A heterogeneous optimization recommendation method and device based on subgraph link prediction

Abstract

A heterogeneous optimization method and device based on subgraph link prediction, the method comprising the steps of: based on the behavior or relationship between users, commodities and shop entities, abstractly constructing a no-weight and no-direction graph required by a model with node labels; implementing closed subgraph sampling extraction of target node pairs on the no-weight and no-direction graph; simply controlling the upper limit of the size of the subgraph and reasonably filtering the samples; calculating the node heterogeneity index of each closed subgraph; generating a new heterogeneous feature vector according to the calculated index data; replacing the obtained heterogeneous feature vector with the original node feature to become a new node feature; extracting subgraph features and performing model training, and finally realizing the prediction of whether an edge exists between the target node pairs; obtaining a recommended candidate list of each user according to the obtained prediction result of the existing edge; and according to the prediction score, completing the sorting of the recommended candidate list obtained by each user to obtain the final recommended result displayed to the user.

Description

Technical Field

[0001] This invention relates to recommender systems, graph neural networks, link prediction, and graph homogeneity-heterogeneity, and is a heterogeneity-optimized recommender method and apparatus based on subgraph link prediction. Background Technology

[0002] Link prediction methods based on graph neural networks (GNNs) are increasingly being applied in various graph data mining scenarios, such as e-commerce, social networks, and biochemistry. A common phenomenon is that many GNN models satisfy the homogeneity principle, meaning the model assumes that specific attributes (e.g., labels, node features) of two connected nodes are often the same or similar. For example, in citation networks, a study typically cites references from papers within the same research field, and users searching for papers often have needs within the same domain. However, recent research indicates that because homogeneous GNNs are theoretically more suitable for highly homogeneous graph data, their performance on heterogeneous graph data is limited.

[0003] This is a noteworthy issue because graph data in the real world often exhibits varying degrees of heterogeneity, meaning that seemingly different or even opposite entities can form connections. In online transaction networks, scammers are more likely to connect with customers; in many social scenarios, most people prefer interacting or dating with members of the opposite sex; and in recommendation tasks in e-commerce, heterogeneous graphs are modeled based on numerous interactions between users and products, shops and friends, and other entities. Heterogeneous graph data is widespread in the real world, and its application prospects are quite broad.

[0004] Attribute network link prediction algorithms based on graph neural networks (GNNs) can be applied to recommendation tasks. Methods proposed for attribute networks can combine graph structure information and attribute information for utilization; however, the heterogeneity of graph data also has a certain impact on model performance. Practical observations show that homogeneous GNNs perform well on highly homogeneous data but poorly on highly heterogeneous data. Even for the same dataset, the model's performance is lower on heterogeneous parts than on homogeneous parts. This means that in practical applications, recommendation system algorithms are affected to varying degrees by the heterogeneity of the data. With predominantly heterogeneous target samples, the model is more likely to avoid connecting two entities of different classes, which affects the practicality and effectiveness of the recommendation results and reduces user experience. For example, users don't always buy the same type of goods, and methods lacking heterogeneity in their recommendations struggle to recommend entirely new products.

[0005] To better handle and utilize highly heterogeneous data, many heterogeneous GNN methods have been proposed in recent years. However, most of these methods consider semantic-level heterogeneity, i.e., sampling the original graph using meta-paths. This requires complex information and the types of meta-paths, and in some cases, it is difficult to obtain meta-paths containing sufficient information from the data. Therefore, a simpler and more effective method is needed to optimize the model's predictive performance on heterogeneous data. Summary of the Invention

[0006] This invention aims to overcome the aforementioned shortcomings of existing technologies by providing a heterogeneous optimization recommendation method and apparatus based on subgraph link prediction. This invention combines graph topology features and heterogeneity features, extracting and utilizing the heterogeneity features of the graph to optimize the performance of the GNN model, improve the overall accuracy of the link prediction algorithm, and enhance the effectiveness of the recommendation system on heterogeneous graphs.

[0007] The technical solution adopted in this invention is a heterogeneous optimization recommendation method based on subgraph link prediction, comprising the following steps:

[0008] S1: Based on the various behaviors or relationships between the three types of entities—users, products, and stores—an unweighted, undirected graph with node labels is constructed to meet the model requirements.

[0009] S2: Perform closed subgraph sampling extraction on the unweighted and undirected graph constructed in step S1 to obtain the extracted subgraph object set.

[0010] S3: For the subgraph sample set obtained in step S2, simply control the upper limit of its subgraph size and perform reasonable sample filtering.

[0011] S4: Based on the subgraph sample set obtained in step S3, calculate the node heterogeneity index of each closed subgraph.

[0012] S5: Generate new heterogeneous feature vectors based on the calculated index data.

[0013] S6: Replace the original node features with the obtained heterogeneous feature vectors to become new node features.

[0014] S7: Use the DCGNN (Deep Graph Convolutional Neural Network) model to extract features from the subgraph, obtain important representations of the graph, train the model, and finally predict whether there are edges between target node pairs.

[0015] S8: Based on step S7, a batch of prediction results with connected edges can be obtained, which is the recommended candidate list for each user.

[0016] S9: For each user's recommended candidate list obtained in step S8, further sort them according to the predicted scores to obtain the final recommendation results displayed to the user.

[0017] In step S1, an unweighted, undirected graph with node labels is constructed based on the various behaviors and relationships between the three entities: users, products, and stores. Specifically, based on the user's historical behavior records in the system logs, a user-product / store and user-user unweighted, undirected graph can be constructed centered on the user. Furthermore, the connections in the graph can be supplemented based on the product catalogs sold by stores, keywords in each store's name, and the similarity of product categories. Finally, each node is labeled according to its entity category, indicating which type of entity the node belongs to. This allows the construction of a complete unweighted, undirected graph with node labels composed of the three types of entities.

[0018] In step S2, the subgraph of the target node pairs is extracted from the constructed unweighted undirected graph to obtain a sampled set of subgraph objects. Specifically: First, the model requires a closed subgraph of order h for the target node pairs. Considering the completeness of information and the operational efficiency of the model, a hop count of 2 is most suitable, i.e., h = 2. After determining the subgraph order, the target node pairs are determined according to the user-product / store format, where one side of the node pair is a user, and the other side can be a product or a store. The sampling method involves obtaining the second-order neighbor sets of the two nodes separately, and then merging these neighbor sets to form a complete second-order subgraph.

[0019] In step S4, based on the set of subgraphs obtained in step S3, the corresponding heterogeneous features are calculated for each subgraph. Specifically:

[0020] The heterogeneity index is explained by the following two calculation formulas:

[0021] Nh i (k) =|{j|j∈Neibor (k) (i), y i ≠y j}| (1)

[0022] Neibor (k) (i) represents the set of k-order neighbors of the target node i, and y represents the class label of the node. Then Nh i (k) The meaning is the number of k-order heterogeneous neighbors of the target node.

[0023]

[0024] Among them Rh i (k)This represents the proportion of heterogeneous neighbors of target node i of order k.

[0025] In step S5, based on the heterogeneity index calculated in step S4, these four indices are concatenated and saved as a one-dimensional vector, i.e., the heterogeneous feature vector of node i is:

[0026] x i =[Nh i (1) Rh i (1) ,Nh i (2) Rh i (2) ]

[0027] In step S6, the new heterogeneous features obtained in step S5 are replaced with the node features in the original graph to complete the new feature vector engineering for all subgraphs.

[0028] In step S7, the DCGNN model is used to extract features from all subgraphs to obtain their representations, and the model is trained. Finally, the prediction of whether there is an edge between target node pairs is achieved. The specific process is as follows:

[0029] Given the adjacency matrix A and its node information matrix X of a subgraph, the graph convolutional layer is:

[0030]

[0031] in It is the angle value matrix, that is W is the graph convolution parameter matrix that can be trained, and f is a non-linear activation function;

[0032] To extract multi-scale substructure features, stacking multiple graph convolutional layers yields the following representation:

[0033]

[0034] Z 0 =X,Z t W is the output of the t-th layer graph convolutional network. t This is the mapping from channel t to channel t+1.

[0035] After performing multiple graph convolutional layers, the outputs of the multiple layers are concatenated laterally, becoming [Z]. 1 , ..., Z hThe feature information is then fed into the pooling layer, whose main function is to sort the feature descriptors in a consistent order, with each feature descriptor corresponding to a node in the original network. Here, a SortPooling layer is used, which sorts the features according to the output values ​​of the last layer of the convolutional network and selects the information from the top-K nodes for pooling.

[0036] For data with high homogeneity, the AttPooling layer can be used. This is a pooling method based on attention mechanism. It uses the self-attention mechanism of graph convolution to calculate the ranking score and selects the information of the top-K nodes for pooling.

[0037] The calculation of self-attention fractions has the following expression:

[0038]

[0039] Where σ is the activation function, θ att These are the attention parameters of AttPool.

[0040] The pooled representation information is then classified through a fully connected layer and a ReLU layer to obtain the model's prediction of whether there are edges between the target node pairs.

[0041] In step S8, based on step S7, a batch of prediction results with connected edges can be obtained, which is the recommended candidate list for each user. Specifically, the prediction results are divided according to the user, thus obtaining the recommended candidate list for each user.

[0042] In step S9, the recommended candidate list for each user in step S8 is further sorted to produce the final recommendation result displayed to the user. Specifically, based on the specific score given by the model during prediction, the entities in the candidate list are sorted from largest to smallest to generate a reasonable recommendation result for each user.

[0043] A second aspect of the present invention relates to a heterogeneous optimization recommendation apparatus based on subgraph link prediction, comprising a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the heterogeneous optimization recommendation method based on subgraph link prediction of the present invention.

[0044] This invention improves the performance of link prediction algorithms for heterogeneous networks, increases prediction accuracy, and enhances the effectiveness of recommendation systems on heterogeneous graphs.

[0045] The advantages of this invention compared to the prior art are:

[0046] (1) In existing technical solutions, the utilization of information such as homogeneity and heterogeneity indicators in recommendation tasks at the link prediction application level is still very limited. This invention can simply and effectively utilize heterogeneity indicators to generate new node feature vectors for the model to perform link prediction, which helps to improve the model's performance on the overall data, thereby enabling more effective recommendations.

[0047] (2) Compared with traditional recommendation methods, this invention does not need to consider too many specific attributes of entities in the information extraction stage, and does not need to generate complicated node representation vectors at the beginning. It only needs to construct the unweighted undirected graph required by the model based on the basic information and make good use of the node label information. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the method of the present invention;

[0050] Figure 2 This is a flowchart illustrating the generation process of heterogeneous feature vectors according to the present invention. Detailed Implementation

[0051] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0052] It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the invention. Furthermore, with respect to numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included in this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0053] Unless otherwise stated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. While only preferred methods and materials have been described herein, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this invention. All references to this specification are incorporated by way of citation to disclose and describe methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0054] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be readily apparent to those skilled in the art. This application specification and embodiments are merely exemplary.

[0055] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0056] Unless otherwise specified, the term "parts" in this invention refers to parts by weight.

[0057] Example 1

[0058] This embodiment relates to a heterogeneity optimization recommendation method based on subgraph link prediction, which is a method for recommending online products, such as... Figure 1 As shown, it includes three main parts: data extraction and preprocessing, heterogeneity vector generation, and target prediction and product recommendation.

[0059] Data extraction and preprocessing include:

[0060] Step S1: Based on the various behaviors or relationships between entities such as users, products, and stores, abstract and construct the unweighted undirected graph with node labels required for the model.

[0061] Shopping platforms can generate and acquire large amounts of data on users, stores, and other entities. Based on users' historical behavior records in the platform's logs—specifically, their purchase history, adding items to their shopping carts, favorited stores, and following other users—an unweighted, undirected graph centered on users can be constructed, connecting them to products / stores and other users. Furthermore, the connections between products and stores can be obtained based on the store's product catalog; relationships between stores can be derived from keywords in their names; and product categories can reveal associations between products. All these relationships are added to the graph. Finally, each node is labeled according to its entity type, indicating whether it is a user, product, or store. This allows for the construction of a complete unweighted, undirected graph composed of these three types of entities.

[0062] Step S2: Sampling of closed subgraphs

[0063] Subgraph extraction of target node pairs is performed on the constructed unweighted undirected graph. After determining that the subgraph order is 2, the target node pairs are determined according to the user-product / store format, that is, one side of the node pair is a user, and the other side is a product or store. It should be noted that the system selects the same other node for each user node. Specifically, with 10 users and 50 products / stores, 500 independent subgraph samples can be obtained.

[0064] Step S3: Control sample size and sample filtering

[0065] Simultaneously, the size of the subgraph needs to be limited to a certain extent when necessary. This invention specifies a maximum upper limit of 128 nodes for a second-order subgraph. Because target nodes with high degree values ​​have many neighbors, discarding some neighbors does not cause significant information loss. This can save data storage space without significantly affecting prediction performance, thereby improving operational efficiency. For example, for users with a large number of historical shopping records, purchase records older than a certain time period can be discarded. Conversely, for overly isolated target nodes, i.e., subgraphs with a very small number of nodes, since they contain almost no information, they are considered meaningless. This invention will filter out subgraph samples with 3 or fewer nodes.

[0066] Heterogeneity vector generation includes:

[0067] Step S4: Calculate the node heterogeneity index for each closed subgraph.

[0068] Using the heterogeneity index calculation formula, for each node in the subgraph, the first and second order heterogeneity and the first and second order heterogeneity ratios can be calculated based on the statistical results of its neighbor labels. For example, if a user node's first-order neighbors include users, products, and shops, then products and shops are its heterogeneous neighbors. Its first-order heterogeneity is the sum of the number of products and shops, and the first-order heterogeneity ratio is the percentage of products and shops in the total neighbor set.

[0069] Step S5: Construct new feature vectors for the subgraph

[0070] The four indicators obtained in the previous step are concatenated and saved as a one-dimensional vector, that is, the heterogeneous feature vector of node i is:

[0071] x i =[Nh i (1) Rh i (1) ,Nh i (2) Rh i (2) ]

[0072] Step S6: Replace with new features

[0073] For each subgraph object, the newly obtained heterogeneous features are used to replace the existing node features in the subgraph, thus updating the subgraph object's attribute information. The specific heterogeneous feature generation process is as follows: Figure 2 As shown.

[0074] Among them, target prediction and product recommendation include:

[0075] Step S7: Use DCGNN to extract features from all subgraphs, train the model, and finally predict the links of the target node pairs.

[0076] Given the adjacency matrix A and its node information matrix X of a subgraph, the graph convolutional layer takes the following form:

[0077]

[0078] in It is the angle value matrix, that is W is the graph convolution parameter matrix that can be trained, and f is a non-linear activation function.

[0079] To extract multi-scale substructure features, stacking multiple graph convolutional layers yields the following representation:

[0080]

[0081] Z 0 =X,Z t W is the output of the t-th layer graph convolutional network. t This is the mapping from channel t to channel t+1.

[0082] After performing multiple graph convolutional layers, the outputs of the multiple GCNs are concatenated laterally, thus becoming [Z 1 , ..., Z h The feature information is then fed into the pooling layer, whose main function is to sort the feature descriptors in a consistent order, with each feature descriptor corresponding to a node in the original network. Here, a SortPooling layer is used, which sorts the data according to the output values ​​of the last layer of the convolutional network and selects the information from the top-K nodes for pooling. The value of K here depends on the distribution of sub-image sample sizes; by default, it is taken as the size of the sub-image ranked in the 60th percentile.

[0083] For data with high homogeneity, the AttPooling layer can be used. This is a pooling method based on an attention mechanism, which uses the self-attention mechanism of graph convolution to calculate the ranking score and selects the information of the top-K nodes for pooling. The default value of K is the same as above.

[0084] The calculation of self-attention fractions has the following expression:

[0085]

[0086] Where σ is the activation function, θ att These are the attention parameters of AttPool.

[0087] The pooled representation information is then classified through a fully connected layer and a ReLU layer to obtain the model's prediction of whether there is a connection between the target node pairs. The specific formula is:

[0088]

[0089] in, This represents the model's prediction results.

[0090] During the training phase, optimization is achieved through backpropagation and gradient descent. The cross-entropy loss function is used, as follows:

[0091]

[0092] Where y is the label for whether the edge actually exists.

[0093] Step S8: Obtain the recommended candidate list for each user.

[0094] There are 10 target users and 50 products or stores in the recommendation pool, meaning the number of subgraph objects is 500. Step S7 determines which of these 500 samples are predicted to have connected edges, and then these results are grouped according to the user's input. This forms the recommendation candidate list for each user.

[0095] Step S9: Sort and recommend based on the predicted scores;

[0096] After obtaining the candidate list to be recommended, the candidate list is sorted from largest to smallest according to the predicted score given by the model (the score range is between 0.5 and 1). The top 10 products / stores in the sorted list are selected as the final recommendation results. If there are fewer than 10 candidates, the list is sorted and recommended directly.

[0097] This invention utilizes a graph neural network model that simultaneously leverages the structural and attribute information of graph data. It conveniently uses heterogeneity index information as new node features to participate in the model's training and prediction processes, effectively optimizing model performance. Based on the model's link prediction results, it generates a candidate recommendation list for users and achieves the final recommendation function based on the specific prediction scores.

[0098] In summary, this invention utilizes a heterogeneity optimization recommendation method based on subgraph link prediction, which optimizes the original internal mechanism of the neural network model, enabling the model to better adapt to both highly homogeneous and highly heterogeneous data, thus achieving superior performance. This is easy to implement in practical applications and yields significant results.

[0099] Example 2

[0100] This embodiment relates to a heterogeneous optimization recommendation device based on subgraph link prediction, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the heterogeneous optimization recommendation method based on subgraph link prediction of Embodiment 1.

[0101] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A heterogeneous optimization recommendation method based on subgraph link prediction, characterized in that, Includes the following steps: S1: Based on the various behaviors or relationships between the three types of entities—users, products, and stores—an unweighted undirected graph with node labels is constructed to meet the requirements of the model. S2: Perform closed subgraph sampling and extraction on the unweighted and undirected graph constructed in step S1 to obtain the set of extracted subgraph objects; S3: For the subgraph sample set obtained in step S2, simply control the upper limit of its subgraph size and perform reasonable sample filtering; S4: Based on the subgraph sample set obtained in step S3, calculate the node heterogeneity index for each closed subgraph; specifically including: The heterogeneity index is explained by the following two calculation formulas: (1) in Let represent the set of k-order neighbors of the target node i, and y represent the class label of the node. The meaning is the number of heterogeneous neighbors of order k of the target node; (2) in This represents the proportion of heterogeneous neighbors of target node i of order k; S5: Generate new heterogeneous feature vectors based on the calculated index data; S6: Replace the original node features with the obtained heterogeneous feature vectors to become new node features; S7: Using the DCGNN model (Deep Graph Convolutional Neural Network), features of the subgraph are extracted to obtain important representations of the graph. The model is then trained to predict the existence of edges between target node pairs. Specifically, this includes: Given the adjacency matrix A and its node information matrix X of a subgraph, the graph convolutional layer takes the following form: (3) in , It is the angle value matrix, that is W is the graph convolution parameter matrix that can be trained. It is a non-linear activation function; To extract multi-scale substructure features, stacking multiple graph convolutional layers yields the following representation: (4) in , That is the output of the t-th layer graph convolutional network. This is the mapping from channel t to channel t+1; After performing multiple graph convolutional layers, the outputs of the multiple GCNs are concatenated laterally, thus becoming... The feature information is then fed into the pooling layer, which sorts the feature descriptors in a consistent order. Each feature descriptor corresponds to a node in the original network. Here, the SortPooling layer is used to sort the features according to the output values ​​of the last layer of the convolutional network and select the information of the top-K nodes for pooling. For data with high homogeneity, the AttPooling layer can be used. This is a pooling method based on attention mechanism. It uses the self-attention mechanism of graph convolution to calculate the ranking score and selects the information of the top-K nodes for pooling. The calculation of self-attention fractions has the following expression: (5) in For activation function, These are the attention parameters of AttPool; The pooled representation information is then classified through a fully connected layer and a ReLU layer to obtain the model's prediction of whether there are edges between the target nodes. S8: Based on step S7, a batch of prediction results with connected edges can be obtained, which means the recommended candidate list for each user can be obtained. S9: For each user's recommended candidate list obtained in step S8, further sort them according to the predicted scores to obtain the final recommendation results displayed to the user.

2. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S1, an unweighted, undirected graph with node labels is constructed based on the various behaviors or relationships between the three entities: users, products, and stores. Specifically, this includes: constructing a user-product / store and user-user unweighted, undirected graph centered on the user based on the user's historical behavior records in the system logs; further supplementing the graph's connections based on the product catalogs sold by stores, keywords in each store's name, and the same product categories; and finally, labeling each node according to the different types of entities to indicate which type of entity the node belongs to. This constructs a complete unweighted, undirected graph with node labels composed of the three types of entities.

3. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S2, the subgraph extraction of target node pairs is performed on the constructed unweighted undirected graph to obtain a sampled set of subgraph objects. Specifically, this includes: First, the model needs a closed subgraph of order h for the target node pairs. Considering the completeness of information and the running efficiency of the model device, it is most appropriate to set the number of hops of the subgraph to 2, i.e., h=2. After determining the order of the subgraph, the target node pairs are determined according to the format of user-product / store, i.e., one side of the node pair is a user, and the other side is a product or a store. The sampling method is to obtain the second-order neighbor sets of the two nodes respectively, and then merge the neighbor sets of the two nodes to form a complete second-order subgraph.

4. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S5, based on the heterogeneity index calculated in step S4, these four indices are concatenated and saved as a one-dimensional vector, i.e., the heterogeneous feature vector of node i is: 。 5. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S6, the new heterogeneous features obtained in step S5 are replaced with the node features in the original graph to complete the new feature vector engineering for all subgraphs.

6. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S8, a batch of prediction results with connected edges can be obtained according to step S7, that is, the recommended candidate list for each user can be obtained. Specifically, it includes: taking the user as the center, dividing the prediction results according to the user, thereby obtaining the recommended candidate list for each user.

7. The heterogeneous optimization recommendation method based on subgraph link prediction according to claim 1, characterized in that... In step S9, the recommended candidate list for each user in step S8 is further sorted to produce the final recommendation result displayed to the user. Specifically, this includes: sorting the entities in the candidate list from largest to smallest according to the specific score given by the model during prediction, and generating a reasonable recommendation result for each user.

8. A heterogeneous optimization recommendation device based on subgraph link prediction, characterized in that, The method includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the heterogeneity optimization recommendation method based on subgraph link prediction as described in any one of claims 1-7.

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