because people's desire to share generates a lot of recipe information. Nowadays, because of the simplicity of the collaborative filtering (Feng et al., [7]; Wang et al., [35]) method, it is applied to most recipe recommendation methods. Such as content-based methods by analysing the similarity between recipes (Meng et al., [18]; Nilesh et al., [19]; Wang et al., [35]). Although this improves the diversity of recommendations, it does not please users. User-based methods define similar users based on overlapping interaction information between user-recipes (Pecune et al., [21]; Roshdy & Hassan, [23]). This does not consider the relationship characteristics between users and the domain knowledge of recipes. Compared with other recommendation methods, recipe recommendation is multi-dimensional. For example, if a user likes a recipe, it may be recommended based on friends because of its ingredients, taste, or because the user's friends like it. The CF method above is not enough to meet the needs of users. Therefore, designing a high-performance and reliable recipe recommendation method for users has become a concern. For example, a user may like a dish because of its ingredients, taste, or because of the user's friends. The traditional recipe recommendation algorithm above has the following defects: (1) The user-recipe collaborative information and recipe domain knowledge are not fully utilised. (2) Ignoring the impact factor of recipe recommendation is a multifaceted problem. (3) The way of learning is coarse-grained enough to meet people's needs. Therefore, designing a high-performance and reliable recipe recommendation method for users has become a concern.

Recently inspired by knowledge graph recommendation methods. Because the Knowledge Graph (KG) is made up of a collection of triples, triples can be viewed as a collection of entities and relations. Therefore, it not only has rich semantic information to provide knowledge for the recommendation system to alleviate problems such as cold start (Li et al., [16]; Panda & Ray, [20]) and data sparsity (Ahmadian et al., [1]; Anwar et al., [2]; Choi et al., [4]), but also has good structural characteristics to allow the recipe recommendation system to learn more fine-grained features. In this way, user preferences can be better captured. The user and recipe feature learning are essential to enhancing the performance of recipe recommendations. That is, using the user-recipe interaction data as the seed to learn the feature representation of entities. In the process of entity feature learning, the relationship among recipes, users, ingredients and recipe attribute information is particularly important, how to use these data to improve recommendation performance is a challenge. In this paper, we leverage advanced techniques on knowledge graphs to address the recipe recommendation problem. We use Chinese recipe data to create a recipe knowledge graph, which serves as a source of considerable information for the model and refines the entity representation. According to how knowledge is used in KG, the recommendation is divided into three categories of methods (Guo et al., [11]): embedding-based methods (Guo et al., [10]; Vani & Saraiva, [28]), connection-based methods (Wang et al., [37]; Xu, Zhang, et al., [40]) and propagation-based methods (Du, Zhu, Chen, Zheng, & Gao, [6]). The embedding-based method needs to use the knowledge embedding algorithm (KGE) (Wang et al., [34]; Zhou et al., [45]; Zhu et al., [46]) to embed it in low latitude, and then obtain the representation of the entity. The main idea is to use the rich semantic knowledge in the knowledge graph to enrich users and items. thing. Although this type of method has good performance in KG recommendation, it does not take into account the information between high-order entities, resulting in poor interpretability. The connection-based method guides the recommendation according to the connection patterns of the knowledge graph. There are mainly two methods to learn the connection information in KG, the first is to compute the similarity between entities based on the meta-graphs and meta-paths in the KG. The other involves encoding the relationship between entities into a vector representation and integrating it into a recommendation system's framework. Although this type of method takes into account high-order relationships, its meta-paths and meta-graphs need to be manually constructed, which requires a lot of energy. It is not feasible for very large-scale knowledge graphs, and it decomposes complex user-item connections. For a single linear path, there will be a loss of information. Propagation-based methods are inspired by embedding-based methods. This type of method achieves learning high-order features by aggregating feature representations of multi-hop neighbours and obtaining fine-grained feature representations of entities. The rich user representations and latent items are then exploited to predict user preferences. This type of method can make up for the shortcomings of path-based and embedding-based and has a good recommendation performance. However, most of the propagation-based methods in the existing work ignore the attribute knowledge of recipes (such as taste, production process, etc.), and do not fully learn the domain knowledge of recipes. Recently inspired by the collaborative knowledge-aware graph attention neural network recommendation method, it provides a new idea for recipe recommendation. In this paper, we propose a new approach to solve this problem.

This work aims to make full use of two types of key information to refine entity representation to improve recommendation performance. we propose a recipe recommendation, Collaborative Knowledge Propagation Graph Attention Network for Recipes Recommendation (CGRS), which is based on the knowledge graph recommendation method. It is composed of a collaborative information propagation layer, graph attention features learning layer and prediction layer. Intuitively speaking, this method collaborative utilises two key pieces of information (historical interaction data and recipe domain knowledge) to meet the non-atomic requirement of recipe recommendation. Specifically, the method uses a collaborative information dissemination strategy to obtain multi-hop triplet sets of users and items, uses a graph attention feature learning network to obtain structural features of the topological proximity of triplet sets, and learns high-order entity representations, The attention aggregator generates refined embedding representations to accurately capture users' potential interest in food. Experiments demonstrate that CGRS has advantages in evaluation indicators such as AUC and F1 compared with the baseline of advanced recommendation models.

We made the following contributions to this paper:

• We believe that user interaction information and recipe domain information are important for the feature learning of users and recipes. In order to learn better, we introduce knowledge graph technology in this method and use Chinese recipe data to construct a food knowledge graph, which is used as the data source of this experiment and input into the recommendation model.
• This paper proposes a new propagation-based personalised recipe recommendation method. This method can make full use of historical interaction and food knowledge graph information to meet the diverse needs of users.
• Through considerable experimentation, we show that our recommended method works. Experimental results show that our recipe recommendation strategy is superior.

The remainder is organised as follows: in Section 2, we discuss the work related to recommendations; in Section 3, we formulate the problem; in Section 4, we describe our proposed CGRS approach in detail; and in Section 5, we provide the details of trials. Section 6 makes a summary of the full text.

We primarily discuss related research on recipe recommendation methods and knowledge graph-based recommendation algorithms in this part.

Among numerous recommendation problems, we only focus on recipe recommendations. Recipe recommendation has received extensive attention in recent years. Traditional recipe recommendations are mainly Content-based approach (CB) and Collaborative filtering approach (CF). For example, Trattner and Elsweiler ([27]) used collaborative filtering methods to recommend recipes, which is better than other methods in LDA. Pecune et al. ([21]) conducted experiments on methods such as BPR, ALS, etc. It is obvious that such methods are easy to implement, but they do not take into account the domain knowledge of recipes. Chen et al. ([3]) proposed a healthy recipe recommendation method, and Yang et al. ([42]) proposed a nutritious diet recommendation method, both of these methods calculated the similarity between recipes to recommend for users. Such methods did not please users. Some scholars and experts try to take user information into consideration information (Khan et al., [14]; Vivek et al., [29]). This type of method defines similar users based on repeated recipes between user interactions. This type of method ignores the relationship between user-recipe, recipe-recipe, and recipe ingredients. Rostami et al. ([24]) proposed an explainable food recommendation based on deep image clustering and community detection. This method uses food image information as the key content of the recommendation to visually capture the user's attention. Rostami et al. ([25]) proposed a new time-aware food recommendation method, which considers multiple dimensions (such as time, food composition, user social interaction, etc.) to overcome the shortcomings of previous systems. For instance, Gao et al. ([8]) proposed the visual perception hierarchical attention learning strategy recipe recommendation approach. This approach combines the collaborative information of user interaction messages and the domain information of recipes to learn entity representation, but this method only considers the representation of ingredients for recipes, while ignoring various relational characteristics (such as taste, craft, etc.). Meng et al. ([18]) proposed a method of heterogeneous fusion of collaborative information (Pine), which can improve performance through multi-task learning, but does not take into account the relationship between components. Jia et al. ([13]) propose an attentional convolutional network. This method uses the attention mechanism to capture the user's component preferences and uses the multi-view convolutional neural network to extract entity features, which greatly improves the recommendation performance. But it ignores the multifaceted influencing factors of recipes. Gao et al. ([9]) presented a new convolution neural network method (FGCN), which uses multi-embedded propagation layers to model high-order entities and enhance expression, but only considers the recipe Attributes of ingredients while ignoring multi-dimensional influencing factors. Although graph learning methods have greatly improved recommendation performance, fine-grained learning of user-recipe collaborative information and recipe domain knowledge is still a great challenge.

Recently, recommendation methods based on knowledge graphs have gained popularity. Connection-based methods, embedding-based methods, and propagation-based methods are the three primary categories of knowledge graph-based recommendation techniques. The rich knowledge in KG is used by the embedding-based recommendation method to enhance the feature representations of the entity. Wang et al. ([32]) presented a recommendation approach for multi-task feature learning (MKR). Compared with the traditional recipe recommendation, this method has greatly improved the recommendation accuracy, but it cannot use the high-level knowledge of the recipe. The main idea of recommending for users based on the connection method is through the connection patterns in KG. This method's primary task is to mine the connections between graph entities. Wang et al. ([37]) presented the knowledge-aware path recurrent approach (KPRN), which utilises both relational and entity semantics to generate path sequences. Although this method has a certain degree of interpretability, it is obvious that such methods decompose complex relationships into independent paths, thus causing recipe information loss. Although embedding-based methods have good scalability and are easy to implement, they do not consider high-order relational information. Although connection-based methods have good interpretability, they face the problem of information loss. The propagation-based method fully utilises the abundant semantic knowledge of KG, aggregates the high-level information of entities and relationships, and provides fine-grained explainable personalised recommendations. For example, Wang et al. ([30]) proposed the approach of propagating user preferences (RippleNet), which automatic iteration expands the potential interests of users along the links of KG to stimulate the propagation of user preferences on knowledge entity sets. Although compared with the above two methods, the recommendation-based approach performance is better, the recommendation system will be affected by noise as the number of propagation layers increases, which will affect the scalability. Wang et al. ([33]) put forward a Knowledge Graph Convolution Network (KGCN). It obtains the correlation between recipes by capturing the relational attributes on the KG. To further promote the prediction accuracy, the author proposed a label smoothing regularisation method (KGNN-LS) (Wang et al., [31]), which adds the idea of label smoothing on the basis of KGCN for propagation, aiming to simultaneously obtain the user's latent preferences and relational features between entities. The Knowledge-Aware Attention (CKAN) strategy was provided by Wang et al. ([39]). Unlike KGNN-LS which uses label information to improve recommendation accuracy, CKAN focuses more on entity and relationship semantic information in the knowledge graph to improve recommendation performance. However, this method ignores the importance of higher-order entity representation sets. Graph-based recommendation methods can exploit the rich semantic information and structural features in graphs to improve recommendation performance, but scalability is still a challenge for them.

After analysis, it is found that the propagation-based method can learn the feature information of recipes in a more fine-grained manner. So influenced by it, we propose the CGRS method. This method makes full use of the user-recipe synergy signal (user-recipe synergy information refers to the synergy behaviour and information that users show when using the recipe recommendation system. (e.g. clicks, favourites, comments, etc.) and recipe domain knowledge (recipe domain knowledge refers to the knowledge of ingredients, preparation process, production process, taste, etc.)), which is expressed by enriching the characteristics of users and recipes, to improve the accuracy of recommendations.

In this part, the primary recommendation tasks of the recommendation approaches are defined after we present a few key ideas and notations.

Definition 1. Recipe knowledge graph

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$\mathcal{G}$ . The recipe knowledge graph mainly contains domain knowledge of recipes (such as dish names, raw materials, techniques, tastes, etc.). A knowledge graph composed of a set of triples can be expressed as

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$\mathcal{G}=\{(h,r,t)|h,t\in E,r\in R\}$ . Among them

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$(h,r,t)$ can be considered as the representation of entities and relationships, the head entity is represented as

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$h$ , the tail entity is represented as

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$t$ , the relationship between entities is represented by

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$r$ ,

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$E$ indicates the set of entity, and

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$R$ indicates the set of relationship. For example, (Korean barbecue ribs, craftsmanship, and charcoal grilling) indicates that the production process of Korean barbecue ribs is charcoal grilling. In a specific graph representation, an entity represents a node, and a relationship represents an edge connecting two nodes.

Definition 2. User-recipe Interaction. It is built from the user-recipe interaction history. User set

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$\mathcal{U}=\{u_1,u_2,...,u_N\}$ and recipe set

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$\mathrm{I}=\{i_1,i_2,...,i_M\}$ constitute user-recipe interaction data, which is a directed graph. According to the user's implicit feedback (such as click, view, favourite, etc.), the user-recipe interaction matrix

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$Y\in R^{N\times M}$ can be constructed, where

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$N$ denotes users amount and

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$M$ denotes recipes amount. We can express it with the following Equation (1):

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$\begin{array}{r}{Y}_{ui}=\{\begin{array}{ll}1,& Iftheuserinteractedwiththerecipe\\ 0,& otherwise\end{array}\end{array}$ (1)

Among them,

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$Y_{ui}=1$ indicates that the user participates in the implicit feedback of the recipe, here it can be considered that the user likes the recipe, and

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$Y_{ui}=0$ indicates the opposite situation. User interaction can also be similarly defined in triple format

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${\mathcal{G}}^{\ast }=$ (

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$R^{\ast }\{(u,r^{\ast },i)|u\in \mathcal{U},r^{\ast }\in R^{\ast },i\in I\}$ ), where

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$r^{\ast }$ denote the set of all interaction types between user

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$u$ and recipe

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$i$ (such as click, view, favourite, etc.). and

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$\mathcal{U}$ and

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$I$ denote the set of user and interactive recipes.

To describe the alignment relationship between recipes in user-recipe interactions and entities in the knowledge graph, we define the set

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$\mathcal{A}=\{(i,e)\}|i\in I,e\in E\}$ , where

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$(i,e)\in \mathcal{A}$ represents the recipe, I interacted by the user can match the knowledge graph entity e. The problem description of this paper will be given in Definition 3.

Definition 3. Problem description. For the recommendation model, our task is to acquire the feature representation of the entity according to the knowledge graph

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$\mathcal{G}$ and the user-recipe interaction graph

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${\mathcal{G}}^{\ast }$ , afterward predict the possibility of the user interacting with the recipe that has not been interacted with. To be more precise, it is to forecast the likelihood of interaction between user u and recipe

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$i$ in light of the prediction function

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${\hat{y}}_{ui}=\mathcal{F}(\mathrm{u},\mathrm{i}|{\mathcal{G}}^{\ast },\mathrm{\Theta },\mathcal{G})$ , where Θ represents the model parameters.

In this part, we give a thorough overview of the proposed CGRS model architecture. The method primarily consists of three stages, as indicated in Figure 1. (1) Collaborative information propagation layer, which learns high-order feature information of users and recipes through user-recipe interaction and propagates collaborative information along the edges of the knowledge graph. (2) Graph attention feature learning layer. Use the attention mechanism to obtain the topological structure of high-order features of users and recipes to learn high-order entity representations to obtain high-order embedding sets; (3) Prediction layer. Entities from different propagation layers are assigned weights through an attention aggregator, the entity embedding is refined, and finally, the inner product of the final entity embedding is used to predict the user-recipe interaction probability.

Graph: Figure 1. The overall framework of CGRS.

As shown in Figure 1, inspired by the paper(Ma et al., [17]; Wang et al., [39]; Zhang et al., [44]), we design a collaborative message propagation layer to initialise and learn high-level feature information of users and recipes. This layer mainly consists of two parts: user interaction information and recipe knowledge graph information. The first part is used to initialise the entity representation, which explicitly encodes the user-recipe implicit feedback to generate the entity (user, recipe) representation. The second component leverages the seed provided by the first interaction to propagate messages in order to gather high-order data about the entities in the KG. These two sections will each be introduced in turn further down.

The major objective of this component, which serves as the foundation of the entire model, is to acquire the user and the starting entity of the recipe that are necessary for the high-order propagation of the recipe knowledge graph. Specifically, we leverage user-recipe interaction data to gather a starting set of pertinent recipes, match those recipes with knowledge graph entities through set

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$\mathcal{A},$ and then gather an entity set that is centred on the entities that match the recipes in the knowledge graph. To a large extent, the recipes that have interacted with the user can reflect the person's preference information, so the user-related entity set can be used to finely represent the user entity u. The user's initial entity set is defined as Equation (2):

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${\mathcal{E}}_u^0=\{e\mid (i,e)\in \mathcal{A}\mathrm{\&}i\in \{i\mid y_{ui}=1\}\}$ (2)

Where

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$\mathrm{\&}$ means and, the same below. Likewise, users who have interacted with the same recipe can be shown to have similar preferences, so these users can contribute to the recipe's feature representation. The role of collaborative propagation here is to use the user-recipe interaction information to query all users who have interacted with recipe I, and then take a collaborative item set of all the recipes these individuals have engaged with. The formula is defined as Equation (3):

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$I_i=\{i_u\mid u\in \{u\mid y_{ui}=1\}\mathrm{\&}{y}_{u{i}_u}=1\}$ (3)

For the purpose of obtain the initial set of the recipe, we filter and obtain it by synthesising the alignment set

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$\mathcal{A}$ and the collaborative item set

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$I_i$ . The formula is defined as Equation (4)

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${\mathcal{E}}_i^0=\{e\mid (i_u,e)\in \mathcal{A}\mathrm{\&}{i}_u\in I_i\}$ (4)

The collaborative propagation layer can explicitly encode the interactive information that most effectively expresses the potential preferences of users into the initial set of users and recipes, thereby describing the feature representation of users and recipes in a fine-grained manner and improving the recommendation performance.

The recipe knowledge graph has rich semantic relationships and entity features, and adjacent entities have strong correlations, so it is a good choice to use it as auxiliary information. Existing studies have proved that if we only consider the neighbour nodes directly connected to the target node to predict the results, this has the same problem as the knowledge graph embedding recommendation method, ignoring the high-order relationship between entities, making it inaccurate to capture user preferences (Guo et al., [11]). Therefore, the significance of studying message dissemination in knowledge graphs lies in the fact that refined entity representations of high-level semantic information associated with entities can be obtained through message dissemination. We leverage the knowledge of entities in the knowledge graph to augment the representations of users and recipes to enhance the quality of receiving user and recipe-oriented information. For example, if a user likes scrambled eggs with tomatoes, we can find that eggs are an ingredient in recipes such as egg drop soup and egg custard. Therefore, obtaining user potential preference information from the knowledge graph depends on all related entities in the KG and the relationship between related entities. From the user's point of view, liking a dish may be because of its author, its ingredients, or its craftsmanship, which is defined according to the user's potential interest in KG. If the user likes the dishes made by a certain blogger, the module will quickly locate all the recipes made by him. In conclusion, entities in KG can provide a finer-grained description of user feature representation and improve recommendation accuracy.

The high-order propagation of the knowledge graph in the CGRS method involves using the central entity discovered through user interaction information to propagate in the KG to obtain a high-order entity set, which effectively increases the potential interest of the user. For convenience, we use placeholder p to represent user u and recipe

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$i$ . Equation (5) is the formula definition.

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${\mathcal{E}}_p^l=\{t\mid (h,r,t)\in \mathcal{G}\mathrm{\&}h\in {\mathcal{E}}_p^{l-1}\},l=1,2,...,L$ (5)

Where

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$l$ represents the number of high-order propagation layers, and

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$h\in {\mathcal{E}}_p^{l-1}$ represents node with h as the head entity,

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${\mathcal{E}}_p^l$ represents the high-order entity set of users or recipes obtained through l-layer propagation. Based on the given user and recipe high-order entity set, the l- layer user and recipe triplet set can be obtained. The formula is defined as Equation (6):

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${\mathcal{S}}_p^l=\{(h,r,t)\mid (h,r,t)\in \mathcal{G}\mathrm{\&}h\in {\mathcal{E}}_p^{l-1}\},l=1,2,...,L$ (6)

In the process of recipe recommendation, different users have different interests in the same recipe. For example, some users are more concerned about the choice of taste, some users are more concerned about the ingredients, and more concerned about the production process, etc. Different relationships and entities have different weights for users. In other words, when the tail entity in the triplet corresponds to different relationships and head entities, t has different weights. For example, users like the dish "Scrambled Eggs with Tomatoes". The ingredients of this dish are both tomatoes and eggs, but the user prefers eggs, so the reason why he likes this dish is that the weight of eggs is higher than that of tomatoes. In order to obtain advanced entity embedding and accurately capture the potential interests of users, we further focus on mining the links between entities and creating a graph attention feature learning network, which is driven by the attention mechanism.

When domain information is collected for a given recipe or user, inspired by the attention mechanism, we build a network for learning graph attention features to learn the weights of different tail entities. Specifically, according to the given triple information, it is judged which domain entity information needs to be collected more. Thus, each instance of the domain depends on the associated preference score

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$\pi (h,r,t)$ . We generate user-oriented domain information by aggregating entity embedding in the domain. Here we consider the triplet set of entities at layer l. The formula is defined as Equation (7):

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$\begin{array}{r}{e}_{N(n)}=\sum _{e_tϵ\mathcal{N}(n)}\tilde{\pi }(h,r,t)e_t\end{array}$ (7)

Where

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$\tilde{\pi }(h,r,t)$ denotes he attention weight, which determines how much the domain entity information is propagated to the head entity.

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$\pi (h,r,t)$ is the attention weight generated by the triple head entity and relation through the attention feature learning network,

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${\mathrm{e}}_t$ denotes the tail entity embedding representation, and the formula is as follow Equation:

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$\begin{array}{rl}& x_0=LeakyReLU(W_{0}concat[e_h,e_r]+b_0)\end{array}$ (8)

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$\begin{array}{rl}& y_0=LeakyReLU(W_1{x}_0+b_1)\end{array}$ (9)

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$\begin{array}{rl}& \pi (h,r,t)=LeakyReLU(W_2{y}_0+b_2)\end{array}$ (10)

Where

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$concat[\cdot ]$ represents the concatenate operation,

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${\mathrm{W}}_0,{\mathrm{W}}_1,{\mathrm{W}}_2$ represents the trainable parameter matrices in different layers, respectively, and

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${\mathrm{b}}_0,{\mathrm{b}}_1,{\mathrm{b}}_2$ represent the bias, respectively. Both

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$LeakyReLU$ represent nonlinear activation functions. The reason why the

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$LeakyReLU$ function is used in this article is that the recipe recommendation generally needs to consider multiple factors such as user preferences, ingredients, and production techniques. Therefore, a model with strong expressive ability is needed for modelling and optimisation. The small slope introduced by

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$LeakyReLU$ can limit the output of neurones and prevent over-fitting of training data, thereby improving the generalisation ability and nonlinear fitting ability of the model. Next, we need to normalise

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$\pi (h,r,t)$ to get

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$\tilde{\pi }(h,r,t)$ .The formula is as Equation (11):

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$\begin{array}{r}\tilde{\pi }(h,r,t)=softmax(\pi (h,r,t))=\frac{\exp (\pi (h,r,t))}{\sum _{(h^{\prime },r^{\prime },t^{\prime })\in {\mathcal{S}}_p^l}\exp (\pi (h^{\prime },r^{\prime },t^{\prime }))}\end{array}$ (11)

Where

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${\mathcal{S}}_p^l$ denote the set of user or recipe triples at layer l. Attention weights can capture which tail entities in the domain entities need to be given more attention, that is, the knowledge association of aggregated tail entities information.

The domain representation

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$e_{N(n)}$ of

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${\mathrm{e}}_t$ is obtained through the attention feature learning network above, and the next step is to aggregate

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${\mathrm{e}}_t$ and

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$e_{N(n)}$ . Here we design a new bilateral aggregator inspired by Knowledge Graph Attention Network (KGAT) (Wang et al., [36]; Xu, Liu, Li, Zhang, & Tang, [40]), the formula is defined as Equation (12):

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$\begin{array}{rl}& Bilateralaggregation:e_{N(n)}^{\mathrm{\prime }}=\sigma (W_a\cdot [e_t||e_{N(n)}]+b_a)\\ & +\sigma (W_b\cdot (e_t+e_{N(n)})+b_b)\end{array}$ (12)

Where

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$\sigma (\cdot )$ represents the nonlinear activation function (such as

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$LeakyReLU$ ),

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$W$ denote the weight matrix,

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$b$ denote the offset, and

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$||$ represents the concatenate operation (Figure 2).

We contrast the two-sided aggregator with the sum aggregator in order to show its efficacy, which is defined as Equation (13):

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$sum:e_{N(n)}^{\mathrm{\prime }}=\sigma (W_c\cdot (e_t+e_{N(n)})+b_c)$ (13)

Where

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$\sigma (\cdot )$ represents the sigmoid activation function.

Graph: Figure 2. Graph Attention Feature Learning Network.

Finally, aggregate all the obtained entity representations

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$e_{N(n)}^{{}^{\mathrm{\prime }}}$ to

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$e_p^{(l)}$ to obtain the triplet set of users and recipes in this layer, and other layers can be obtained in the same way The aggregated set of triples of all layers, the formula is as Equation (14):

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$e_p^{(l)}=\sum _{e_t\in {\epsilon }_p^l}{\mathit{e}}_{N(n)},l=1,2,...,L$ (14)

There is a problem that needs attention in this section. The initial entity set is the closest to the original representation of users and recipes. They are closely related to the original users and recipes, and can most intuitively reflect the potential interests of users. Therefore, the initial entity set has strong interaction information and collaboration information. Correspondingly, we need to take the initial physical machines into account. Here we use the 0-order neighbourhood to represent them. The formula is defined as Equation (15):

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$e_p^{(0)}=\frac{\sum _{e\in {\epsilon }_p^{0}e}}{{\epsilon }_p^0}$ (15)

In particular, because the most original recipe can be mapped with the nodes in the KG through set

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$\mathcal{A}$ . As a result, the entity that was obtained through knowledge graph mapping can serve as

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$i$ original representation, and the formula is defined as Equation (16):

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$e_i^{(org)}=\frac{\sum _{e\in \{e|(e,i)\in \mathcal{A}\}}e}{|\{e|(e,i)\in \mathcal{A}\}|}$ (16)

Finally, after the knowledge-aware attention mechanism embedding, we can get the user and recipe representation set containing the attention weight, the formula is expressed as follows:

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$\begin{array}{rl}& {\mathcal{T}}_u=\{e_u^{(0)},e_u^{(1)},...,e_u^{(l)}\}\end{array}$ (17)

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$\begin{array}{rl}& {\mathcal{T}}_i=\{e_i^{(o\mathrm{rg})},e_i^{(0)},e_i^{(1)},...,e_i^{(l)}\}\end{array}$ (18)

The goal at this layer seeks to forecast the likelihood that the user and the recipe will interact by generating the final entity representation. Through the attention feature learning layer, the recipe representation set

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${\mathcal{T}}_i$ and the user representation set

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${\mathcal{T}}_u$ including weights can be obtained. Here we use

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${\mathcal{T}}_p$ to replace them, and use p to represent users and recipes. For

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$p$ , different layers

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${\mathcal{T}}_p$ have different weights. To put it simply, the closer the target entity is, the stronger the direct correlation between them, and these entities can most intuitively reflect the potential interest of the user, so the assigned weight should be larger. They are far away from the target entity and connected by indirect correlation, which contributes less than direct correlation, so the assigned weight should be small. If we do not process

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${\mathcal{T}}_p$ , but only aggregate them by concatenate or sum, this will lead to inaccurate capture of user interest. For explore the contribution of the representation sets of different layers in

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${\mathcal{T}}_p$ to the final representation of

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$p$ , we design an attention aggregator to generate the final user and recipe representation

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$e_p$ , the idea comes from the attention mechanism (Hu, [12]; Yang et al., [43]). Specifically, for each layer of

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${\mathrm{e}}_p^{(i)}\in {\mathcal{T}}_p$ We first use an attention network to learn the weights

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$a_p^{(i)}$ , and then normalise the attention weight to get

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${\tilde{a}}_p^{(i)}$ , and finally carry out weighted aggregate according to

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$a_p^{(i)}$ , to obtain the final characterise. The formula is defined as follows:

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$\begin{array}{rl}& a_p^{(i)}=w^{\mathrm{T}}tanh(W_1{e}_p^{(i)})\end{array}$ (19)

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$\begin{array}{rl}& {\tilde{a}}_p^{(i)}=softmax(a_p^{(i)})\end{array}$ (20)

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$\begin{array}{rl}& e_p=\sigma (W_2\sum _{e_p^{(i)}\in {\mathcal{T}}_p}{\tilde{a}}_p^{(i)}\bullet {\mathrm{e}}_b^{(i)}+b_1)\end{array}$ (21)

Where

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$\tanh (\bullet )$ and

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$\sigma (\bullet )$ represent the nonlinear activation function, the latter is a sigmoid function,

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$w$ represents the weight vector,

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$W_1,W_2$ represent the weight matrix and

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$b$ represents the offset.

For the sake of proving the rationality and effectiveness of our proposed attention aggregator, we design a connection aggregator here for the following comparison. Defined as follows Equation (22):

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$e_p=\sigma (W_3(e_p^{(i_1)}||e_p^{(i_2)}||...||e_p^{(i_n)})+b_3)$ (22)

After the above series of operations, the final user and recipe representations

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$e_u$ and

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$e_i$ can be obtained. We calculate the interaction probability between the user and the recipe through the prediction function

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${\hat{y}}_{ui}$ . Defined as follows Equation (23):

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$\begin{array}{r}{\hat{y}}_{ui}=F(e_u,e_i)=e^{\mathrm{T}}\bullet e_i\end{array}$ (23)

CGRS uses a negative sampling method to increase the model's performance and learning effectiveness. For every user, the same number of positive and negative samples are taken. Defined as follows Equation (24):

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$\mathcal{L}=\sum _{u\in \mathcal{U}}\left(\sum _{i\in \{i|(u,i)\in {\mathcal{P}}^{+}\}}\mathcal{I}(y_{ui},{\hat{y}}_{ui})-\sum _{i\in \{i|(u,i)\in {\mathcal{P}}^{-}\}}\mathcal{I}(y_{uv},{\hat{y}}_{ui})\right)+\lambda ||\mathrm{\Theta }|{|}_2^2$ (24)

Where

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$\mathcal{I}(y_{ui},{\hat{y}}_{ui})$ represents the cross-entropy loss,

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${\mathcal{P}}^{+}$ and

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${\mathcal{P}}^{-}$ denote the positive and negative samples of the user-recipe pair set, respectively.

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$\mathrm{\Theta }=\{E,R,w,W_i,b_j,\mathrm{\forall }i\in \{0,1,2,a,b,c\},\mathrm{\forall }j\in \{0,1,2,a,b,c\}\}$ represents the Parameter set, the hyper-parameter of L2 regularisation is balanced using

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$\lambda$ .

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$||\mathrm{\Theta }|{|}_2^2$ represents the L2-regulariser.

We perform experiments in this section. The experimental data is based on the real food knowledge graph created by oneself and the interaction of user recipes. The following are the details of the experiment.

In our task, we use crawler technology to grab recipe-related data and user comment data from the Chinese food platform, and then use data processing technology to convert them into knowledge graphs represented by CSV documents (note that the CSV document here has three columns: (entity, relation, entity), which is equivalent to the triplet of the knowledge graph). Then use encoding technology to process the Chinese characters in the CSV file into digital form. Finally, do further processing according to the needs of the model, and apply it to the model to learn the representation of users and recipes.

The datasets used in this manuscript (sample datasets: https://github.com/Eimo-Bai/Ta-da-recipe-dataset). It is the real and reliable basic data of recipes stored on the Chinese gourmet platform, including the interaction history information between users and recipes, recipe name, main ingredients, auxiliary ingredients, production process, production time, production difficulty, the taste of recipes, etc. The user-recipe interaction and recipe knowledge graph are created after several data processing steps, among which there are 108,248 pieces of user interaction data and 149,127 pairs of triples in the recipe knowledge graph. We have obtained experimental data through continuous improvement and debugging data. The details of this experimental data set are as Table 1.

Table 1. Data details.

In this section, we put the target dataset into multiple models for experiments to obtain their respective AUC and F1 baselines. The advancement of the food recommendation model CGRS proposed in this paper is demonstrated by comparing these baselines.

• BPRMF (Rendle et al., [22]): This method is a personalised ranking algorithm based on Bayesian posterior optimisation, which occupies a large proportion of recipe recommendations.
• MKR (Wang et al., [32]): This method is an embedding-based method, which makes up of two modules, one is the recommendation module and the other is the KGE module, which is connected by cross-compression units to achieve knowledge sharing and learning knowledge graph entities and high-level interaction information of items in the recommendation module.
• KPRN (Wang et al., [37]): The approach is connection-based, which generates paths according to the semantics of entities and relationships, and obtains user potential preferences by designing a weighted pool to distinguish weight information that cannot be pathed.
• Ripple Net (Wang et al., [30]): This method is based on propagation. It spreads through multiple layers on the knowledge graph, which is equivalent to spreading the user's interest on the knowledge graph to achieve the purpose of extracting the user's features, thereby predicting the user's potential points of interest.
• KGCN (Wang et al., [33]): This method is a paradigm based on propagation methods and is an end-to-end framework. It combines the convolutional neural network and the knowledge graph, obtains the knowledge association between items by mining the relevant attributes in the knowledge graph, and performs entity representation by aggregating domain information.
• KGCN-LS (Wang et al., [31]): This method is also based on a propagation model, which incorporates the idea of weighting in the knowledge graph, and then incorporates a label smoothing mechanism in the neural network to calculate personalised item embeddings.
• CKAN (Wang et al., [39]): This method contains an attention mechanism model, which encodes user and entity information in heterogeneous transmission, then learns domain weights through the attention mechanism, and finally aggregates through three aggregators to generate the final user and item representations.

In experiments, we will compare the effectiveness of our proposed CGRS models using Chinese recipe datasets on each model. We divide the recipe dataset into three parts: training set, test set, and evaluation set with a ratio of 6:2:2. Each experiment was repeated 10 times to calculate the average performance. For the parameter setting of the comparative experimental model and the training and optimisation of the experimental results, we follow the description in the original paper and use the default values in the original code. For the CGRS model proposed in the manuscript, we implemented it in Porch and used Adam (Darban & Valipour, [5]) as the optimiser for the method, using grid search to tune the hyperparameters. we explore the coefficient ϵ of L2 normalisation in {10-5,10-4,10-3,10-2,10-1}, and in

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$\{0.001,0.005,0.01,0.05\}$ to explore the learning rate δ, and in

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$\{1,2,3,4,5\}$ to debug the recursion depth of message passing. In

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$\{8,16,32,64,128,256,512\}$ to debug the dimension d of the best user and entity embedding. Each experiment was repeated 10 times and the best performance results were averaged.

For the evaluation metrics of this experiment, we will evaluate our model using two scenarios, Top-K recommendation, and click-through rate (CTR) prediction. We predict interactions in the test datasets by using the trained model, in CTR prediction, and we will evaluate the CTR prediction through two evaluation metrics, AUC and F1; The K items with the highest click-through rate in our test data set are predicted by the trained model in the Top-K recommendation, and we evaluate Top-K recommendation by three evaluation indicators,

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$Recall@K$ ,

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$Precision@K$ and

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$NDCG@K$ . Where

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$Recall@K$ ,

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$Precision@K$ and

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$NDCG@K$ are defined as follows:

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$\begin{array}{rl}& Precision@K=\frac{1}{N}{\sum }_{u=1}^N\frac{|R_u(k)\cap T_u|}{|T_u|}\end{array}$ (25)

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$\begin{array}{rl}& Recall@K=\frac{1}{N}{\sum }_{u=1}^N\frac{|R_u(k)\cap T_u|}{k}\end{array}$ (26)

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$\begin{array}{rl}& NDCG@K=\frac{{\sum }_{i=1}^k\frac{re{l}_i}{lo{g}_2(i+1)}}{{\sum }_{i=1}^{|REL|}\frac{re{l}_i}{lo{g}_2(i+1)}}\end{array}$ (27)

Where

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$R_u(k)$ represents a set of top-k recommended by the model for the user, and

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$T_u$ represents the set of recipes accessed by the user during the testing process.

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$re{l}_i$ represents the true relevance score of the itch result.

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$|REL|$ indicates that the results are sorted from large to small according to the real correlation, and the number of sets composed of the first k results is taken. The formulas for AUC and F1 are defined as follows:

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$\begin{array}{rl}& AUC=\frac{{\sum }_{i\in positiveClass}ran{k}_i-\frac{t_{pos}(1+t_{pos})}{2}}{t_{pos}\times t_{neg}}\end{array}$ (28)

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$\begin{array}{rl}& F1=2\frac{Recall\times Precision}{Recall+Precision}\end{array}$ (29)

Where

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$ran{k}_i$ is the probability that the predicted sample is a positive example,

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$t_{pos}$ denote positive sample count, and

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$t_{neg}$ denote negative examples count.

We use real recipe data to conduct comparative experiments, and the statistics of the Top-K. experimental results are shown in Figures 3 and 4, and the statistics of the CTR prediction results of each model are shown in Table 2. It is found that CGRS has a large improvement over the baselines of other models. Through the outcomes of the experiment, we highlight the following points:

• We can see the sophisticated nature of our suggested CGRS model by contrasting the baseline state-of-the-art model with it. This also shows our assumption that fully utilising user interaction information and recipe neighbourhood information to refine entity representation, and distinguishing complex relationships between multi-layer entity representation sets can capture user preferences well and improve recommendation performance.
• By comparing with other models on NDCG and Precision indicators, we can find that CGRS also has good performance. This also demonstrates the advancement and effectiveness of our CGRS.
• Compared with CKAN, the recommendation performance of CGRS is significantly better. This shows that through the improvement of its activation function, the bilateral aggregator designed in the attention feature learning layer and the attention aggregator added in the prediction layer can enhance the feature representation of users and recipes and improve the recommendation performance.
• Both CGRS and CKAN outperform MKR, RippleNet, and KGCN in performance metrics in experiments. This not only proves that CGRS and CKAN can tap the potential interests of users by using both the user-recipe interaction information and the rich semantic knowledge in KG, but also proves that heterogeneous propagation can well combine the two aspects of knowledge, enhancing the embedded representation of entities.
• Through the experimental results, it can be observed that the propagation-based method significantly outperforms the traditional methods, connection-based and embedding-based, which demonstrates that the high-order message of the knowledge graph can be exploited by the propagation-based model. Therefore, the feature representation of fine-grained users and recipes is obtained, and the recommendation performance is improved.
• All based on knowledge graph methods except KPRN outperform traditional methods, which shows that using knowledge graph as auxiliary information for recommendation can improve recommendation performance. The reason why KPRN may be the lowest is that the path-based method needs to rely on the manual definition of meta-paths, so it is difficult to obtain optimal meta-paths on complex graphs.
• KGCN, RippleNet, CKAN, CGRS, KGNN-LS, and other propagation-based methods perform better than embedding (MKR)-based methods in most cases. This shows that it is hard to get accurate recommendation effects by only considering the domain nodes directly with the target node in KG without using rich semantic information. On the contrary, high-order propagation may capture user preferences and improve recommendation performance by using knowledge connections of knowledge graphs.

Graph: Figure 3. Comparison of different models in Top-K recommendation (Recall@K and Precision@K).

Graph: Figure 4. Comparison of different models in NDCG@K.

Table 2. CTR predicts AUC and F1 outcomes.

For a comprehensive comprehension of CGRS, we study the influence of some parameters on it. First, we study the effect of depth, then we study the effect of embedding dimension, and finally study the effect of attention aggregator.

We study the change in recommendation performance by changing the depth of knowledge propagation of the CGRS model. The number of layers determines the richness of the information of the aggregated and iterative entities. If the number of layers is too small, the knowledge association of the knowledge graph cannot be fully utilised. If the number of layers is too large, the noise will affect the recommendation performance. In this experiment, we conduct research between

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$\{1,2,3,4,5\}$ . The experimental analysis results are as Table 3. Through the experimental data, conclusions can be obtained:

• According to the experimental data, we found that in layers 1-3, as the depth of CGRS increases, the model performance is significantly improved. This demonstrates how modelling second and third-order propagation can enhance entity information, thereby improving the accuracy of the recommendation
• As the model's depth continues to rise in layers 4-5, its performance seems to degrade. The possible reason for this is that although the fourth- and fifth-order connections can increase the richness of promotion, too many irrelevant nodes may be used, and the noise will also increase, which will interfere with the recommendation accuracy.

Table 3. AUC and F1 experimental results at different depths.

For the embedding of relationships and entities in the KG, we set them to the same dimension to facilitate subsequent calculations and explore the different embedding impacts on approach recommendation. We change the embedding dimension in

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$\{4,8,16,32,64,128,256,512\}$ to study the performance variation. The experiment's findings are shown in Table 4. Through analysis, we can draw the following conclusions:

• In a certain interval, the model recommendation performance can be improved by improving the entity embedding dimension. The possible reason is that within a certain range, the embedding dimension size can determine the amount of encoded information, and a larger dimension can encode more information.
• When the embedding dimension reaches 512, we discovered that the model's performance tends to deteriorate. This shows that when the embedding dimension exceeds a certain threshold, overfitting will occur, which will affect the performance of the recommendation.

Table 4. AUC and F1 experimental results at different embedding dimensions.

We study its impact on model performance with different aggregators. In this experiment, we use two aggregators, a sum aggregator, and a bilateral aggregator, denoting them as CGRS-GCN and CGRS-BI respectively. The experiment's findings are shown in Table 5. Through this table, we can find that the performance of CGRS-GCN is lower than that of CGRS-BI. The possible reason is that CGRS-BI adds additional feature interactions to improve the representation of entities, which also verifies the effectiveness and rationality of the proposed aggregator.

Table 5. AUC and F1 experimental results at the different aggregator.

For the sake of confirming the impact of the attention aggregator on the model, we replaced the attention aggregator with ordinary connection aggregation, and the formula is as follows. For convenience, here we use p to represent users and recipes. Table 6 shows the comparative experimental results. We found that the AUC and F1 of the attention aggregator are significantly higher than that of the connection aggregator. The possible reason is that the attention aggregator distinguishes the importance of different layers and can better capture the user's interest.

Table 6. AUC and F1 experimental results at different component.

The impact factors for food recommendations are diverse. We need to acquire entity representations in a fine-grained learning manner. Based on this, this paper proposes a personalised recipe recommendation method CGRS. This method is a kind of knowledge graph recommendation in popular fields, which is of great significance for grasping the frontiers of science and technology, academic trends, and research work. And an efficient and reliable recipe recommendation method is also of great significance to the industry. It can not only promote food nutrition and health management, but also promote food production and sales, intelligent services based on data analysis, and food innovation and research and development. In CGRS, first of all, through the design of collaborative knowledge dissemination layer, dissemination is carried out from the perspective of users and recipes, to make full use of the two types of key information to achieve the purpose of diversification. Then a graph attention feature learning network is proposed to capture the topological proximity structure features of entities and achieve the purpose of fine-grained learning by superimposing multi-layer networks to obtain high-order semantic information. Among them, a neighbourhood aggregator is proposed to better aggregate domain information. Finally, in the prediction layer, we use an attention aggregator to distinguish the importance of entity representation sets in different layers, to refine the representation of users and recipes. We conduct experiments on real recipe data, and the results prove the rationality and effectiveness of our proposed CGRS. Additionally, we perform experiments on a few parameters to provide readers with a deeper grasp of the CGRS model and demonstrate the authenticity of our model.

Healthy eating has drawn increasing public attention in recent years, as poor eating habits can also contribute to several ailments. The Communist Party of China's Nineteenth National Congress made a significant resolution about the "Healthy China" plan and mentioned the upkeep of national health from the standpoint of national strategy. And recently Li et al. ([15]) proposed a health-guided recipe recommendation method with good results. Therefore, in the future, we will study a personalised recommendation method that considers user health and preferences.

No potential conflict of interest was reported by the authors.

Some data from the Ta-da dataset are used in this study and will be gradually opened after the completion of subsequent laboratory projects. The sample data is part of the Ta-da data set and can be accessed at https://github.com/Eimo-Bai/Ta-da-recipe-dataset, visited on December 17, 2022.