Knowledge graph link prediction method based on quaternion and multi-objective evolutionary learning

Abstract

The invention discloses a knowledge graph link prediction method based on quaternion and multi-objective evolutionary learning, and relates to a knowledge graph link prediction method. The method comprises the complete processes of knowledge graph preprocessing, quaternion representation, Hamilton product fusion, convolution feature extraction, drug interaction score calculation and multi-objective evolution optimization. The objective of the invention is to solve key technical problems of limited expression ability, insufficient asymmetric modeling, difficulty in multi-relation fusion, difficulty in parameter optimization and the like of an existing knowledge graph link prediction method based on a deep learning model in drug interaction prediction. A quaternion representation method and a Hamilton product fusion mechanism are introduced, feature extraction is performed in combination with a convolutional neural network architecture, and intelligent parameter optimization is performed by using an improved multi-objective evolutionary learning algorithm, so that precise modeling and efficient prediction of a complex interaction relationship between drugs are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to a knowledge graph link prediction method, in particular to a knowledge graph link prediction method based on quaternions and multi-objective evolutionary learning. BACKGROUND

[0002] According to statistics, drug interaction is one of the important reasons for adverse drug events. Drug interaction refers to the mutual influence of two or more drugs when used at the same time. This influence may enhance or weaken the efficacy of the drug, or even cause serious adverse reactions. With the increasing popularity of clinical multiple drug therapy, especially in elderly patients and patients with chronic diseases, the average number of drugs used can reach 5-10. The complex drug use mode significantly increases the risk of drug interaction, which has become a major hidden danger to patient medication safety. Traditional drug interaction identification mainly relies on clinical trials and pharmacological experiments. Therefore, it is urgent to develop efficient and accurate drug interaction prediction technology to provide scientific basis for clinical safe medication.

[0003] In recent years, link prediction technology based on knowledge graph has provided a new solution for drug interaction prediction. The knowledge graph describes drugs and their mutual relationships in the form of triples (head entity, relationship, tail entity), such as ("aspirin", "interaction", "warfarin") representing the interaction relationship between aspirin and warfarin. As shown in the formula, the core task of knowledge graph completion is to infer the missing link relationship through known entity relationship information. By analyzing known drug interaction data, link prediction technology can infer the possible interaction relationship between unknown drug pairs, thereby realizing rapid screening and prediction of large-scale drug interactions. However, there are inevitably a large number of missing relationships in the construction process of the drug knowledge graph. Therefore, it is necessary to complete the missing relationship information through link prediction technology, which is the core technical challenge of drug interaction prediction. Figure 1

[0004] At present, deep learning model-based is a mainstream knowledge graph link prediction method. Deep learning models (such as ConvE, LPBERT, etc.) introduce the nonlinear transformation and hierarchical feature extraction capabilities of neural networks, which can capture complex interaction patterns between entities and relationships in higher-dimensional embedding spaces. Compared with traditional methods, deep learning models can combine entity and relationship attribute features, context information, and multi-modal data to significantly enhance the semantic compatibility of embedding representations. However, there are four key technical problems in the application of existing deep learning model-based knowledge graph link prediction methods in drug interaction prediction: ​First, the expressiveness limitation. Existing methods mainly rely on real-valued scalar embedding to represent knowledge, which is difficult to fully express the complex multi-relational interactions among drug molecules. Drug interactions involve nonlinear coupling of biochemical processes such as enzyme inhibition and carrier competition. These multi-level and multi-dimensional characteristics are difficult to accurately model through linear combination of real-valued vectors, resulting in loss of key information and affecting prediction accuracy.

[0005] Second, the lack of asymmetric modeling. Drug interactions often have obvious directional characteristics, that is, the influence of drug A on drug B may be completely different from the influence of drug B on drug A. For example, a strong CYP3A4 inhibitor can significantly affect the metabolism of CYP3A4 substrates, but the reverse effect is usually small. However, existing real-valued embedding methods calculate similarity based on symmetric inner product or Euclidean distance, which is difficult to effectively capture this asymmetric information. This limitation is particularly prominent when dealing with drug interactions with clear directionality, resulting in large prediction bias.

[0006] Third, the difficulty of multi-relational fusion. In a complex drug interaction network, the same pair of drugs may interact through multiple different mechanisms, such as both pharmacokinetic and pharmacodynamic interactions. Existing methods often use simple vector splicing or linear weighting to fuse, which is prone to information redundancy, feature confusion, and dimension explosion. This rough fusion method cannot effectively integrate multi-source heterogeneous information, limiting the model's understanding ability of complex drug interaction patterns.

[0007] Fourth, the difficulty of parameter optimization. Deep learning models contain a large number of hyperparameters, such as learning rate, embedding dimension, dropout rate, batch size, etc. The setting of these parameters directly affects the model performance. Traditional manual parameter tuning methods are not only inefficient, but also difficult to find the globally optimal parameter combination. Especially in the application scenario of drug interaction prediction which requires high precision, small differences in parameter settings may lead to significant changes in prediction results. In addition, there is a complex interdependence between different parameters, and optimizing each parameter separately often cannot achieve the overall optimal effect, while exhaustive search faces the problem of high computational complexity. SUMMARY

[0008] In view of the deficiencies of the prior art described above, the purpose of the present application is to provide a knowledge graph link prediction method based on quaternions and multi-objective evolutionary learning, aiming to solve the key technical problems such as limited expression ability, insufficient asymmetric modeling, difficult multi-relation fusion and difficult parameter optimization that the existing knowledge graph link prediction method based on deep learning model faces in drug interaction prediction. By introducing the quaternion representation method and Hamilton product fusion mechanism, combining convolutional neural network architecture for feature extraction, and using an improved multi-objective evolutionary learning algorithm for intelligent parameter optimization, accurate modeling and efficient prediction of complex interaction relationships between drugs are realized.

[0009] The technical scheme provided by the present application is as follows: A knowledge graph link prediction method based on quaternions and multi-objective evolutionary learning, the method comprising the following steps: Step 1: Establish a data preprocessing module for converting drug interaction data in the original knowledge graph into a standard knowledge graph triple format, generating a triple data set, and encoding all N drug entities and M relationships in the triple data set; Step 2: Establish a quaternion representation module for converting drug entities and relationships in the standardized triple data set into high-dimensional feature representations in the form of quaternions, constructing a quaternion embedding matrix for drug entities and a quaternion embedding matrix for relationships; Step 3: Establish an entity relationship nonlinear fusion module for nonlinear fusion of the drug entity quaternion embedding matrix and the relationship quaternion embedding matrix to generate a head entity-relationship composite representation vector; Step 4: Establish a convolution feature extraction module for feature extraction of the head entity-relationship composite representation vector through a convolutional neural network to obtain a fusion feature vector; Step 5: Establish a drug interaction score calculation module for extracting quaternion embeddings of all N drug entities from the drug entity quaternion embedding matrix as candidate tail entity quaternion embeddings, performing inner product calculation on the fusion feature vector and all candidate tail entity quaternion embeddings to generate interaction score vectors for the head entity-relationship combination and each candidate drug; Step 6: Cascade the data preprocessing module, the quaternion representation module, the entity relationship nonlinear fusion module, the convolution feature extraction module and the drug interaction score calculation module in sequence to establish a quaternion-convolutional neural network model; Step 7: Improve the traditional multi-objective differential evolution algorithm: use the opposite learning method to expand the search range during population initialization and relearning after each generation of population evolution; use the existing Q-learning-based strategy adjustment method to enable each individual in the population to dynamically adjust the differential evolution mutation strategy according to whether it is located on the Pareto front archive; Step 8: The improved multi-objective differential evolution algorithm is used to automatically optimize the hyperparameters of the quaternion-convolutional neural network model, and the quaternion-convolutional neural network model with the optimal hyperparameter configuration is called OLRL-QuatCNN evolutionary deep learning model; Step 9: The drug pair to be predicted is input into the OLRL-QuatCNN evolutionary deep learning model to obtain a drug interaction score, and the score is compared with a preset threshold. If the score exceeds the preset threshold, it is considered that there is an interaction between the drug pair; if the score is lower than the preset threshold, it is considered that there is no interaction link between the drug pair in the knowledge graph.

[0010] Further, according to the knowledge graph link prediction method, the processing flow of the quaternion representation module includes the following steps: Step 2.1: According to formula (1), each drug entity in the standardized triple data set is represented as a quaternion form: ; wherein is a real value vector of a real part, are real value vectors of three imaginary parts, respectively, is an imaginary unit; Step 2.2: According to formula (2), each drug interaction relationship in the standardized triple data set is represented as a quaternion form: ; wherein is the square root of -1, called an imaginary unit, satisfying Hamilton's rule: ; ; Step 2.3: According to formula (5), a quaternion embedding matrix is constructed for N drug entities and a quaternion embedding matrix is constructed for M relationships according to the same method , and the Xavier initialization method is used to initialize the quaternion embedding matrix Q; ; wherein is the real part of each quaternion in the quaternion embedding matrix Q; are the three imaginary parts of each quaternion in the quaternion embedding matrix Q, respectively; is a random angle in the interval [-π, π], is randomly generated from the interval [-1 / (2k), 1 / (2k)], and k is the embedding dimension.

[0011] Furthermore, according to the aforementioned knowledge graph link prediction method, the processing flow of the entity relationship nonlinear fusion module includes the following steps: Step 3.1: Embed the relation quaternions into the matrix according to equation (6). Normalized to a unit quaternion: ; Step 3.2: Embed the head entity quaternion in the matrix using drug entity quaternions. Normalized relation quaternions embedded in a relation quaternion matrix Hamiltonian products are used to achieve nonlinear fusion of entity relationships, generating a head entity-relationship composite representation vector that captures the asymmetric features of drug interactions. ; in This represents the Hamiltonian product operation, which has a non-commutative property. It can naturally capture the directional characteristics of drug interactions.

[0012] Furthermore, according to the knowledge graph link prediction method described above, the processing flow in the convolutional feature extraction module includes the following steps: Step 4.1: Combine the head entity-relationship representation vector real part With three imaginary parts , , They are stacked as independent channels to form a 4-channel tensor. ,in It is a real number; Step 4.2: Apply convolutional layers to the 4-channel tensor Perform local feature extraction; Step 4.3: The output of the convolutional layer is sequentially processed through batch normalization, ReLU activation, and Dropout operations to obtain convolutional features; Step 4.4: Through the Flatten operation and fully connected layers, the convolutional features are mapped into a fusion feature vector of local interaction patterns in the hypercomplex space.

[0013] Furthermore, according to the knowledge graph link prediction method, in step 5, the inner product of the fused feature vector and the quaternion embeddings of all candidate tail entities is calculated through a 1-N scoring mechanism.

[0014] Furthermore, based on the aforementioned knowledge graph link prediction method, the improved multi-objective differential evolution algorithm includes the following steps: Step 7.1: Using the prediction accuracy metrics of the quaternion-convolutional neural network model and model complexity indicator as the objective function of multi-objective optimization: ; wherein ; The parameter quantity refers to the total number of all trainable parameters in the quaternion-convolutional neural network model. Step 7.2: Randomly generate NP initial individuals, and generate the opposite solution for each initial individual, thereby expanding the total number of individuals in the population to 2NP; wherein each individual represents a set of hyperparameter combinations of the quaternion-convolutional neural network model; Step 7.3: Evaluate the target function for the expanded 2NP candidate individuals, sort the individuals by layer using the non-dominated sorting method in the NSGA-II algorithm, and sort them by distribution density within the same layer using the crowding degree calculation method, finally select the first NP individuals as the initial population, and the non-dominated solutions among them as the current Pareto front archive; Step 7.4: In the differential evolution operation stage of population evolution, each individual is regarded as an intelligent agent, and the individual is allowed to select a mutation strategy according to the current Pareto front archive state through a reinforcement learning mechanism to evolve the population; Step 7.5: Relearning process based on opposite learning: after the differential evolution of the current population is completed, opposite learning is further introduced to enhance the diversity of the population, and the Pareto front archive is updated; Step 7.6: Multi-objective optimization iteration: repeat steps 7.4-7.5 until the preset termination condition is met.

[0015] Further, according to the knowledge graph link prediction method, in step 7.4, the state corresponds to the performance state in the training process of the quaternion-convolutional neural network model, that is, the state s is encoded according to the position of the individual in the current Pareto front archive: if the individual is in the Pareto front archive, s=1; otherwise, s=0.

[0016] Further, according to the knowledge graph link prediction method, the action a is selected from three commonly used standard mutation strategies in the differential evolution algorithm: a_1: DE / rand / 1 strategy a_2: DE / current-to-best / 1 strategy a_3: DE / best / 1 strategy.

[0017] Further, according to the knowledge graph link prediction method, in the reinforcement learning mechanism: a SoftMax action selection policy is used to select the next action, that is, the mutation strategy to be executed; after the action is selected, the agent representing the individual of the population executes the corresponding mutation operation to generate a mutation vector V; a binomial crossover operation is adopted to cross the parent individual and the mutation vector V to obtain a trial individual U; the trial individual U and the parent individual X are compared, and a reward is obtained according to the advantage relationship between the trial individual and the parent individual; finally, the Q value is updated according to the Bellman equation.

[0018] Further, according to the knowledge graph link prediction method, the step 7.5 is specifically: for each individual in the current population, an opposite solution is generated by using opposite learning, and the opposite solution is combined with the parent and trial individuals to form a larger candidate population; the combined population is selected by using non-dominated sorting and congestion calculation, so that the optimal NP individuals are selected to form the next generation population, and the Pareto front archive is updated.

[0019] Compared with the prior art, the present application has the following beneficial effects: (1) Significantly enhance the expression ability of complex interaction relationship Since the quaternion has four dimensions (one real part and three imaginary parts) as a hypercomplex number system, compared with the traditional real scalar embedding which can only perform linear combination, the quaternion representation can encode entity and relationship information in a higher-dimensional representation space through its rich algebraic structure. Specifically, the Hamilton product operation of the quaternion has a non-commutative property, and this non-commutative feature enables the quaternion to naturally express complex non-linear interaction patterns. However, biochemical processes such as enzyme inhibition, carrier competition and receptor antagonism, which are prevalent in drug interaction mechanisms, have the characteristics of nonlinearity and multi-level coupling. Therefore, by embedding entities and relationships into the quaternion space, the present application can capture richer semantic information under the same parameter scale, significantly improving the modeling accuracy of complex multi-relationship interactions between drug molecules.

[0020] (2) Effectively solve the problem of asymmetric information modeling Since the Hamilton product operation satisfies The non-commutative property of quaternion ensures that the head entity to tail entity transformation and the tail entity to head entity transformation produce different results when the quaternion representation of the head entity and the quaternion representation of the relationship are fused by Hamilton product, which exactly corresponds to the directionality feature widely existing in drug interactions. For example, the influence of a potent enzyme inhibitor on the enzyme substrate is usually much greater than the reverse influence, and this asymmetric interaction mode can be accurately modeled by the non-commutative property of Hamilton product. Therefore, the present application can accurately capture the direction dependence of drug interactions, and significantly improve the accuracy of drug pair interaction prediction with obvious directionality feature.

[0021] (3) Efficient and lossless fusion of multi-relation information Since the quaternion space has a natural four-dimensional structure, different types of relationship information can be encoded into the real part and three imaginary parts, avoiding the dimension explosion and information redundancy problems caused by vector splicing or linear weighting in traditional methods. At the same time, Hamilton product operation can nonlinearly fuse the information of multiple quaternions, and the operation result still maintains the algebraic structure of quaternion, ensuring the mathematical consistency of the information fusion process. This fusion mechanism enables the multiple interactions of the same pair of drugs through different mechanisms (such as pharmacokinetics and pharmacodynamics) to be integrated and represented in a unified mathematical framework, avoiding the feature confusion and information loss problems in traditional fusion methods. Therefore, the present application can better handle the coexistence of multiple relationships in complex drug interaction networks, and improve the comprehensive prediction ability of multi-mechanism drug interactions.

[0022] (4) Intelligent parameter optimization based on multi-objective evolutionary learning to maximize overall performance Since the traditional manual parameter tuning method cannot effectively handle the complex interdependent relationship among numerous hyperparameters in the deep learning model, and is prone to fall into a local optimal solution, the application introduces a multi-objective evolutionary learning algorithm that integrates the opposite learning and reinforcement learning mechanism to realize the end-to-end intelligent optimization of the quaternion-convolutional neural network model. Specifically, the combination of hyperparameters is regarded as an individual, the opposite learning strategy expands the coverage range of the search space by one time by generating opposite solutions for each individual, and significantly improves the initial population diversity; the reinforcement learning mechanism enables each individual to adaptively select the optimal mutation strategy according to the current state, avoiding the low search efficiency caused by the fixed strategy; the multi-objective optimization strategy automatically finds the optimal balance point between the prediction accuracy and the model complexity, ensuring that a practical parameter configuration is obtained; the end-to-end integrated design enables the network architecture and the optimization algorithm to cooperate, avoiding the local optimal problem of modular optimization. Therefore, the application can automatically find the globally optimal combination of hyperparameters, significantly reduce the manual parameter tuning workload, maximize the overall system performance, and obtain a solution that achieves the best balance between prediction accuracy and computational efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 A knowledge graph link prediction schematic diagram; Figure 2 A flowchart of the knowledge graph link prediction method based on quaternion and multi-objective evolutionary learning in the embodiment of the application; Figure 3 A flowchart of the improved evolutionary deep learning algorithm in the embodiment of the application. DETAILED DESCRIPTION

[0024] In order to facilitate the understanding of the present application, the present application will be described more fully below with reference to the relevant drawings.

[0025] Figure 2 A flowchart of the knowledge graph link prediction method based on quaternion and multi-objective evolutionary learning in the embodiment of the application, including the complete flow of knowledge graph preprocessing, quaternion representation, Hamilton product fusion, convolution feature extraction, drug interaction score calculation and multi-objective evolutionary optimization, realizing the accurate prediction of drug knowledge graph link prediction, i.e. drug interaction. As shown in the figure, the method comprises the following steps: Figure 2 Step 1: Establish a data preprocessing module for preprocessing the original drug interaction knowledge graph data to generate a standardized triple data set and an entity relationship mapping dictionary.

[0026] The data processing module of the embodiment is established to perform format processing and encoding conversion on the obtained original drug interaction knowledge graph data, generate a standardized triple data set and an entity relationship mapping table, and specifically comprises the following steps: ​Step 1.1: Uniformly convert the drug interaction data in the knowledge graph into the standard knowledge graph triple format to generate a standardized triple data set; In this embodiment, the drug interaction data in the knowledge graph is first uniformly converted into the standard triple format, i.e., (head entity, relation, tail entity), where the head entity and the tail entity represent drugs, and the relation represents the interaction type between drugs. For example: ("aspirin", "synergistic enhancement of anticoagulation", "warfarin") indicates that aspirin and warfarin used together can synergistically enhance the anticoagulation effect and increase the risk of bleeding; ("ketoconazole", "CYP3A4 enzyme inhibition", "simvastatin") indicates that ketoconazole affects the metabolism of simvastatin by inhibiting CYP3A4 enzyme; ("digoxin", "carrier competitive interaction", "verapamil") indicates that verapamil and digoxin compete for P-glycoprotein carriers, affecting the clearance of digoxin.

[0027] Step 1.2: Encode all N drug entities and M relations in the triple data set, map each drug entity name and relation name to a unique integer number, and generate an entity-relation mapping dictionary; In this embodiment, an entity dictionary E_dict = {entity_name: entity_id} and a relation dictionary R_dict = {relation_name: relation_id} are established, each drug name and relation name is mapped to a unique integer number, and an entity-relation mapping dictionary is generated, where entity_name and entity_id represent the name and corresponding integer number of the drug entity, respectively, and relation_name and relation_id represent the name and corresponding integer number of the relation entity, respectively, to facilitate subsequent numerical calculations. For example, the entity dictionary E_dict = {"aspirin": 0, "warfarin": 1, "ketoconazole": 2, "simvastatin": 3, "digoxin": 4, "verapamil": 5,...}, and the relation dictionary R_dict = {"synergistic enhancement of anticoagulation": 0, "CYP3A4 enzyme inhibition": 1, "carrier competitive interaction": 2, "pharmacodynamic antagonism": 3, "liver enzyme induction": 4,...}.

[0028] Step 1.3: Divide the standardized triple data set into a training set; In this embodiment, the standardized triple data set is divided into a training set, a validation set, and a test set in a ratio of 8:1:1.

[0029] Step 2: Establish a quaternion representation module for converting drug entities and relationships in the standardized triple data set into high-dimensional feature representations in the form of quaternions, and constructing a quaternion embedding matrix of drug entities and relationships.

[0030] The quaternion representation module established in this embodiment includes the following processing steps: Step 2.1: According to formula (1), each drug entity in the standardized triple data set is represented as a quaternion: wherein is a real-valued vector of the real part, are real-valued vectors of the three imaginary parts, respectively, is the imaginary unit; Step 2.2: According to formula (2), each drug interaction relationship in the standardized triple data set is represented as a quaternion: wherein is the square root of -1, called the imaginary unit, and satisfies the Hamilton rule: Step 2.3: Construct a quaternion embedding matrix Q for N drug entities according to formula (5): and construct a quaternion embedding matrix R for M relationships according to the same method: and initialize the quaternion embedding matrix Q using the Xavier initialization method; wherein is the real part of each quaternion in the quaternion embedding matrix Q; are the three imaginary parts of each quaternion in the quaternion embedding matrix Q, respectively; is a random angle in the interval [-π, π], is randomly generated in the interval [-1 / (2k), 1 / (2k)], and k is the embedding dimension.

[0031] Step 3: Establish an entity relationship nonlinear fusion module for nonlinear fusion of the drug entity quaternion embedding matrix and the relationship quaternion embedding matrix obtained in step 2 using Hamilton product, to generate a head entity-relationship composite representation vector that captures the asymmetric characteristics of drug interactions.

[0032] In this embodiment, the processing flow of the entity relationship nonlinear fusion module includes the following steps: ​​​​​​​Step 3.1: Embedding the relationship quaternion into the matrix according to formula (6) Normalization to unit quaternion: ; Step 3.2: Head entity quaternion is embedded into the matrix by drug entity quaternion Hamilton product of the normalized relationship quaternion embedded in the relationship quaternion embedding matrix The Hamilton product realizes the nonlinear fusion of entity relationships, generating a head entity-relation composite representation vector that captures the asymmetric characteristics of drug interactions: ; Where represents the Hamilton product operation, and its non-commutative property can naturally capture the directional features of drug interactions.

[0033] Hamilton product realizes the rotation transformation of the head entity in the quaternion space, rotates the head entity from the initial position to the target position through the isogonal rotation operation, and generates a comprehensive representation containing entity and relationship interaction information.

[0034] Step 4: Establish a convolution feature extraction module to extract features of the head entity-relation composite representation vector through a convolutional neural network, and obtain a fusion feature vector of local interaction patterns in hypercomplex space.

[0035] In this embodiment, the processing flow in the convolution feature extraction module includes the following steps: Step 4.1: Stack the real part and three imaginary parts , , , of the head entity-relation composite representation vector respectively as independent channels to form a 4-channel tensor , where is a real number; Step 4.2: Local feature extraction of the 4-channel tensor using the convolution layer; Step 4.3: The convolution layer output successively undergoes batch normalization, ReLU activation and Dropout operation to obtain convolution features, improving the nonlinear ability of feature expression and model robustness; Step 4.4: Through the Flatten operation and the fully connected layer, the convolution features are mapped to the fusion feature vector of local interaction patterns in hypercomplex space.

[0036] Step 5: Establish a drug interaction score calculation module for calculating the inner product of the fusion feature vector and all candidate tail entity quaternion embeddings by the 1-N scoring mechanism to generate the interaction prediction score vector of the head entity-relation combination and each candidate drug.

[0037] In the present embodiment, the processing flow in the drug interaction score calculation module includes the following steps: Step 5.1: Extract the quaternion embeddings of all N drug entities from the drug entity quaternion embedding matrix constructed in step 2.3 as candidate tail entity quaternion embeddings, and establish a candidate tail entity set, denoted as , where represents the quaternion embedding of the i-th drug entity, and these embeddings constitute all possible tail entity candidates in link prediction.

[0038] Step 5.2: For each head entity-relation pair to be predicted , calculate the inner product of the fusion feature vector v and each candidate tail entity quaternion embedding vector according to formula (8) to obtain the interaction prediction score, thereby obtaining the drug interaction score vector , where N is the total number of drug entities in the knowledge graph.

[0039]

[0040] , where represents the prediction confidence score of the triple having a drug interaction relationship.

[0041] Step 6: Cascade the data preprocessing module, quaternion representation module, entity relationship nonlinear fusion module, convolution feature extraction module, and drug interaction score calculation module in sequence to establish a quaternion-convolutional neural network model.

[0042] Step 7: Improve the traditional multi-objective differential evolution algorithm: use the opposite learning method to expand the search range during population initialization and relearning after each generation of population evolution; use the existing Q-learning-based strategy adjustment method to allow each individual in the population to dynamically adjust the differential evolution mutation strategy according to the current population state, i.e., whether the individual is located on the Pareto front archive; The core of the improvement of the traditional multi-objective differential evolution algorithm in the present embodiment is to organically integrate the opposite learning and reinforcement learning mechanisms into the traditional differential evolution (DE) framework, thereby achieving the expansion of the diversity of population individuals and the adaptive adjustment of the search strategy, and solving the current problems of the traditional multi-objective differential evolution algorithm. For example, Figure 3 ​​As shown, the improved multi-objective differential evolution algorithm comprises three core stages: population initialization and adversarial learning, reinforcement learning-based population evolution, and adversarial learning-based relearning. Specifically, it overcomes the problem of traditional random initialization failing to adequately cover the feasible region by using adversarial learning methods to expand the search range during population initialization and relearning after each generation of population evolution. During evolution, a reinforcement learning module (emphasizing existing Q-learning-based policy adjustment methods) is embedded, allowing each individual in the population to dynamically adjust its differential evolution mutation strategy based on the current population state (whether the individual is located in the Pareto front archive), thus effectively balancing global search and local fine-grained optimization. The improved multi-objective differential evolution algorithm is as follows: Figure 3 As shown, it includes the following steps: Step 7.1: Using the prediction accuracy metrics of the quaternion-convolutional neural network model and model complexity metrics As the objective function for multi-objective optimization: ; in ; The number of parameters refers to the total number of all trainable parameters in a quaternion-convolutional neural network model. Step 7.2: Randomly generate NP initial individuals and generate their complementary solutions for each initial individual, thereby expanding the total number of individuals in the population to 2NP; where each individual represents a set of hyperparameter combinations of the quaternion-convolutional neural network model; In the population initialization phase, traditional random initialization methods often fail to adequately cover the entire search space, easily leading to an overly localized initial population distribution and affecting the overall search performance. Therefore, this invention employs an adversarial learning strategy to expand the initial individuals, thereby achieving more comprehensive population coverage. The specific steps are as follows: Randomly generate initial individuals Within the given upper and lower bounds L and U of the independent variables, the standard initialization method of the multi-objective differential evolution algorithm is used to randomly initialize each dimension of each individual according to the existing formula 10:

[0043] in, For the first i The individual in the first j Initialization values ​​on the hyperparameters, i For individual indexes (NP individuals in total). j This is the index for the hyperparameter dimensions (a total of D hyperparameters). and They represent the first j The lower and upper bounds of each hyperparameter.rand (0,1) represents a random number uniformly distributed between [0,1]. Through the formula, NP individuals can be generated , where each individual contains the initial values of D hyperparameters. In this embodiment, the individual corresponds to a set of hyperparameter combinations of the quaternion-convolutional neural network model, such as a set of specific numerical values of parameters such as learning_rate, dropout_rate, embedding_dim, etc.

[0044] Generate opposite solutions: for each initial individual , use the standard opposite solution generation formula 11 in the opposite learning theory to generate the opposite solution value of each dimension of the individual respectively:

[0045] By performing the above calculation on all D dimensions of each individual , j =1,2,...,D), the complete opposite solution of the individual can be obtained, and is obtained. Repeat this process for NP initial individuals to finally obtain NP opposite solution individuals , thereby expanding the total number of individuals in the population (the population corresponds to a set of multiple hyperparameter combinations, i.e., a group containing multiple different parameter configuration schemes) to 2NP. Among them, is the opposite solution value of the i th individual in the j th dimension of the hyperparameter.

[0046] Step 7.3: Evaluate the target function for the expanded 2NP candidate individuals, use the non-dominated sorting method in the NSGA-II algorithm to stratify the individuals, use the crowding degree calculation method to sort by distribution density within the same layer, and finally select the top NP individuals as the initial population, and the non-dominated solutions among them as the current Pareto front archive; Step 7.4: In the differential evolution operation stage of population evolution, each individual is regarded as an intelligent agent, and through the reinforcement learning mechanism, the individual autonomously selects a mutation strategy for population evolution according to the current Pareto front archive state; In this embodiment, the state corresponds to the performance state in the training process of the quaternion-convolutional neural network model, and whether it is in the Pareto front archive, i.e., the state s is coded according to the position of the individual in the current Pareto front archive: if the individual is in the Pareto front archive, it is recorded as s=1; otherwise, it is recorded as s=0. The action a is one of the three commonly used DE mutation strategies, i.e., the action is selected from the three commonly used standard mutation strategies in the differential evolution algorithm: a_1: DE / rand / 1 strategy a_2: DE / current-to-best / 1 strategy a_3: DE / best / 1 strategy To realize the autonomous learning ability of the agent, the method configures an independent Q table for each agent to record the state-action value function, and the structure of the Q table is shown in Table 1. According to the state coding and the action set, the Q table has two rows representing different states and three columns representing different strategies, wherein the state S0 represents that the individual is not in the Pareto front file, and the state S1 represents that the individual is in the Pareto front file. In addition, since different agents have different effects at different evolution stages of the same problem, each agent has an independent Q table to guide in the embodiment.

[0047] Table 1 Structure of Q table

[0048] Wherein, the meanings of the values in the Q table: Q(0,0): the expected return value of selecting the DE / rand / 1 strategy when the individual is not in the Pareto front file; Q(0,1): the expected return value of selecting the DE / current-to-best / 1 strategy when the individual is not in the Pareto front file; Q(0,2): the expected return value of selecting the DE / best / 1 strategy when the individual is not in the Pareto front file; Q(1,0): the expected return value of selecting the DE / rand / 1 strategy when the individual is in the Pareto front file; Q(1,1): the expected return value of selecting the DE / current-to-best / 1 strategy when the individual is in the Pareto front file; Q(1,2): the expected return value of selecting the DE / best / 1 strategy when the individual is in the Pareto front file.

[0049] Action selection and execution: Since there is no experience to draw on, the default values in the initial Q table are all zero. The agent first obtains the current state according to the state coding method defined at the beginning of step 7.4, and then selects the next action, i.e. the mutation strategy to be executed, according to the Q table using the existing SoftMax action selection strategy (as shown in formula 12). After selecting the action, the population individual (agent) performs the corresponding mutation operation to generate a mutation vector V.

[0050]

[0051] In the formula, represents the probability of selecting the action by the agent in the state , represents the corresponding state and action in the Q table at time t The value n represents the number of candidate actions. This represents a control parameter used to adjust the probability interval of the selected action. When When the probability approaches 0, the probability of choosing the optimal action approaches 1; when As the value approaches infinity, the probability of choosing each action approaches 1 / n.

[0052] Crossover and generation of experimental individuals: According to the existing formula 13, a binomial crossover operation is used to cross the parent individual with the mutation vector V to obtain the experimental individual U.

[0053]

[0054] in, Indicates the experimental individual U. The first individual Dimensional parameter values, Represents the mutation vector V. The first individual Dimensional parameter values, Represents the parent individual X. The first individual Dimensional parameter values. For crossover probability, It is the first The random number corresponding to the dimension, and It is guaranteed that at least one dimension of the newly generated individual is provided by the mutation vector V. Through the crossover operation, the generated experimental individuals inherit the desirable characteristics of the parent solution and also incorporate the exploratory information from the mutated solution.

[0055] Rewards and Q-table updates: Compare the experimental individual U with its parent individual X, and award a reward based on the dominance relationship between the experimental individual and its parent individual.

[0056] Finally, the Q-values ​​at the corresponding positions in the Q-table are updated according to the Bellman equation (as shown in Equation 15). In turn, the updated Q-table can provide more effective guidance for the agent to select the next mutation strategy.

[0057]

[0058] in, At any moment Execute action Then, the immediate reward from environmental feedback, i.e., the reward calculated by formula 14; and Representing the state and action updates respectively Time and before update Q value at time t, Indicates the learning rate. It is a discount factor. Indicates a new state The highest expected return that can be obtained.

[0059] This reinforcement learning-based population evolution mechanism enables each individual to autonomously choose the most suitable mutation strategy based on historical experience, balancing global exploration and local development, thereby improving the convergence speed and diversity of the overall population.

[0060] Step 7.5: Relearning process based on opposition learning: After the differential evolution of the current population is completed, opposition learning is introduced to further enhance the diversity of the population; After differential evolution of the current population is completed, opposition learning is introduced to further enhance the diversity of the population and improve the global search capability of the algorithm. Specifically, for each individual X in the current population, opposition learning (Equation 11) is used to generate its opposition solution. The opposition solution is then merged with the parent and trial individuals to form a larger candidate population. Using non-dominated sorting and crowding calculation, environmental selection is performed on the merged population to select the optimal NP individuals to form the next generation population, and the Pareto front archive is updated. After updating the Pareto front archive, the process returns to step 7.4. Individuals in the population will re-evaluate their own state based on the updated Pareto front archive (i.e., re-determine whether the individual is in the Pareto front archive), and autonomously choose mutation operations based on the new state information through reinforcement learning to generate better offspring. Through the relearning process of opposition learning, not only is the search space of the population expanded, but the opposition solutions added after each generation of evolution can effectively prevent premature convergence of the algorithm, thereby ensuring that the solution set has better diversity and balance in the global scope.

[0061] Step 7.6: Multi-objective optimization iteration: Repeat the iterative loop formed by steps 7.4 (population evolution based on reinforcement learning) and 7.5 (relearning process based on opposition learning). That is, in each iteration, first execute step 7.4 to let individuals choose mutation strategies for population evolution based on the current Pareto frontier archive state, then execute step 7.5 to perform opposition learning relearning and update the Pareto frontier archive, and then return to step 7.4 to continue evolution based on the new archive state until the preset termination condition is met.

[0062] Step 8: The improved multi-objective differential evolution algorithm is used to automatically optimize the hyperparameters of the quaternion-convolutional neural network model to achieve the optimal hyperparameter configuration that achieves the best balance between prediction accuracy and model complexity. The quaternion-convolutional neural network model with the optimal hyperparameter configuration is called the OLRL-QuatCNN evolutionary deep learning model. Step 9: input the drug pair to be predicted into the OLRL-QuatCNN evolved deep learning model to obtain a drug interaction score, and predict whether there is an interaction between the drug pair to be predicted by comparing the score with a preset threshold, specifically, if the score exceeds the preset threshold, it is predicted that there is an interaction between the drug pair; if the score is lower than the preset threshold, it is predicted that there is no interaction link between the drug pair in the knowledge graph. In this embodiment, the OLRL-QuatCNN evolved deep learning model is used for feature extraction, drug interaction prediction score calculation and interaction relationship judgment of the drug pair to be predicted, and the knowledge graph link prediction result and confidence score of drug interaction are output. Specifically: (1) The data preprocessing module in the OLRL-QuatCNN evolved deep learning model encodes the data preprocessing module: the drug pair to be predicted is converted into a corresponding head entity-relation-tail entity triple form.

[0063] (2) The drug pair to be predicted is represented by the quaternion representation module, the entity relationship nonlinear fusion module, the convolution feature extraction module and the drug interaction score calculation module in the OLRL-QuatCNN evolved deep learning model for quaternion representation, Hamilton product fusion, convolution feature extraction and drug interaction score calculation.

[0064] (3) Compare the drug interaction score with the preset threshold to determine whether there is an interaction between the drug pair: if the score exceeds the preset threshold, it is predicted that there is a drug interaction between the drug pair, which needs to be paid attention to in clinical practice; if the score is lower than the preset threshold, it is predicted that there is no interaction link between the drug pair in the knowledge graph; (4) Finally, the drug interaction score is converted into a probability value between 0 and 1 by the Sigmoid function, which represents the confidence of the predicted drug interaction link.

[0065] Example 1

[0066] The main data set used in the experiment is the ogbl-ddi data set, which is composed of interaction relationships between multiple drugs, and is used to predict the missing drug interaction link relationships in the drug knowledge graph. The data set essentially constitutes a large-scale knowledge graph link prediction task, that is, predicting the corresponding tail entity when given the head entity and relationship. The statistical information of the data set is shown in Table 2. The challenge of this data set is that the drug interactions in the ogbl-ddi data set often have complex chemical and pharmacological dependence structures, and many relationships have non-symmetry and incomplete symmetry. Therefore, the ogbl-ddi data set can be used as an ideal test platform for testing whether the method of the present application can effectively capture complex drug interaction structures, because the non-commutative property of Hamilton product in quaternion representation is exactly suitable for modeling such non-symmetric drug interaction relationships. Therefore, ogbl-ddi not only has practical significance for drug interaction prediction, but also has challenges, which exactly matches the design motivation of the method of the present application and is an ideal platform for testing the effectiveness of the method of the present application.

[0067] Table 2 Statistical information of ogbl-ddi data set

[0068] The commonly used evaluation index of ogbl-ddi data set is Hits@k (Hits@20 is used in the present embodiment), and the definition and calculation formula are as follows: Hits@k: This index refers to the average proportion of triples ranked less than k in link prediction. The Hits@k index is used to measure whether the link prediction model can rank the correct entity or relationship in the top k positions in the link prediction task. The calculation method is as follows: wherein is the total number of test samples, is the ranking of the real tail entity in the th sample, is an indicator function, and if the ranking of the real tail entity does not exceed , the score of the sample is 1, otherwise it is 0. This index directly reflects whether the link prediction model can rank the correct answer in the front position in the candidate results. The larger the index, the higher the prediction accuracy of the model.

[0069] The experimental parameter settings of the OLRL-QuatCNN evolution deep learning model in the experiment are shown in Table 3. In the actual experiment, for the consideration of time cost, the Hits@20 index calculated on the test set at the 30th epoch is selected as the performance evaluation basis. The optimal model parameters of the OLRL-QuatCNN evolution deep learning model are: learning_rate = 0.003159, embedding_dim = 320, input_drop = 0.196, and hidden_dropout = 0.422. The parameter combination of the OLRL-QuatCNN evolution deep learning model realizes the best balance between prediction accuracy and model complexity, which embodies the significant advantage of the multi-objective evolution learning algorithm in automatic optimization of hyperparameters.

[0070] Table 3 Parameter settings

[0071] In order to further verify the performance of the method, the OLRL-QuatCNN evolution deep learning model of the present embodiment is used for experiment on the drug prediction data set ogbl-ddi, and compared with the currently more typical algorithm, and the specific results are shown in Table 4. QuatCNN is a quaternion-convolutional neural network model, and the model result is obtained by manual parameter tuning. The OLRL-QuatCNN evolution deep learning model is the result obtained by fine-tuning the quaternion-convolutional neural network model using the improved multi-objective evolution learning algorithm.

[0072] Table 4 Model results in ogbl-ddi data set Model Test@20 Validation@20 Matrix Factorization 0.1368 ± 0.0475 0.3370 ± 0.0264 Common Neighbor 0.1773 ± 0.0000 0.0947 ± 0.0000 Node2vec 0.2246 ± 0.0290 0.3292 ± 0.0121 SEAL 0.3056 ± 0.0386 0.2849 ± 0.0269 GCN 0.3707 ± 0.0507 0.5550 ± 0.0208 QuatCNN 0.4855 ± 0.0116 0.8515 ± 0.0098 OLRL-QuatCNN 0.4910 ± 0.0097 0.8705 ± 0.0106 As shown in Table 4, there is a significant difference in the performance of Hits@20 of each model on the ogbl-ddi dataset. From the experimental results, it can be seen that the OLRL-QuatCNN evolutionary deep learning model is significantly better than all the comparative methods in the Hits@20 index. For example, compared with the traditional matrix decomposition method, the test score of the QuatCNN quaternion-convolutional neural network model is increased by about 3.5 times; compared with the GCN and other graph neural network models, there is also a relative increase of nearly 30%. This significant performance difference shows that the quaternion embedding combined with Hamilton product and convolution feature extraction has obvious advantages in capturing the complex interaction between drugs and the characteristics of asymmetric entity relationships. After parameter adjustment, the performance index is further improved, and the OLRL-QuatCNN evolutionary deep learning model is 1.1% higher than the hand-tuned quaternion-convolutional neural network model in the test set, and the standard deviation is smaller (0.0097 vs 0.0116), which shows that the optimized model not only has higher accuracy, but also has better stability. This fully proves the effectiveness of the OLRL-QuatCNN evolutionary deep learning model proposed in the application in the deep learning parameter tuning task.

[0073] Reason analysis of the excellent performance of the application in Hits@20: (1) The representation ability of quaternions is significantly enhanced: the application uses quaternion representation technology to encode entity and relationship information in a higher-dimensional representation space through the rich algebraic structure of its four dimensions (one real part and three imaginary parts). The non-commutative property of Hamilton product operation enables quaternions to naturally express complex nonlinear interaction patterns, effectively capturing the nonlinear and multi-level coupling characteristics of biochemical processes such as enzyme inhibition, carrier competition, and receptor antagonism in drug interaction mechanisms. Compared with traditional scalar embedding, which can only perform linear combination, quaternion representation can capture more rich semantic information under the same parameter size. Experimental results show that it is about 3.5 times higher than traditional matrix decomposition methods, proving the significant advantages of quaternion representation.

[0074] (2) Accurate modeling of non-symmetry information: Hamilton product operation satisfies the non-commutative property of a⊗b≠b⊗a, which naturally has the mathematical foundation to handle non-symmetric relationships. When using Hamilton product to fuse the head entity quaternion and the relationship quaternion, the non-commutative property of the operation ensures that the transformation from the head entity to the tail entity and the transformation from the tail entity to the head entity produce different results, accurately corresponding to the direction dependence in drug interactions. For example, the influence of a strong CYP3A4 inhibitor on CYP3A4 substrates is usually much greater than the reverse influence, and this asymmetric feature is accurately modeled by Hamilton product, avoiding the limitations of traditional symmetric calculation methods.

[0075] (3) Efficient and lossless fusion of multi-relation information: The natural four-dimensional structure of quaternion space enables different types of relation information to be encoded into the real part and three imaginary parts, respectively, avoiding the dimension explosion and information redundancy problems caused by traditional vector splicing or linear weighting methods. Hamilton product operation can non-linearly fuse the information of multiple quaternions, and the operation result still maintains the algebraic structure of quaternion, ensuring the mathematical consistency of the information fusion process. This enables the integration of multiple interactions of the same pair of drugs through different mechanisms (such as pharmacokinetics and pharmacodynamics) in a unified mathematical framework, effectively avoiding feature confusion and information loss.

[0076] (4) Intelligent global optimization of parameters: The improved multi-objective evolutionary learning algorithm of the invention expands the search space coverage by one-fold through the opposite learning strategy, significantly improving the initial population diversity; the reinforcement learning mechanism enables each individual to adaptively select the optimal mutation strategy based on the current state, avoiding the search efficiency problem of fixed strategies; the multi-objective optimization strategy automatically finds the optimal balance point between prediction accuracy and model complexity. Experimental results show that the OLRL-QuatCNN evolutionary deep learning model improves the absolute performance on the test set by 1.1% compared to the hand-tuned quaternion-convolutional neural network model, with a smaller standard deviation (0.0097 vs 0.0116), proving the significant advantage of the algorithm in achieving globally optimal parameter configuration and overcoming the low efficiency of traditional hand-tuning.

[0077] In addition, based on the fused quaternion representation, the model extracts entity position features in the hypercomplex space through convolution layers. This operation not only captures the fine-grained structure in entity and relationship interactions, but also achieves multi-scale information fusion through multiple convolution layers. After the convolution layer, batch normalization, ReLU activation, and Dropout processing are performed to effectively alleviate the overfitting problem and improve the robustness of the model. This feature extraction method enables the model to better identify specific local patterns and relationship patterns in the ogbl-ddi dataset, further improving the Hits@20 indicator.

[0078] In summary, the experimental results of the model on the ogbl-ddi dataset in this paper fully demonstrate that the use of quaternion representation and its Hamilton product can effectively capture the complex multi-dimensional interaction information between entities and relationships, and the convolution layer further extracts local patterns based on this, enhancing the prediction accuracy of the model. At the same time, the multi-objective evolutionary learning algorithm expands the search space through the opposite learning strategy and realizes adaptive strategy selection through the reinforcement learning mechanism, successfully achieving global optimization of hyperparameters and avoiding the limitations of traditional hand-tuning. The improvement in the Hits@20 indicator not only proves the excellent performance of the model on the experimental dataset, but also indicates that the method has high application value in actual link prediction tasks.

[0079] It should be understood that, under the inspiration of the technical concept of the present application, those skilled in the art can make various improvements or changes according to the above content without departing from the basis of the present application, which still falls within the protection scope of the present application.

Claims

1. A knowledge graph link prediction method based on quaternions and multi-objective evolutionary learning, characterized in that, The method includes the following steps: Step 1: Establish a data preprocessing module to convert the drug interaction data in the original knowledge graph into a standard knowledge graph triple format, generate a triple dataset, and encode all N drug entities and M relations in the triple dataset; Step 2: Establish a quaternion representation module to convert drug entities and relations in the standardized triplet dataset into high-dimensional feature representations in quaternion form, and construct the quaternion embedding matrix of drug entities and the quaternion embedding matrix of relations; Step 3: Establish an entity-relationship nonlinear fusion module to perform nonlinear fusion of the drug entity quaternion embedding matrix and the relation quaternion embedding matrix to generate a head entity-relationship composite representation vector; Step 4: Establish a convolutional feature extraction module, which is used to extract features from the head entity-relationship composite representation vector through a convolutional neural network to obtain a fused feature vector; Step 5: Establish a drug interaction score calculation module, which is used to extract the quaternion embeddings of all N drug entities from the drug entity quaternion embedding matrix as candidate tail entity quaternion embeddings, and perform inner product calculation on the fused feature vector and all candidate tail entity quaternion embeddings to generate the interaction score vector of head entity-relationship combination and each candidate drug. Step 6: Cascade the data preprocessing module, quaternion representation module, entity relationship nonlinear fusion module, convolutional feature extraction module, and drug interaction score calculation module in sequence to establish a quaternion-convolutional neural network model; Step 7: Improve the traditional multi-objective differential evolution algorithm: use the opposition learning method to expand the search range during population initialization and relearning after each generation of population evolution; adopt the existing Q-learning-based policy adjustment method in the evolution to allow each individual in the population to dynamically adjust the differential evolution mutation strategy according to whether it is located in the Pareto front archive. Step 8: The improved multi-objective differential evolution algorithm is used to automatically optimize the hyperparameters of the quaternion-convolutional neural network model, and the quaternion-convolutional neural network model with the optimal hyperparameter configuration is called the OLRL-QuatCNN evolutionary deep learning model. Step 9: Input the drug pair to be predicted into the OLRL-QuatCNN evolutionary deep learning model to obtain the drug interaction score, and compare the score with a preset threshold. If the score exceeds the preset threshold, it is considered that there is an interaction between the drug pair; if it is below the preset threshold, it is considered that there is no interaction link between the drug pair in the knowledge graph.

2. The knowledge graph link prediction method according to claim 1, characterized in that, The processing flow of the quaternion representation module includes the following steps: Step 2.1: According to Equation (1), each drug entity in the standardized triplet dataset is... Represented in quaternion form: ； in Let be a real-valued vector with the real part. These are real-valued vectors with three imaginary parts, The imaginary unit; Step 2.2: According to Equation (2), each drug interaction relationship in the standardized triplet dataset is... Represented in quaternion form: ； In the formula It is the square root of -1, called the imaginary unit, and satisfies Hamilton's rule: ； ； Step 2.3: Construct a quaternion embedding matrix for N drug entities according to equation (5). And construct quaternion embedding matrices for M relations using the same method. The quaternion embedding matrix Q is initialized using the Xavier initialization method. ; in, Let Q be the real component of each quaternion in the quaternion embedding matrix Q; These are the three imaginary components of each quaternion in the quaternion embedding matrix Q; Let be a random angle within the interval [-π, π]. Randomly generated from the interval [-1 / (2k), 1 / (2k)], where k is the embedding dimension.

3. The knowledge graph link prediction method according to claim 1, characterized in that, The processing flow of the entity relationship nonlinear fusion module includes the following steps: Step 3.1: Embed the relation quaternions into the matrix according to equation (6). Normalized to a unit quaternion: ; Step 3.2: Embed the head entity quaternion in the matrix using drug entity quaternions. Normalized relation quaternions embedded in a relation quaternion matrix Hamiltonian products are used to achieve nonlinear fusion of entity relationships, generating a head entity-relationship composite representation vector that captures the asymmetric features of drug interactions. ; in This represents the Hamiltonian product operation, which has a non-commutative property. It can naturally capture the directional characteristics of drug interactions.

4. The knowledge graph link prediction method according to claim 2, characterized in that, The processing flow in the convolutional feature extraction module includes the following steps: Step 4.1: Combine the head entity-relationship representation vector real part With three imaginary parts , , They are stacked as independent channels to form a 4-channel tensor. ,in It is a real number; Step 4.2: Apply convolutional layers to the 4-channel tensor Perform local feature extraction; Step 4.3: The output of the convolutional layer is sequentially processed through batch normalization, ReLU activation, and Dropout operations to obtain convolutional features; Step 4.4: Through the Flatten operation and fully connected layers, the convolutional features are mapped into a fusion feature vector of local interaction patterns in the hypercomplex space.

5. The knowledge graph link prediction method according to claim 1, characterized in that, In step 5, the inner product of the fused feature vector and the quaternion embeddings of all candidate tail entities is calculated using a 1-N scoring mechanism.

6. The knowledge graph link prediction method according to claim 1, characterized in that, The improved multi-objective differential evolution algorithm includes the following steps: Step 7.1: Using the prediction accuracy metrics of the quaternion-convolutional neural network model and model complexity metrics As the objective function for multi-objective optimization: ； in ; The number of parameters refers to the total number of all trainable parameters in a quaternion-convolutional neural network model. Step 7.2: Randomly generate NP initial individuals and generate their complementary solutions for each initial individual, thereby expanding the total number of individuals in the population to 2NP; where each individual represents a set of hyperparameter combinations of the quaternion-convolutional neural network model; Step 7.3: Evaluate the objective function for the expanded 2NP candidate individuals. Use the non-dominated sorting method in the NSGA-II algorithm to stratify the individuals. Within the same stratum, sort them according to the distribution density using the crowding calculation method. Finally, select the top NP individuals as the initial population and use the non-dominated solutions among them as the current Pareto front archive. Step 7.4: In the differential evolution operation stage of population evolution, each individual is regarded as an intelligent agent. Through reinforcement learning mechanism, the individual is allowed to autonomously select mutation strategy to carry out population evolution based on the current Pareto frontier archive state. Step 7.5: Relearning process based on opposition learning: After the differential evolution of the current population is completed, opposition learning is introduced to further enhance the diversity of the population and update the Pareto frontier archive; Step 7.6: Multi-objective optimization iteration: Repeat steps 7.4-7.5 until the preset termination condition is met.

7. The knowledge graph link prediction method according to claim 6, characterized in that, In step 7.4, the state corresponds to the performance state during the training process of the quaternion-convolutional neural network model. That is, the state s is encoded according to the individual's position in the current Pareto frontier: if the individual is in the Pareto frontier, it is recorded as s=1; otherwise, it is recorded as s=0.

8. The knowledge graph link prediction method according to claim 6, characterized in that, Action a is to select from three commonly used standard mutation strategies in differential evolution algorithms: a_1: DE / rand / 1 strategy a_2: DE / current-to-best / 1 strategy a_3: DE / best / 1 strategy.

9. The knowledge graph link prediction method according to claim 6, characterized in that, In the reinforcement learning mechanism: the SoftMax action selection strategy is used to select the next action, i.e., the mutation strategy to be executed; after the action is selected, the agent representing the population individual performs the corresponding mutation operation to generate the mutation vector V; a binomial crossover operation is used to cross the parent individual with the mutation vector V to obtain the test individual U; the test individual U is compared with the parent individual X, and a reward is obtained according to the dominance relationship between the test individual and the parent individual; finally, the Q value is updated according to the Bellman equation.

10. The knowledge graph link prediction method according to claim 9, characterized in that, Step 7.5 specifically involves: for each individual in the current population, generating its opposite solution using opposite learning, merging the opposite solution with the parent and experimental individuals to form a larger candidate population; using non-dominated sorting and crowding calculation, performing environmental selection on the merged population to select the optimal NP individuals to form the next generation population, and updating the Pareto frontier archive.

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