A graph embedding distance prediction method and system based on adaptive landmarks and multi-scale perception
Patent Information
- Application Number
- CN202611167364.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-03
- Publication Date
- 2026-10-13
AI Technical Summary
[0006]为解决现有技术在大规模图最短路径距离预测中存在的时间空间复杂度高、精度不足、泛化能力弱等问题，本发明的目的是提供一种大规模图上最短路径距离预测的方法，实现快速、精准且通用的最短路径距离预测
[0034]本发明通过地标局部与全局信息协同挖掘，在多种真实图数据集上的均优于主流方法，结果见图2，最优变体在部分数据集上误差降低超70%。方法时间复杂度与节点数呈线性相关，空间复杂度避免传统方法的O()开销。仅依赖节点基本属性，如仅依赖图结构本身的拓扑信息（包括节点邻接关系、边权重、PageRank值及介数中心性等结构特征），无需场景特定特征，可适配社交网络、道路网络等多种图结构。
Smart Images
Figure CN122903905A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computer technology and relates to a graph embedding distance prediction method and system based on adaptive landmarks and multi-scale perception. Background Technology
[0002] In recent years, with the explosive growth of graph data in social networks and transportation networks, shortest path distance prediction for large-scale graphs has become one of the core requirements of graph data management, and is widely used in practical scenarios such as travel route planning, community association mining, and network resource scheduling.
[0003] Traditional shortest path algorithms, such as Dijkstra's algorithm and Floyd's algorithm, perform calculations by precisely traversing the nodes and edges of the graph to complete path search and distance calculation. However, in real-world applications, the limitations of these algorithms become increasingly apparent. Limited by the number of nodes and edges in large-scale graphs, the time and space complexity of traditional algorithms increases exponentially; calculating a single path can take hours or even days, far exceeding the storage and computing capabilities of ordinary computers.
[0004] With the widespread application of deep learning, many learning-based methods have been proposed to address the complexity issues of traditional methods. However, existing learning-based methods either focus only on local or global single-dimensional location information, resulting in insufficient prediction accuracy, or they rely excessively on scene-specific features, such as the latitude and longitude information of road networks, leading to weak generalization ability. Some decision tree-based methods also struggle to meet the multi-distance output requirements in complex scenarios.
[0005] Therefore, how to ensure that the algorithm can adapt to large-scale graph data and take into account computational efficiency, while freeing the model from the dependence on scene-specific features and improving prediction accuracy, has become an urgent problem to be solved in the field of shortest path distance prediction. Summary of the Invention
[0006] To address the problems of high time and space complexity, insufficient accuracy, and weak generalization ability in existing technologies for shortest path distance prediction on large-scale graphs, this invention aims to provide a method for shortest path distance prediction on large-scale graphs, achieving fast, accurate, and universal shortest path distance prediction. This invention proposes a dynamic influence landmark selection strategy, combining graph convolutional networks and multi-view deep neural network models to deeply mine local and global node location information; and achieves efficient dual-embedding fusion through a neural network predictor, improving prediction performance in complex scenarios without relying on scene-specific features.
[0007] like Figure 1As shown, this invention focuses on improving the efficiency and accuracy of shortest path distance prediction for complex, large-scale graph structures. It proposes an embedding method based on adaptive landmarks and multi-scale perception to achieve deep mining of graph node location information and shortest path distance prediction, including the following steps:
[0008] Step 1: Dynamic Influence Landmark Filtering
[0009] A hybrid importance distribution is constructed based on the PageRank score and betweenness centrality of nodes. From this distribution, a dynamically updated set of landmark nodes is sampled. "Dynamically" refers to adaptive selection based on the graph structure, with the optimal update frequency synchronized with the graph data update cycle. Simultaneously, an edge pruning strategy based on the Jaccard coefficient is introduced to remove redundant connections and construct a simplified sparse adjacency matrix. The specific threshold setting rules and procedures for edge pruning are as follows: For each edge (u,v) in the graph, its Jaccard coefficient is calculated, and the pruning threshold is set to 0.1 (this threshold is determined on the validation set through grid search, ranging from [0.05, 0.30], with a step size of 0.05, selecting the value that minimizes the MAE of the validation set). If J(u,v) < 0.1, the edge is considered a redundant connection and is pruned; otherwise, it is retained. The distance from each node to the landmark node is calculated to form an initial local embedding, which is then input into the graph convolutional network. This generates a local encoding embedding that captures local topological and location information through neighborhood feature aggregation. A two-layer graph convolutional network (GCN) is used, with the following structure: input layer (dimension d, which is the number of landmark nodes) → GCN layer 1 (output dimension 128) → ReLU activation → Dropout (0.2) → GCN layer 2 (output dimension 64) → ReLU activation → Dropout (0.2) → output layer (output dimension 64).
[0010] The aggregation formula for each layer of GCN is:
[0011] ,
[0012] in, It is a sparse adjacency matrix with self-loops. For degree matrix, For learnable parameters, This is the ReLU activation function.
[0013] Step 2: Anchor Set Selection and Global Embedding Generation
[0014] Based on Bourgain's theorem, log₂n groups are sampled, each group containing log₂n anchor point sets (n being the number of nodes). The i-th group of anchor point sets is then sorted by probability. The algorithm includes nodes, balancing computational overhead with information integrity. For each node, the maximum distance from it to all nodes in the anchor set is used as the embedding feature corresponding to that anchor set, forming the initial global embedding. This initial embedding is then input into a multi-view deep neural network, training an independent deep neural network for each view. The neural network structure for each view is identical, consisting of two fully connected layers: Input layer (dimension d, the size of each anchor set) → Fully connected layer 1 (dimension 256) → BatchNorm → ReLU → Dropout (0.3) → Fully connected layer 2 (dimension 128) → BatchNorm → Output layer (dimension 64). The average value of each dimension is calculated to obtain the final global encoded embedding.
[0015] In step two, the view networks are jointly trained under a unified loss function (sharing backpropagation).
[0016] Step 3: Embedded Fusion Prediction
[0017] A neural network predictor is used to achieve fusion prediction of local and global embeddings: first, prediction is based on local embeddings, then the global embeddings are combined with another neural network, the global prediction is optimized through local results, and the final predicted distance is output.
[0018] The first-level local predictor takes node pairs as input. The local embeddings are concatenated, with a dimension of 64×2=128, and the output is the local predicted distance. Network structure: Input layer (128) → Fully connected layer 1 (dimension 64) → BatchNorm → ReLU → Dropout (0.3) → Fully connected layer 2 (dimension 32) → BatchNorm → Output layer (dimension 1).
[0019] The second-level global tuning predictor takes node pairs as input. The global embedding is concatenated with the first-level output, with a dimension of 64×2+1=129. The output is the final predicted distance. Network structure: Input layer (129) → Fully connected layer 1 (dimension 64) → BatchNorm → ReLU → Dropout (0.3) → Fully connected layer 2 (dimension 32) → BatchNorm → Output layer (dimension 1).
[0020] Step 4: Model Training and Iterative Optimization
[0021] The mean squared error is used as the loss function to minimize the deviation between the predicted and actual distances. The graph convolutional network encoder, the multi-view deep neural network encoder, and the predictor are trained iteratively to optimize the model parameters until the preset number of training epochs or loss convergence is achieved.
[0022] Specific hyperparameter settings for model training:
[0023] Optimizer type: Adam optimizer ,
[0024] Learning rate settings: Initial learning rate lr=0.001, using cosine annealing strategy, decaying to 0.000001 every 50 rounds.
[0025] Batch size: The sampling batch size for training node pairs is 1024.
[0026] Training rounds preset value: maximum training rounds 10000.
[0027] Define the rate of change of relative loss ,in Let be the average loss of the t-th training round. If the rate of change is less than 0.000001 for 10 consecutive rounds, the loss is considered to have converged, and training is terminated early. If the loss on the validation set does not decrease for 20 consecutive rounds, training is stopped.
[0028] Based on the above, this invention also proposes a graph embedding distance prediction system based on adaptive landmarks and multi-scale perception, the system comprising:
[0029] The dynamic landmark filtering and local embedding module is used to construct a hybrid importance distribution based on the node's PageRank score and betweenness centrality, and to sample the dynamically updated landmark node set; it uses an edge pruning strategy based on the Jaccard coefficient to construct a sparse adjacency matrix; it calculates the distance from the node to the landmark node to obtain the initial local embedding, and generates the local encoded embedding through a graph convolutional network.
[0030] The global anchor embedding module is used to sample multiple sets of anchor points based on Bourgain's theorem, form an initial global embedding with the maximum distance from the node to the anchor set, and generate the final global encoded embedding through a multi-view deep neural network.
[0031] The two-level fusion prediction module is used to employ a two-level neural network predictor. First, it outputs the local prediction distance based on the local encoding embedding of node pairs. Then, it combines the global encoding embedding and the local prediction distance for optimization and outputs the final shortest path prediction distance.
[0032] The training optimization module is used to iteratively train the network parameters of each module using mean squared error as the loss function until the preset number of training rounds or loss convergence is reached.
[0033] The embedding method and system based on adaptive landmark and multi-scale perception disclosed in this invention have the following beneficial effects:
[0034] This invention, through the collaborative mining of local and global landmark information, outperforms mainstream methods on various real-world graph datasets, as shown in the results. Figure 2The optimal variant reduces error by over 70% on some datasets. The method's time complexity is linearly related to the number of nodes, and its space complexity avoids the O(n log n) of traditional methods. Low overhead. It only relies on basic node attributes, such as the topological information of the graph structure itself (including node adjacency relationships, edge weights, PageRank values, and betweenness centrality, etc.), without requiring scene-specific features, and can be adapted to various graph structures such as social networks and road networks. Attached Figure Description
[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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.
[0036] Figure 1 This is a schematic diagram illustrating the workflow of the shortest path distance prediction method of the present invention;
[0037] Figure 2 This is a schematic diagram comparing the accuracy experimental results of the present invention with those of existing methods;
[0038] Figure 3 This is a schematic diagram comparing the experimental results of distance prediction time of the present invention and existing methods (unit: ns).
[0039] Figure 4 This is a schematic diagram comparing the experimental results of embedding and model memory size of the present invention and existing methods (unit: KB).
[0040] Figure 5 This is a schematic diagram illustrating the experimental proof of the effectiveness of the dual-path prediction of the present invention. Detailed Implementation
[0041] The invention will be further described in detail below with reference to the specific embodiments and accompanying drawings. Except for the contents specifically mentioned below, the processes, conditions, and experimental methods for implementing the invention are all common knowledge and general knowledge in the art, and the invention does not have any particular limitations.
[0042] This invention discloses a node distance metric learning technique applicable to complex, large-scale graph structures. In the field of graph data management, calculating the shortest path between any two nodes is a core, fundamental operation with wide-ranging applications, covering multiple practical areas such as route planning and community-wide search. Traditional algorithms generally suffer from excessively high time and space complexity when processing large-scale graph data. Existing learning-based methods not only struggle to achieve high-accuracy distance prediction in complex graph structures, but some methods also exhibit strong dependence on scene-specific data, resulting in poor generalization performance. To effectively address these technical challenges, this invention proposes a graph embedding framework that integrates adaptive landmark selection and multi-scale perception capabilities. This method first constructs a dynamic landmark set based on node influence sampling. It then generates local encoding embeddings containing rich topological details through neighborhood feature aggregation using a graph convolutional network, and generates global encoding embeddings reflecting the global relative positions of nodes through a multi-view deep neural network. By performing distance decoding and calibration operations in the latent space, high-precision, low-latency inference of the distance between any pair of nodes is ultimately achieved. Comprehensive experimental results show that the proposed method exhibits excellent effectiveness and efficiency on various real-world graph datasets. Compared with existing mainstream methods, it not only significantly improves the accuracy of shortest path distance prediction but also effectively reduces time and space overhead. It can efficiently adapt to large-scale graph application scenarios and support high-throughput query requirements.
[0043] This invention uses the mean squared error (MSE) loss function to measure the deviation between the predicted distance and the true distance, and it is used to optimize model parameters during training. The function is defined as follows:
[0044]
[0045] In formula (1), T is the training sample. For node pairs and The true shortest path distance, This loss function predicts distances for the model. It effectively minimizes prediction bias, ensuring the model learns the mapping between node locations and path distances.
[0046] In the dynamic influence landmark selection, the sampling probability of a node is defined as:
[0047]
[0048] in, For nodes PageRank value, For betweenness centrality, λ is the balance coefficient. λ is the normalization function. The value of λ ranges from [0,1]. The optimal value is searched on the validation set using cross-validation with a search step size of 0.1. Experiments show that for most graph structures, the model performance is optimal when λ=0.6.
[0049] like Figure 1 As shown, the shortest path distance prediction method of the present invention includes the following steps:
[0050] Step 1: Dynamic Influence Landmark Filtering
[0051] A hybrid importance distribution is constructed based on node PageRank scores and betweenness centrality, from which a dynamically updated set of landmark nodes is sampled. Simultaneously, an edge pruning strategy based on the Jaccard coefficient is introduced to eliminate redundant connections and construct a simplified sparse adjacency matrix. The distance from each node to the landmark node is calculated to form an initial local embedding, which is then input into a graph convolutional network. Local encoding embeddings capturing local topological and location information are generated through neighborhood feature aggregation.
[0052] Step 2: Anchor Set Selection and Global Embedding Generation
[0053] Based on Bourgain's theorem, log₂n groups are sampled, each group containing log₂n anchor point sets (n being the number of nodes). The i-th group of anchor point sets is then sorted by probability. It includes nodes, balancing computational overhead and information integrity. For each node, the maximum distance from it to all nodes in the anchor set is used as the embedding feature corresponding to that anchor set, forming an initial global embedding. This is then input into a multi-view deep neural network, where an independent deep neural network is trained for each view. The final global encoded embedding is obtained by averaging the view embeddings.
[0054] Step 3: Embedded Fusion Prediction
[0055] A neural network predictor is used to achieve fusion prediction of local and global embeddings: first, prediction is based on local embeddings, then the global embeddings are combined with another neural network, the global prediction is optimized through local results, and the final predicted distance is output.
[0056] Step 4: Model Training and Iterative Optimization
[0057] The mean squared error is used as the loss function to minimize the deviation between the predicted and actual distances. The graph convolutional network encoder, the multi-view deep neural network encoder, and the predictor are trained iteratively to optimize the model parameters until the preset number of training epochs or loss convergence is achieved.
[0058] The overall implementation algorithm is as follows:
[0059] Algorithm: Overall Training Algorithm
[0060] Input:
[0061] Image: G
[0062] Number of training rounds:
[0063] Output:
[0064] Embedding matrix: ,
[0065] Predictor:
[0066]
[0067] Assuming graph G is used as input, complete the encoder. , and predictor Initialization.
[0068] The second line describes the selection of landmarks. Anchor set and training node pair set .
[0069] The third line calculates the actual distance d between training node pairs.
[0070] The fourth row generates the initial embedding matrix. , .
[0071] Execute lines 5-14 Rotation training:
[0072] Line 6 initializes the loss for this round.
[0073] Lines 7 and 8 are respectively passed through , coding , get , .
[0074] Lines 9-12 iterate through the set of training node pairs. Each node pair in:
[0075] Line 10 embeds the node into the predictor. , to obtain the predicted distance .
[0076] Line 11 accumulates the loss based on the actual distance.
[0077] Line 13 optimizes the encoder using loss. , and predictor To minimize losses.
[0078] Line 15 returns the embedding matrix. , and predictor .
[0079] Example
[0080] The method described in this invention focuses on shortest path distance prediction on large-scale graphs. As a specific embodiment, the process is as follows:
[0081] This invention uses a real-world node distance prediction system based on a graph-structured data learning architecture as an experimental case, employing five publicly available datasets and comparing it with nine other existing methods. The core task of this distance prediction system is to perform a series of complex processing steps on the node relationships and structural information in complex topological graphs to achieve accurate modeling and prediction of distances between nodes. The method of this invention is based on distance embedding using graph convolutional networks and multi-view deep neural networks.
[0082] Taking Dongguan's route planning as an example, the road network map G = (V, E) in Dongguan's central urban area contains |V| = 7,633 intersection nodes and |E| = 10,499 road edges, with edge weights equal to the actual distance (kilometers). The traditional Dijkstra algorithm takes an average of approximately 150ms per query, which cannot meet the demands of high-concurrency real-time navigation.
[0083] Offline phase
[0084] Step 1: Dynamic Influence Landmark Filtering
[0085] Landmark selection: A hybrid importance distribution was constructed based on the PageRank (reflecting the intersection's hub status as a city-wide transportation hub) and betweenness centrality (reflecting the intersection's bridging ability as a bridge between different towns and streets) of intersections. The Jaccard coefficients of adjacent intersections were calculated, with a threshold τ=0.10 (the proportion of shared neighbors among adjacent intersections in Dongguan's road network is relatively low, and the overlap of neighbors at intersections of branch roads and main roads is small; therefore, the threshold was appropriately lowered to retain key connections). After pruning, approximately 9,200 edges were retained, and the edge density of the graph was reduced from 1.82 × 10⁻⁻⁻⁶. 4 Reduced to 1.59 × 10⁻ 4 .
[0086] The shortest travel distance from each intersection to 120 landmarks (approximately 1.6% of the total number of nodes) is pre-calculated, input into the GCN network with the structure described in the implementation method, and the output is a local coding embedding (7633×64).
[0087] Step 2: Anchor Set Selection and Global Embedding Generation
[0088] Based on Bourgain's theorem, we sample m = ⌈log2 7600⌉ = 13 sets of anchor points, each set containing 13 anchor points. The i-th set (i = 1, ..., 13) is distributed according to probability. For each intersection, calculate the maximum and shortest distance from it to all nodes in the i-th set of anchor points as the embedding feature of that set, forming the initial global embedding (7600×13).
[0089] Multi-view deep neural network configuration: There are 13 independent view networks, each corresponding to a set of anchor points, with the structure as described in the implementation method, and the output is a global encoding embedding (7633×64).
[0090] Step 3: Embedded Fusion Prediction
[0091] The input consists of a two-stage predictor, with the predictor network structure as described in the implementation method.
[0092] Step 4: Model Training and Iterative Optimization
[0093] One million node pairs were randomly selected as training samples. These were then divided into a training set (800,000 pairs), a validation set (100,000 pairs), and a test set (100,000 pairs) in an 8:1:1 ratio. Mean squared error was used as the loss function to minimize the deviation between the predicted and actual distances. The graph convolutional network encoder, the multi-view deep neural network encoder, and the predictor were iteratively trained to optimize the model parameters until the preset number of training iterations or loss convergence was achieved.
[0094] Online phase
[0095] Query performance was analyzed on a test set of 100,000 node pairs: a single prediction took 1.27 µs, and the total query time for 100,000 test samples was 0.127 s. In comparison, the traditional Dijkstra algorithm takes approximately 12.22 seconds to process a query of the same size, representing a speedup of approximately 96 times. This mechanism allows local prediction to handle "short-range fine estimation" (relative error 0.2125), while global prediction handles "long-range structural correction" (relative error 0.1917). Together, they reduce the relative error of the entire test set to 0.0521.
[0096] The code in this example is implemented using Python 3.12 and deployed on an Intel i9-10900K CPU, a GeForce RTX 3080 GPU, and 128GB of memory.
[0097] To accurately assess the accuracy of distance prediction, the Mean Absolute Error (MAE) and Mean Relative Error (MRE) were calculated. Experimental results are as follows: Figure 2As shown, the model achieves best or second-best accuracy on five datasets compared to other existing methods.
[0098] To accurately evaluate the runtime and storage performance of distance prediction, the actual runtime, as well as the memory size of the embedding and model, were recorded. Experimental results are as follows: Figure 3 and 4 As shown, the model prediction time (ns) and storage cost (kb) are reduced and within an acceptable range while maintaining accuracy.
[0099] To verify the effectiveness of the joint prediction of global and local embeddings provided by this invention, their accuracy was implemented and recorded. Experimental results are as follows: Figure 5 As shown, accuracy drops significantly in variants that use only local or global embedding of landmarks.
[0100] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
[0101] As used in this invention, the term "comprising" is an open-ended expression, meaning it includes the contents specified in this invention but does not exclude other aspects.
[0102] As used in this invention, the term "and / or" includes any one or more of the related listed items and all combinations thereof.
[0103] The scope of protection of this invention is not limited to the above embodiments. All variations and advantages that can be conceived by those skilled in the art within the technical scope disclosed in this invention are included in this invention and are protected by the appended claims.
Claims
1. A graph embedding distance prediction method based on adaptive landmarks and multi-scale perception, characterized in that, Includes the following steps: Step 1: Construct a hybrid importance distribution based on the node's PageRank score and betweenness centrality, and sample to obtain a dynamically updated set of landmark nodes; A sparse adjacency matrix is constructed by eliminating redundant connections using an edge pruning strategy based on the Jaccard coefficient. The distance from each node to the landmark node is calculated to obtain the initial local embedding. The initial local embedding is then input into the graph convolutional network to aggregate neighborhood features and generate the local encoded embedding. Step 2: Based on Bourgain's theorem, sample multiple sets of anchor points, and use the maximum distance from each node to all nodes in the corresponding anchor point set as the embedding feature of that anchor point set to form the initial global embedding; The initial global embedding is input into a multi-view deep neural network, and an independent deep neural network is trained for the view corresponding to each set of anchor points. The outputs of each view are then fused to obtain the final global encoding embedding. Step 3: Use a two-level neural network predictor to perform fusion prediction of local encoding embedding and global encoding embedding. First, output the local prediction distance based on the local encoding embedding of the node pair, and then combine the global encoding embedding and local prediction distance of the node pair for optimization, and output the final shortest path prediction distance of the node pair. Step 4: Using the mean squared error as the loss function, iteratively optimize the parameters of the graph convolutional network, the multi-view deep neural network, and the two-level neural network predictor until the preset training rounds are reached or the loss converges.
2. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step one, the formula for calculating the sampling probability of a node is: ； In the formula, For nodes PageRank value, For betweenness centrality, λ is the balance coefficient. This is the normalization function.
3. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step one, the edge pruning strategy calculates the Jaccard coefficient for each edge (u,v) in the graph and sets a pruning threshold. If the Jaccard coefficient of an edge is less than the threshold, it is determined to be a redundant connection and pruned; otherwise, it is retained. The pruning threshold is determined on the validation set through grid search, with a value range of [0.05, 0.30] and a search step size of 0.
05.
4. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 3, characterized in that, The pruning threshold is 0.
1.
5. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step one, the graph convolutional network is a two-layer GCN structure, consisting of an input layer, a first GCN layer, a ReLU activation layer, a first Dropout layer, a second GCN layer, a ReLU activation layer, a second Dropout layer, and an output layer; the aggregation formula for each GCN layer is: ， In the formula, It is a sparse adjacency matrix with self-loops. For degree matrix, For learnable parameters, This is the ReLU activation function.
6. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step two, based on Bourgain's theorem, log₂n sets of anchor points are sampled, each set containing log₂n anchor points, where n is the total number of nodes in the graph; the i-th set of anchor points is then sorted by probability. Includes nodes in the graph.
7. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step two, the deep neural network corresponding to each view is a two-layer fully connected network, which includes an input layer, a first fully connected layer, a BatchNorm layer, a ReLU activation layer, a Dropout layer, a second fully connected layer, a BatchNorm layer, and an output layer. The output embedding of each view's deep neural network is averaged dimension by dimension to obtain the final global encoding embedding.
8. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step three, the two-stage neural network predictor includes a first-stage local predictor and a second-stage global tuning predictor: The input to the first-level local predictor is the concatenated vector of local encoding embeddings of two nodes, and the output is the local prediction distance. The input to the second-level global tuning predictor is a vector formed by concatenating the global encoding embedding of two nodes with the local prediction distance, and the output is the final prediction distance.
9. The graph embedding distance prediction method based on adaptive landmarks and multi-scale perception according to claim 1, characterized in that, In step four, the mean squared error loss function is defined as follows: ； In the formula, T is the set of training node pairs. For node pairs and The true shortest path distance, Predict distances for the model.
10. A graph embedding distance prediction system based on adaptive landmarks and multi-scale perception, characterized in that, The system comprising the method described in any one of claims 1-9, wherein the method is: The dynamic landmark filtering and local embedding module is used to construct a hybrid importance distribution based on the node's PageRank score and betweenness centrality, and to sample the dynamically updated landmark node set; it uses an edge pruning strategy based on the Jaccard coefficient to construct a sparse adjacency matrix; it calculates the distance from the node to the landmark node to obtain the initial local embedding, and generates the local encoded embedding through a graph convolutional network. The global anchor embedding module is used to sample multiple sets of anchor points based on Bourgain's theorem, form an initial global embedding with the maximum distance from the node to the anchor set, and generate the final global encoded embedding through a multi-view deep neural network. The two-level fusion prediction module is used to employ a two-level neural network predictor. First, it outputs the local prediction distance based on the local encoding embedding of node pairs. Then, it combines the global encoding embedding and the local prediction distance for optimization and outputs the final shortest path prediction distance. The training optimization module is used to iteratively train the network parameters of each module using mean squared error as the loss function until the preset number of training rounds or loss convergence is reached.