Group discovery method and device for dynamic metabolic network

Abstract

The invention relates to the technical field of biological analysis, discloses a group discovery method and device for a dynamic metabolic network, introduces the concept of time smoothness to solve the problem of instability of a group structure in the dynamic network, and improves the stability and accuracy of the group structure. Based on the thought of evolution clustering and semi-nonnegative matrix factorization, the model fuses node similarity into network analysis, the topological structure and the similarity relation between the nodes in the metabolic network are comprehensively considered, and the problem that group division is insufficient in other methods is effectively solved. Meanwhile, by processing the microstructure of the metabolic network, the system can effectively solve the problem of data sparseness, and enables the relation between the nodes in the group to be tighter. Besides, the system effectively improves the distinction degree among the groups and reduces the influence of noise through a method based on semi-non-negative matrix factorization (Semi-NMF), thereby improving the accuracy and reliability of group discovery.

Description

Technical Field

[0001] The present invention relates to the field of biological analysis technology, and in particular to a group discovery method and device for a dynamic metabolic network. Background Art

[0002] As an important carrier of chemical reactions in organisms, metabolic networks play a vital role in maintaining homeostasis and stability in organisms. The discovery of group structures in networks is that studying network functions can help people better understand the connections and transformations between metabolic pathways, and has important research value. For this research topic, traditional methods still have three types of shortcomings. First, because only the topological structure or attribute similarity of the network is considered, the complexity of the metabolic network is ignored, resulting in limited performance. Secondly, most traditional methods are oriented to static networks, that is, the network structure is assumed to be fixed, while the chemical reactions and metabolite concentrations in the actual metabolic network are constantly changing. This makes the metabolic network a dynamic and complex network, and the connections between nodes will continue to change over time. Ignoring the modeling of the temporal characteristics of this network will make it difficult to apply the model to dynamic scenarios. In addition, the existing technology has failed to make good use of the association properties of nodes in the metabolic network, resulting in insufficient links between nodes within the group and insufficient distinction between groups. According to the survey, there is currently a lack of effective methods to deal with these shortcomings.

[0003] Group discovery methods often use community discovery algorithms. In the 1960s, Herbert Simon first proposed the concept that complex systems have modular structural characteristics. The study of communities actually evolved from the subgraph segmentation problem. The binary algorithm proposed by Kernighan-Lin made the subgraph segmentation problem gradually become the focus of attention in the field of graph mining at that time. In addition, in the field of sociology, sociologists have also discovered the universal existence of community structures in various complex networks. After entering the 21st century, community research began to be valued by researchers, and in recent years, with the rise of social networks, the attention to this field has greatly increased.

[0004] At present, traditional group discovery methods include modularity-based, spectral clustering-based, label propagation-based, clustering coefficient-based, etc. The modularity method usually uses a greedy algorithm or a simulated annealing algorithm to search and optimize the group structure. The spectral clustering-based method can map the nodes in the network into a low-dimensional space, thereby realizing the clustering analysis of the network, which usually includes the calculation of the Laplace matrix, the selection of eigenvectors, and clustering analysis. The label propagation-based method is a group discovery algorithm based on local information propagation, which discovers the group structure through information transmission between nodes. The clustering coefficient-based method is a group discovery algorithm based on the relationship between node degree and neighbor node degree, and usually uses spectral clustering, hierarchical clustering and other technologies to realize the discovery and analysis of group structure. The group of the metabolic network needs to comprehensively consider factors such as the topological structure of the network and the similarity of the properties of metabolites. Traditional methods are difficult to reflect the global structural characteristics of the group. The topological method may classify nodes with close links but dissimilar properties into the same group, while the similarity law may misjudge nodes with similar properties but loose links as the same group. In addition, due to the sparse data structure of complex networks, the connections between microstructures are weak, but the existence of group structures can enhance the similarities between them.

[0005] Traditional methods usually only consider the topological structure or attribute similarity of the network, resulting in inaccurate detection. For example, in the patent "VANET community discovery method based on node similarity" (CN108712287B), a method is described that can accurately discover the group structure in the VANET network based on node similarity, which can improve the communication efficiency between vehicles. However, the limitation of this patent is that it only considers node similarity, and does not fully consider the connection information between nodes, which may cause the connection within the group to be not tight enough; in the patent "A method and system for discovering communities in overlapping complex networks based on topological potential" (CN103500168B), a new group discovery method is proposed, which uses a topological potential field to construct the topological structure of a given complex network, and then determines the representative node by finding the peak in the topological potential field, and expands the entire group. However, the concept of topological potential used in this method is relatively abstract, and it is difficult to find a specific representation method in practical applications. In addition, this method has high requirements for the preprocessing of network data, and the original data needs to be normalized, which may impose certain restrictions on the data scale and dimension.

[0006] Most traditional grouping methods are based on static networks, that is, they assume that the network structure is fixed, while the biological metabolic network in reality is often dynamically changing, and the connection between nodes will also change over time. Therefore, this type of method ignores the relationship between nodes in the time series network that changes over time. For example: the patent "A secure community discovery method for social networks" (CN115423639A) introduces a method for group discovery based on the trust of nodes in social networks and the similarity between nodes. The method first constructs a weighted adjacency matrix based on the trust value between nodes, and then clusters the adjacency matrix to obtain groups through an algorithm based on node similarity. However, the patent only performs group discovery on static networks, and has not yet involved group discovery on dynamic networks. In addition, the trust calculation method and similarity algorithm mentioned in the patent have certain limitations in practical applications and need further improvement and optimization; the patent "A semi-supervised community discovery method that integrates node attributes and graph structure" (CN110442800B) uses the label information of some known nodes, spreads the label information to unknown nodes through a label propagation algorithm, and uses the propagated label information as node attributes for subsequent group discovery. However, this method is mainly aimed at semi-supervised static network group discovery problems, and has not yet involved the group discovery problem of dynamic networks. In addition, in the process of calculating the similarity of node attributes, this method uses a Gaussian kernel function. Although this method works well in practical applications, it is sensitive to the selection of parameters and requires certain experience or parameter adjustment process.

[0007] Traditional methods ignore the fusion of rich features of nodes in the network, making it difficult to make the links between nodes within the group more closely connected, and at the same time, the nodes within the group have better attribute similarity, resulting in the inability to reflect the homogeneity of the group. In the patent "A community discovery method based on k-truss decomposition with NUMA perception" (CN114265691A), a group discovery algorithm based on k-truss decomposition is proposed, which uses the NUMA perception method when decomposing k-truss. At the same time, scalable hash table technology is introduced to solve the problem of memory usage in large-scale graph structures. However, this method performs poorly when processing some special network structures or network data with large noise, and cannot adapt well to the dynamic characteristics of metabolic networks. In addition, due to the inability to reflect the changes in node attributes and metabolic flows well, the application effect of this method is subject to certain limitations. The patent "A maximum clique greedy expansion community discovery method and system based on average mutual information" (CN111464343B) uses average mutual information to evaluate the correlation between nodes, uses the maximum clique to divide groups, and uses a greedy algorithm for expansion. It performs well in terms of grouping accuracy and scalability. However, this method does not work well when dealing with complex network structures and is easily affected by noise in the network. In addition, this method does not consider factors such as node attributes and network dynamics, and is not suitable for processing network data with special properties. Summary of the invention

[0008] The purpose of the present invention is to provide a method and device for group discovery of a dynamic metabolic network with higher accuracy and reliability.

[0009] In order to achieve the above object, the present invention provides a group discovery method of a dynamic metabolic network, comprising:

[0010] S1: construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and simulates the dynamic evolution of the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot;

[0011] S2: For each node in the network snapshot, calculate the neighbor node set of the node at different time moments, and calculate the similarity of the neighbor node set at different time moments; then, fuse the similarities of the nodes at different time moments to obtain the comprehensive similarity measure of the nodes, and use the comprehensive similarity measure of the nodes as the adjacency matrix;

[0012] S3: Modeling the group structure based on semi-non-negative matrix decomposition, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider the changes in the group structure between adjacent time steps; constructing an objective function according to the adjacency matrix, the cluster centroid matrix and the group member matrix, iterating the objective function based on an optimization method based on the gradient descent method until the objective function value converges, and obtaining the group partition matrix of the node based on the objective function after the iterative operation.

[0013] As a preferred solution, in step S1, time is divided into multiple discrete time steps, and changes in factors such as metabolite concentration and enzyme activity are considered to establish a dynamic metabolic network; in this dynamic metabolic network, the states of metabolite and enzyme nodes will change over time, and the occurrence or non-occurrence of metabolic reactions will also change the topological structure of the dynamic metabolic network over time;

[0014] For any dynamic metabolic network G = (V, E), where V = {v1, v2, ..., v n} represents a vertex set, E = {e1, e2, …, e m} represents the link set; the dynamic metabolic network is dynamic, where each moment contains a network snapshot, and all moments are represented by the binary adjacency matrix X t Indicates that t is the corresponding network slice, and the complex network matrix element X t,ij Indicates whether node i is directly connected to node j in snapshot t, that is, there is an edge connecting them. If there is an edge, then X t,ij =1, otherwise X t,ij =0.

[0015] As a preferred solution, step S2 includes:

[0016] S201, according to the adjacency matrix X in step S1 t Calculate first-order proximity

[0017] S202, according to the first-order proximity S (1) The second-order proximity matrix is ​​calculated by the collection of

[0018] S203, introduce the weight coefficient η, and according to the first-order proximity S (1) and the second-order proximity matrix S (2) , calculate the final adjacency matrix S, S = S (1) +ηS (2) , where η>0.

[0019] As a preferred solution, the similarity of the neighbor node sets is calculated by using a similarity metric based on the graph structure.

[0020] As a preferred solution, the graph structure-based similarity measurement uses a cosine similarity algorithm.

[0021] As a preferred solution, in step S201, the first-order proximity It is a measure used to describe the similarity between nodes in social networks. (1) It measures the most intuitively observed proximity probability between two nodes; when there is a connection between node i and node j, its similarity score X ij If it is positive, it indicates that there is a strong correlation between node i and node j. On the contrary, if there is no correlation between node i and node j, the similarity score is 0, indicating that there is no direct proximity relationship between node i and node j.

[0022] In step S202, if there is no directly connected edge between two nodes, but they have many common neighbor nodes, then they can still be considered similar;

[0023] In step S203, it is assumed that represents the set of first-order proximity between node i and all other nodes, according to N i With N j The similarity between them can determine the second-order proximity; here, cosine similarity is used to calculate the second-order proximity matrix. For nodes i and j, Where ||N|| represents the norm of N; according to the properties of cosine similarity, the value of the second-order proximity can be obtained between 0 and 1; in order to maintain the trade-off between the first-order and second-order proximity properties, a weight variable is used to connect them, that is, S = S (1) +ηS (2) , where η>0.

[0024] As a preferred solution, in step S3, the objective function includes a cost function, and the cost function is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost.

[0025] As a preferred solution, in step S3, a cluster centroid matrix F=(f1, f2, ..., f k ), where each column represents the central node of the corresponding group, usually with positive and negative attributes;

[0026] The group membership matrix G is a non-negative matrix that indicates the input data nodes belong to specific groups. It is defined as follows:

[0027]

[0028] where s i represents the node labeled i in the input matrix, c krepresents the group numbered k; the group member matrix G represents s i Is it c k Cluster, where if the element g ik is equal to 1, then s i Belongs to c k cluster, otherwise 0;

[0029] Assuming that K-means clustering is performed on the input adjacency matrix S, the objective function of K-means clustering can be expressed as:

[0030]

[0031] In order to consider the mutual influence between adjacent time steps, a time smoothness constraint is introduced and added to the group member matrix; specifically, the time cost is defined, which represents the probability that the group member structure changes significantly between t-1 and t, which directly reflects the quality of group discovery: a lower time cost means that the group member structure is relatively stable over time, which indicates that the quality of group discovery is higher, that is, the group discovery quality is an inverse expression of the time cost, and the higher the group discovery quality is, the lower the time cost is; by adding the time cost of network topology modeling and the time cost of the smoothness constraint, a total time cost is obtained, and the time cost function is the sum of the current community discovery quality and the historical time cost. The time cost function is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost. Therefore, the resulting cost function is as follows:

[0032]

[0033] Among them, the weight parameter α of the time smoothing constraint is a very critical parameter. Usually, its value range is a decimal between 0 and 1. The function of this parameter is to balance the changes in the group member structure and the consumption of time cost. Based on this, the objective function is in the following form:

[0034]

[0035] Excluding the first time slice, the gradient descent method is used to solve the objective function to obtain an iterative algorithm, which uses relevant update rules and takes the convergence of the objective function value as the iteration termination condition, so as to obtain the final group structure and then the group partition matrix of the node.

[0036] As a preferred solution, the process of using the gradient descent method to solve the objective function is as follows:

[0037] When fixed G t When F t By minimizing formula (2), it can be simplified into the following form:

[0038]

[0039] In order to meet the non-negativity constraint, the Lagrange multiplier matrix λ is introduced and incorporated into the objective function. The constraints are adjusted using the Lagrange multiplication method to obtain the objective function with constraints. The obtained objective function is as follows:

[0040]

[0041] Assume that the partial differential is taken,

[0042]

[0043] Introducing the KKT fixed point condition, we can get:

[0044]

[0045] According to the derivation results, formula (7) is transformed equivalently:

[0046]

[0047] Therefore, F t The update transformation formula of the variable is:

[0048]

[0049] Similarly, when F t Fixed and G t When an update is required, G is constrained by introducing a non-negative Lagrange multiplier matrix λ t The non-negative property of G t The update transformation formula of the variable is as follows:

[0050]

[0051] The present invention also provides a group discovery device for a dynamic metabolic network, comprising:

[0052] A dynamic metabolic network construction unit is used to construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and performs dynamic evolution simulation on the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot;

[0053] The node attribute fusion unit is used to calculate the neighbor node set of each node in the network snapshot at different time moments, and calculate the similarity of the neighbor node set at different time moments; then, the similarity of the node at different time moments is fused to obtain the comprehensive similarity measurement of the node, and the comprehensive similarity measurement of the node is used as the adjacency matrix;

[0054] A group clustering detection unit is used to model the group structure based on semi-non-negative matrix decomposition, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider the change of the group structure between adjacent time steps; an objective function is constructed according to the adjacency matrix, the cluster centroid matrix and the group member matrix, and the objective function is iteratively calculated based on an optimization method based on a gradient descent method until the objective function value converges, and the group partition matrix of the node is obtained based on the objective function after the iterative calculation.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The present invention makes the metabolic network a dynamic network with time series characteristics by introducing time information. When analyzing, the network topology and time series information are used to make each group obtained by division represent a group of nodes with similar behaviors in time, so as to better understand the biological functions and physiological processes of the metabolic network. In addition, in the network snapshot analysis, the similarity between nodes in the network is quantified, and the comprehensive similarity measurement of the nodes is obtained as an adjacency matrix, the node similarity is fused, and the topological structure of the nodes is combined with the attribute similarity, so as to more comprehensively consider the relationship between the nodes in the network, which can well solve the problem of data sparsity in the metabolic network and make the links between the nodes in the group closer. When constructing the group structure, the concept of time smoothness is introduced to constrain the change threshold between adjacent time slices, solve the influence of time changes between nodes in the time series network, and then improve the performance of the model; and based on semi-non-negative matrix decomposition, the influence of noise is effectively reduced, the discrimination between groups is improved, and the group discovery results are more accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a flow chart of a group discovery method of a dynamic metabolic network according to an embodiment of the present invention;

[0058] Figure 2 is a processing schematic diagram of a group discovery method for a dynamic metabolic network according to an embodiment of the present invention;

[0059] Figure 3 is a flowchart of the fusion node similarity of step S2 of an embodiment of the present invention;

[0060] Figure 44 is a schematic diagram for comparing the performance of different methods in the embodiments of the present invention. DETAILED DESCRIPTION

[0061] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0062] Terminology explanation:

[0063] Complex network: A network structure consisting of a large number of nodes and the connections between them, in which the relationship between nodes and connections is usually highly nonlinear and random. In a complex network, nodes can represent various types of entities, such as individuals, organizations, molecules, physical systems, etc., and connections can represent the relationship between them, such as friendships in social networks, interactions in protein networks, etc.

[0064] Link prediction: Given partial information about a network, try to predict connections that have not yet appeared in the network in order to further analyze the structure and properties of the network.

[0065] Group detection: Group detection (also known as community discovery) refers to dividing nodes into several groups in a large network, so that nodes in the same group have closer connections, while the connections between different groups are weaker. Group detection is an important problem in complex network analysis and a research hotspot in practical applications such as social networks, biological networks, and logistics networks.

[0066] Embodiment 1

[0067] like Figure 1 to Figure 2 As shown, a group discovery method of a dynamic metabolic network in a preferred embodiment of the present invention includes:

[0068] S1: construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and simulates the dynamic evolution of the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot;

[0069] S2: For each node in the network snapshot, calculate the neighbor node set of the node at different time moments, and calculate the similarity of the neighbor node set at different time moments; then, fuse the similarities of the nodes at different time moments to obtain the comprehensive similarity measure of the nodes, and use the comprehensive similarity measure of the nodes as the adjacency matrix;

[0070] S3: Modeling the group structure based on semi-non-negative matrix decomposition, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider the changes in the group structure between adjacent time steps; constructing an objective function according to the adjacency matrix, the cluster centroid matrix and the group member matrix, iterating the objective function based on an optimization method based on the gradient descent method until the objective function value converges, and obtaining the group partition matrix of the node based on the objective function after the iterative operation.

[0071] This embodiment introduces time information to make the metabolic network a dynamic network with time series characteristics. When analyzing, the network topology and time series information are used to make each group obtained by division represent a group of nodes with similar behaviors in time, so as to better understand the biological functions and physiological processes of the metabolic network. In addition, in the network snapshot analysis, the similarity between nodes in the network is quantified, and the comprehensive similarity measurement of the nodes is obtained as the adjacency matrix. The node similarity is fused, and the topological structure of the nodes is combined with the attribute similarity, so as to more comprehensively consider the relationship between the nodes in the network, which can well solve the problem of data sparsity in the metabolic network and make the links between the nodes in the group closer. When constructing the group structure, the concept of time smoothness is introduced to constrain the change threshold between adjacent time slices, solve the influence of time changes between nodes in the time series network, and then improve the performance of the model; and based on semi-non-negative matrix decomposition, the influence of noise is effectively reduced, the discrimination between groups is improved, and the group discovery results are more accurate and reliable.

[0072] Embodiment 2

[0073] The difference between this embodiment and the first embodiment is that, based on the first embodiment, this embodiment further explains step S1.

[0074] S1: Construct a dynamic metabolic network, which uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and simulates the dynamic evolution of the network; the dynamic metabolic network is dynamic, and each moment contains a network snapshot.

[0075] In step S1, time is divided into multiple discrete time steps, and a dynamic metabolic network is established by considering the changes in factors such as metabolite concentration and enzyme activity. In this dynamic metabolic network, the states of metabolites and enzyme nodes will change over time, and the occurrence or non-occurrence of metabolic reactions will also change the topological structure of the dynamic metabolic network over time. For any dynamic metabolic network G = (V, E), where V = {v1, v2, ..., v n} represents a vertex set, E = {e1, e2, …, e m} represents the link set; the dynamic metabolic network is dynamic, where each moment contains a network snapshot, and all moments are represented by the binary adjacency matrix X t Indicates that t is the corresponding network slice, and the complex network matrix element X t,ij Indicates whether node i is directly connected to node j in snapshot t, that is, there is an edge connecting them. If there is an edge, then X t,ij =1, otherwise X t,ij =0.

[0076] Step S1 first uses metabolites and enzymes as nodes and metabolic reactions as edges to establish a static network. Secondly, time information is introduced to model the dynamic process of metabolic reactions as a time series, and the network is dynamically evolved. Specifically, time is divided into multiple discrete time steps, and changes in factors such as metabolite concentration and enzyme activity are considered to establish a dynamic metabolic network model. In this metabolic network, the state of metabolite and enzyme nodes will change over time, and the occurrence or non-occurrence of metabolic reactions will also change the topological structure of the network over time.

[0077] The other steps of this embodiment are the same as those of the first embodiment and will not be described again here.

[0078] Embodiment 3

[0079] The difference between this embodiment and the second embodiment is that, based on the second embodiment, this embodiment further explains step S2.

[0080] In the network snapshot analysis, it is considered how to quantify the similarity between nodes in the network. To this end, this method proposes a method for calculating a comprehensive similarity measure. Specifically, for each node in the network snapshot, this method calculates the set of neighbor nodes of the node at different time moments, and calculates the similarity of the set of neighbor nodes at different time moments. Here, this method adopts some similarity measurement methods based on graph structure, such as cosine similarity. Then, the similarities of the nodes at different time moments are fused to obtain a comprehensive similarity measure of the nodes. Finally, this measurement result replaces the original adjacency matrix as the algorithm input data, so that the relationship and similarity between nodes can be more accurately described.

[0081] Therefore, this embodiment provides step S2: for each node in the network snapshot, the neighbor node set of the node at different time moments is calculated, and the similarity of the neighbor node set at different time moments is calculated; then, the similarities of the nodes at different time moments are fused to obtain a comprehensive similarity measure of the nodes, and the comprehensive similarity measure of the nodes is used as an adjacency matrix.

[0082] Step S2 calculates the similarity of the neighbor node set by using a similarity measurement based on the graph structure. Specifically, the similarity measurement based on the graph structure adopts a cosine similarity algorithm.

[0083] Step S2 includes:

[0084] S201, according to the adjacency matrix X in step S1 t Calculate first-order proximity

[0085] In step S201, the first-order proximity It is a measure used to describe the similarity between nodes in social networks. (1) It measures the most intuitively observed proximity probability between two nodes; when there is a connection between node i and node j, its similarity score X ij If it is positive, it indicates that there is a strong correlation between node i and node j. On the contrary, if there is no correlation between node i and node j, the similarity score is 0, indicating that there is no direct proximity relationship between node i and node j.

[0086] S202, according to the first-order proximity S (1) The second-order proximity matrix is ​​calculated by the collection of

[0087] When dealing with similarities between nodes in a complex network, this embodiment generally uses the adjacency matrix X ij As a first-order proximity matrix to describe the proximity between nodes. However, in practice, the edges in complex networks are usually sparse, with only a few edges between nodes, so using first-order proximity to describe the similarity between nodes may be too simple. To overcome this problem, a second-order proximity matrix is ​​introduced here The similarity between nodes can be described more accurately. Specifically, if there is no direct edge connecting two nodes, but they have many common neighbor nodes, then they can still be considered similar.

[0088] S203, introduce the weight coefficient η, and according to the first-order proximity S (1) and the second-order proximity matrix S (2) , calculate the final adjacency matrix S, S = S (1) +ηS (2) , where η>0;

[0089] In step S203, it is assumed that represents the set of first-order proximity between node i and all other nodes, according to N i With N j The similarity between them can determine the second-order proximity; here, cosine similarity is used to calculate the second-order proximity matrix. For nodes i and j, Where ||N|| represents the norm of N; according to the properties of cosine similarity, the value of the second-order proximity can be obtained between 0 and 1; in order to maintain the trade-off between the first-order and second-order proximity properties, a weight variable is used to connect them, that is, S = S (1) +ηS (2) , where η>0. In actual situations, the value of η can be adjusted as needed. The specific process is as follows Figure 3 shown.

[0090] The other steps of this embodiment are the same as those of the second embodiment and will not be described again here.

[0091] Embodiment 4

[0092] The difference between this embodiment and the third embodiment is that, based on the third embodiment, this embodiment further explains step S2.

[0093] Step S3: Modeling the group structure based on semi-non-negative matrix decomposition, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider changes in the group structure between adjacent time steps; constructing an objective function based on the adjacency matrix, the cluster centroid matrix and the group member matrix, iterating the objective function based on an optimization method based on the gradient descent method until the objective function value converges, and obtaining the group partition matrix of the node based on the objective function after the iterative operation.

[0094] The objective function of this embodiment includes a cost function, which is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost.

[0095] This step considers the mutual influence between adjacent time steps and controls the change of the group membership matrix by introducing a time smoothing constraint. Specifically, the comprehensive similarity measure of the nodes is taken as input, and a time smoothing constraint is added to the group membership matrix to consider the change of the group structure between adjacent time steps. This method defines the time cost as the probability that the group membership structure changes significantly between t-1 and t, and combines the time cost of the smoothing constraint with the time cost of network topology modeling, and defines the time cost function as the sum of the current time cost and the historical time cost, where "the time cost of the smoothing constraint" refers to the "current time cost" and "the time cost of network topology modeling" refers to the "historical time cost".

[0096] This embodiment proposes an optimization method based on the gradient descent method, which maximizes the current group discovery quality and minimizes the historical cost. Specifically, this method designs an objective function, in which the group discovery quality and the historical cost are assigned different weights to balance the relationship between them. By iteratively calculating the gradient of the objective function, the final group result can be obtained.

[0097] The specific process is as follows: The present invention relates to a data network matrix, which is unconstrained and performs group structure modeling based on the condition of semi-nonnegative matrix decomposition. Specifically, the cluster centroid matrix F = (f1, f2, ..., f k ), where f i represents the central node of the corresponding group, which is calculated based on the characteristics of the data points in the group and usually has positive and negative attributes. Group member matrix G = (g 11 ,g 12 ,…,g ik ) is a non-negative matrix, indicating that the input data nodes belong to specific groups, and is defined as follows:

[0098]

[0099] where s i represents the node labeled i in the input matrix, c k represents the group numbered k. The group member matrix G represents s i Is it c k Cluster, where if the element g ik is equal to 1, then s i Belongs to c k cluster, otherwise 0.

[0100] Assuming that K-means clustering is performed on the input matrix S, the objective function of K-means clustering can be expressed as:

[0101]

[0102] In order to consider the mutual influence between adjacent time steps, a time smoothness constraint is introduced and added to the group membership matrix. Specifically, this method defines a time cost, which represents the probability that the group membership structure changes significantly between t-1 and t, which directly reflects the quality of group discovery: a lower time cost means that the group membership structure is more stable over time, indicating that the quality of group discovery is higher. In other words, the quality of group discovery is an inverse expression of the time cost, and the higher the group discovery quality is, the lower the time cost. By adding the time cost of network topology modeling and the time cost of the smoothness constraint, a total time cost is obtained. The time cost function is the sum of the current community discovery quality and the historical time cost. To solve this problem, the time cost function is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost. Therefore, the resulting time cost function is as follows:

[0103]

[0104] Among them, the weight parameter α of the time smoothing constraint is a very critical parameter. Usually, its value range is a decimal between 0 and 1. The function of this parameter is to balance the change of the group member structure and the consumption of time cost. Based on this, the objective function proposed by the present invention is in the form of:

[0105]

[0106] Excluding the first time slice, the gradient descent method is used to solve the objective function (2) to obtain an iterative algorithm, which uses the relevant update rule and takes the convergence of the objective function value as the iteration termination condition, so that the detected group member structure can be obtained.

[0107] The specific update rule is proved as follows: Due to the properties of non-negative matrix factorization, its solution space is non-convex and discrete, and there is no global optimal solution. However, when a parameter is fixed, a local optimal solution can be found. When G is fixed t When F t By minimizing formula (2), it can be simplified into the following form:

[0108]

[0109] In order to satisfy the non-negativity constraint, the Lagrange multiplier matrix λ is introduced and incorporated into the objective function to obtain the optimal solution. When the Lagrange multiplier is 0, the objective function can be simplified to a form without constraints. Specifically, this method uses the Lagrange multiplication method to adjust the constraints to obtain an objective function with constraints. In this process, the matrix λ constrains S tThe non-negativity of enables this method to obtain stable and feasible results in the solution process, and obtain the following objective function:

[0110]

[0111] Assume that the partial differential is taken,

[0112]

[0113] Introducing the KKT fixed point condition, we can get:

[0114]

[0115] According to the derivation results obtained by this method, this method can perform equivalent transformation of formula (7):

[0116]

[0117] Therefore, F t The update transformation formula of the variable is:

[0118]

[0119] Similarly, when F t Fixed and G t When an update is required, G is constrained by introducing a non-negative Lagrange multiplier matrix λ t The non-negative property of G. t The partial derivative of is 0. This method can also use a series of mathematical operations, such as introducing KKT fixed point conditions, to further simplify and optimize G t Through these operations, we can get G t The update transformation formula of the variable is as follows:

[0120]

[0121] To evaluate the performance of the group discovery method, this method uses two performance metrics. Accuracy (AC) is a metric used to compare the difference between the group membership matrix obtained by the algorithm and the group membership matrix in the actual network. In short, AC can be considered as the error rate, which is defined as follows:

[0122] AC=||ZZ T -Z'Z' T || F (11)

[0123] Where Z and Z′ represent the group membership matrix obtained by the dynamic group discovery algorithm and the group membership matrix of the real network, respectively, ||·|| FIndicates the Frobenius norm. In this process, the smaller the AC value, the more accurate the results obtained by the model.

[0124] Normalized mutual information (NMI) is one of the accuracy criteria of the detection model. This indicator is only applicable to static networks and networks with true values. Therefore, this method calculates NMI at each time step. The similarity measure between the group division obtained by this method and the true group structure can be expressed by the following formula:

[0125]

[0126] In this formula, H(Z) and H(Z′) represent the entropy of Z and Z′ respectively, and their values ​​range from 0 to 1. When the NMI value is closer to 1, it means that the model matches the real result better.

[0127] The model is run on an artificial attribute network, and the performance of the model is quantitatively evaluated using Normalized Mutual Information (NMI) and Accuracy (AC). In an artificial attribute network, each node carries an attribute vector, which consists of multiple attributes. This method converts the attribute vector into a node feature vector by encoding these attributes into a binary vector, and combines it with a node similarity measure to obtain the input data. This method runs the proposed method on this dataset and compares it with several other classic group discovery methods.

[0128] To create synthetic datasets that are more representative of real-world situations, this method uses an improved LFR model. The model generates networks using embedded real group structures, which are composed of subgraphs with similar topological features, each of which consists of a specific arrangement of group members. To evaluate the performance of this method, a synthetic network containing 1000 nodes was constructed, and different synthetic networks were created by varying the model parameters over 10 time steps. Specifically, this method sets the following basic parameters: μ is a mixing parameter that controls the edge level between different groups and is set to 0.7; p is the probability of transition between group nodes and is set to 0.5; the number of groups is set to 36; the average degree of nodes is set to 10; and the time step T is 10.

[0129] The example results of the temporal network generated by the LFR model are as follows Figure 4 The results show that compared with other baseline methods, this method performs better in network generation. Figure 4 As can be seen on the left, in this data set, the highest normalized mutual information (NMI) value of other models is 0.965, while the NMI value of this method is 0.968-0.97. Figure 4 On the right side, the performance of the proposed method is relatively weak, but as the time step increases, its performance gradually improves. In the 5th to 10th time slices, the NMI results of the proposed method are 0.01 to 0.04 higher than the maximum values ​​of the other methods. In addition, except for the first time step with low accuracy, the performance of all time steps shows a high level. This is because the system initially used a randomly initialized decomposition of the matrix, and the system has been greatly improved over time and evolution. The model created by the proposed method has a lower error and can detect dynamic groups more accurately. These results show that the proposed method is more robust than other benchmark methods and has broad application prospects.

[0130] The other steps of this embodiment are the same as those of the third embodiment and will not be described again here.

[0131] Embodiment 5

[0132] This embodiment provides a group discovery device for a dynamic metabolic network, including:

[0133] A dynamic metabolic network construction unit is used to construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and performs dynamic evolution simulation on the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot; the dynamic metabolic network construction unit of this embodiment is used to implement the above step S1.

[0134] The node attribute fusion unit is used to calculate, for each node in the network snapshot, the set of neighbor nodes of the node at different time moments, and calculate the similarity of the neighbor node sets at different time moments; then, the similarities of the nodes at different time moments are fused to obtain a comprehensive similarity measure of the nodes, and the comprehensive similarity measure of the nodes is used as an adjacency matrix; the node attribute fusion unit of this embodiment is used to implement the above step S2.

[0135] The group clustering detection unit is used to model the group structure based on semi-non-negative matrix decomposition, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider the change of the group structure between adjacent time steps; an objective function is constructed according to the adjacency matrix, the cluster centroid matrix and the group member matrix, and an optimization method based on the gradient descent method is used to iterate the objective function until the objective function value converges, and the group partition matrix of the node is obtained based on the objective function after the iterative operation. The group clustering detection unit of this embodiment is used to implement the above step S3.

[0136] This device introduces the concept of temporal smoothness to solve the problem of instability of group structure in dynamic networks, and improves the stability and accuracy of group structure. Based on the ideas of evolutionary clustering and semi-non-negative matrix decomposition, the model integrates node similarity into network analysis, comprehensively considers the topological structure and similarity relationship between nodes in the metabolic network, and effectively solves the problem of insufficient group division in other methods. At the same time, by processing the microstructure of the metabolic network, this device can effectively solve the problem of data sparsity and make the connection between nodes within the group closer. In addition, the system effectively improves the distinction between groups and reduces the impact of noise through a method based on semi-non-negative matrix decomposition (Semi-NMF), thereby improving the accuracy and reliability of group discovery.

[0137] In summary, the embodiment of the present invention provides a group discovery method for a dynamic metabolic network, which is based on a group discovery method that fuses node similarity and network embedding by semi-non-negative matrix decomposition (Semi-NMF). The method uses the principle of semi-non-negative matrix decomposition, fuses node similarity, and uses the gradient descent method to solve the calculation while considering the dynamic changes of the network. It is mainly based on the following three points: First, the algorithm based on the principle of semi-non-negative matrix decomposition has a better effect in the group detection task, can reduce the influence of noise, and can make the distinction between groups higher, so that the group discovery result is more accurate and reliable; second, the present invention introduces the concept of time smoothness, constrains the change threshold between adjacent time slices, solves the influence of time changes between nodes in the time series network, and thus improves the performance of the model; third, the fusion of node similarity and the addition of group structure to network embedding can provide effective and rich information to solve the data sparsity problem in the microstructure, and can also make the learned node representation more discriminative.

[0138] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A method for discovering groups in a dynamic metabolic network, characterized in that: include: S1: construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and simulates the dynamic evolution of the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot; S2: For each node in the network snapshot, calculate the neighbor node set of the node at different time moments, and calculate the similarity of the neighbor node set at different time moments; then, fuse the similarities of the nodes at different time moments to obtain the comprehensive similarity measure of the nodes, and use the comprehensive similarity measure of the nodes as the adjacency matrix; S3: group structure modeling based on semi-non-negative matrix factorization, the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider the changes of the group structure between adjacent time steps; An objective function is constructed according to the adjacency matrix, the cluster centroid matrix and the group member matrix, and the objective function is iteratively calculated based on an optimization method based on the gradient descent method until the objective function value converges, and the group partition matrix of the node is obtained based on the objective function after the iterative calculation.

2. The method for group discovery of dynamic metabolic networks according to claim 1, characterized in that: In step S1, time is divided into multiple discrete time steps, and a dynamic metabolic network is established by considering the changes in factors such as metabolite concentration and enzyme activity; in this dynamic metabolic network, the states of metabolite and enzyme nodes will change over time, and the occurrence or non-occurrence of metabolic reactions will also change the topological structure of the dynamic metabolic network over time; For any dynamic metabolic network G = (V, E), where V = {v1, v2, ..., v n } represents a vertex set, E = {e1, e2, …, e m } represents the link set; the dynamic metabolic network is dynamic, where each moment contains a network snapshot, and all moments are represented by the binary adjacency matrix X t Indicates that t is the corresponding network slice, and the complex network matrix element X t,ij Indicates whether node i is directly connected to node j in snapshot t, that is, there is an edge connecting them. If there is an edge, then X t,ij =1, otherwise X t,ij =0.

3. The method for group discovery of dynamic metabolic networks according to claim 2, characterized in that: Step S2 includes: S201, according to the adjacency matrix X in step S1 t Calculate first-order proximity S202, according to the first-order proximity S (1) The second-order proximity matrix is ​​calculated by the collection of S203, introduce the weight coefficient η, and according to the first-order proximity S (1) and the second-order proximity matrix S (2) , calculate the final adjacency matrix S, S = S (1) +ηS (2) , where η>0.

4. The method for group discovery of dynamic metabolic networks according to claim 3, characterized in that: The similarity of neighbor node sets is calculated using a similarity measure based on the graph structure.

5. The method for group discovery of dynamic metabolic networks according to claim 4, characterized in that: The graph structure-based similarity measurement uses a cosine similarity algorithm.

6. The method for group discovery of a dynamic metabolic network according to claim 5, characterized in that: In step S201, the first-order proximity It is a measure used to describe the similarity between nodes in social networks. (1) It measures the most intuitively observed proximity probability between two nodes; When there is a relationship between node i and node j, its similarity score is X ij If it is positive, it indicates that there is a strong correlation between node i and node j. On the contrary, if there is no correlation between node i and node j, the similarity score is 0, indicating that there is no direct proximity relationship between node i and node j. In step S202, if there is no directly connected edge between two nodes, but they have many common neighbor nodes, then they can still be considered similar; In step S203, it is assumed that represents the set of first-order proximity between node i and all other nodes, according to N i With N j The similarity between them can determine the second-order proximity; here, cosine similarity is used to calculate the second-order proximity matrix. For nodes i and j, Where ||N|| represents the norm of N; according to the properties of cosine similarity, the value of the second-order proximity can be obtained between 0 and 1; in order to maintain the trade-off between the first-order and second-order proximity properties, a weight variable is used to connect them, that is, S = S (1) +ηS (2) , where η>0.

7. The method for group discovery of a dynamic metabolic network according to claim 6, characterized in that: In step S3, the objective function includes a cost function, which is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost.

8. The method for group discovery of dynamic metabolic networks according to claim 7, characterized in that: In step S3, the cluster centroid matrix F = (f1, f2, ..., f k ), where each column represents the central node of the corresponding group, usually with positive and negative attributes; The group membership matrix G is a non-negative matrix that indicates the input data nodes belong to specific groups. It is defined as follows: where s i represents the node labeled i in the input matrix, c k represents the group numbered k; the group member matrix G represents s i Is it c k Cluster, where if the element g ik is equal to 1, then s i Belongs to c k cluster, otherwise 0; Assuming that K-means clustering is performed on the input adjacency matrix S, the objective function of K-means clustering can be expressed as: In order to consider the mutual influence between adjacent time steps, a time smoothness constraint is introduced and added to the group member matrix. Specifically, a time cost is defined, which represents the probability that the group member structure changes significantly between t-1 and t. It directly reflects the quality of group discovery: a lower time cost means that the group member structure is more stable over time, which indicates that the quality of group discovery is higher. That is, the quality of group discovery is an inverse expression of the time cost. The higher the quality of group discovery, the lower the time cost. By adding the time cost of network topology modeling and the time cost of smoothing constraints, a total time cost is obtained. The time cost function is the sum of the current group discovery quality and the historical time cost. The time cost function is determined by maximizing the group discovery quality at the current moment and minimizing the historical cost. Therefore, the resulting cost function is as follows: Among them, the weight parameter α of the time smoothing constraint is a very critical parameter. Usually, its value range is a decimal between 0 and 1. The function of this parameter is to balance the changes in the group member structure and the consumption of time cost. Based on this, the objective function is in the following form: Excluding the first time slice, the gradient descent method is used to solve the objective function to obtain an iterative algorithm, which uses relevant update rules and takes the convergence of the objective function value as the iteration termination condition, so as to obtain the final group structure and then the group partition matrix of the node.

9. The method for group discovery of a dynamic metabolic network according to claim 8, characterized in that: The process of solving the objective function using the gradient descent method is as follows: When fixed G t When F t By minimizing formula (2), it can be simplified into the following form: In order to meet the non-negativity constraint, the Lagrange multiplier matrix λ is introduced and incorporated into the objective function. The constraints are adjusted using the Lagrange multiplication method to obtain the objective function with constraints. The obtained objective function is as follows: Assume that the partial differential is taken, Introducing the KKT fixed point condition, we can get: According to the derivation results, formula (7) is transformed equivalently: Therefore, F t The update transformation formula of the variable is: Similarly, when F t Fixed and G t When an update is required, G is constrained by introducing a non-negative Lagrange multiplier matrix λ t The non-negative property of G t The update transformation formula of the variable is as follows:

10. A group discovery device for a dynamic metabolic network, characterized in that: include: A dynamic metabolic network construction unit is used to construct a dynamic metabolic network, wherein the dynamic metabolic network uses metabolites and enzymes as nodes, metabolic reactions as edges connecting nodes, introduces time information, models the dynamic process of metabolic reactions as a time series, and performs dynamic evolution simulation on the network; the dynamic metabolic network is dynamic, wherein each moment contains a network snapshot; The node attribute fusion unit is used to calculate the neighbor node set of each node in the network snapshot at different time moments, and calculate the similarity of the neighbor node set at different time moments; then, the similarity of the node at different time moments is fused to obtain the comprehensive similarity measurement of the node, and the comprehensive similarity measurement of the node is used as the adjacency matrix; A group cluster detection unit, used for modeling a group structure based on semi-non-negative matrix factorization, wherein the group structure includes a cluster centroid matrix and a group member matrix, and a time smoothing constraint is added to the group member matrix to consider changes in the group structure between adjacent time steps; An objective function is constructed according to the adjacency matrix, the cluster centroid matrix and the group member matrix, and the objective function is iteratively calculated based on an optimization method based on the gradient descent method until the objective function value converges, and the group partition matrix of the node is obtained based on the objective function after the iterative calculation.

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