A protein classification method based on an interpretable dimensional graph neural network

Abstract

The application discloses a protein classification method based on an interpretable dimension graph neural network, obtains an adjacency symmetric matrix based on graph data of a protein molecule; estimates a node representation vector dimension of a protein graph structure by using the adjacency matrix as an optimal estimation dimension, and constructs a candidate set of the optimal estimation dimension; trains an interpretable dimension graph neural network model based on the candidate set of the optimal estimation dimension, and in the training, the protein graph structure is embedded into the best fitting dimension; and performs a protein classification task based on the trained graph neural network model to obtain a predicted type of the protein. The application is used for solving the problem that the existing method ignores dimension estimation, resulting in poor protein classification accuracy and low efficiency.

Description

Technical Field

[0001] This invention belongs to the field of protein classification technology, and in particular relates to a protein classification method based on an interpretable dimensional graph neural network. Background Technology

[0002] Graph data, composed of nodes and edges, provides a unified modeling approach for various systems in the real world. To address the challenge of directly applying vector-based machine learning algorithms to graph data, graph representation learning techniques (also known as graph representation learning) have emerged, mapping graph data to vectorized representations (also called embedded vectors). In recent years, graph neural networks (GNNs) have become the mainstream method for graph representation learning.

[0003] Protein molecules are composed of amino acids through a process of "dehydration condensation," which can be naturally represented by graphical data.

[0004] Existing protein classification methods, while employing graph neural networks (GNNs), fail to consider the dimensionality issue. They neither embed the protein graph structure into a uniform dimension nor use different graph representation dimensions for proteins with different topological structures, resulting in suboptimal embedding results. Representation dimension, as a hyperparameter, significantly impacts the performance of GNN models: too low a dimension reduces model performance, while too high a dimension leads to overfitting and increases model parameters and complexity.

[0005] For the dimensionality estimation problem, current graph neural network (GNN) training schemes generally treat dimension as a hyperparameter, tuning it based on domain knowledge or experience. This typically involves training multiple GNN models with different dimensions using grid search or exhaustive methods to determine the optimal embedding dimension. Heuristic dimension selection methods like grid search require significant time and computational resources and often fail to yield the optimal representation dimension, resulting in poor GNN training performance. For example, grid search enumerates dimensions at intervals of N, but cannot precisely find the optimal dimension within that interval; while exhaustive search can provide an accurate optimal dimension, this method lacks theoretical basis, and the resulting optimal dimension is not interpretable. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a protein classification method based on an interpretable dimensional graph neural network, which solves the problem that existing methods neglect dimensionality estimation, resulting in poor protein classification accuracy and low efficiency.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a protein classification method based on an interpretable dimensional graph neural network, comprising the following steps:

[0008] S10, Obtain the adjacency symmetric matrix from the graph data of protein molecules;

[0009] S20, the node representation vector dimension of the protein graph structure is estimated based on the adjacency matrix, and used as the optimal estimation dimension;

[0010] S30, obtain the candidate set of the optimal estimation dimension based on the optimal estimation dimension;

[0011] S40, based on the candidate set of the optimal estimated dimension, trains the interpretable dimension graph neural network model, in which the protein graph structure is embedded into the best-fit dimension during training.

[0012] S50 performs a protein classification task based on a trained graph neural network model to obtain the predicted protein type.

[0013] Furthermore, in step S10, the nodes of the graph structure in the graph data represent amino acids, and the edges of the graph structure represent chemical bonds between amino acids; the adjacency matrix corresponding to the chemical bonds between amino acids is obtained from the graph data of the protein molecule.

[0014] Here, the adjacency matrix A is an N*N two-dimensional array used to represent the protein graph structure, where N is the number of amino acids in the protein.

[0015] Furthermore, in S20, estimating the node representation vector dimension of the protein graph structure based on the adjacency matrix as the estimation dimension includes the following steps:

[0016] S21, define the attribute entropy as a measure of the uncertainty of the properties of protein graph structural nodes. The attribute entropy is calculated from the number of amino acids and the vector dimension of the amino acids.

[0017] S22, find the multi-order adjacency matrix of the protein adjacency matrix;

[0018] S23, perform graph Laplace normalization on the multi-order adjacency matrix;

[0019] S24, calculates the structural entropy that measures the global and local uncertainties of the amino acid diagram;

[0020] S25, Calculate the relative probability p based on the structural entropy. i , which serves as a weighting coefficient when fusing adjacency matrices of different orders;

[0021] S26, fusion of adjacency matrices and degree diagonal matrices of protein graph structures at various orders;

[0022] S27. Calculate the higher-order structural entropy of the protein graph structure using the fused adjacency matrix.

[0023] S28, obtain the estimated dimension based on the higher-order structural entropy and attribute entropy.

[0024] Furthermore, in step S22, the multi-order adjacency matrix of the protein adjacency matrix includes...

[0025]

[0026] The first-order, second-order, and third-order adjacency matrix structures of the graph were measured respectively, indicating whether amino acids can be connected to each other through paths of length one, two, and three chemical bonds, respectively.

[0027] A+I adds an amino acid to its own chemical bond in the representation of the original structure.

[0028] Furthermore, in step S23, graph Laplace normalization is performed on the multi-order adjacency matrix;

[0029] get:

[0030] in, D is a diagonal matrix of degree for each order of adjacency matrix. i The degree diagonal matrix of the normalized adjacency matrices of each order The defined D i [u][v] represents the information passed from amino acid u to amino acid v in the GNN model.

[0031] Furthermore, in step S24, the structural entropy, which measures the global and local uncertainties of the amino acid graph structure, is calculated;

[0032] The structural entropy is:

[0033] in, It is a coding tree, g α Defined as D i [u][v] sums the values ​​of nodes not in the subtree rooted at α, and v sums the values ​​of nodes in the subtree rooted at α. vol(α) represents the sum of the degrees of all nodes in the subtree rooted at α, and γ is the root node.

[0034] Furthermore, in step S25, the relative probability p i for:

[0035]

[0036] In step S26, the adjacency matrices and degree diagonal matrices of the protein graph structure are fused to obtain...

[0037] in

[0038] Furthermore, the higher-order structural entropy of the protein diagram is calculated:

[0039] The estimated dimension is obtained from the higher-order structural entropy and property entropy: the estimated amino acid representation vector dimension d is given by the inequality. It is confirmed that the formula is the attribute entropy H. Att ≈logN 2 -0.24d and structural entropy The sum of the values ​​is less than or equal to the intrinsic entropy of the graph, which is a sufficient condition.

[0040] Furthermore, in step S30, clustering is performed based on the optimal estimated dimension. Graphs from different clusters are embedded into different dimensions in the last graph convolutional layer of the GNN to obtain a candidate set of the optimal estimated dimension, including the following steps:

[0041] K-means clustering with K=1 is performed on the optimal dimension of all protein graph structures to obtain the cluster center value C0;

[0042] K-means clustering with K=k cluster numbers is performed on the optimal dimension of all protein graph structures to obtain cluster center values ​​C1, C2, ..., C k These central values ​​constitute a candidate set for the optimal estimated dimension;

[0043] Assign a C to each protein graph structure Gi, based on its cluster. i value.

[0044] Furthermore, in step S40, based on the candidate set of optimal estimated dimensions, the interpretable dimensional graph neural network model is trained, during which the protein graph structure is embedded into the best-fit dimension, including the following steps:

[0045] Train an interpretable dimensional graph neural network model based on a candidate set of optimally estimated dimensions;

[0046] In the explained dimensional graph neural network model, all graph convolutional layers except the last one have a unified hidden representation dimension C0; the last graph convolutional layer is actually composed of k graph convolutional layers, and the output dimensions of the k graph convolutional layers are C1, C2, ..., C0, respectively. k ;

[0047] The training strategy involves sequentially inputting all protein graph structures into the interpretable dimensional graph neural network model. In the last graph convolutional layer, the graphs are processed according to the C-order of their respective clusters. i The value is assigned to the output dimension C. i The convolutional layer.

[0048] The beneficial effects of adopting this technical solution are:

[0049] The protein classification method proposed in this invention is based on obtaining the adjacency symmetric matrix from the graph data of protein molecules; using the adjacency matrix to estimate the node representation vector dimension of the protein graph structure as the optimal estimated dimension, and constructing a candidate set of optimal estimated dimensions; training an interpretable dimensional graph neural network model based on the candidate set of optimal estimated dimensions, during which the protein graph structure is embedded into the best-fit dimension; and performing a protein classification task based on the trained graph neural network model to obtain the predicted protein type. This incorporates dimensionality estimation, improving protein classification accuracy and computational efficiency.

[0050] The interpretable dimensional graph neural network model proposed in this invention improves the classification accuracy of traditional GNN models: experiments show that it improves classification accuracy compared with various GNN models on supervised graph classification tasks.

[0051] This invention effectively reduces time complexity: it not only improves the classification accuracy of GNNs but also reduces time complexity. Specifically, this invention improves the time efficiency of GNNs for graph classification tasks in two aspects. First, compared with grid search-based heuristic methods, this invention can estimate the optimal graph representation dimension in a shorter time. Second, GNN models using the estimation results of this invention as the graph representation dimension have higher operating efficiency compared with GNN models using other representation dimensions.

[0052] This invention improves interpretability: Based on the principle of minimum entropy, it directly calculates the optimal dimension using computational methods, eliminating the need for additional neural network training and thus offering better interpretability. Compared to heuristic methods based on grid search, it has theoretical support based on information theory.

[0053] This invention has a wide range of applications: The protein classification method based on GNNs with solvable dimensions proposed in this invention improves the performance of the original GNN model and can be applied to various GNN models. Furthermore, it can be applied to tasks other than protein classification. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of a protein classification method based on an interpretable dimensional graph neural network according to the present invention.

[0055] Figure 2 This is a flowchart illustrating the optimal dimension estimation process in an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram illustrating the process of training an interpretable dimensional graph neural network model in an embodiment of the present invention;

[0057] Figure 4 This is a schematic diagram of the structure of an interpretable dimensional graph neural network model in an embodiment of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings.

[0059] In this embodiment, see Figure 1 As shown, this invention proposes a protein classification method based on an interpretable dimensional graph neural network, comprising the following steps:

[0060] S10, Obtain the adjacency symmetric matrix from the graph data of protein molecules;

[0061] S20, the node representation vector dimension of the protein graph structure is estimated based on the adjacency matrix, and used as the optimal estimation dimension;

[0062] S30, obtain the candidate set of the optimal estimation dimension based on the optimal estimation dimension;

[0063] S40, based on the candidate set of the optimal estimated dimension, trains the interpretable dimension graph neural network model, in which the protein graph structure is embedded into the best-fit dimension during training.

[0064] S50 performs a protein classification task based on a trained graph neural network model to obtain the predicted protein type.

[0065] As an optimization scheme 1 of the above embodiment, in step S10, the nodes of the graph structure in the graph data represent amino acids, and the edges of the graph structure represent chemical bonds between amino acids; the adjacency matrix corresponding to the chemical bonds between amino acids is obtained from the graph data of the protein molecule.

[0066] Here, the adjacency matrix A is an N*N two-dimensional array used to represent the protein graph structure, where N is the number of amino acids in the protein;

[0067] In the adjacency matrix A, if the distance between amino acid i and amino acid j is less than 6 Å, they are considered to have a chemical bond. Therefore, A... ij =1.

[0068] As an optimization scheme 2 of the above embodiments, such as Figure 2 As shown, in step S20, the node representation vector dimension of the protein graph structure is estimated based on the adjacency matrix as the estimation dimension, including the following steps:

[0069] S21, define the attribute entropy as a measure of the uncertainty of the properties of protein graph structural nodes. The attribute entropy is calculated from the number of amino acids and the vector dimension of the amino acids.

[0070] S22, find the multi-order adjacency matrix of the protein adjacency matrix;

[0071] S23, perform graph Laplace normalization on the multi-order adjacency matrix;

[0072] S24, calculates the structural entropy that measures the global and local uncertainties of the amino acid diagram;

[0073] S25, Calculate the relative probability p based on the structural entropy. i , which serves as a weighting coefficient when fusing adjacency matrices of different orders;

[0074] S26, fusion of adjacency matrices and degree diagonal matrices of protein graph structures at various orders;

[0075] S27. Calculate the higher-order structural entropy of the protein graph structure using the fused adjacency matrix.

[0076] S28, obtain the estimated dimension based on the higher-order structural entropy and attribute entropy.

[0077] Specific implementation process:

[0078] S21, define the attribute entropy as a measure of the uncertainty of the properties of protein graph structural nodes. The attribute entropy is calculated from the number of amino acids and the vector dimension of the amino acids.

[0079] The specific form of attribute entropy is H Att ≈logN 2 -0.24d, where N represents the number of amino acids and d represents the vector dimension.

[0080] S22, find the multi-order adjacency matrix of the protein adjacency matrix, including...

[0081]

[0082] The first-order, second-order, and third-order adjacency matrix structures of the graph were measured respectively, indicating whether amino acids can be connected to each other through paths of length one, two, and three chemical bonds, respectively.

[0083] A+I adds an amino acid to its own chemical bond in the representation of the original structure.

[0084] S23, Perform graph Laplacian normalization on the multi-order adjacency matrix to obtain:

[0085] in, D is a diagonal matrix of degree for each order of adjacency matrix. i The degree diagonal matrix of the normalized adjacency matrices of each order The defined D i [u][v] represents the information passed from amino acid u to amino acid v in the GNN model.

[0086] S24, calculates the structural entropy that measures the global and local uncertainties of the amino acid diagram;

[0087] The structural entropy is:

[0088] in, It is a coding tree. Taking a three-layer coding tree as an example, the root node γ represents the entire graph, the tree nodes in the second layer represent communities of the graph, and the nodes in each community constitute the third layer of the tree, i.e., the leaf nodes. This definition constructs the hierarchical information of the graph by using community partitioning, introducing the local distribution of nodes into the structural entropy that only considers the global distribution in the traditional approach. In order to calculate high-dimensional structural entropy, community detection algorithms are needed to construct the coding tree, such as the highly efficient Leuven algorithm. α Defined as D i [u][v] sums the values ​​of nodes not in the subtree rooted at α, and v sums the values ​​of nodes in the subtree rooted at α. vol(α) represents the sum of the degrees of all nodes in the subtree rooted at α, and γ is the root node.

[0089] S25, Calculate the relative probability p based on the structural entropy. i , which serves as a weighting coefficient when fusing adjacency matrices of different orders;

[0090] relative probability p i for:

[0091]

[0092] S26, by fusing the adjacency matrices and degree diagonal matrices of the protein graph structure at various orders, we obtain...

[0093] in because It represents more complex structural information about proteins, so its structural entropy is higher than that of proteins. Larger. Direct addition can lead to redundancy and oversmoothing, so each item is assigned a probability during fusion.

[0094] S27. Using the fused adjacency matrix, calculate the higher-order structural entropy of the protein graph structure. The calculation method is the same as that for S24.

[0095] S28, Obtain the estimated dimension based on higher-order structural entropy and property entropy: Estimate the vector dimension d of the amino acid representation, where d is determined by the inequality It is confirmed that the formula is the attribute entropy H. Att ≈logN 2 -0.24d and structural entropy The sum of the values ​​is less than or equal to the intrinsic entropy of the graph, which is a sufficient condition.

[0096] As an optimization scheme 3 of the above embodiment, in step S30, such as Figure 3 As shown, clustering is performed based on the optimal estimation dimension. Graphs in different clusters are embedded into different dimensions in the last graph convolutional layer of the GNN to obtain a candidate set of the optimal estimation dimension.

[0097] Including the following steps:

[0098] K-means clustering with K=1 is performed on the optimal dimension of all protein graph structures to obtain the cluster center value C0;

[0099] K-means clustering with K=k cluster numbers is performed on the optimal dimension of all protein graph structures to obtain cluster center values ​​C1, C2, ..., C k These central values ​​constitute a candidate set for the optimal estimated dimension;

[0100] Assign a C to each protein graph structure Gi, based on its cluster. i value.

[0101] As an optimization of the above embodiment, in step S40, such as Figure 3 As shown, an interpretable dimensional graph neural network model is trained based on a candidate set of optimal estimated dimensions. During training, the protein graph structure is embedded into the best-fit dimension, including the following steps:

[0102] Train an interpretable dimensional graph neural network model based on a candidate set of optimally estimated dimensions;

[0103] In the explained dimensional graph neural network model, all graph convolutional layers except the last one have a unified hidden representation dimension C0; the last graph convolutional layer is actually composed of k graph convolutional layers, and the output dimensions of the k graph convolutional layers are C1, C2, ..., C0, respectively. k ;

[0104] The training strategy involves sequentially inputting all protein graph structures into the interpretable dimensional graph neural network model. In the last graph convolutional layer, the graphs are processed according to the C-order of their respective clusters. i The value is assigned to the output dimension C. i Convolutional layers;

[0105] The interpretable dimensional graphical neural network model is formally expressed as follows:

[0106]

[0107]

[0108]

[0109]

[0110] This invention adds a dimensionality estimation step to the traditional GNN training process. For protein classification problems, the training process and GNN model are further modified to embed different protein graph structures into different dimensions.

[0111] To fully utilize the structural information of graphs, the dimension estimation method of this invention is based on the principle of minimum entropy. This metric considers the global and local topological structure of the graph, resulting in a better dimension estimate on graph data. This dimension estimate is based on information theory and has good interpretability.

[0112] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A protein classification method based on an interpretable dimensional graph neural network, characterized in that, Including the following steps: S10, Obtain the adjacency matrix from the graph data of protein molecules; S20, estimating the node representation vector dimension of the protein graph structure based on the adjacency matrix, as the optimal estimation dimension, includes the following steps: S21, define the attribute entropy as a measure of the uncertainty of the properties of protein graph structural nodes. The attribute entropy is calculated from the number of amino acids and the vector dimension of the amino acids. S22, find the multi-order adjacency matrix of the protein adjacency matrix; S23, perform graph Laplace normalization on the multi-order adjacency matrix; S24, calculates the structural entropy that measures the global and local uncertainties of the amino acid diagram; S25, Calculate the relative probability p based on the structural entropy. i , which serves as a weighting coefficient when fusing adjacency matrices of different orders; S26, fusion of adjacency matrices and degree diagonal matrices of protein graph structures at various orders; S27. Calculate the higher-order structural entropy of the protein graph structure using the fused adjacency matrix. S28, obtain the estimated dimension based on the higher-order structural entropy and attribute entropy; S30, obtain the candidate set of the optimal estimation dimension based on the optimal estimation dimension; S40, based on the candidate set of the optimal estimated dimension, trains the interpretable dimension graph neural network model, in which the protein graph structure is embedded into the best-fit dimension during training. S50 performs a protein classification task based on a trained graph neural network model to obtain the predicted protein type.

2. The protein classification method based on an interpretable dimensional graph neural network according to claim 1, characterized in that, In step S10, the nodes of the graph structure in the graph data represent amino acids, and the edges of the graph structure represent chemical bonds between amino acids; the adjacency matrix corresponding to the chemical bonds between amino acids is obtained from the graph data of the protein molecule. Here, the adjacency matrix A is an N*N two-dimensional array used to represent the protein graph structure, where N is the number of amino acids in the protein.

3. The protein classification method based on an interpretable dimensional graph neural network according to claim 1, characterized in that, In step S22, the multi-order adjacency matrix of the protein adjacency matrix is ​​calculated, including... The first-order, second-order, and third-order adjacency matrix structures of the graph were measured respectively, indicating whether amino acids can be connected to each other through paths of length one, two, and three chemical bonds, respectively. A+I adds an amino acid to its own chemical bond in the representation of the original structure.

4. The protein classification method based on an interpretable dimensional graph neural network according to claim 3, characterized in that, In step S23, graph Laplacian normalization is performed on the multi-order adjacency matrix; get: in, D is a diagonal matrix of degree for each order of adjacency matrix. i The degree diagonal matrix of the normalized adjacency matrices of each order The defined D i [u][v] represents the information passed from amino acid u to amino acid v in the GNN model.

5. The protein classification method based on an interpretable dimensional graph neural network according to claim 4, characterized in that, In step S24, the structural entropy, which measures the global and local uncertainties of the amino acid graph structure, is calculated; The structural entropy is: in, It is a coding tree. Defined as D i [u][v] sums the values ​​of nodes not in the subtree rooted at α, and v sums the values ​​of nodes in the subtree rooted at α. vol(α) represents the sum of the degrees of all nodes in the subtree rooted at α, and γ is the root node.

6. The protein classification method based on an interpretable dimensional graph neural network according to claim 5, characterized in that, In step S25, the relative probability p i for: In step S26, the adjacency matrices and degree diagonal matrices of the protein graph structure are fused to obtain... in 7. The protein classification method based on an interpretable dimensional graph neural network according to claim 6, characterized in that, Calculate the higher-order structural entropy of the protein diagram: The estimated dimension is obtained from the higher-order structural entropy and property entropy: the estimated amino acid representation vector dimension d is given by the inequality. It is confirmed that the formula is the attribute entropy H. Att ≈logN 2 -0.24d and structural entropy The sum of the values ​​is less than or equal to the intrinsic entropy of the graph, which is a sufficient condition.

8. A protein classification method based on an interpretable dimensional graph neural network according to any one of claims 1-7, characterized in that, In step S30, clustering is performed based on the optimal estimated dimension. Graphs from different clusters are embedded into different dimensions in the last graph convolutional layer of the GNN to obtain a candidate set of the optimal estimated dimension. This includes the following steps: K-means clustering with K=1 is performed on the optimal dimension of all protein graph structures to obtain the cluster center value C0; K-means clustering with K=k cluster numbers is performed on the optimal dimension of all protein graph structures to obtain cluster center values ​​C1, C2, ..., C k These central values ​​constitute a candidate set for the optimal estimated dimension; Assign a C to each protein graph structure Gi, based on its cluster. i value.

9. A protein classification method based on an interpretable dimensional graph neural network according to claim 8, characterized in that, In step S40, the interpretable dimensional graph neural network model is trained based on the candidate set of optimal estimated dimensions. During training, the protein graph structure is embedded into the best-fit dimension, including the following steps: Train an interpretable dimensional graph neural network model based on a candidate set of optimally estimated dimensions; In the explained dimensional graph neural network model, all graph convolutional layers except the last one have a unified hidden representation dimension C0; the last graph convolutional layer is actually composed of k graph convolutional layers, and the output dimensions of the k graph convolutional layers are C1, C2, ..., C0, respectively. k ; The training strategy involves sequentially inputting all protein graph structures into the interpretable dimensional graph neural network model. In the last graph convolutional layer, the graphs are processed according to the C-order of their respective clusters. i The value is assigned to the output dimension C. i The convolutional layer.

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