High-order link prediction method and device based on co-occurrence node guide topology embedding model

Abstract

The invention provides a high-order link prediction method and device based on a co-occurrence node guide topology embedding model, and the method comprises the following steps: (1) converting original time series data into a dynamic high-order network, and extracting a timestamp and a simplex structure; (2) quantifying the interaction strength of the node pairs, and generating a time-varying weight matrix; (3) predicting a closing probability based on an interaction weight mean value; (4) generating a node walk sequence of time sequence perception, and capturing a dynamic behavior mode; (5) analyzing high-dimensional topological features (such as rings and holes), and extracting a stable structure; (6) dynamic node embedding is generated, and the characterization capacity of the closed structure is enhanced; (7) optimizing the stability of the prediction model, and preventing overfitting; and (8) fusing local interaction and global topological features, and outputting a final closure probability. According to the invention, through dynamic time sequence modeling and multi-modal feature fusion, accurate prediction of the high-order closed structure is realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of complex network analysis and prediction, and particularly relates to a high-order link prediction method and device based on a co-occurrence node guided topology embedding model. BACKGROUND

[0002] With the rapid development of complex systems such as social networks, biological information networks, and transportation networks, analyzing high-order interaction relationships (such as multi-node simultaneous interaction) in networks has become a key to understanding the evolution mechanism and function of the network. Traditional link prediction (LP) mainly focuses on the direct connection between pairs of nodes, while higher-order link prediction (HLP) needs to predict high-order structures (such as hyperedges, simplices) involving multiple nodes, which has important application value in disease transmission analysis, group behavior prediction, resource allocation optimization, etc. However, high-order interaction has complex nonlinear characteristics and dynamic evolution characteristics, and existing technologies face significant challenges in dealing with such problems. The existing technical means are as follows: 1. Topological feature-based method: by extending traditional pairwise link prediction indicators (such as common neighbors CN, Adamic-Adar AA) to the high-order scene, the local topological similarity of nodes in high-order structures is calculated. For example, by calculating the mean value of the topological features of all node pairs in the hyperedge as the basis for high-order structure prediction.

[0003] 2. Matrix optimization-based method: using hypergraph Laplacian matrix or tensor decomposition technology, the high-order interaction is mapped to a low-dimensional matrix, and the missing hyperedge is predicted by optimizing the objective function. For example, the Coordinate Matrix Minimization (CMM) method converts hyperedge prediction into a matrix completion problem.

[0004] 3. Embedding-based method: graph embedding technology (such as Node2Vec, Graph Convolutional Network GCN) is used to learn the low-dimensional vector representation of nodes or high-order structures, and the potential interaction is predicted by vector similarity. For example, the Neural Hyperlink Predictor (NHP) uses GCN to model the embedding features of nodes in the hypergraph.

[0005] The existing technology has the following problems: 1. Limited representation ability of high-order structures for topological feature method: the simple extension of traditional topological indicators (such as CN, AA) cannot effectively capture the complex nonlinear relationships between multiple nodes, resulting in the loss of high-order feature information. For example, the local feature mean value of node pairs in the hyperedge cannot reflect the global interaction pattern.

[0006] 2. High computational complexity of matrix optimization method: matrix decomposition or tensor operation needs to handle large-scale sparse data, which consumes a lot of computing resources and is difficult to extend to large-scale networks, limiting the practical application scenarios.

[0007] 3. Overfitting and Insufficient Generalization of Embedding Methods: Deep learning-based embedding models (such as GCNs) are susceptible to data sparsity, prone to overfitting on small datasets, and lack the ability to model dynamic evolution processes. For example, static embeddings cannot adapt to the temporal changes in co-occurrence nodes (CoNs), leading to decreased prediction stability. Furthermore, existing methods often extract features from a single perspective, failing to integrate the dynamic formation process of higher-order structures (such as simple complex closure events) with multi-node interaction patterns, thus limiting prediction accuracy. Therefore, an innovative technique that balances computational efficiency, dynamic modeling, and high-order feature fusion is needed. Summary of the Invention

[0008] This invention proposes a high-order link prediction method and apparatus based on a co-occurrence node-guided topology embedding model. Through time-series dynamic modeling, high-order topology analysis, contrastive learning optimization, and gated ensemble, the accuracy and robustness of high-order link prediction (HLP) are significantly improved.

[0009] The first aspect of this invention provides a high-order link prediction method based on a co-occurring node-guided topology embedding model, comprising: Extract all simplex records with timestamps from the time-series dataset, map the simplex s to a simplex structure, and obtain a higher-order network; the higher-order network includes: a node set V h Simplex set S h and timestamp set T h ; For the node set V h For each node pair in the process, the dynamic link weight matrix M(t0) of the node pair is obtained based on the decay rate. Based on the dynamic link weight matrix M(t0), a time-aware node walk sequence set walks is generated. From the simplex set S h The closed dynamic simplex sequence is extracted, and the Vietoris-Rips complex is constructed on the dynamic simplex sequence to obtain the simplex lifetime. Based on the simplex lifetime, the embedding vector weighting coefficients are obtained. Based on the node walk sequence set walks and the node set V h A dynamic adjacency matrix A and a node feature matrix X are constructed. A multi-head attention mechanism is employed to generate a graph attention network (GAT) embedding Φ based on the dynamic adjacency matrix A and the node feature matrix X. GAT ( v The GAT embedding is optimized through comparative learning to obtain the optimized embedding Φ. contrast ( v Based on comparison, optimize the embedded Φ contrast ( v), obtain a Hadamard aggregated simplex embedding vector Φ s ); According to the simplex embedding vector Φ s ) and the embedding vector weighting coefficient, a weighted simplex embedding vector Φ weighted ( s ) is obtained; The simplex embedding vector Φ weighted ( s ) is subjected to MLP and spectral normalization processing to obtain a closure probability P CTE ; According to the local interaction closure probability P MI and the closure probability P CTE , the final closure probability P is obtained by using the formula ; Wherein, P MI is obtained based on the multi-dimensional interaction MI model, and β is a preset coefficient.

[0010] Optionally, for each node pair in the node set V h , a dynamic link weight matrix M(t0) of the node pair is obtained based on a decay rate, including: For each node pair in the node set V h , the corresponding dynamic link weight is obtained by using the formula ; According to the corresponding dynamic link weight of each node pair, the dynamic link weight matrix M(t0) of the node pair is obtained; Wherein, , and are the total weight of the node v i and the node v j in the time window ; λ is a decay rate, t 0 is the current time, t s is the timestamp of the simplex s , is an indicator function, which is 1 if , otherwise 0.

[0011] Optionally, according to the dynamic link weight matrix M(t0), a time series aware node walk sequence set walks is generated, including: Traverse the node set V h , and from each node v iDeparture, commencement l s Each independent walk yields all node walk sequences, which are then used as a set of node walk sequences. In each node's walk sequence, the current node v current The next node v next Based on the dynamic link weight matrix within the corresponding time window, the formula is used. Sure; in, Represents a node v The set of adjacent nodes.

[0012] Optionally, the dynamic simplex sequence is denoted as K( t () indicates time t The simplex; c is a preset value. t s For closed simplex s The closing timestamp; Closed simplex in dynamic simplex sequence s Duration of life per (pers) s )= t death - t birth ,in, t birth For the time of birth, t death Time of death; Closed simplex s Embedding vector weighting coefficients ,in, Among them, | s | is the order of the simplex s. N ( s Let be the neighborhood of simplex s, and let be a closed simplex that shares at least one node with simplex s. .

[0013] Optional, local interaction closure probability ; Among them, S MIA It is the arithmetic mean. ; S MIG It is the geometric mean. , S MIH Harmonic mean: ; in, k Represents the set of nodes Vh the total number of nodes, mi( v i , v j ) represents the weight of the edge, v i , v j ) represents the weight of the edge, .

[0014] Optionally, the time window Δt is a dynamic adjustment window or a periodic window; the periodic window Δt= T period ; the dynamic adjustment window ; wherein, T period is a preset period, w min is a preset minimum window, θ is a time density threshold, .

[0015] The second aspect of the present application provides a high-order link prediction device based on a co-occurrence node guided topology embedding model, which is used to perform the method of any one of the first aspect.

[0016] The third aspect of the present application provides a computer readable storage medium, the computer readable storage medium stores at least one instruction, the instruction is loaded and executed by the processor to realize the operation performed by the method of any one of the first aspect.

[0017] The present application provides a high-order link prediction method and device based on a co-occurrence node guided topology embedding model, which significantly overcomes the limitations of the prior art and achieves a breakthrough in prediction accuracy, computational efficiency and dynamic modeling capability through the following technical innovations: 1. Dynamic high-order network modeling and time perception mechanism, overcoming the time sequence modeling defects of static network In the prior art, network modeling usually adopts a static graph structure or a fixed time window, which cannot capture the time evolution characteristics of data, especially when dealing with multi-node interactions (such as email groups, drug formulations), the dynamic closure process of high-order structure is difficult to accurately represent. The present application solves this problem through the following technical breakthroughs: (1) Timestamp binding and dynamic simplex filtering: embedding timestamps into high-order network construction (such as G h ={V h ,S h ,T h} ), only closed simplices (such as stable groups formed by closure events) are retained, effectively eliminating noise data (such as temporary groups or invalid formulas) (2) Dynamic weight calculation and exponential decay mechanism: introduce a weighted co-occurrence formula with decay rate λ, automatically adjust the weight proportion of recent interactions, solve the problem of ignoring time sensitivity in traditional fixed window.

[0018] 2. Multi-dimensional interaction model and persistent homology analysis, enhance the feature representation ability of high-order structure Traditional methods usually rely on a single indicator (such as co-occurrence) or low-dimensional topological features (such as node degree), which is difficult to capture the complex associations of high-order closed structures. The invention realizes multi-dimensional feature fusion through the following technical innovations: (1) Multi-mean integrated closure determination: combined with the integrated prediction value P of arithmetic, geometric and harmonic mean MI , improve the robustness of local interaction model.

[0019] (2) Persistent homology and high-dimensional topology modeling: extract 0-d topological features (such as loops, voids) through Vietoris-Rips complex, combine with persistent lifetime weight, identify long-term stable high-order structure, d is a positive integer.

[0020] 3. Dynamic graph attention network and contrastive learning, improve embedding representation and generalization ability Existing graph embedding methods often ignore temporal dynamics and have insufficient ability to distinguish closed structures. The technical optimization of the invention includes: (1) Dynamic adjacency matrix and multi-head attention: generate time-varying adjacency matrix based on random walk sequence, combine dynamic mask to capture the temporal evolution pattern of node behavior.

[0021] (2) Simplex contrastive learning: optimize embedding representation through positive and negative sample contrast, use loss function to enhance the model's ability to distinguish closed and non-closed structures.

[0022] 4. Gated MLP and dynamic integrated prediction, ensure model stability and prediction accuracy Traditional prediction models are prone to failure due to overfitting or local optimum, the invention realizes stable and efficient integrated prediction through the following design: (1) Gating mechanism and spectral normalization: replace the fully connected layer with a gated linear unit (GLU) to enhance non-linear modeling capability; spectral normalization constrains the spectral norm of the weight matrix to prevent gradient explosion and overfitting.

[0023] (2) Dynamic integration framework: weightedly fuse the prediction results of local interaction model and global topology model, adaptively balance local and global features. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 This is a flowchart illustrating the high-order link prediction method based on a co-occurring node-guided topology embedding model provided by the present invention. Detailed Implementation

[0025] To make the objectives, technical methods, and advantages of the invention easier to understand, the invention will be further described in detail below with reference to schematic diagrams and implementation examples. It should be understood that the specific implementation examples described herein are merely illustrative and not intended to limit the scope of the invention.

[0026] The technical solution, implementation steps, and advantages of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] This invention proposes a high-order link prediction framework based on topological embedding and multiple interaction mode fusion (CTE-MIP) guided by co-occurrence nodes (CoNs).

[0028] like Figure 1 As shown, the overall architecture of the technical solution of the present invention is as follows: The CTE-MIP framework includes core modules: (1) Network preprocessing and network construction: The original time series data is transformed into a dynamic high-order network, and the timestamps and simplex structure are extracted.

[0029] (2) Dynamic weight calculation: Quantify the interaction strength of node pairs and generate a time-varying weight matrix.

[0030] (3) Closure event determination (MI model): predict the closure probability based on the mean of interaction weights.

[0031] (4) Dynamic random walk: Generate time-aware node walk sequences to capture dynamic behavior patterns.

[0032] (5) High-order topology modeling: Analyze high-dimensional topological features (such as rings and holes) and extract stable structures.

[0033] (6) Graph attention network embedding: Generate dynamic node embeddings to enhance the ability to represent closed structures.

[0034] (7) Gated MLP and spectral normalization: optimize the stability of the prediction model and prevent overfitting.

[0035] (8) Integrate local interaction and global topological features to output the final closure probability.

[0036] The objective of this invention is to achieve accurate prediction of high-order closed structures through dynamic temporal modeling and multimodal feature fusion.

[0037] In certain embodiments, the core modules of the technical solutions provided by the present application are as follows: 1. Dynamic network modeling and weight calculation This module aims to capture the evolution characteristics of node interaction through time-series dynamic modeling and construct a dynamic weight matrix. First, based on the co-occurrence frequency and decay rate (λ) of nodes within a time window, the dynamic weight of node pairs is calculated: The dynamic matrix M(t) stores the weights of all node pairs in real time. For different network types, the time window is adaptively selected: a fixed window is used for periodic networks (such as transportation networks); a dynamic window is used for non-periodic networks (such as social networks).

[0038] 2. High-order algebraic topology modeling (Topology Embedding) High-order structural features are captured through algebraic topology and graph attention network (GAT). First, the Vietoris-Rips complex is constructed to extract the persistence of dynamic simplices, and the weight is calculated based on the neighborhood topological stability: After normalization, the embedding vector is injected to enhance topological stability. Second, GAT is designed based on the dynamic adjacency matrix A(t): the node feature matrix is divided into 8 independent projections, the attention coefficient is calculated, and the node embedding Φ GAT ( v ) is generated by multi-head aggregation to dynamically filter non-neighbor noise.

[0039] 3. Contrastive learning and embedding optimization The contrastive loss is used to enhance the embedding's ability to distinguish between closed and unclosed simplices. Positive samples are generated by time perturbation or node discard; negative samples are randomly sampled from unclosed simplices at a ratio of 1:5. The contrastive loss is defined as: where τ = 0.07 is the temperature coefficient, and Φ( s ) is calculated by Hadamard aggregation of node embeddings. The GAT and MLP parameters are jointly optimized, with a learning rate η = 0.001, and an early stopping mechanism is used to prevent overfitting.

[0040] 4. Gated integrated prediction The multi-dimensional interaction (MI) model and the topological embedding (CTE) model are integrated to improve generalization. The MI model integrates the interaction weights of node pairs through arithmetic, geometric, and harmonic mean, and outputs the closure probability P MI ; the CTE model processes the embedding vector through a gated MLP: where σ is the Sigmoid function, and the spectral normalization constraint parameter prevents overfitting. The final prediction value is weighted integrated: .

[0041] Exemplarily, in a specific embodiment, the implementation steps of the present application include: 1.1 Temporal data preprocessing and high-order network construction Step description: (1) Raw data parsing: Extract all simplex records with timestamps from the time series data set. For example, in the email-Eu data set, each record contains the sender, the recipient list, and the email sending time.

[0042] (2) High-order network modeling: Map each simplex (e.g., 3-simplex v 1, v 3, v 5} to a simplex structure to construct a high-order network G h ={ V h , S h , T h}. Wherein: V h : Node set, representing entities such as users, drug ingredients, etc.

[0043] S h : Simplex set, each simplex s contains multiple nodes and corresponding timestamps t .

[0044] T h : Timestamp set, recording the closing time of each simplex.

[0045] Example: In the NDC-substances data set, simplex v 1, v 3, v 5} represents a drug ingredient, v 1, v 3, v 5 participates in a certain drug formula at the same time t 3.

[0046] 1.2 Edge weight and simplex weight calculation Step: Temporal weight calculation and dynamic matrix construction: Input: Time-stamped simplex set S h ={ s 1( t 1), s2( t 2),..., s m ( t m )}, current time t 0, decay rate λ .

[0047] Output: Dynamic link weight matrix .

[0048] (1) Interaction counting statistics: For each node pair ( v i , v j ), and statistically analyze its time window Weighted co-occurrence count within: ,in t s For simplex s timestamp, For indicator functions (if) The value is 1 if it is 1, otherwise it is 0.

[0049] (2) Calculation of dynamic link weights: Introducing an exponential decay factor, the calculation is performed. ,in, and These represent the total weight of the node within the time window.

[0050] Represents a node v i The cumulative number of occurrences of all simplexes within the current time window. Represents a node v j The cumulative number of occurrences of all simplexes within the current time window.

[0051] Dynamic matrix construction: updating matrix M ( t 0), Stores the dynamic weights of all node pairs: .

[0052] in, Co-occurrence frequency refers to v i and v j The number of co-occurrences within the time window. The decay rate λ is a preset value. The larger this value, the faster the decay, indicating that the model pays more attention to recent events. The smaller the value, the slower the decay, and the more historical information is retained.

[0053] 1.3 Closure Event Determination and Output Step-by-step instructions: (1) Multidimensional interaction (MI) model prediction: Calculate the mean interaction weights of node pairs within the simplex: Arithmetic mean: , Geometric mean: , Harmonic mean: , If the integrated prediction value P If the value is greater than or equal to 0.5, the simplex is determined to have a closure event; otherwise, it is marked as unclosed.

[0054] The mean of the interaction weights is the average of the above averages.

[0055] Here, k-simplex represents a higher-order structure consisting of k nodes; for example, 3-simplex represents a structure consisting of 3 nodes. k(k-1) / 2 is the number of sides of the simplex. mi( v i , v j ) means ( v i , v j The weight of the edge is taken as a value in matrix M(t).

[0056] For example, the time t used in the dynamic weight matrix is ​​the end time of the time window for predictive analysis, such as three time windows [t0,t1], [t1,t2], [t2,t3]. When the analysis reaches time t2, the data up to t2 is used to predict whether the closure event is in the time after t2 (e.g., within the time window [t2,t3]). Therefore, the dynamic weight matrix at time point t2 is used.

[0057] (2) Output closure probability ,in .

[0058] 1.4 Dynamic CoN-guided random walk Step 1: Adaptive Time Window Sampling Input: timestamp sequence T h ={ t 1, t 2,…, t m Time density threshold θ .

[0059] Output: Adaptive window size Δt .

[0060] (1) Window type selection: Periodic window (e.g. traffic network): fixed window Δt = T period (e.g. morning and evening peak periods).

[0061] Exponential decay period (social / mail network): dynamic adjustment window where w min is a preset minimum window (e.g. can be set as 3 by default), control time coverage density (default is 0.8, if the data is sparse, reduce to 0.6 to cover a wider time range). Time density threshold θ This parameter is used to control the dynamic time window coverage density, for example, when the value is 0.8, the sliding window observes the number of current window events, if the number of events is too small, the window is widened a little bit to accommodate enough events; if the number of events is already enough, the window does not need to be widened.

[0062] (2) Sliding window update: According to the current time t 0, the sliding window range is , and the expired interaction is dynamically truncated.

[0063] Step 2: Dynamic walk sequence generation Input: dynamic weight matrix M(t0), walk length l n , sampling times l s .

[0064] Output: a set of timestamped walk sequences walks.

[0065] (1) Walk initialization: for each node v i , start l s independent walks, and each walk starts from v i record the starting time t start .

[0066] (2) Dynamic transition probability: at the l x step of the walk, the current node is v current , and the next node v next is selected according to the dynamic weight: where is the set of adjacent nodes of v ; where, representing the dynamic weight of the node pair in matrix M at time t and .

[0067] (3) Time-aware walk: update the current time at each transition t current = t start + l x ·Δ t , dynamically adjust the weight matrix M( t current ).

[0068] 1.5 High-order algebraic topology modeling Step 1: Dynamic simplex construction and time slice division Input: timestamped simplex set S h ={ s 1( t 1), s 2( t 2),..., s m ( t m )},time window size Δ t .

[0069] Output: dynamic simplex sequence , K( t ) represents the simplex at time t .

[0070] (1) Time slice division: divide the time axis into consecutive windows[ t - cΔt, t ] (exemplarily, set c =5), and the closed simplex in each window constitutes the instantaneous simplex: , where t s is the closed timestamp of simplex s , and only the closed simplex formed by the closed event is retained.

[0071] where the closed simplex refers to all node pairs in the simplex that have interacted within the time window, such as the triple (A, B, C), which requires that the three pairs of nodes (A, B), (B, C), and (A, C) have interacted within the time window.

[0072] (2) Dynamic filtering: discard open simplices to ensure that K( t ) only contains closed structures.

[0073] Step 2: Persistent Cohomology Barcodes Extraction Input: Dynamic Simplex Sequence {K( t )} with upper bound of topological feature dimension d = 4 Output: Persistence Lifetime pers(s) of each simplex s.

[0074] (1) Vietoris-Rips Complex Construction for capturing high-dimensional topological features: For each window, compute the persistent cohomology of each dimension (0-d) according to the filtered sequence: 0-dimensional cohomology: Number of connected components (e.g., how many independent small circles in the user group).

[0075] 1-dimensional cohomology: Survival time of loop structures (e.g., how many independent small circles in the user group).

[0076] d-dimensional cohomology (d ≥ 2): Evolution process of high-dimensional cavities (e.g., four users form a hollow tetrahedron).

[0077] 0-dimensional hole (an independent connected component): Birth: When a node (e.g., a user) first appears, an independent connected component is born.

[0078] Death: When an edge (e.g., {A, B} two-person event) connects two originally independent nodes A and B, a connected component dies because it is merged into a larger component.

[0079] For example, the 0-dimensional cohomology calculation result is n, indicating n connected components, i.e., n 0-dimensional holes. Each connected component feature has an independent birth and death time in the barcode, so n components produce n sets of time data.

[0080] Here, the barcode is the core output form of persistent cohomology, recording the dimension, birth time, and death time of each detected topological feature.

[0081] 1-dimensional hole (loop): Birth: There are three nodes A, B, C. When edges {A, B} and {B, C} already exist, the appearance of the third edge {A, C} closes the three edges into a loop. This loop is born at this moment. Its birth time t_birth is the time of the latest appearing edge among the three edges.

[0082] Death: After the loop has existed for a period of time, a three-person event {A, B, C} occurs. This event is a solid triangular face in topology, which exactly fills the hole formed by the three edges before. This loop dies at this moment. Its death time t_death is the time when the three-person event occurs.

[0083] 2-dimensional hole (cavity / hole): Birth: Four nodes D, E, F, G. When all four triangular faces (three-person events, such as {D, E, F}, {D, E, G}, etc.) appear and are spliced into a closed, pyramid-like hollow shell, the hole inside the hollow shell is born. Its birth time is the time of the latest appearance of the four triangular faces.

[0084] Death: When a four-person event {D, E, F, G} occurs, it forms a "solid tetrahedron" and fills the previous hole. The hole dies at this moment.

[0085] For example, it can be understood that the calculation of holes of more dimensions can be derived using the above method, and the present application does not repeat it.

[0086] (2) Barcode mapping: Record the birth time of the closed simplex s t birth and the death time t death Calculate the persistent life: pers( s )= t death − t birth If s still alive at the end of the window, then ( is the minimum value). t end is the end time of the window.

[0087] Among them, the minimum value is set to be the minimum 5% of all life distribution as the minimum threshold.

[0088] Step 3: Persistent weight calculation and embedding injection Input: Simplex persistent life set {pers( s )} Output: Weighted embedding vector Φ weighted ( s ).

[0089] (1) Neighborhood simplex extraction: for each s ∈K( t ), define its neighborhood N ( s ) as the closed simplex that shares at least one node: ; where s'∈K( t ) represents any simplex s' in K( t ). ​

[0090] Example 1: Triangles {A, B, C} and {A, B, D} are “1-hop neighbors” because they share an edge {A, B}.

[0091] Example 2: Edges {A, B} and {B, C} are “1-hop neighbors” because they share a vertex {B}.

[0092] Example 3: Tetrahedrons {A, B, C, D} and {A, B, C, E} are “1-hop neighbors” because they share a triangular face {A, B, C}.

[0093] (2) Persistence weight formula: combining the lifetime of s and the stability of neighborhood topology, the weight is calculated as: ; where |s| is the order of simplex s (e.g., |s|=3 for a 3-simplex). s s

[0094] (3) Weight normalization: max-min normalization of the weight: .

[0095] (4) Embedding vector weighting: inject the weight into the original embedding: where .

[0096] 1.6 Graph Attention Network (GAT) Embedding Step 1: Dynamic Adjacency Matrix Construction and Feature Initialization Input: Dynamic CoN-guided random walk sequence set walks, node set V h , embedding dimension d =128.

[0097] Output: Dynamic adjacency matrix , node feature matrix .

[0098] (1) Dynamic Adjacency Matrix Construction: Generate a weighted adjacency matrix based on the co-occurrence frequency of nodes in the walk sequence: ; where count counts the number of co-occurrences of node pairs within the window t , l s (sampling times) and l n (walk length) are parameters defined in step 3.

[0099] (2) Node Feature Initialization: Initialize the feature matrix using the pre-trained Word2Vec embedding Φ( v ):​​ .

[0100] Step 2: Multi-head attention mechanism design Input: Dynamic adjacency matrix A(t), node feature matrix X, number of heads H = 8.

[0101] Output: Multi-head attention weights , aggregated node embedding Φ GAT ( v ).

[0102] (1) Linear transformation and multi-head segmentation: linear projection and segmentation of feature matrix X into H heads: where is a learnable parameter, and each head performs feature transformation independently.

[0103] (2) Attention coefficient calculation: for each head h , calculate the attention coefficient of node pair ( v i , v j ): where is the projection matrix of the query and key, and || represents vector concatenation; where a is the learnable parameter vector of each attention head in GAT, used to calculate the attention score of node pairs, which determines the weight distribution of each neighbor when aggregating information.

[0104] (3) Dynamic mask and normalization: filter non-neighbor nodes using dynamic adjacency matrix A(t), and normalize the attention weight: .

[0105] (4) Multi-head aggregation and concatenation: aggregate the output of each head and concatenate it into the final embedding: where is the value projection matrix, and || represents vector concatenation.

[0106] Step 3: High-order contrastive learning design Input: GAT embedding Φ GAT ( v ), simplex set S h , temperature coefficient τ = 0.07, negative sampling ratio 5:1.

[0107] Output: contrastive loss L c , optimized embedding Φ contrast ( v ).

[0108] (1) Positive and negative sample generation: Positive samples, for each closed simplex s + , augmented samples are generated by randomly discarding nodes (probability p = 0.2) or time perturbation (offset Δ t ~ U (0, 1) s aug . Negative samples, randomly sampled from non-closed simplices s − , ensure that the ratio of positive and negative samples is 1:5.

[0109] (2) Contrastive loss calculation: Define the simplex-level contrastive loss function: , where sim(·) is the cosine similarity, .

[0110] Step 4: Parameter optimization Input: GAT embedding module, contrastive loss module, MLP prediction module, learning rate η = 0.001.

[0111] Output: Jointly optimized model parameters

[0112] (1) Joint training process: Forward propagation:

[0113] Loss calculation:

[0114] Backpropagation: Update parameters through Adam optimizer, gradient clipping threshold ; where ω MLP is the weight parameter of the MLP prediction module, which determines how the MLP maps input features to output results. It is randomly initialized and continuously optimized through backpropagation during training. Spectral normalization is also performed to improve the stability of the model.

[0115] (2) Early stopping mechanism: If the validation set loss does not decrease for 5 consecutive rounds, terminate training.

[0116] 1.7 Gated MLP and spectral normalization Step 1: MLP architecture and gating mechanism design Input: Hadamard aggregated simplex embedding vectors Φ( s ) ∈ R d , number of hidden layer neurons h = 512, activation function selection.

[0117] Output: Gated enhanced MLP outputP CTE (1) Gate Linear Unit (GLU) replaces the original fully connected layer: Replace the MLP with GLU architecture: where , ∈R h×d is the learnable weight, σ is the Sigmoid function, and ⊗ denotes element-wise multiplication.

[0118] where superscripts (1), (2), 1, 2, etc. represent different weights and bias parameters of the main branch and gating branch of the GLU gating unit, respectively, for the calculation of the main linear transformation and the gating signal. The main branch produces the main information flow, and the gating branch produces the gating signal (decides which part of the main information flow is retained or suppressed). In these two hidden layers, each layer independently has its own weights and biases.

[0119] Step 2: Spectral Normalization Input: MLP weight matrix , number of iterations 1.

[0120] Output: Spectrally normalized weights ω SN .

[0121] (1) Power iteration method to calculate the spectral norm: for each weight matrix ω ∈R m×n , initialize a random vector u ∈R m , iteratively update: , After repeating 3 times, calculate the largest singular value (spectral norm): σ ( ω )= u T ωv .

[0122] (2) Weight normalization: scale the weights by the spectral norm: .

[0123] (3) Dynamic update mechanism: recalculate σ ( ω ) after each batch of training to ensure continuous constraints.

[0124] Step 3: Parameter optimization Input: training set C Φ(s) , loss function L =MSE+λL c learning rate η = 0.001.

[0125] Output: Optimized gated MLP parameters.

[0126] (1) Forward propagation: First hidden layer (GLU + spectral normalization): .

[0127] Second hidden layer: Same structure as the first layer.

[0128] Output layer (Sigmoid):

[0129] (2) Backpropagation and gradient clipping: Calculate the gradient , update the parameters using the Adam optimizer. Gradient clipping threshold , to prevent gradient explosion.

[0130] where MSE is the mean square error loss, used to measure the difference between the model's predicted output and the true label.

[0131] 1.8 Dynamic ensemble prediction Input: MI model prediction value P MI , CTE model prediction value P CTE .

[0132] Output: Final prediction value P .

[0133] , by β dynamically balancing local interaction and global topological features.

[0134] The following describes the present application by taking social network dynamic group closure prediction as an example: Scenario: In the email-Eu dataset, predict whether a user group will form a stable closed group within a certain time window.

[0135] Implementation steps: (1) Data preprocessing: Extract the sender, recipient list and sending time of each email. Construct high-order network G h , where the node set V h is the user, the simplex set S h is all email communication groups, and the timestamp set T h records the sending time of each email.

[0136] (2) Edge weight calculation: Count the co-occurrence times of users within the last 7 days and weight the exponential decay.

[0137] (3) Closure event determination: Calculate the average interaction weight of the simplex pair (arithmetic, geometric, harmonic mean), get the integrated prediction value P MI .

[0138] (4) Dynamic random walk and embedding: Starting from the node, generate a walk sequence according to the dynamic weight matrix, and use it to construct a dynamic adjacency matrix.

[0139] (5) Graph attention network and contrastive learning: Through GAT embedding and contrastive learning optimization, predict the closure probability P CTE .

[0140] (6) Weighted integrated prediction value: Get the final prediction value P by weighted integration P MI and P CTE .

[0141] Results: Predict the time period after an event, the user group will form a stable collaboration team, and the system outputs the closure probability as P .

[0142] The following describes the application by taking drug combination prediction in biological networks as an example: Scenario: In the NDC-substances dataset, analyze the time series data of drug ingredient combinations, and predict whether a specific ingredient combination will become an effective formula (closed simplex) in the future.

[0143] Implementation steps: (1) Data preprocessing and high-order network construction: Extract drug formula records, node set V h Drug ingredients, simplex set S h All formula combinations, and timestamp records the approval time of the formula.

[0144] (2) Edge weight calculation: Count the co-occurrence times of the ingredient pair in the last 30 days.

[0145] (3) Closure event determination: Calculate the average interaction weight of the simplex, get the integrated prediction value P P MI .

[0146] (4) High-order topology modeling: Extract 2D barcodes (such as detecting tetrahedral voids), and the persistence of ingredient combinations reflects their stability.

[0147] (5) Dynamic integrated prediction: The negative sampling ratio of contrastive learning is 5:1, the spectral normalization is used in the gated MLP to prevent overfitting, and the CTE model prediction value P P CTE is obtained, and the final prediction value P P.

[0148] Results: The system outputs a closed probability that a combination of ingredients will be approved as an effective drug formulation within a time period after a certain event P .

[0149] The above merely describes one specific implementation of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A high-order link prediction method based on a co-occurring node-guided topology embedding model, characterized in that, include: Extract all simplex records with timestamps from the time-series dataset, map the simplex s to a simplex structure, and obtain a higher-order network; the higher-order network includes: a node set V h Simplex set S h and timestamp set T h ; For the node set V h For each node pair in the process, the dynamic link weight matrix M(t0) of the node pair is obtained based on the decay rate. Based on the dynamic link weight matrix M(t0), a time-aware node walk sequence set walks is generated. From the simplex set S h The closed dynamic simplex sequence is extracted, and the Vietoris-Rips complex is constructed on the dynamic simplex sequence to obtain the simplex lifetime. Based on the simplex lifetime, the embedding vector weighting coefficients are obtained. Based on the node walk sequence set walks and the node set V h A dynamic adjacency matrix A and a node feature matrix X are constructed. A multi-head attention mechanism is employed to generate a graph attention network (GAT) embedding Φ based on the dynamic adjacency matrix A and the node feature matrix X. GAT ( v The GAT embedding is optimized through comparative learning to obtain the optimized embedding Φ. contrast ( v Based on comparison, optimize the embedded Φ contrast ( v ), obtain the simplex embedding vector Φ after Hadamard aggregation. s ); According to the simplex embedding vector Φ( s The weighted simplex embedding vector Φ is obtained by combining the weighting coefficients of the embedding vector and the embedding vector. weighted ( s ); For the simplex embedding vector Φ weighted ( s MLP and spectral normalization are performed to obtain the closure probability. P CTE ; Based on the local interaction closure probability P MI Sum of closure probability P CTE Using formula Obtain the final closure probability P; Among them, P MI The result is predicted based on the multidimensional interactive MI model, where β is a preset coefficient.

2. The high-order link prediction method based on a co-occurrence node-guided topology embedding model according to claim 1, characterized in that, For the node set V h For each node pair in the matrix, the dynamic link weight matrix M(t0) of the node pair is obtained based on the decay rate, including: For the node set V h Each node pair in the formula Obtain the corresponding dynamic link weight. ; Based on the dynamic link weight of each node Obtain the dynamic link weight matrix M(t0) of the node pairs; in, , and They are nodes v i and nodes v j In the time window The total weight within; λ is the decay rate. t 0 represents the current time. t s For simplex s timestamp, For indicator functions, if If it is 1, then it is 1; otherwise, it is 0.

3. The high-order link prediction method based on a co-occurrence node-guided topology embedding model according to claim 2, characterized in that, Based on the dynamic link weight matrix M(t0), a time-aware node walk sequence set walks is generated, including: Traverse the node set V h From each node v i Departure, commencement l s Each independent walk yields all node walk sequences, which are then used as a set of node walk sequences. In each node's walk sequence, the current node v current The next node v next Based on the dynamic link weight matrix within the corresponding time window, the formula is used. Sure; in, Represents a node v The set of adjacent nodes.

4. The high-order link prediction method based on a co-occurrence node-guided topology embedding model according to claim 3, characterized in that, The dynamic simplex sequence is denoted as K( t () indicates time t The simplex; c is a preset value. t s For closed simplex s The closing timestamp; Closed simplex in dynamic simplex sequence s Duration of life per (pers) s )= t death - t birth ,in, t birth For the time of birth, t death Time of death; Closed simplex s Embedding vector weighting coefficients ,in, Among them, | s | is the order of the simplex s. N ( s Let be the neighborhood of simplex s, and let be a closed simplex that shares at least one node with simplex s. .

5. The high-order link prediction method based on a co-occurrence node-guided topology embedding model according to claim 2, characterized in that, Local interaction closure probability ; Among them, S MIA It is the arithmetic mean. ; S MIG It is the geometric mean. , S MIH Harmonic mean: ; in, k Represents the set of nodes V h The total number of nodes, mi( v i , v j )express( v i , v j The weight of the edge. .

6. The high-order link prediction method based on a co-occurrence node-guided topology embedding model according to claim 2, characterized in that, The time window Δt can be a dynamically adjusted window or a periodic window; Periodic window Δt= T period ; Dynamically adjust window ; in, T period For the preset period, w min To preset the smallest window, θ The time density threshold, .

7. A high-order link prediction device based on a co-occurrence node-guided topology embedding model, characterized in that, Used to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, which is loaded and executed by a processor to perform the operation performed by the method as described in any one of claims 1 to 7.

Images