Protein function prediction method based on multi-modal fusion and dynamic label network

Abstract

The invention discloses a protein function prediction method based on multi-modal fusion and a dynamic label network, and belongs to the technical field of biological information, an adjacent matrix of a label association network can be smoothly updated in a model training process, and the protein function prediction method can be used for predicting protein functions by extracting various modal information of protein. The redundant relation among multiple modes is removed, the prediction effect of protein functions is improved, meanwhile, a training method combining a protein function association network and a tag association network is used, the influence of multiple tags on protein function prediction is considered, and protein function prediction is achieved by fusing the sequence, structure and structural domain information of protein. According to the method, the complementarity of various data is fully utilized, so that the prediction capability of the model is improved, and compared with a traditional method using a static label relationship, the scheme dynamically updates the label relationship in model training, so that the generalization capability of the model is further improved.

Description

Technical Field

[0001] This invention belongs to the field of bioinformatics technology, specifically relating to a protein function prediction method based on multimodal fusion and dynamic tagging networks. Background Technology

[0002] Protein function prediction is one of the core tasks in the field of bioinformatics. Accurately identifying protein functions is of great significance for revealing biological processes, disease mechanisms, and new drug development.

[0003] However, due to the complexity of protein function and the scarcity of data annotation, traditional prediction methods have the following drawbacks.

[0004] 1. Multimodal fusion methods simply splice features, ignoring the relationships between different modalities. While post-processing ensures that the prediction results conform to the hierarchical relationship between labels, the lack of explicit modeling of the correlation between multiple labels can lead to some related labels not being accurately predicted.

[0005] 2. Existing protein association networks and tag association networks are usually statically constructed based on prior data or statistical methods. However, this limits the model's predictive power and generalization ability. If there is noise or bias in the data, the model's predictive performance will deteriorate. Summary of the Invention

[0006] To address the problems mentioned in the background art, this invention provides a protein function prediction method based on multimodal fusion and dynamic tag network, which solves the problems of insufficient accuracy, weak generalization ability, and failure to fully utilize tag co-occurrence and hierarchical relationships in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A protein function prediction method based on multimodal fusion and dynamic tagging networks includes the following steps:

[0009] S1: Construct a tag association network; build a tag co-occurrence matrix based on tags with known protein functions, calculate a tag similarity matrix by combining tag hierarchical relationships, and then weight and fuse the tag co-occurrence matrix and tag similarity matrix to obtain the tag association network G. f adjacency matrix W f Simultaneously, a protein function association network G was constructed. p It is used to characterize the functional similarity between proteins;

[0010] S2: Extract multimodal features of proteins; extract domain features, sequence features and structural features of proteins respectively. Domain features are obtained based on domain identification and embedding calculation, sequence features are obtained based on residue feature construction, sequence encoding and attention weighting, and structural features are obtained based on the protein three-dimensional structure residue map and then learning and pooling through graph neural network.

[0011] S3: Construct the model and combine it with the label association network G f Predicting protein function, specifically:

[0012] S31: Construct a prediction model; the prediction model includes a shared feature extraction network for extracting common information across modalities, a private feature extraction network for extracting unique information for each modality, and a function prediction network for outputting function prediction results;

[0013] S32: Multimodal feature fusion; The prediction model uses a shared-private representation learning method to fuse the multimodal features obtained from S2, and adds regularization constraints to reduce information redundancy between modalities to obtain protein representation;

[0014] S33: Model training optimization; based on protein functional association network G p A total loss function with multi-dimensional loss terms is constructed, and the model parameters of the prediction model are optimized with the goal of minimizing the total loss. During training, the label association network G is dynamically updated based on the current prediction results. f adjacency matrix W f ;

[0015] S34: Functional prediction; Input the multimodal features of the protein to be predicted into the optimized prediction model and output the protein function prediction results.

[0016] Preferably, in S1, the specific method for constructing the tag co-occurrence matrix is ​​as follows: construct a protein-tag binary tag matrix based on the known functional tags of the protein samples, where a value of 1 in the matrix element indicates that the corresponding protein has the functional tag, and a value of 0 indicates that it does not have the functional tag; calculate the tag co-occurrence matrix based on the binary tag matrix, and normalize the tag co-occurrence matrix to obtain the tag co-occurrence matrix.

[0017] Preferably, the formula for calculating the tag co-occurrence matrix is: ;

[0018] Where Y is the protein-tag binary label matrix, p represents a single protein, and f a f b Each represents a different functional label, C(f) a ,f b ) for label f a with f b The number of times they co-occur;

[0019] The normalization formula is: .

[0020] Preferably, in S1, the label hierarchy is as follows: In the gene ontology GO, the labels are organized in a hierarchical relationship using a directed acyclic graph (DAG).

[0021] When calculating the label similarity matrix, the shortest path length between terms in the DAG is used as the basis. A Gaussian kernel function is then used to calculate the label similarity, resulting in the label similarity matrix. The formula for the Gaussian kernel function is:

[0022] ;

[0023] Where d(f) a ,f b ) represents the shortest path length, and σ is the smoothing parameter;

[0024] The adjacency matrix is ​​represented as:

[0025] ;

[0026] Where λ is a hyperparameter.

[0027] Preferably, in S1, the protein function association network G p The construction method is as follows: the functional association degree between proteins is calculated based on protein sequence similarity or functional annotation similarity, and a protein functional association network is constructed with proteins as nodes and association degree as edge weights. Its adjacency matrix is ​​denoted as W. p W p (i,j) represents the functional association weight between protein i and protein j.

[0028] Preferably, in S2, the specific process for extracting domain features is as follows: The protein sequence is scanned using the InterProScan tool to identify the domains to which the protein belongs and represent them as a one-hot vector IPR. Then, the features are extracted using the formula... Computational domain embedding representation , The learningable embedding matrix yields the structural domain features;

[0029] The specific process for extracting sequence features is as follows: constructing a residue feature matrix based on the physicochemical properties of amino acids, the BLOSUM scoring matrix, and site conservation. The hidden layer output is obtained through bidirectional LSTM (Bi-LSTM) encoding. Calculate sequence-weighted features using a self-attention mechanism The global sequence features are then obtained by weighted averaging. .

[0030] Preferably, in S2, the specific process for extracting structural features is as follows: based on the three-dimensional structural information of proteins in the PDB library, using residues as nodes, and combining the initial features of the residues to construct initial node features. When constructing the residue map, if two residues p and q... Atomic Euclidean distance d pq If the value is less than 10 Å, an edge is added between the two nodes, and each residue is connected to its nearest predetermined number of residues. After updating the residue features through a graph neural network, the structural feature Z is obtained through pooling. str .

[0031] Preferably, in S32, the regularization constraints include private representation decorrelation constraints and shared-private representation separation constraints;

[0032] Private representation decorrelation constraints are implemented using the following formula:

[0033] ;

[0034] Where T is the matrix transpose. ⋅ Denotes the Frobenius norm;

[0035] The shared-private representation separation constraint is achieved through the following formula:

[0036] ;

[0037] Z sh To achieve cross-modal shared features, the output of the shared feature extraction network is calculated after weighted fusion of multimodal features.

[0038] Preferably, in S33, the total loss function includes the protein function association network regularization loss, the label association network regularization loss, and the supervision loss. The formula for the total loss function is:

[0039] ;

[0040] in, Z is the protein function prediction score vector. final Represented as a protein, by Z sh It is obtained by weighted fusion with the private representations of each modality. For monitoring loss, μ and λ are hyperparameters.

[0041] Preferably, L f The formula for calculating (F) is:

[0042] ;

[0043] Among them W p(i,j) represents the protein function association network G. p The edge weights of proteins i and j in the protein-function association network G, where n is the edge weight of protein i and j. p The number of proteins in the protein, K is the tag association network G. f The number of tags, D p The degree matrix in the protein function association network and , Let be the prediction score of the i-th protein for the k-th label;

[0044] L c The formula for calculating (F) is:

[0045] ;

[0046] Among them W f (u,v) represents the label association network G. f The edge weights of labels u and v, D f Let be the degree matrix in the label association network and , Let be the prediction score of the i-th protein for the u-th label. Let be the prediction score of the j-th protein for the v-th tag.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] This invention proposes a protein function prediction method based on multimodal fusion and dynamic label association network. The adjacency matrix of the label association network in this application is smoothly updated during model training. Furthermore, this application improves the prediction effect of protein function by extracting multimodal information of proteins and removing redundant relationships between multiple modalities. At the same time, it uses a training method that combines protein function association network and label association network, taking into account the impact of multiple labels on protein function prediction. By fusing protein sequence, structure and domain information, it makes full use of the complementarity of various types of data, thereby improving the model's prediction ability. Compared with traditional methods that use static label relationships, this solution dynamically updates label relationships during model training, further improving the model's generalization ability. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the process of this application;

[0050] Figure 2 This is a flowchart illustrating the multimodal feature extraction stage of this application;

[0051] Figure 3 This is a flowchart illustrating the feature fusion and functional prediction stages of this application. Detailed Implementation

[0052] To facilitate understanding of the technical content of this invention by those skilled in the art, the invention will be further described in detail below with reference to the accompanying drawings and specific examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the scope of the invention.

[0053] This embodiment proposes a protein function prediction method based on multimodal fusion and dynamic tag association network. This method first utilizes the STRING database to construct a protein function association network G. p Its adjacency matrix is ​​W p The Gene Ontology (GO) database was used to obtain GO terms and their hierarchical relationships. The frequency of protein-shared tags was statistically analyzed using a tag co-occurrence matrix to statically initialize the tag association network G. f adjacency matrix W f During the training process, W f By employing a smooth dynamic update mechanism and fusing model prediction information, the network structure is gradually optimized to improve the model's generalization ability and accuracy. Specifically:

[0054] 1. Construct a tag association network based on the tag co-occurrence matrix and tag hierarchy;

[0055] In order to fully consider the relationships between tags in protein function prediction, this approach constructs a tag association network to explicitly model the potential relationships between tags.

[0056] Step 1: Calculate the label co-occurrence matrix C;

[0057] In protein function prediction tasks, certain labels often appear simultaneously in the annotations of the same protein; that is, if two labels f a and f b If tags frequently appear in different protein tag sets, they may have a strong correlation.

[0058] Let Y be a protein-tag binary label matrix, where Y p,f =1 indicates that protein p has tag f, otherwise it is 0.

[0059] ;

[0060] in, Represents the tag f a and f b The number of times a protein co-occurs on the same protein.

[0061] Since the annotation frequencies of different labels may vary significantly, we normalize the co-occurrence matrix to make the weight distribution more even and prevent high-frequency categories from dominating the entire network.

[0062] ;

[0063] This represents the normalized structure. The formula is similar to cosine similarity, which controls the numerical range between [0,1].

[0064] Step 2: Construct a tag association network by combining the tag hierarchy;

[0065] Gene Ontology (GO) provides a hierarchical way of organizing label relationships. The hierarchical relationships between GO terms are generally organized through a directed acyclic graph (DAG), which defines the inheritance, inclusion, and similarity relationships between labels.

[0066] Let the path length between GO term tags be d(f) a ,f b ), that is, from the term f a to f b The shortest path in a DAG.

[0067] Similarity is calculated using the Gaussian kernel function:

[0068] ;

[0069] Where σ is a smoothing parameter that controls the degree of similarity decay.

[0070] Step 3: Construct the adjacency matrix W of the final label association network by combining the label co-occurrence matrix and GO relations. f ;

[0071] Will and Perform weighted fusion:

[0072] ;

[0073] Wherein, λ is a hyperparameter that controls the weight ratio between co-occurrence information and hierarchical information.

[0074] Tag co-occurrence matrix It primarily utilizes statistical co-occurrence information to reflect data-driven similarity of protein functions and GO hierarchical relationships. By defining it using biological knowledge, the prior structural information of protein function is captured.

[0075] By using weighted fusion, combining statistical data with biological knowledge, a more reasonable label association network is constructed.

[0076] 2. Protein multimodal feature extraction;

[0077] This scheme employs shared-private representation learning for multimodal fusion, combining domain information, protein 3D structure, and sequence information to improve the multi-label prediction capability of protein function.

[0078] Step 1: Extract structural domain feature information;

[0079] In protein function prediction, domain information is a crucial feature because protein function is often determined by its domains. A domain is a self-contained folded unit within a protein, typically responsible for performing a specific biological function. For example, a protein may contain multiple domains, each responsible for a different function, such as catalysis, binding, or signal transduction. Therefore, incorporating domain features helps improve the accuracy and generalization of function prediction.

[0080] This method uses InterProScan to scan protein sequences, identify the corresponding protein domains, and represent the results as one-hot vectors. , where m is the total number of possible domains in the InterPro database. If a protein contains a domain, the corresponding position is set to 1; otherwise, it is set to 0.

[0081] Next, the structure domain embedding is computed using a learnable embedding matrix:

[0082] ;

[0083] in It is a representation of protein domain embedding. It is a learnable embedding matrix. This represents the dimension after mapping IPR.

[0084] Step 2: Extract protein sequence feature information;

[0085] First, an initial residue feature matrix of the protein sequence is constructed using information such as amino acid physicochemical properties (e.g., hydrophobicity, charge), BLOSUM score matrix, and site conservation. Where L is the protein sequence length, i.e., the number of residues. The feature dimension for each residue.

[0086] Next, a bidirectional LSTM (Bi-LSTM) is used to encode the sequence:

[0087] ;

[0088] in, It is the hidden layer output of Bi-LSTM. This represents the dimension of each residue after bidirectional LSTM.

[0089] Traditional methods typically employ pooling (such as average pooling or max pooling) to obtain global sequence features, while this approach uses a self-attention mechanism to acquire information about the most functionally critical residues in the protein sequence:

[0090] ;

[0091] ;

[0092] in, For learnable parameters, Attention weights represent the correlation between different positions in a sequence. As a weighted feature representation of the sequence.

[0093] Finally, we calculate the global sequence features using a weighted average. :

[0094] ;

[0095] in, This represents the characteristic representation of the o-th amino acid in a protein sequence. In this way, we avoid the information loss that pooling may cause and retain the information of key residues.

[0096] Step 3: Extract protein structural feature information;

[0097] In this approach, the third modality (protein structure information) constructs a protein structure map using residues as nodes and defines edges based on the distances between residues. The introduction of structural information captures the spatial topological relationships of proteins, providing three-dimensional folding characteristics that sequence information cannot reveal, thereby improving the accuracy of protein function prediction.

[0098] The 3D structure information of proteins is obtained from the PDB library. For each protein, we construct a residue-level graph. The features of each initial node are represented as follows: ,in Representing geometric features, it consists of the three-dimensional coordinates of the residues. This represents the initial residue feature matrix in the second step, where \ indicates the splicing operation.

[0099] If the two residues p and q are... Atomic Euclidean distance d pq If the distance is less than 10 Å, an edge is added between node p and node q. To ensure graph connectivity, each residue is connected to its nearest kn residues.

[0100] For each edge (p, q), the edge's eigenvector e pq It can be represented as , where dpq Represented as residues Atomic Euclidean distance:

[0101] ;

[0102] in Distance formula, and These represent the three-dimensional coordinates of the p-th and q-th residues, respectively.

[0103] This is represented as the following direction information:

[0104] ;

[0105] After constructing the structural diagram, this scheme uses a graph neural network to update the residue features. In each layer of the GNN calculation, the feature h of residue p is updated. p It will be updated based on the information of neighboring nodes:

[0106] ;

[0107] W1, W2, W3 are learnable parameters, Z p It is a normalization factor expressed in terms of p-node degree, where N(p) is the neighbor of residue p, where , This represents the initial characteristics of the p-th residue.

[0108] Finally, pooling layers are used to obtain the structural features of the protein:

[0109] ;

[0110] Where L represents the number of residues. This represents the last layer of the graph network. , Dimensions representing the structural features of proteins.

[0111] 3. Protein function prediction using joint tag association networks;

[0112] Firstly, to avoid redundant information among multiple modalities, which could lead to inaccurate predictions, this scheme employs a multimodal fusion method based on shared-private representation learning to extract common information across modalities. A shared space is introduced, projecting all modalities onto the same common representation. .

[0113] ;

[0114] This method uses cross-modal feature fusion, first mapping the dimensions of different modal features uniformly, where... Then sum them up, and then extract the shared features using MLP. .

[0115] Then through a private coding network Extract the private information for each modality:

[0116] ;

[0117] ;

[0118] ;

[0119] Final protein representation It is obtained by fusing private and shared representations:

[0120] ;

[0121] in , , These are learnable parameters used to control the contribution of the private representation to the final fused features.

[0122] To further strengthen the decoupling of shared and private information, two regularization terms are added:

[0123] Decorrelation constraints on private representations:

[0124] ;

[0125] in The purpose of representing the Frobenius norm is to make the private representations of different modalities orthogonal, thereby reducing redundant information.

[0126] Separation of shared and private representations:

[0127] ;

[0128] The goal is to make shared representations and private representations as different as possible.

[0129] Next, we performed protein function prediction.

[0130] ;

[0131] Where F represents the protein functional prediction score vector, and here, F is defined as follows: i k denoted as the predicted score for the k-th function of the i-th protein.

[0132] For multi-label prediction tasks, in order to capture the correlation between functional labels, this invention introduces the label association network G constructed in this scheme. f .

[0133] Therefore, the total loss function of the model is:

[0134] ;

[0135] in Represented as a protein-function association network G p Regularization ensures the consistency of protein labels on the STRING network. µ and λ represent hyperparameters that control the importance of different loss terms. Represented as label association network G f Regularization ensures that the relationships between tags are utilized. This is represented as supervised loss, ensuring that the prediction results conform to the known labels. This is a loss during the modal fusion stage.

[0136] ;

[0137] Among them W p (i,j) represents the edge weight between protein i and protein j in the protein function association network, n represents the number of proteins in the protein function association network, K represents the number of labels in the label association network, and D p For degree matrix, The goal of this loss function is to ensure that proteins i and j with similar biological functions have as similar predicted labels as possible.

[0138] ;

[0139] Among them W f (u,v) represents the edge weight between labels u and v in the label association network, D f For degree matrix, This loss function ensures that if labels u and v are closely related, then the predicted value of protein i for label u should be close to the predicted value of protein j for label v.

[0140] ;

[0141] Where Y represents the known protein-function label matrix (the label indicating whether a protein has a certain label). This loss term ensures that the model-learned F is as close as possible to the true label.

[0142] During the training process, W f It's not fixed, but rather it continuously optimizes as the model's predictions evolve:

[0143] ;

[0144] in Let be the adjacency matrix of the label association network during training round t. The category similarity matrix is ​​calculated based on the current predictions of the model, and α controls the smoothness of the dynamic updates.

[0145] In this way, the model not only utilizes static prior knowledge (label co-occurrence information + label hierarchical relationship) during training, but also dynamically adjusts the weights between labels to make them more consistent with the actual protein functional distribution.

Claims

1. A protein function prediction method based on multimodal fusion and dynamic tagging network, characterized in that, Includes the following steps: S1: Construct a tag association network; build a tag co-occurrence matrix based on tags with known protein functions, calculate a tag similarity matrix by combining tag hierarchical relationships, and then weight and fuse the tag co-occurrence matrix and tag similarity matrix to obtain the tag association network G. f adjacency matrix W f Simultaneously, a protein function association network G was constructed. p It is used to characterize the functional similarity between proteins; S2: Extracting multimodal features of proteins; The domain features, sequence features, and structural features of the protein were extracted respectively. The domain features were obtained based on domain identification and embedding calculation, the sequence features were obtained based on residue feature construction, sequence encoding, and attention weighting, and the structural features were obtained based on the residue map constructed from the three-dimensional protein structure and then learned and pooled by graph neural network. S3: Construct the model and combine it with the label association network G f Predicting protein function, specifically: S31: Construct a prediction model; the prediction model includes a shared feature extraction network for extracting common information across modalities, a private feature extraction network for extracting unique information for each modality, and a function prediction network for outputting function prediction results; S32: Multimodal feature fusion; The prediction model uses a shared-private representation learning method to fuse multimodal features obtained from S2, and adds regularization constraints to reduce information redundancy between modalities to obtain protein representations; S33: Model training optimization; based on protein functional association network G p A total loss function with multi-dimensional loss terms is constructed, and the model parameters of the prediction model are optimized with the goal of minimizing the total loss. During training, the label association network G is dynamically updated based on the current prediction results. f adjacency matrix W f ; S34: Functional prediction; Input the multimodal features of the protein to be predicted into the optimized prediction model and output the protein function prediction results.

2. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 1, characterized in that, In S1, the specific method for constructing the tag co-occurrence matrix is ​​as follows: construct a protein-tag binary tag matrix based on the known functional tags of the protein samples, where a value of 1 in the matrix element indicates that the corresponding protein has the functional tag, and a value of 0 indicates that it does not have the functional tag; calculate the tag co-occurrence matrix based on the binary tag matrix, and normalize the tag co-occurrence matrix to obtain the tag co-occurrence matrix.

3. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 2, characterized in that, The formula for calculating the tag co-occurrence matrix is: ； Where Y is the protein-tag binary label matrix, p represents a single protein, and f a f b Each represents a different functional label, C(f) a ,f b ) for label f a with f b The number of times they co-occur; The normalization formula is: 。 4. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 3, characterized in that, In S1, the label hierarchy is as follows: In the gene ontology GO, the labels are organized in a hierarchical relationship using a directed acyclic graph (DAG). When calculating the label similarity matrix, the shortest path length between terms in the DAG is used as the basis. A Gaussian kernel function is then used to calculate the label similarity, resulting in the label similarity matrix. The formula for the Gaussian kernel function is: ； Where d(f) a ,f b ) represents the shortest path length, and σ is the smoothing parameter; The adjacency matrix is ​​represented as: ； in, This is a hyperparameter.

5. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 4, characterized in that, In S1, the protein function association network G p The construction method is as follows: the functional association degree between proteins is calculated based on protein sequence similarity or functional annotation similarity, and a protein functional association network is constructed with proteins as nodes and association degree as edge weights. Its adjacency matrix is ​​denoted as W. p W p (i,j) represents the functional association weight between protein i and protein j.

6. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 5, characterized in that, In S2, the specific process for extracting domain features is as follows: the InterProScan tool is used to scan the protein sequence, identify the domains to which the protein belongs, and represent them as one-hot vectors. Then through the formula Computational domain embedding representation , The learningable embedding matrix yields the structural domain features; The specific process for extracting sequence features is as follows: constructing a residue feature matrix based on the physicochemical properties of amino acids, the BLOSUM scoring matrix, and site conservation. The hidden layer output is obtained through bidirectional LSTM (Bi-LSTM) encoding. Calculate sequence-weighted features using a self-attention mechanism The global sequence features are then obtained by weighted averaging. .

7. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 6, characterized in that, In S2, the specific process for extracting structural features is as follows: Based on the three-dimensional structural information of proteins in the PDB library, initial features of nodes are constructed using residues as nodes and combined with the initial features of residues. When constructing the residue graph, if two residues p and q... Atomic Euclidean distance d pq If the value is less than 10 Å, an edge is added between the two nodes, and each residue is connected to its nearest predetermined number of residues. After updating the residue features through a graph neural network, the structural feature Z is obtained through pooling. str .

8. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 7, characterized in that, In S32, regularization constraints include private representation decorrelation constraints and shared-private representation separation constraints; Private representation decorrelation constraints are implemented using the following formula: ； Where T is the matrix transpose. ⋅ Denotes the Frobenius norm; The shared-private representation separation constraint is achieved through the following formula: ； Z sh To achieve cross-modal shared features, the output of the shared feature extraction network is calculated after weighted fusion of multimodal features.

9. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 8, characterized in that, In S33, the total loss function includes the protein function association network regularization loss, the label association network regularization loss, and the supervision loss. The formula for the total loss function is: ； in, Z is the protein function prediction score vector. final Represented as a protein, by Z sh It is obtained by weighted fusion with the private representations of each modality. For monitoring loss, μ and λ are hyperparameters.

10. The protein function prediction method based on multimodal fusion and dynamic tagging network according to claim 9, characterized in that, L f The formula for calculating (F) is: ； Among them W p (i,j) represents the protein function association network G. p The edge weights of proteins i and j in the protein-function association network G, where n is the edge weight of protein i and j. p The number of proteins in the protein, K is the tag association network G. f The number of tags, D p The degree matrix in the protein function association network and , Let be the prediction score of the i-th protein for the k-th label; L c The formula for calculating (F) is: ； Among them W f (u,v) represents the label association network G. f The edge weights of labels u and v, D f Let be the degree matrix in the label association network and , Let be the prediction score of the i-th protein for the u-th label. Let be the prediction score of the j-th protein for the v-th tag.

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