A method for identifying individual-level cancer driver genes based on PMF and HGNN

Abstract

The application discloses a method for identifying individual-level cancer driver genes based on PMF and HGNN, which comprises three steps: 1) after the preprocessing of single nucleotide variation and gene expression data, the low-dimensional latent features of genes and patients are extracted by using probability matrix factorization PMF, and the biological correlation between the two is preliminarily modeled; 2) a heterogeneous graph containing two types of nodes, i.e., genes and patients, is constructed, three types of correlations, i.e., gene interaction, patient similarity and gene-patient regulation, are integrated, the node position embedding is learned through a constrained random walk and a Skip-gram model, and an enhanced feature matrix fusing attribute and topological information is obtained by splicing; and 3) the heterogeneous graph neural network HGNN is input, the high-order representation of nodes is learned through a multi-layer heterogeneous message passing mechanism, and the prediction result of individual-level cancer driver genes is output. The method can deeply mine deep semantic information of multi-omics data, fully utilize the topological structure characteristics of a heterogeneous network, effectively improve the recognition accuracy of individual-level cancer driver genes, and provide a new idea for tumor target screening.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics technology, specifically to a method for identifying individual-level cancer driver genes by fusing multi-omics data of cancer with heterogeneous graph network topology features. Background Technology

[0002] Cancer is a major and complex disease that seriously threatens human health. Its occurrence and development are a multi-gene, multi-stage process. Cancer driver genes are genes that, after gain-of-function or loss-of-function mutations, can drive the transformation of normal cells into malignant cells and promote tumor occurrence and progression. They are the core targets of cancer pathogenesis and the key basis for targeted drug development. In recent years, the identification of individual-level cancer driver genes has gradually become a research hotspot, with the goal of identifying specific driver genes for each patient.

[0003] Existing individual-level cancer driver gene identification methods are gradually moving towards joint modeling of gene-patient relationships and their interactions, but significant limitations remain. For example, the DawnRank method uses PageRank to propagate mutation effects in the network, the Prodigy method combines mutation and expression data to calculate pathway interference scores, and the IMCDriver method uses inductive matrix completion to infer functional similarity. The core reliance of these methods is still on direct gene-patient association measurement, assessing the degree of gene-patient association solely through shallow data correlation calculations. This fails to fully explore the deep semantic information hidden in multi-omics data, nor does it consider the crucial role of the topological position of genes and patients in the association network on functional impact. Consequently, they struggle to capture higher-order biological regulatory relationships, limiting further improvements in identification performance.

[0004] Therefore, there is an urgent need to develop an individual-level cancer driver gene identification method that can adaptively learn high-order representations of nodes from heterogeneous biological networks and integrate multi-source biological information to improve identification accuracy. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing individual-level cancer driver gene identification methods, which tend to focus on shallow association calculations, lack deep semantic information mining, and have limited utilization of network topology features. This invention proposes a method (named PHDriver) for identifying individual-level cancer driver genes based on Probabilistic Matrix Factorization (PMF) and High-Gen Neural Network (HGNN). This method extracts latent features through probabilistic matrix factorization, constructs a gene-patient heterogeneous graph to fuse multiple biological associations, and combines it with a heterogeneous graph neural network to learn high-order node representations, effectively improving the identification performance of individual-level cancer driver genes.

[0006] The technical solution to achieve the objective of this invention is:

[0007] A method for identifying individual-level cancer driver genes based on PMF and HGNN includes the following steps:

[0008] 1) Using PMF to extract genes and potential characteristics of patients

[0009] Assuming that both genes and patients can be represented as latent low-dimensional feature vectors, these features are implicit in the data and need to be extracted through model learning. First, relevant genes and patients are screened using two types of genomic data: single nucleotide variants and gene expression. The gene expression data from the screened patients is preprocessed to obtain a gene expression matrix. The gene expression matrix is ​​then decomposed using PMF (Proteinized Factor Model), resulting in the product of two low-dimensional matrices, which preliminarily characterize the biological association between genes and patients. The resulting low-dimensional matrices are the gene latent feature matrix and the patient latent feature matrix: in the gene latent feature matrix, the column represents the gene and the column represents the genomic attributes; in the patient latent feature matrix, the column represents the patient and the column represents the patient's genomic representation. The following details the specific steps for extracting latent features of genes and patients using PMF.

[0010] (1.1) Data preprocessing

[0011] First, only patients and genes possessing both SNVs data and gene expression data for a specific cancer type are retained, with patients having at least three mutated genes. To eliminate dimensional differences in gene expression levels and improve the stability and convergence speed of subsequent model training, the data for each gene in the gene expression data is standardized, i.e., a standardized score for each gene in each sample is calculated. The specific calculation is expressed as shown in Formula 1:

[0012] (1)

[0013] in, Indicates gene In patients The expression value on and They represent genes respectively. The mean expression value and standard deviation were calculated. Next, to identify the aberrantly expressed genes in each patient, a specific aberration threshold was set for each gene. The specific calculation is expressed in Formula 2:

[0014] (2)

[0015] in, and They represent genes respectively. At the 95th and 5th percentiles of the standardized expression values. (By taking...) and The smaller of the two absolute values ​​is used as a threshold to capture values ​​indicating significantly high or low gene expression. If the gene... In patients Standardized expression values ​​in Greater than Then determine the gene In patients Abnormal expression was detected. Only genes that were mutated or abnormally expressed in at least one patient were retained for subsequent analysis.

[0016] (1.2) Perform probabilistic matrix decomposition on gene expression data to obtain the latent features of genes and patients.

[0017] Preprocessed gene expression matrix ( Represents a gene set. The patient set (represented by the patient set) approximately follows a Gaussian distribution. The PMF algorithm is used to decompose... Obtain the gene latent feature matrix Patient latent feature matrix The calculation process is shown in Formula 12:

[0018] (12)

[0019] in, This represents the PMF function. Therefore, high-dimensional genomic data is transformed into 16-dimensional feature representations of genes and patients, thus establishing a preliminary biological association model between genes and patients.

[0020] 2) Construct a gene-patient heterogeneity map and generate an enhanced feature matrix.

[0021] To integrate gene interactions, patient similarity, and gene-patient regulatory relationships, a gene-patient heterogeneity map was constructed. Based on this heterogeneity map, positional embedding matrices for genes and patients were obtained. In the resulting matrices, the former uses genes as the column and columns as the gene positional embedding feature matrix, while the latter uses patients as the patient positional embedding feature matrix. Finally, the positional embedding feature matrices were concatenated with the latent feature matrices extracted by PMF (Prognostics and Predictive Factor Analysis) to form enhanced feature matrices, which are used to characterize the comprehensive representation of genes and patients in multi-omics data. The following details the construction process of the heterogeneity map and the generation process of the enhanced feature matrices.

[0022] (2.1) Constructing a gene-patient heterogeneity map

[0023] Constructed gene-patient undirected heteromorphism Using genes and patients as nodes, the edges are based on three types of associations: gene-to-gene associations, patient-to-patient associations, and gene-to-patient associations. First, gene-to-gene interactions are constructed using a PPI network, retaining only interactions with a confidence level of at least 0.65 as gene-to-gene association edges. Genes are used as nodes and gene-gene association edges are used. The gene association subgraph is constructed, and the adjacency matrix of the gene association subgraph is formed. As shown in Formula 3:

[0024] (3)

[0025] in, This represents the confidence level of the interaction between gene i and gene j in the PPI network. Secondly, the similarity between patients is quantified by calculating the Pearson correlation coefficient using their latent feature matrix, as shown in Equation 13.

[0026] (13)

[0027] in, Indicates the patient The mean of the latent feature vectors, Indicates the patient The mean of the latent feature vectors. Furthermore, patient-patient association edges are constructed by connecting patient pairs with a correlation coefficient of at least 0.9. Treat patients as nodes and associate them with patient-patient edges. The patient-to-patient relationship subgraph is constructed, and the adjacency matrix of the patient-to-patient relationship subgraph is formed. As shown in Formula 4:

[0028] (4)

[0029] Finally, the association between genes and patients is defined by mutation and abnormal expression events: if a gene mutates or is abnormally expressed in a specific patient, a connection is established between the corresponding gene node and the patient node. This forms the gene-patient association edge. Genes and patients are used as nodes, with gene-patient association edges. The gene-patient association subgraph is composed of the adjacency matrix of the gene-patient association subgraph. As shown in Formula 5:

[0030] (5)

[0031] Based on the above description, a gene-patient undirected heterogeneous graph with two types of nodes and three types of edges was constructed. ;

[0032] (2.2) Genetic and patient feature enhancement matrix

[0033] Based on the gene-patient heterogeneous graph constructed in step (2.1), a random walk strategy based on node type constraints was used to generate sequences. Each walk started from a gene node, and the next node was dynamically selected according to the current node type: if the current node was a gene node, the next node was randomly selected from its neighboring nodes, which could be either gene or patient nodes; if the current node was a patient node, only gene nodes were randomly selected from its neighboring nodes, thus ensuring that the walk path propagated alternately between the two types of nodes. By setting the walk length and the number of repetitions, all walk sequences for location nesting feature learning were obtained.

[0034] To map nodes in the sequence to low-dimensional vectors, the Skip-gram model is used for embedding learning, and its calculation process is shown in Equation 14:

[0035] (14)

[0036] in, The matrix represents the location embedding of genes. The patient's location embedding matrix is ​​represented. Indicates the use of heterogeneous graphs The generated set of walk sequences, This represents the Skip-gram function.

[0037] Finally, the location embedding matrices of the genes and patients are concatenated with the preceding latent feature matrices along the feature dimension to form a 32-dimensional enhanced feature matrix, formally represented as shown in Equations 6 and 7:

[0038] (6)

[0039] (7)

[0040] These two enhanced feature matrices integrate the intrinsic properties of nodes with contextual information in the heterogeneous graph structure, providing a more expressive representational basis for subsequent identification of individual-level cancer driver genes.

[0041] 3) Train the HGNN model and make predictions

[0042] An HGNN model adapted to the gene-patient heterogeneous graph from step 2 is constructed. This model takes the gene-enhanced feature matrix and the patient-enhanced feature matrix as input and performs feature learning and semantic fusion layer by layer through three HGNN modules. Within each HGNN module, the model simultaneously utilizes the three types of edge relationships in the gene-patient heterogeneous graph and jointly updates the features of the two types of nodes through a heterogeneous message passing mechanism. After multi-layer information aggregation, the HGNN model finally outputs the prediction results of individual-level cancer driver genes based on the learned gene feature representation. The process of training the HGNN model and making predictions will be described in detail below.

[0043] The core idea of ​​HGNN is to learn a set of independent weight parameter matrices for each edge relationship, enabling the HGNN model to effectively distinguish different types of associations and capture their unique information propagation patterns. The three constructed HGNN modules have similar structures, but the input and output dimensions change layer by layer. The specific architecture of each HGNN module is as follows: the output feature matrix of the previous module and the gene-patient undirected heterogeneous graph... The edge relationships are used as input to the current HGNN module. Each HGNN module uses an independent GAT structure to process different edge types and updates the feature representations of genes and patients through a heterogeneous message passing mechanism, which then serves as input to the next HGNN module. The definition of the node feature representation matrix obtained using GAT in different edge types is shown in Equation 15-18:

[0044] (15)

[0045] (16)

[0046] (17)

[0047] (18)

[0048] in, This represents the message passed from one gene to another in gene-gene relationships. This represents the message that genes convey to patients in gene-patient associations. This represents the message that the patient transmits to the gene in the gene-patient association. This refers to the messages that patients exchange with each other in a patient-to-patient relationship. Indicates HGNN module The i-th GAT submodule, This refers to the GAT function. Indicates gene nodes in the HGNN module The output feature matrix, This indicates that the patient node is in the HGNN module. The output feature matrix, Representing heterogeneous graphs Only subgraphs showing gene relationships are retained. Representing heterogeneous graphs Only subgraphs with gene-patient relationships are retained. Representing heterogeneous graphs Only subgraphs with patient-gene relationships are retained. Representing heterogeneous graphs Only subgraphs containing patient-to-patient relationships are retained. Subsequently, for gene nodes, all messages passed to the gene are... and Gene aggregation message obtained by element-wise addition For the patient node, all messages sent to the patient... and Obtain the aggregated message of the patient by element-wise addition. To ensure that the HGNN model can utilize both low-level details and high-level semantics simultaneously, and to enhance the discriminative power of node representations, residual connections and the ReLU activation function are added to the HGNN module. The specific definition of this operation is shown in Equation 8-9:

[0049] (8)

[0050] (9)

[0051] in, This represents the output feature matrix updated by the gene node in HGNN module k. This represents the output feature matrix updated by the patient node in HGNN module k. and Let represent the learnable weight matrix and bias vector, respectively.

[0052] Through propagation and aggregation of multiple HGNN modules, the HGNN model obtains a gene node embedding representation that integrates information from multiple types of edge relationships and neighbors. Finally, the sigmoid function is used to convert the real-valued output into probability values, resulting in the final prediction structure. As shown in Formula 10:

[0053] (10)

[0054] in, This represents the Sigmoid activation function. Furthermore, binary cross-entropy is used as the loss function, as shown in Equation 11:

[0055] (11)

[0056] in, Indicates gene The true label, Indicates gene The prediction results.

[0057] This technical solution overcomes the limitations of existing methods that rely on shallow correlation calculations by fusing probabilistic matrix factorization (PMF) and heterogeneous graph neural networks (HGNN), and achieves more accurate personalized cancer driver gene identification.

[0058] The advantages of this technical solution are mainly reflected in the following aspects: 1) It uses PMF to extract low-dimensional potential features of genes and patients from sparse gene expression data, and initially captures the global biological association between the two; 2) It constructs a heterogeneous graph that includes gene interactions, patient similarity and gene-patient regulatory relationships, and dynamically learns node representations through a heterogeneous message passing mechanism, making full use of node position information and deep semantic associations in the network; 3) Compared with methods that rely solely on mutation frequency or direct association measures, this technical solution can more effectively mine synergistically driven gene modules in individual patients. Experimental results on multiple cancer datasets show that its average F1 score, AUC and other indicators are significantly better than existing methods, and enrichment analysis verifies the consistency of biological functions of candidate genes, which has high explanatory potential. Attached Figure Description

[0059] Figure 1 Here is the overall flowchart of the PHDriver method;

[0060] Figure 2 This is a diagram showing the overall structure of a heterogeneous graph neural network model.

[0061] Figure 3 This is a schematic diagram illustrating the information aggregation and updating process of the HGNN module.

[0062] Figure 4 A comparison of average precision in identifying BRCA cancer driver genes at the individual level;

[0063] Figure 5 A comparison of the average recall rate for identifying BRCA cancer driver genes at the individual level;

[0064] Figure 6 Comparison of mean F1 scores for identifying BRCA cancer driver genes at the individual level;

[0065] Figure 7 A comparison of average precision in identifying GBM cancer driver genes at the individual level;

[0066] Figure 8 A comparison of the average recall rate for identifying GBM cancer driver genes at the individual level;

[0067] Figure 9 Comparison of average F1 scores for identifying GBM cancer driver genes at the individual level;

[0068] Figure 10 A comparison of average precision in identifying LIHC cancer driver genes at the individual level;

[0069] Figure 11 A comparison of the average recall rate for identifying LIHC cancer driver genes at the individual level;

[0070] Figure 12 Comparison of average F1 scores for identifying LIHC cancer driver genes at the individual level;

[0071] Figure 13 A comparison of the average precision in identifying PAAD cancer driver genes at the individual level;

[0072] Figure 14 A comparison of the average recall rate for identifying PAAD cancer driver genes at the individual level;

[0073] Figure 15 Comparison of average F1 scores for identifying PAAD cancer driver genes at the individual level;

[0074] Figure 16 A comparison of average precision in identifying STAD cancer driver genes at the individual level;

[0075] Figure 17 A comparison of the average recall rate for identifying STAD cancer driver genes at the individual level;

[0076] Figure 18 Comparison of average F1 scores for identifying STAD cancer driver genes at the individual level;

[0077] Figure 19 GO enrichment analysis of BRCA candidate cancer driver genes;

[0078] Figure 20 GO enrichment analysis of GBM candidate cancer driver genes;

[0079] Figure 21 GO enrichment analysis of LIHC candidate cancer driver genes;

[0080] Figure 22 GO enrichment analysis of PAAD candidate cancer driver genes;

[0081] Figure 23 GO enrichment analysis of STAD candidate cancer driver genes;

[0082] Figure 24KEGG enrichment analysis diagram of BRCA candidate cancer driver genes;

[0083] Figure 25 KEGG enrichment analysis diagram of GBM candidate cancer driver genes;

[0084] Figure 26 KEGG enrichment analysis diagram of LIHC candidate cancer driver genes;

[0085] Figure 27 KEGG enrichment analysis diagram of PAAD candidate cancer driver genes;

[0086] Figure 28 KEGG enrichment analysis of STAD candidate cancer driver genes. Detailed Implementation

[0087] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the following.

[0088] Example: This experiment uses the Ubuntu operating system to build and train the model, implements the algorithm using the Python language, and plots the results using the matplotlib library.

[0089] 1. Experimental environment and parameter settings

[0090] The experimental environment configuration for this example is shown in Table 1. The model hyperparameters are kept consistent across the five cancer type datasets, and the specific parameter settings are shown in Table 1 (continued).

[0091] Table 1 Parameter Settings

[0092]

[0093] 2. Experimental Dataset

[0094] The genomic and transcriptomic data used in this example are both from TCGA, covering five cancer types: BRCA, GBM, LIHC, PAAD, and STAD. Regarding biological networks, this example integrates PPI data from STRING using NDEx and maps multi-omics features to the PPI network, thereby generating datasets for the five cancer types. The positive and negative labels for the experiment come from the same source as TGCN. The dataset descriptions for this experiment are shown in Table 2.

[0095] Table 2. Description of Experimental Datasets

[0096]

[0097] 3. Specific Implementation Steps

[0098] The flowchart of the PHDriver method is as follows: Figure 1 As shown, the specific steps are as follows: 1) Use PMF to extract the potential features of genes and patients; 2) Construct a gene-patient heterogeneous graph and obtain the enhanced feature matrix of genes and patients; 3) Train the heterogeneous graph neural network model and predict the individual-level cancer driver genes of patients.

[0099] 1) Using PMF to extract genes and potential characteristics of patients

[0100] This example assumes that both genes and patients can be represented as potential low-dimensional feature vectors, which are implicit in the data and need to be extracted through model learning. For example... Figure 1 As shown, this example first uses two types of genomic data—single nucleotide variants and gene expression—to screen for relevant genes and patients. The gene expression data from the screened patients is preprocessed to obtain a gene expression matrix. PMF is then used to decompose the obtained gene expression matrix, resulting in the product of two low-dimensional matrices, which preliminarily characterize the biological association between genes and patients. The resulting low-dimensional matrices are the gene latent feature matrix and the patient latent feature matrix: the former represents genes, with columns indicating genomic attributes; the latter represents patients, with columns indicating the patient's genomic characteristics. The following details the specific steps for extracting gene and patient latent features using PMF.

[0101] (1.1) Data preprocessing

[0102] First, only patients with both SNVs data and gene expression data for a specific cancer type are retained, and these patients must have at least three mutated genes. To eliminate dimensional differences in gene expression levels and improve the stability and convergence speed of subsequent model training, the data for each gene in the gene expression data is standardized, i.e., a standardized score for each gene in each sample is calculated. The specific calculation is expressed as shown in Formula 1:

[0103] (1)

[0104] in, Indicates gene In patients The expression value on and They represent genes respectively. The mean expression value and standard deviation were calculated. Next, to identify the aberrantly expressed genes in each patient, a specific aberration threshold was set for each gene. The specific calculation is expressed in Formula 2:

[0105] (2)

[0106] in, and They represent genes respectively. The 95th and 5th percentiles of standardized expression values ​​are used as thresholds. By taking the smaller of the absolute values ​​of these two values, significantly high or low gene expression levels can be identified. If the gene... In patients Standardized expression values ​​in Greater than Then determine the gene In patients Abnormal expression was observed. In this case, only genes with mutations or abnormal expression in at least one patient were retained for subsequent analysis.

[0107] (1.2) Perform probabilistic matrix decomposition on gene expression data to obtain the latent features of genes and patients.

[0108] Preprocessed gene expression matrix ( Represents a gene set. The patient set (represented by the patient set) approximately follows a Gaussian distribution. The PMF algorithm is used to decompose... Obtain the gene latent feature matrix Patient latent feature matrix The calculation process is shown in Formula 12:

[0109] (12)

[0110] Therefore, this example transforms high-dimensional genomic data into 16-dimensional feature representations of genes and patients, and initially establishes a biological association model between genes and patients.

[0111] 2) Construct a gene-patient heterogeneity map and generate an enhanced feature matrix.

[0112] To integrate gene interactions, patient similarity, and gene-patient regulatory relationships, this example constructs a gene-patient heterogeneity map. Based on this heterogeneity map, positional embedding matrices for genes and patients are obtained. In the resulting matrices, the former uses the column as the gene's positional embedding feature matrix, and the latter uses the patient's positional embedding feature matrix. Finally, the positional embedding feature matrices are concatenated with the latent feature matrices extracted by the Product-Modal Matrix (PMF) to form enhanced feature matrices, which are used to characterize the comprehensive representation of genes and patients in multi-omics data. The following details the construction process of the heterogeneity map and the generation process of the enhanced feature matrices.

[0113] (2.1) Constructing a gene-patient heterogeneity map

[0114] The gene-patient undirected heterogeneous graph constructed in this example Using genes and patients as nodes, the edges are based on three types of associations: gene-to-gene associations, patient-to-patient associations, and gene-to-patient associations. First, the gene-to-gene interactions are constructed using a PPI network, retaining only interactions with a confidence level of at least 0.65 as gene-to-gene association edges. Its adjacency matrix As shown in Formula 3:

[0115] (3)

[0116] in, This represents the confidence level of the interaction between genes i and j in the PPI network. Secondly, the similarity between patients is quantified by calculating the Pearson correlation coefficient using their latent feature matrix, as shown in Equation 13.

[0117] (13)

[0118] in, Indicates the patient The mean of the latent feature vectors, Indicates the patient The mean of the latent feature vectors. Furthermore, patient-patient association edges are constructed by connecting patient pairs with a correlation coefficient of at least 0.9. Treat patients as nodes and associate them with patient-patient edges. The patient-to-patient relationship subgraph is constructed, and the adjacency matrix of the patient-to-patient relationship subgraph is formed. As shown in Formula 4:

[0119] (4)

[0120] Finally, the association between genes and patients is defined by mutation and abnormal expression events: if a gene mutates or is abnormally expressed in a specific patient, a connection is established between the corresponding gene node and the patient node. This forms the gene-patient association edge. Genes and patients are used as nodes, with gene-patient association edges. The gene-patient association subgraph is composed of the adjacency matrix of the gene-patient association subgraph. As shown in Formula 5:

[0121] (5)

[0122] Based on the above description, a gene-patient undirected heterogeneous graph with two types of nodes and three types of edges was constructed. .

[0123] (2.2) Genetic and patient feature enhancement matrix

[0124] On the constructed gene-patient heterogeneous graph, this example employs a random walk strategy based on node type constraints to generate sequences. Each walk begins with a gene node, and the next node is dynamically selected based on the current node type: if the current node is a gene node, the next node is randomly selected from its neighboring nodes, which can be either gene or patient nodes; if the current node is a patient node, only gene nodes are randomly selected from its neighboring nodes, thus ensuring that the walk path propagates alternately between the two types of nodes. By setting the walk length and the number of repetitions, all walk sequences for location nesting feature learning are obtained.

[0125] To map nodes in the sequence to low-dimensional vectors, the Skip-gram model is used for embedding learning, and its calculation process is shown in Equation 14:

[0126] (14)

[0127] in, The matrix represents the location embedding of genes. The patient's location embedding matrix is ​​represented. Indicates the use of heterogeneous graphs The generated set of wandering sequences.

[0128] Finally, the location embedding matrices of the genes and patients are concatenated with the preceding latent feature matrices along the feature dimension to form a 32-dimensional enhanced feature matrix, the formal representation of which is shown in Equations 6 and 7:

[0129] (6)

[0130] (7)

[0131] These two enhanced feature matrices integrate the intrinsic properties of nodes with contextual information in the heterogeneous graph structure, providing a more expressive representational basis for subsequent identification of individual-level cancer driver genes.

[0132] 3) Train the HGNN model and make predictions

[0133] This example constructs an HGNN model adapted to the gene-patient heterogeneity map described above, and its overall structure is as follows: Figure 2As shown, the model takes the constructed gene-enhanced feature matrix and patient-enhanced feature matrix as input, and performs feature learning and semantic fusion layer by layer through three HGNN modules. Within each HGNN module, the HGNN model simultaneously utilizes the three types of edge relationships in the gene-patient heterogeneous graph, and jointly updates the features of the two types of nodes through a heterogeneous message passing mechanism. After multi-layer information aggregation, the HGNN model finally outputs the prediction results of individual-level cancer driver genes based on the learned gene feature representation. The following will detail the process of training the HGNN model and making predictions.

[0134] The core idea of ​​HGNN is to learn an independent set of weight parameter matrices for each edge relationship, enabling the HGNN model to effectively distinguish different types of associations and capture their unique information propagation patterns. The three HGNN modules constructed in this example have similar structures, but the input and output dimensions change layer by layer. The specific architecture of each HGNN module is as follows: Figure 3 As shown: The output feature matrix of the previous HGNN module and the gene-patient undirected heterogeneous graph The edge relationships are used as input to the current HGNN module. Internally, the HGNN module uses independent GAT structures to process different edge types and updates the feature representations of genes and patients through a heterogeneous message passing mechanism, which then serves as input to the next HGNN module. The definition of the node feature representation matrix obtained using GAT in different edge relationship types is shown in Equation 15-18:

[0135] (15)

[0136] (16)

[0137] (17)

[0138] (18)

[0139] in, This represents the message passed from one gene to another in gene-gene relationships. This represents the message that genes convey to patients in gene-patient associations. This represents the message that the patient transmits to the gene in the gene-patient association. This refers to the messages that patients exchange with each other in a patient-to-patient relationship. Indicates HGNN module The i-th GAT submodule, This refers to the GAT function. Indicates gene nodes in the HGNN module The output feature matrix, This indicates that the patient node is in the HGNN module. The output feature matrix, Representing heterogeneous graphs Only subgraphs showing gene relationships are retained. Representing heterogeneous graphs Only subgraphs with gene-patient relationships are retained. Representing heterogeneous graphs Only subgraphs with patient-gene relationships are retained. Representing heterogeneous graphs Only subgraphs containing patient-to-patient relationships are retained. Subsequently, for gene nodes, all messages passed to the gene are... and Gene aggregation message obtained by element-wise addition For the patient node, all messages sent to the patient... and Obtain the aggregated message of the patient by element-wise addition. To ensure that the HGNN model can utilize both low-level details and high-level semantics, and to enhance the discriminative power of node representations, this example adds residual connections and the ReLU activation function to the HGNN module. The specific definition of this operation is shown in Equation 8-9:

[0140] (8)

[0141] (9)

[0142] in, This represents the output feature matrix updated by the gene node in HGNN module k. This represents the output feature matrix updated by the patient node in HGNN module k. and Let represent the learnable weight matrix and bias vector, respectively.

[0143] Information gene node embedding representation Finally, the sigmoid function is used to convert the real-valued output into probability values, resulting in the final prediction structure. As shown in Formula 10:

[0144] (10)

[0145] in, This represents the Sigmoid activation function. Furthermore, this example uses binary cross-entropy as the loss function, as shown in Equation 11:

[0146] (11)

[0147] in, This indicates the number of genes in the training set. Indicates gene The true label, Indicates gene The prediction results.

[0148] 4. Performance Evaluation Indicators

[0149] Consistent with most comparative methods, this example uses leave-one-out cross-validation's mean precision, mean recall, and mean F1 score as performance metrics for individual-level cancer driver gene identification. The specific steps of leave-one-out cross-validation are as follows: Assume the dataset contains... One patient is selected from a pool of patients each time as the test set, and the rest... Using a set of patients as the training set, the model is trained and then used to predict the results of the test patients; this process is repeated. This process is repeated to ensure that each patient is used as part of the test set exactly once. Finally, all... The prediction results are aggregated, and the average performance metric is calculated as the overall evaluation result of the model. Similar to TGCN, PHDriver uses the average AUC and average AUPRC from ten five-fold cross-validations at the cohort level as evaluation metrics. The F1 score is defined as shown in Equation 19:

[0150] (19)

[0151] The F1 score is the harmonic mean of precision and recall, with equal weighting for both. A higher F1 score indicates better model performance. Because it comprehensively reflects the model's ability and accuracy in identifying positive patients, the F1 score is particularly suitable for imbalanced data problems such as cancer driver gene identification.

[0152] 5. Comparison based on individual levels

[0153] To evaluate the performance of PHDriver in identifying driver genes at the individual level, this example compares it with six representative methods. To ensure a fair comparison, all deep learning-based methods used the same biological features and PPI network. The parameter settings for each comparison method were either based on the original text or appropriately adjusted to achieve optimal performance. The following is the process for obtaining evaluation values ​​for deep learning-based methods: Using a leave-one-out method, one patient was used as the test set each time, and all other patients were used as the training set. The trained model was used to calculate the prediction score for each mutated gene in that patient. Subsequently, the 16 mutated genes with the highest scores were extracted as candidate driver genes at the individual level for that patient, and their Precision, Recall, and F1 scores were calculated using them along with positive and negative labels. The above process was repeated for all patients, and the average Precision, average Recall, and average F1 score of all patients were used as the evaluation metrics for the model's individual-level identification performance. For non-learning methods, the average Precision, average Recall, and average F1 score were directly calculated using their output patient prediction results.

[0154] Figure 4-6 The average precision, average recall, and average F1 score of each method in identifying BRCA cancer driver genes at the individual level are presented. PHDriver achieved an average precision of 0.4141, an average recall of 0.6844, and an average F1 score of 0.4489 on the BRCA dataset, all of which outperformed the comparison methods.

[0155] Performance comparisons of various methods in identifying GBM cancer driver genes at the individual level, for example Figure 7-9 As shown, on the GBM dataset, PHDriver achieved average precision, average recall, and average F1 score of 0.4096, 0.6665, and 0.4441, respectively. Except for average recall, which was slightly lower than IMCDriver, all other metrics were significantly better than the comparison methods.

[0156] In the task of identifying LIHC cancer driver genes at the individual level, PHDriver outperformed all comparable methods. Figure 10-12 As shown, its average Precision, average Recall and average F1 score on the LIHC dataset reached 0.4075, 0.4896 and 0.3907 respectively, all ranking first.

[0157] Figure 13-15The average precision, average recall, and average F1 score of each method in identifying PAAD cancer driver genes at the individual level are presented. Experimental results show that PHDriver achieves an average precision of 0.4459, an average recall of 0.7467, and an average F1 score of 0.5011 on the PAAD dataset. Although PHDriver's average precision and average recall are slightly lower than TGCN, it significantly outperforms the other methods in all metrics.

[0158] Figure 16 -18 shows the mean precision, mean recall, and mean F1 score of each method in identifying STAD cancer driver genes at the individual level. PHDriver achieved a mean precision of 0.4780, a mean recall of 0.4007, and a mean F1 score of 0.3501 on the STAD dataset, all of which are superior to the comparison methods.

[0159] 6. Comparison based on queue level

[0160] Since it is impossible to directly obtain the specific driver gene information of patients, this study, referencing existing individual-level cancer driver gene research, compared the performance of PHDriver and six comparative methods in identifying cohort-level cancer driver genes across five single-cancer datasets. Tables 3-4 show the mean AUC and mean AUPRC of each method in identifying single-cancer driver genes at the cohort level. PHDriver achieved the best performance on all five datasets. Its mean AUC values ​​reached 90.83%, 90.74%, 90.65%, 90.46%, and 91.57%, respectively, and its mean AUPRC values ​​were 82.93%, 84.20%, 84.28%, 84.59%, and 83.60%, respectively. All indicators were significantly higher than those of the comparative methods. The experimental results fully demonstrate the superiority and stability of PHDriver in identifying driver genes.

[0161] Table 3. Mean AUC for identifying single cancer driver genes at the cohort level

[0162]

[0163] Table 4. Average AUPRC of single-cancer driver genes identified at the cohort level.

[0164]

[0165] 7. Enrichment Analysis

[0166] In the individual-level prediction results, this example references existing research and uses a voting strategy to screen candidate cancer driver genes for each cancer type by summarizing the predicted scores of each patient's mutated genes. The Condorcet method compares candidates pairwise and selects the candidate that receives the most support in the majority vote as the winner. In this experiment, each patient is considered a voter, and the mutated genes in the top 50% of their predicted scores are considered as one vote for that patient, thus constructing a ranking list of candidate genes for each cancer type. Finally, the top 16 genes in each type are identified as candidate cancer driver genes. The specific list of candidate genes is shown in Table 5.

[0167] Table 5. Candidate cancer driver genes predicted by PHDriver

[0168]

[0169] To verify the biological importance of the candidate cancer driver genes predicted by PHDriver, this study performed GO and KEGG enrichment analyses on the candidate genes to reveal their enrichment characteristics at the functional and pathway levels. The specific enrichment analysis results are as follows:

[0170] (1) GO enrichment analysis

[0171] GO enrichment analysis results of BRCA candidate cancer driver genes are as follows: Figure 19 As shown in the figure, in terms of biological processes, the candidate genes are significantly enriched in processes such as cerebellar cortex formation, endoderm cell differentiation, regulation of axonal regeneration, ERK1 / 2 cascade reactions, placental vascular development, and Schwann cell development, suggesting that the candidate genes are widely involved in nervous system development, organ morphogenesis, and cell fate determination. In terms of cellular components, the candidate genes are significantly enriched in subcellular structures such as spindle polar bodies, early endosomes, late endosomes, focal adhesions, endoplasmic reticulum, centrosomes, Golgi apparatus, and mitochondria, indicating that the proteins encoded by the candidate genes are mostly located in key regions related to cell division, membrane transport, and energy metabolism. In terms of molecular function, the candidate genes are significantly enriched in functions such as MAP kinase scaffold activity, MAP kinase kinase activity, protein serine / threonine kinase activity, protein tyrosine kinase activity, calcium ion binding, and miRNA binding, further revealing the potential molecular mechanisms of the candidate genes in kinase signal transduction, second messenger regulation, and posttranscriptional modification. These enrichment features collectively suggest that BRCA candidate genes may play a potential driving role in tumorigenesis and progression by regulating development-related signaling pathways, kinase cascade reactions, and organelle functions.

[0172] GO enrichment analysis results of GBM candidate cancer driver genes are as follows: Figure 20As shown in the figure, in terms of biological processes, the candidate genes were significantly enriched in hypoxia detection, positive regulation of ferroptosis, regulation of intestinal lipid absorption and cholesterol metabolism, sphingomyelin and ceramide metabolism, anion transmembrane transport, and positive regulation of calcium ion transport, suggesting that the candidate genes are widely involved in cellular stress response, lipid metabolism reprogramming, and ion homeostasis maintenance. In terms of cellular components, the candidate genes were significantly enriched in multiple subcellular structures, including dense core vesicles, microvilli, postsynaptic specialized structures, U2 spliceosomes, perinuclear chromatin filaments, and the cell membrane, indicating that the candidate gene-encoded proteins are located in key regions related to signal transduction, RNA processing, and membrane transport. In terms of molecular function, the candidate genes were significantly enriched in ATP-gated cation channel activity, volume-sensitive anion channel activity, sphingomyelin phosphodiesterase activity, fatty acid ligase activity, estrogen-responsive element binding, and histone binding, further revealing the potential molecular mechanisms of the candidate genes in ion channel regulation, lipid metabolism enzyme activity, and epigenetic regulation. These enrichment features suggest that GBM candidate genes may play an important role in the development and progression of cancer by influencing tumor microenvironment perception, metabolic reprogramming, membrane signaling, and gene expression regulation.

[0173] GO enrichment analysis results of LIHC candidate cancer driver genes are as follows: Figure 21 As shown in the figure, in terms of biological processes, the candidate genes are mainly enriched in the regulation of voltage-gated sodium channel activity, membrane depolarization, muscle contraction, positive regulation of tumor necrosis factor production, negative regulation of the Hippo signaling pathway, regulation of the NF-κB signaling pathway, neuronal neurite extension, lipid metabolism, and vesicle-mediated transport, suggesting that the candidate genes are widely involved in signal transduction, cytoskeleton dynamics, and metabolic regulation. In terms of cellular components, the candidate genes are significantly enriched in membrane structures and organelles such as the plasma membrane, sarcolemma, Z-disc, mitochondrial membrane, endoplasmic reticulum membrane, cytoplasmic vesicles, M-band, and FAR / SIN / STRIPAK complex, indicating that the proteins encoded by the candidate genes are mostly located in the cell membrane or subcellular organelle membranes and may be involved in cell polarity, contraction, and intracellular transport. In terms of molecular function, the candidate genes are significantly enriched in calcium ion binding, phospholipid binding, protein tyrosine kinase activity, fibroblast growth factor receptor activity, NF-κB binding, protein-macromolecule adapter activity, and various transporter activities, further supporting the potential functions of the candidate genes in receptor signal transduction, ion homeostasis, and transmembrane transport. In summary, these enrichment features reveal that LIHC candidate genes may play a driving role in tumor cell proliferation, migration, invasion, and drug resistance by interfering with key pathways such as cell signal transduction, membrane transport, and metabolic homeostasis.

[0174] GO enrichment analysis results of PAAD candidate cancer driver genes are as follows: Figure 22As shown in the figure. In terms of biological processes, they are significantly enriched in mRNA processing, RNA splicing, telomere maintenance and regulation, and negative regulation of DNA recombination, indicating that candidate genes are widely involved in post-transcriptional regulation and genome stability maintenance. In terms of cellular components, they are significantly enriched in subcellular structures such as nuclear plaques, nucleoplasm, nuclear membrane, PML bodies, chromosome telomere regions, and mitochondrial matrix, with particularly prominent enrichment in nuclear plaques and nucleoplasm, suggesting that candidate gene-encoded proteins are mostly located in regions related to RNA metabolism and nuclear tissue. In terms of molecular function, they are significantly enriched in DNA binding, transcriptional regulatory region binding, RNA binding, and mRNA binding. 6 The enrichment features, including A-methyltransferase activity, DNA helicase activity, GTPase activity, and chromatin binding, further revealed the potential molecular mechanisms by which candidate genes play a role in transcriptional regulation, RNA modification, and chromatin remodeling. These enrichment characteristics collectively suggest that PAAD candidate genes may play a crucial driving role in tumor cell proliferation, immortalization, and gene expression dysregulation by regulating key processes such as RNA processing, telomere homeostasis, and chromatin structure.

[0175] GO enrichment analysis results of STAD candidate cancer driver genes are as follows: Figure 23 As shown in the figure, the candidate genes are significantly enriched in fatty acid metabolism and biosynthesis, long-chain fatty acid coenzyme A metabolism, receptor-mediated endocytosis, cell differentiation, spermatogenesis, and mesenchymal-epithelial transition, suggesting that they are widely involved in tumor-related pathways such as metabolic reprogramming, signal transduction, and cell fate determination. In terms of cellular components, they are significantly enriched in subcellular regions such as mitochondria, cytoplasm, mitochondrial matrix, lysosomal membrane, endocytic vesicle membrane, and ciliary structures, indicating that the proteins encoded by the candidate genes are mostly located in energy metabolism centers and membrane transport systems, and may play a key role in energy adaptation and material exchange in tumor cells. In terms of molecular function, they are significantly enriched in fatty acid coenzyme A ligase activity, scavenger receptor activity, nucleotide binding, sequence-specific DNA binding, and the activity of various amino acid metabolic enzymes, further supporting the potential molecular mechanisms of the candidate genes in lipid metabolism regulation, transcriptional regulation, and membrane recognition. These enrichment characteristics collectively suggest that the STAD candidate genes may play an important driving role in the development and evolution of cancer by regulating the metabolic reprogramming, membrane transport, and signal sensing capabilities of tumor cells.

[0176] (2) KEGG enrichment analysis

[0177] KEGG enrichment analysis results of BRCA candidate cancer driver genes are as follows: Figure 24As shown in the figure, the candidate genes were significantly enriched in various solid tumors and hematologic malignancies, including thyroid cancer, bladder cancer, melanoma, acute myeloid leukemia, glioma, chronic myeloid leukemia, non-small cell lung cancer, renal cell carcinoma, and endometrial cancer, further validating the broad association between the candidate genes and multiple cancer types. In terms of signal transduction pathways, they were significantly enriched in the HIF-1 signaling pathway, estrogen signaling pathway, FcεRI signaling pathway, cholinergic synapses, serotonergic synapses, and long-term enhancement / inhibition pathways, suggesting that the candidate genes are widely involved in hypoxia response, hormonal regulation, and neurotransmitter-mediated signal transduction. Furthermore, the significantly enriched pathways also included central carbon metabolism in cancer and resistance to EGFR tyrosine kinase inhibitors, indicating that the candidate genes may play a key role in tumor metabolic reprogramming and targeted drug resistance mechanisms. These results collectively suggest that BRCA candidate genes may play a potential driving role in tumorigenesis and progression by interfering with multiple cancer-related signaling pathways and metabolic networks.

[0178] The results of KEGG enrichment analysis of GBM candidate cancer driver genes are as follows: Figure 25 As shown in the figure, the enrichment of the taste transduction pathway was the most significant, suggesting that the candidate gene may influence tumor microenvironment perception by regulating taste receptor-related signals. The sphingolipid metabolism pathway was also significantly enriched, indicating that lipid metabolism reprogramming plays an important role in driving gene regulatory networks. Furthermore, the olfactory transduction pathway, the neuroactive ligand-receptor interaction pathway, and the endocytic pathway all showed some degree of enrichment, further supporting the candidate gene's broad involvement in cell membrane receptor signal transduction, extracellular stimulus response, and membrane transport processes. These results collectively reveal that the GBM candidate gene may play a potential driving role in tumor cell proliferation, migration, and microenvironment adaptation by interfering with key pathways such as cell metabolism, signal sensing, and endocytosis.

[0179] KEGG enrichment analysis results of LIHC candidate cancer driver genes are as follows: Figure 26 As shown in the figure, the enrichment of endocytosis pathway was the most significant, suggesting that candidate genes play an important role in cell membrane transport and receptor-mediated endocytosis. In addition, cholesterol metabolism and thyroid hormone synthesis pathways were also significantly enriched, indicating a potential link between lipid metabolism and hormone signaling in the driver gene regulatory network. Regarding cancer-specific pathways, enrichment was observed in melanoma, prostate cancer, breast cancer, and central carbon metabolism in cancer, further validating the direct correlation between candidate genes and multiple tumor types. Other significantly enriched pathways included ubiquitin-mediated proteolysis, cytochrome P450-related drug metabolism, and chemical carcinogenesis. These results collectively reveal that LIHC candidate genes are widely involved in malignant processes such as tumor cell proliferation, metabolic reprogramming, drug detoxification, and genomic instability.

[0180] KEGG enrichment analysis results of PAAD candidate cancer driver genes are as follows: Figure 27 As shown in the figure, the enrichment of the olfactory transduction pathway was the most significant, suggesting that the candidate gene may influence tumor microenvironment perception or cell migration behavior by regulating olfactory receptor-related signals. Regarding cancer-specific pathways, it was significantly enriched in various solid tumors and hematologic malignancies, including thyroid cancer, bladder cancer, melanoma, glioma, chronic myeloid leukemia, non-small cell lung cancer, endometrial cancer, pancreatic cancer, prostate cancer, breast cancer, colorectal cancer, and gastric cancer, further validating the broad association between the candidate gene and multiple cancer types. In addition, significantly enriched pathways also included central carbon metabolism in cancer, miRNAs in cancer, nerve growth factor signaling pathway, sphingolipid signaling pathway, and mitophagy, indicating that the candidate gene is widely involved in malignant processes such as metabolic reprogramming, epigenetic regulation, signal transduction, and cellular homeostasis maintenance in tumor cells. These results collectively suggest that the PAAD candidate gene may play a potential driving role in tumorigenesis and progression by interfering with multiple cancer-related signaling pathways and metabolic networks.

[0181] KEGG enrichment analysis results of STAD candidate cancer driver genes are as follows: Figure 28 As shown in the figure, the enrichment of fatty acid biosynthesis and fatty acid degradation pathways was the most significant, indicating that lipid metabolism reprogramming is a core biological process involving candidate genes. In addition, glycine, serine, and threonine metabolism, as well as one-carbon unit metabolism pathways, were also significantly enriched, suggesting that amino acid metabolism and one-carbon unit cycling play important roles in the driver gene regulatory network. Other significantly enriched pathways include GPI-anchored biosynthesis, Th17 cell differentiation, JAK-STAT signaling pathway, and mTOR signaling pathway. Although the enrichment levels were lower, these results further support the broad involvement of candidate genes in malignant processes such as tumor immune regulation, cell growth, and metabolic adaptation. These results collectively suggest that STAD candidate genes may play a potential driving role in tumorigenesis and progression by regulating fatty acid metabolism, amino acid metabolism, and key signaling pathways.

[0182] From a biological perspective, candidate genes from various cancer types are enriched in pathways closely related to their tumor characteristics: BRCA is enriched in the ERK1 / 2 cascade, MAP kinase activity, and developmental processes, consistent with the hormone signaling crossover and invasive phenotype of breast cancer; GBM is significantly enriched in hypoxia response, ferroptosis, and sphingolipid metabolism, reflecting glioblastoma's dependence on metabolic stress and microenvironment adaptation; LIHC involves Hippo, NF-κB, and voltage-gated channel activity, which play a key role in hepatocellular carcinoma metastasis and immune escape; PAAD is enriched in mRNA processing, telomere maintenance, and DNA helicase activity, suggesting significant genomic instability and abnormal post-transcriptional regulation in pancreatic cancer; STAD is concentrated in fatty acid metabolism, amino acid metabolism, and endocytosis, highly correlated with metabolic reprogramming and abnormal membrane transport in gastric cancer. At the molecular function and cellular component level, multiple cancer types are co-enriched in kinase activity, calcium ion binding, and membrane-bound organelles, indicating that candidate genes are widely involved in core cellular processes such as signal transduction, energy metabolism, and intracellular transport. KEGG pathway analysis further revealed that candidate genes for PAAD and BRCA were significantly enriched in the MAPK signaling pathway, while GBM and STAD were involved in sphingolipid signaling and fatty acid metabolism, respectively, which corroborates the above GO results.

[0183] In summary, the candidate driver genes predicted by PHDriver not only cover known core cancer pathways but also reveal multi-level synergistic mechanisms involving metabolic reprogramming, epigenetic regulation, and cellular stress responses. These results validate the biological rationale for PHDriver's identification of driver genes at the individual level from a functional annotation perspective and provide a referable list of candidate genes and pathway clues for subsequent molecular mechanism research targeting specific cancer types.

[0184] 8. Ablation test

[0185] To systematically evaluate the contributions of input features and model components to PHDriver, this example conducts ablation experiments at the cohort level using five cancer datasets. As shown in Tables 6-7, by systematically removing specific features from the feature enhancement matrices of genes and patients, and eliminating core modules from the PHDriver framework, and observing changes in average AUC and average AUPRC, the impact of each component on PHDriver performance is quantified.

[0186] The variant names in the ablation experiments are explained below. "Large-endian features only" means that only the latent feature portion of the gene and patient feature enhancement matrices is retained. Similarly, "Local embedding features only" means that only the location embedding feature portion of the gene and patient feature enhancement matrices is retained. "Gene-patient association only" means that the gene and patient location embedding features only consider gene-patient associations, and only gene-patient associations are considered in the HGNN module. Likewise, "No inter-gene associations" means that inter-gene associations are removed from the gene and patient location embedding features and also removed from the HGNN module, while "No inter-patient associations" means that inter-patient associations are removed from both the gene and patient location embedding features and the HGNN module. "No PMF" means that gene expression data is directly used as biofeedback instead of PMF to extract latent features of genes and patients. "GraphSAGE instead of GAT" means that a graph aggregation network (Graph SAmpleand aggreGatE, GraphSAGE) is used in the HGNN module instead of GAT to obtain node feature representation matrices in different edge type relationships. Ablation experiments showed that using PMF to extract potential features of genes and patients simultaneously, integrating gene-patient associations, gene-patient associations, and patient-patient associations to construct a gene-patient heterogeneity map, and fully preserving each module of the model, is crucial for improving the performance of PHDriver.

[0187] Table 6 Mean AUC of PHDriver Ablation Experiments

[0188]

[0189] Table 7. Mean AUPRC of PHDriver Ablation Experiments

[0190] .

Claims

1. A method for identifying individual-level cancer driver genes based on PMF and HGNN, characterized in that, Includes the following steps: 1) Extracting genes and potential patient characteristics: Patients and genes with both single nucleotide variant data and gene expression data were screened. After preprocessing the gene expression data of the screened patients, a gene expression matrix was obtained. Probabilistic matrix factorization (PMF) was used to decompose the matrix to obtain the gene latent feature matrix and the patient latent feature matrix. 2) Constructing a gene-patient heterogeneous graph and generating an enhanced feature matrix: Using genes and patients as nodes, we construct links between genes based on a protein-protein interaction (PPI) network, links between patients based on the similarity of their latent features, and gene-patient links based on gene mutations and abnormal expression events. These links form a gene-patient undirected heterogeneous graph. We perform a random walk with node type constraints on this heterogeneous graph to generate sequences, and generate gene and patient location embedding matrices using a Skip-gram model. We concatenate the gene latent feature matrix and the gene location embedding matrix to obtain the gene enhanced feature matrix, and concatenate the patient latent feature matrix and the patient location embedding matrix to obtain the patient enhanced feature matrix. 3) Train the heterogeneous graph neural network (HGNN) model and make predictions: Input the gene enhancement feature matrix and the patient enhancement feature matrix into the HGNN model, and perform feature aggregation and updates on different types of edges through a multi-layer heterogeneous message passing module. Finally, output the cancer driver gene prediction results at the individual patient level.

2. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 1, characterized in that, The preprocessing in step 1) includes standardization and setting an abnormal expression threshold: The data for each gene in the gene expression data were standardized separately, that is, the standard score of each gene in each sample was calculated. The specific calculation is expressed as shown in Formula 1: (1) in, Indicates gene In patients The expression value on and They represent genes respectively. The mean expression value and standard deviation; to identify abnormally expressed genes in each patient, an abnormal expression threshold was set for each gene. The specific calculation is expressed in Formula 2: (2) in, and They represent genes respectively. At the 95th and 5th percentiles of the standardized expression values, by taking and The smaller of the two absolute values ​​is used as a threshold to capture values ​​indicating significantly high or low gene expression. In patients Standardized expression values ​​in Greater than Then determine the gene In patients Abnormal expression in Chinese.

3. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 1, characterized in that, The matrix decomposition process using Probabilistic Matrix Factorization (PMF) in step 1) is as follows: The preprocessed gene expression matrix... It approximates a Gaussian distribution, where Represents a gene set. Represent the patient set; decompose using the PMF algorithm. Obtain the gene latent feature matrix Patient latent feature matrix d represents the potential feature dimension, and preliminary modeling is performed to establish the biological association between genes and patients.

4. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 3, characterized in that, The three types of association edge construction rules for the gene-patient undirected heterogeneous graph in step 2) are as follows: Gene-gene association edges: Based on the PPI network, interactions with a confidence level of at least 0.65 are retained as gene-gene association edges. Using gene sets Genes in the data are used as nodes and gene-gene association edges. The gene association subgraph is constructed, and the adjacency matrix of the gene association subgraph is formed. As shown in Formula 3: (3) Patient-to-patient association edges: Calculate the Pearson correlation coefficient of the latent feature vectors of patients, and retain patient pairs with a correlation coefficient of not less than 0.9 as patient-to-patient association edges. Patient pooling The patient is treated as a node and associated with a patient-patient edge. The patient-to-patient relationship subgraph is constructed, and the adjacency matrix of the patient-to-patient relationship subgraph is formed. As shown in Formula 4: (4) Gene-patient association edge: If a gene is mutated or abnormally expressed in the corresponding patient, a gene-patient association edge is established. Using gene sets Genes and patient sets The patient is treated as a node and associated with the gene-patient edge. The gene-patient association subgraph is composed of the adjacency matrix of the gene-patient association subgraph. As shown in Formula 5: (5)。 5. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 1, characterized in that, The random walk rule for node type constraints in step 2) is as follows: the walk starts from a gene node. If the current node is a gene node, the next node is randomly selected from the gene or patient neighbors of that node; if the current node is a patient node, the next node is randomly selected only from the gene neighbors of that node, ensuring that the walk path propagates alternately between the two types of nodes. An embedding learning process is performed on the walk sequence using a Skip-gram model to obtain a 16-dimensional gene position embedding matrix. Embedded matrix with patient location .

6. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 1, characterized in that, The enhanced feature matrix in step 2) is generated by concatenating the gene latent feature matrix and the gene location embedding matrix along the feature dimension to obtain the gene enhanced feature matrix, as shown in Formula 6: (6) The patient latent feature matrix and the patient location embedding matrix are concatenated along the feature dimension to obtain the patient enhanced feature matrix, as shown in Equation 7: (7)。 7. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 1, characterized in that, The HGNN model described in step 3) consists of three cascaded HGNN modules. The processing procedure for each HGNN module is as follows: For four types of edge relationships—gene-to-gene, gene-to-patient, patient-to-gene, and patient-to-patient—an independent graph attention network (GAT) submodule is used for message passing to obtain the message matrix for the corresponding edge type. For gene nodes, aggregate the associations between genes and the patient-gene associations to obtain gene aggregation messages; For patient nodes, aggregate patient aggregate messages by aggregating messages related to relationships between patients and gene-patient relationships; By introducing residual connections and the ReLU activation function, node feature updates are completed. The specific definitions of the node feature update operation are shown in Equations 8 and 9. (8) (9) in, This represents the output feature matrix updated by the gene node in HGNN module k. This represents the output feature matrix updated by the patient node in HGNN module k. and Let represent the learnable weight matrix and bias vector, respectively.

8. The method for identifying individual-level cancer driver genes based on PMF and HGNN according to claim 7, characterized in that, In step 3), the HGNN model ultimately converts the real-valued output into probability values ​​using the Sigmoid function, resulting in the final prediction structure. As shown in Formula 10: (10) in, The Sigmoid activation function is used, and the binary cross-entropy is used as the loss function, as shown in Equation 11: (11) in, Indicates gene The true label, Indicates gene The prediction results.

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