A gene regulation relationship prediction method based on matrix enhancement and feature fusion

Abstract

The application discloses a gene regulation relationship prediction method based on matrix enhancement and feature fusion, and comprises the following steps: 1, obtaining N genes G and their regulation relationship R; 2, calculating the directed adjacency matrix of the genes according to R; 3, generating the similarity matrix of the source genes and normalizing the similarity matrix; 4, generating the similarity matrix of the target genes and normalizing the similarity matrix; 5, processing the normalized source gene similarity matrix and the normalized target gene similarity matrix respectively by adopting an EASNN method, and performing matrix enhancement processing on the adjacency matrix; 6, generating the covariance matrix Co of the genes, and selecting the neighborhood gene pair set of any gene pair according to Co; 7, obtaining the total histogram set Mg of each gene pair according to G; 8, obtaining the total enhanced histogram set Ma of each gene pair; and 9, constructing a CNN network to obtain the probability that a regulation relationship exists between each gene pair. The application can effectively fuse the gene expression features and the enhanced network structure features, so that the regulation relationship between the genes can be more accurately predicted.

Description

Technical Field

[0001] This invention belongs to the field of gene regulation relationship prediction, specifically a gene regulation relationship prediction method based on matrix enhancement and feature fusion. Background Technology

[0002] Transcriptional regulation is crucial for cells, allowing them to adapt to changing environments and dynamically regulate gene expression in response to external stimuli. Transcription factors (TFs) exert their effects by regulating themselves and their corresponding target genes (tgs). Transcription factors, target genes, and their interactions constitute gene regulatory networks (GRNs). GRNs aim to capture the dependencies between these molecular entities, such as transcription factors and target genes. GRNs play a vital role in the growth and development of organisms by controlling gene expression. Specifically, GRNs are core elements in maintaining life processes, controlling biochemical reactions, and regulating compound levels, playing a significant role in various organisms and systems. Therefore, accurately constructing GRNs can improve our understanding of gene regulation mechanisms and the molecular mechanisms of organisms.

[0003] To better understand the regulatory mechanisms between genes, many algorithms have been developed in recent years for constructing Gene-Recurrent Neural Networks (GRNs). Information-theoretic methods quantify the statistical dependencies between genes based on their correlations, predicting the GRN structure from the resulting correlation matrix. Boolean network-based methods use Boolean variables to represent gene states and then use Boolean functions to calculate the relationships between genes, capturing dynamic interactions between them. Feature selection is also increasingly being applied to GRN inference, such as GENIE3, dynGENIE3, Jump3, and BiXGBoost. With the development of deep learning, more and more deep learning methods are being applied to GRN inference, such as CNN, TDL, and DeepDRIM.

[0004] The methods described above extract features from gene expression data to make predictions, ignoring the rich network structure information in GRNs. Compared to using gene expression features alone, integrating gene expression features and network structure features can significantly improve the accuracy of GRN predictions. However, the adjacency matrix generated by GRNs is very sparse, which can affect the final prediction results. CNNs are highly capable of feature extraction from image data. When extracting network structure features of genes, directly using the adjacency matrix as input to the CNN may negatively impact the prediction performance. Summary of the Invention

[0005] The present invention aims to address the shortcomings of the existing technologies by proposing a gene regulatory relationship prediction method based on matrix enhancement and feature fusion. This method aims to effectively integrate gene expression features and enhanced network structure features, thereby enabling more accurate prediction of the regulatory relationships between genes.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] The gene regulatory relationship prediction method based on matrix enhancement and feature fusion of this invention is characterized by the following steps:

[0008] Step 1: Obtain N genes G = {g1, g2, ..., g...} i ..., g N} and its regulatory relationship R, and any i-th gene g i It contains the expression values ​​of M genes; i∈[1,N];

[0009] Step 2: Calculate the directed adjacency matrix Adj = {adj} based on the regulatory relationship R. 1，1 , adj 1，2 ..., adj c，k ..., adj N，N}, where adj c，k Represents the c-th gene g c Does it regulate the k-th gene g? k If adjusted, it will cause adj c，k =1, otherwise, let adj ck =0; c, k∈[1,N];

[0010] Given that R is directional, the genes are treated as source genes or target genes respectively and processed accordingly;

[0011] Step 3: After generating and normalizing the source gene similarity matrix, the normalized source gene similarity matrix RS = {RS(s1, s1), RS(s1, s2), ..., RS(s1, s2)} is obtained. c s k ), ..., RS(s) N s N )}, where s c Representing the c-th source gene, s k Representing the k-th source gene, RS(s) c s k ) represents the c-th source gene s c With the k-th source gene s k The similarity, c, k∈[1,N];

[0012] Step 4: After generating and normalizing the target gene similarity matrix, the normalized target gene similarity matrix RT = {RT(t1, t2), RT(t1, t2), ..., RT(t3, t4)} is obtained. c , t k ), ..., RT(t) N , t N )}, where t c Representing the c-th target gene, t k Representing the k-th target gene, RT(t) c , t k ) represents the c-th target gene t c With the kth target gene t k The similarity; c, k∈[1,N];

[0013] Step 5: Input RS, RT, and Adj into the EASNN method, perform matrix augmentation on Adj, and obtain the augmented adjacency matrix MEAdj = {MEadj}. 1，1 MEadj 1，2 , ..., MEadj c，k ..., MEadj N，N}, where MEadj c，k Represents the c-th gene g c Regulating the k-th gene g k The probability of MEadj c，k ∈[0,1];

[0014] Step 6: Generate the covariance matrix Co = {Co} from N genes G. 1，1 Co 1，2 , ..., Co c，k ..., Co N，N}; where Co c，k Indicates the c-th gene g c and the kth gene g k The covariance between them;

[0015] Based on Co, select the c-th gene g c The gene with the highest positive covariance among the genes is designated as the c-th gene g. c Neighboring genes, denoted as {g c，1 g c，2 , ..., g c，b , ..., g c，B}, g c，b Indicates the c-th gene g c The b-th neighboring gene; the c-th gene g c Each gene pair forms a gene pair with its neighboring genes {(g c g c，1), (g c g c，2 ), ..., (g c g c，b ), ..., (g c g c，B )};

[0016] Based on Co, select the k-th gene g k The genes with the highest positive covariance values ​​(ranked Bth) among the genes are considered as the kth gene g. k Neighboring genes, denoted as {g k，1 g k，2 , ..., g k，b , ..., g k，B}, g k，b Represents the k-th gene g k The b-th neighboring gene; the k-th gene g k Each of its neighboring genes constitutes a gene pair {(g k g k，1 (g) k g k，2 ), ..., (g k g k，b ), ..., (g k g k，B )};

[0017] The c-th gene g c and the kth gene g k Each of them constitutes a gene pair {(g)} with itself c g c ), (g k g k )};

[0018] From {(g c g c ), (g k g k ), (g c g c，1 ), (g c g c，2 ), ..., (g c g c，B ), (g k g k，1 ), (g k g k，2 ), ..., (g k g k，B )} constitutes the c-th gene g c and the kth gene g k Gene pairs between (g) c g kThe set of neighboring gene pairs;

[0019] Step 7: Generate the c-th gene g c With the k-th gene g k Histogram Mg′ between c，k ;

[0020] Gene c is generated. c and the kth gene g k The set of neighborhood gene pairs between them corresponds to the set of neighborhood histograms Mg″. c，k ; by Mg′ c，k and Mg″ c，k Gene pairs (g) c g k ) total histogram Mg c，k Thus, the total histogram set of each gene pair, Mg = {Mg 1，1 Mg 1，2 , ...Mg c，k , ..., Mg N，N};

[0021] Step 8: Based on the c-th gene g c The set {MEadj} consisting of the probabilities of regulation of all genes c，1 MEadj c，2 , ..., MEadj c，N} and the kth gene g k The set {MEadj} consisting of the probabilities of regulation of all genes k，1 MEadj k，2 , ..., MEadj k，N Generate the c-th gene g c With the k-th gene g k Enhanced histogram Ma′ between c，k ;

[0022] Gene c is generated. c and the kth gene g k The set of enhanced neighborhood histograms Ma″ corresponding to the set of neighboring gene pairs between them c，k , by Ma′ c，k and Ma" c，k Gene pairs (g) c g k The total enhanced histogram Ma c，k Thus, the total enhancement histogram set Ma = {Ma} for each gene pair is obtained. 1，1 Ma 1，2 ,...,Ma c，k ,...,Ma N，N};

[0023] Step 9: Construct the CNN network, including: convolutional pooling layers, fully connected layers, fusion layers, and output layers;

[0024] The convolutional pooling layer processes Mg and Ma to obtain the gene expression feature tensor u. Mg and the enhanced adjacency matrix feature tensor u Ma After being processed by a fully connected layer, a one-dimensional gene feature v is obtained. Mg and one-dimensional enhanced gene features v Ma ;

[0025] The fusion layer will u Mg and u Ma After fusion, a one-dimensional fusion feature V is obtained;

[0026] The output layer supports gene features v Mg Enhance gene characteristics v Ma After splicing the fusion feature V and processing it through another fully connected layer and the sigmoid function, the probability of regulatory relationships between gene pairs is obtained.

[0027] The gene regulation relationship prediction method of the present invention is characterized in that step 3 generates a source gene similarity matrix according to the following process:

[0028] Using equation (1), the c-th source gene s before normalization is obtained. c With the k-th source gene s k Similarity RS′(s c s k ):

[0029]

[0030] In equation (1), r sl This indicates that based on the c-th source gene s c With the k-th source gene s k For the l-th source gene s l The corresponding weights assigned to the regulatory relationship, l∈{1,2,3,...,N}:

[0031] When l = c or l = k, that is, the c-th source gene s c With the k-th source gene s k If a regulatory relationship exists, then let

[0032] When l ≠ c, k, i.e., the c-th source gene s c With the k-th source gene s k There is no regulatory relationship, and the c-th source gene s c With the k-th source gene s kFor each of the other l-th genes s l If the same regulatory relationship exists, then let r = r w ;

[0033] When l ≠ c, k, i.e., the c-th source gene s c With the k-th source gene s k There is no regulatory relationship, and the c-th source gene s c With the k-th source gene s k For each of the other l-th genes s l If different regulatory relationships exist, then let r = -r w ;

[0034] And there are:

[0035]

[0036] In equation (2), δ represents the confidence level, and δ > 1.

[0037] The EASNN method in step 5 is performed according to the following steps:

[0038] Step 5.1: Transfer the c-th source gene s c The one-dimensional matrix formed by the similarity scores with all other source genes is denoted as rs′. c , for rs′ c After sorting in descending order, the resulting one-dimensional matrix is ​​denoted as rs. c Find the position a that satisfies equation (3):

[0039] rs c (a)-rs c (a+L)<rs c (a+L)-rs c (a+3L) (3)

[0040] In equation (3), L represents the step size, rs c (a) represents the sorted one-dimensional matrix rs c The sum of the similarities of the first a positions, and Among them, RS c (A) represents the sorted one-dimensional matrix rs c The similarity ranking A in the middle;

[0041] Step 5.2: Use equation (4) to obtain the c-th source gene s after filtering. c With the k-th source gene s k Similarity between S(s) c s k ):

[0042]

[0043] In equation (4), SNN(s) c ) represents the sorted one-dimensional matrix rs c In the context, RS(s) is the set of the first a largest similarities; c s k ) represents the c-th source gene s c With the k-th source gene s k The similarity between them;

[0044] Step 5.3: The c-th target gene t c The one-dimensional matrix formed by the similarity to all other target genes is denoted as rt′. c , for rt′ c The sorted matrix obtained by performing a descending sort is denoted as rt. c Find the position a′ that satisfies equation (3):

[0045] rt c (a′)-rt c (a′+L)<rt c (a′+L)-rt c (a′+3L) (5)

[0046] In equation (5), L represents the step size, rt c (a′) represents the sorted one-dimensional matrix rt c The sum of the similarities of the first a′ positions, and Among them, RT c (A) represents the sorted one-dimensional matrix rt c The similarity ranking A in the middle;

[0047] Step 5.4: Use equation (6) to obtain the c-th target gene t after filtering. c With the kth target gene t k Similarity between T(t) c , t t ):

[0048]

[0049] In equation (6), SNN(t) c ) represents the sorted one-dimensional matrix rt c The set consisting of the first a′ largest similarities; RT(t) c , t k ) represents the c-th target gene t c With the kth target gene t k Similarity;

[0050] Step 5.5: Construct source gene s using equation (7)c Interaction spectrum A s (s c ):

[0051]

[0052] In equation (8), w n Indicates the relationship with the source gene s c The weight factor of the source gene ranked nth in similarity, and w n =r n-1 *S(s c ,s n ), r represents the control weight w n The attenuation factor, and r∈[0,1], Indicates source gene s c The normalization term, and

[0053] Step 5.6: Construct the target gene t using equation (9). c Interaction profile of target genes A t (t c ):

[0054]

[0055] In equation (9), w' n' Indicates the relationship with target gene t c The weighting factor of the target gene ranked n' in similarity, and w' n =r' n-1 *T(t c ,t n r' represents the control weight w' n' The attenuation factor, and r∈[0,1], Indicates target gene t c The normalization term, and

[0056] Step 5.7: Obtain the new interaction spectrum A using equation (10). st :

[0057]

[0058] In equation (10), μ and v represent the control factors of source gene fusion rate and target gene fusion rate, respectively;

[0059] Step 5.8: Enhance the original adjacency matrix Adj using equation (11) to obtain the enhanced adjacency matrix MEAdj:

[0060] MEAdj = max(Adj, A st )) (11).

[0061] In step 7, the histogram is generated according to the following process:

[0062] For any pair of genes (g c ,g k ), and the c-th gene g c The expression range of the M expression values ​​is divided into several equal parts; the expression range of the k-th gene g is divided into several equal parts. k The expression ranges of the M expression values ​​are divided into equal parts;

[0063] The c-th gene g c The x-axis is divided into several equal parts, and the k-th gene g is used as the x-axis value. k The y-axis is divided into several equal parts, thus establishing a two-dimensional coordinate system;

[0064] Statistical analysis of the c-th gene g c and the kth gene g k The number of values ​​whose expression values ​​fall within the same equally divided range in a two-dimensional coordinate system is obtained, and the set of numbers H is obtained. c,k The final histogram Mg' is obtained using equation (12). c,k :

[0065]

[0066] The fusion layer in step 9 is to combine u Mg and u Ma After multiplying the corresponding elements, we get the initial fusion feature U. We then perform convolutional pooling on U to get the local fusion feature U'. Finally, we flatten U' to get the flattened feature U'". We then concatenate U' and U' and input them into another fully connected layer to obtain the fusion feature V.

[0067] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the gene regulation relationship prediction method, and the processor is configured to execute the program stored in the memory.

[0068] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the gene regulation relationship prediction method.

[0069] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0070] 1. Network structure, as an important feature of genes, is extracted from the adjacency matrix. However, because the adjacency matrix is ​​too sparse, this invention combines the obtained similarity matrix of source and target genes and uses the EASNN method to enhance the adjacency matrix, effectively overcoming the problem of the sparse adjacency matrix; thus, it can more accurately predict the regulatory relationships between genes.

[0071] 2. In order to better utilize the advantages of CNN in extracting image features, this invention generates corresponding total histograms and total enhancement histograms based on the adjacency matrices of gene expression and enhancement, respectively; by using a visual approach, the data becomes easier to analyze and understand, thereby improving the accuracy and reliability of gene regulation relationship prediction.

[0072] 3. Gene expression and network structure are two different aspects of gene features. When integrating them, it is necessary to consider not only the specific information of each feature, but also the synergistic effect between the two features. Therefore, this invention splices gene expression features, enhanced adjacency matrix features, and fused features obtained by a fusion method. This not only considers the specific information of the two features, but also their synergistic effect. Through this feature fusion, this invention can enhance the model's ability to understand and analyze gene expression features and network structure features, thereby improving the accuracy of gene regulation relationship prediction. Attached Figure Description

[0073] Figure 1 This is the overall flowchart of the present invention;

[0074] Figure 2 This is a process diagram of the enhanced adjacency matrix of the present invention;

[0075] Figure 3 This is a flowchart illustrating the process of histogram generation in this invention.

[0076] Figure 4 The plot shows the area under the receiver operating characteristic (AUC) and the area under the precision and recall curves for each method under ten runs of five-fold cross-validation on the benchmark dataset DREAM4.

[0077] Figure 5 The plot shows the area under the receiver operating characteristic (AUC) and area under the precision and recall curves for each method under ten runs of five-fold cross-validation in three different networks of the benchmark dataset *E. coli*. Detailed Implementation

[0078] In this embodiment, a gene regulatory relationship prediction method based on matrix enhancement and feature fusion is presented, such as... Figure 1 As shown, the procedure is as follows:

[0079] Step 1: Obtain N genes G = {g1, g2, ..., g...} i …,g N} and its regulatory relationship R, and any i-th gene g i It contains the expression values ​​of M genes; i∈[1,N];

[0080] Among them, gene expression value Figure 3 As shown, it is represented by an N*M two-dimensional matrix, where each row represents a gene, each column represents a sample, and the M values ​​in each gene represent the expression values ​​of the gene in M ​​different samples.

[0081] Step 2: Calculate the directed adjacency matrix Adj = {adj} based on the regulatory relationship R. 1，1 , adj 1，2 ..., adj c，k ..., adj N，N}, where adj c，k Represents the c-th gene g c Does it regulate the k-th gene g? k If adjusted, it will cause adj c，k =1, otherwise, let adj ck =0; c, k∈[1,N];

[0082] Given that R is directional, genes are treated as source genes or target genes respectively and processed accordingly.

[0083] Step 3, as follows Figure 2 As shown, after generating and normalizing the source gene similarity matrix, the normalized source gene similarity matrix RS={RS(s1,s1), RS(s1,s2), ..., RS(s1,s2) , ... ,RS ... c s k ), ..., RS(s) N s N )}, where s c Representing the c-th source gene, s k Representing the k-th source gene, RS(s) c s k ) represents the c-th source gene s c With the k-th source gene s k The similarity, c, k∈[1,N];

[0084] Among them, RS(s) in the generated source gene similarity matrix c s k The value of ) is obtained by using equation (1) to get the c-th source gene s before normalization. c With the k-th source gene s k Similarity RS′(s c sk ):

[0085]

[0086] In equation (1), This indicates that based on the c-th source gene s k With the k-th source gene s k For the l-th source gene s l The corresponding weights assigned to the regulatory relationship, l∈{1,2,3,...,N}:

[0087] When l = c or l = k, that is, the c-th source gene s c With the k-th source gene s k If a regulatory relationship exists, then let

[0088] When l ≠ c, k, i.e., the c-th source gene s c With the k-th source gene s k There is no regulatory relationship, and the c-th source gene s c With the k-th source gene s k For each of the other l-th genes s l If the same regulatory relationship exists, then let r = r w ;

[0089] When l ≠ c, k, i.e., the c-th source gene s c With the k-th source gene s k There is no regulatory relationship, and the c-th source gene s c With the k-th source gene s k For each of the other l-th genes s l If different regulatory relationships exist, then let r = -r w ;

[0090] And there are:

[0091]

[0092] In equation (2), δ represents the confidence level, and δ > 1.

[0093] Step 4, as follows Figure 2 As shown, after generating and normalizing the similarity matrix of the target genes, the normalized target gene similarity matrix RT = {RT(t1, t2), RT(t1, t2), ..., RT(t3, t4)} is obtained. c , t k ), ..., RT(t) N , t N )}, where t c Representing the c-th target gene, t k Representing the k-th target gene, RT(t)c , t k ) represents the c-th target gene t c With the kth target gene t k The similarity; c, k∈[1,N].

[0094] Step 5, as follows Figure 2 As shown, RS, RT, and Adj are input into the EASNN method, and matrix augmentation is performed on Adj to obtain the augmented adjacency matrix MEAdj={MEadj 1，1 MEadj 1，2 , ..., MEadj c，k ..., MEadj N，N}, where MEadj c，k Represents the c-th gene g c Regulating the k-th gene g k The probability of MEadj c，k ∈[0,1].

[0095] The steps of the EASNN method are as follows:

[0096] Step 5.1: Transfer the c-th source gene s c The one-dimensional matrix formed by the similarity scores with all other source genes is denoted as rs′. c , for rs′ c After sorting in descending order, the resulting one-dimensional matrix is ​​denoted as rs. c Find the position a that satisfies equation (3):

[0097] rs c (a)-rs c (a+L)<rs c (a+L)-rs c (a+3L) (3)

[0098] In equation (3), L represents the step size, rs c (a) represents the sorted one-dimensional matrix rs c The sum of the similarities of the first a positions, and Among them, RS c (A) represents the sorted one-dimensional matrix rs c The similarity ranking A in the middle;

[0099] Step 5.2: Use equation (4) to obtain the c-th source gene s after filtering. c With the k-th source gene s k Similarity between S(s) c s k ):

[0100]

[0101] In equation (4), SNN(s) c ) represents the sorted one-dimensional matrix rs c In the context, RS(s) is the set of the first a largest similarities; c s k ) represents the c-th source gene s c With the k-th source gene s k The similarity between them;

[0102] Step 5.3: The c-th target gene t c The one-dimensional matrix formed by the similarity to all other target genes is denoted as rt′. c , for rt′ c The sorted matrix obtained by performing a descending sort is denoted as rt. c Find the position a′ that satisfies equation (3):

[0103] rt c (a′)-rt c (a′+L)<rt c (a′+L)-rt c (a′+3L) (5)

[0104] In equation (5), L represents the step size, rt c (a′) represents the sorted one-dimensional matrix rt c The sum of the similarities of the first a′ positions, and Among them, RT c (A) represents the sorted one-dimensional matrix rt c The similarity ranking A in the middle;

[0105] Step 5.4: Use equation (6) to obtain the c-th target gene t after filtering. c With the kth target gene t k Similarity between T(t) c , t k ):

[0106]

[0107] In equation (6), SNN(t) c ) represents the sorted one-dimensional matrix rt c The set consisting of the first a′ largest similarities; RT(t) c , t k ) represents the c-th target gene t c With the kth target gene t k Similarity;

[0108] Step 5.5: Construct source gene s using equation (7)c Interaction spectrum A s (s c ):

[0109]

[0110] In equation (8), w n Indicates the relationship with the source gene s c The weight factor of the source gene ranked nth in similarity, and w n =r n-1 *S(s c s n ), r represents the control weight w n The attenuation factor, and r∈[0,1], Indicates source gene s c The normalization term, and

[0111] Step 5.6: Construct the target gene t using equation (9). c Interaction profile of target genes A t (t c ):

[0112]

[0113] In equation (9), w′ n′ Indicates the relationship with target gene t c The weighting factor of the target gene ranked n' in similarity, and w′ n =r′ n-1 *T(t c , t n r′ represents the control weight w′ n′ The attenuation factor, and r∈[0,1], Indicates target gene t c The normalization term, and

[0114] Step 5.7: Obtain the new interaction spectrum A using equation (10). st :

[0115]

[0116] In equation (10), μ and v control the fusion rates of the source gene and the target gene, respectively;

[0117] Step 5.8: Enhance the original adjacency matrix Adj using equation (11) to obtain the enhanced adjacency matrix MEAdj:

[0118] MEAdj = max(Adj, A) st (11)

[0119] Among them, A st The values ​​in A are decimals between 0 and 1, while the values ​​in Adj are integers of 0 or 1. For A... st Compare the values ​​of A and B with the value of Adj, and take the larger of the two values ​​to replace the 0 value in Adj. (This is done through A...) st The values ​​in the adjacency matrix are padded to reduce errors or biases in data analysis and processing, and improve data integrity and analytical accuracy. This also addresses the problem of the original adjacency matrix being too sparse to some extent.

[0120] Step 6: Generate the covariance matrix Co = {Co} from N genes G. 1，1 Co 1，2 , ..., Co c，k ..., Co N，N}; where Co c，k Indicates the c-th gene g c and the kth gene g k The covariance between them;

[0121] Based on Co, select the c-th gene g c The gene with the highest positive covariance among the genes is designated as the c-th gene g. c Neighboring genes, denoted as {g c，1 g c，2 , ..., g c，b , ..., g c，B}, g c，b Indicates the c-th gene g c The b-th neighboring gene; the c-th gene g c Each gene pair forms a gene pair with its neighboring genes {(g c g c，1 ), (g c g c，2 ), ..., (g c g c，b ), ..., (g c g c，B )};

[0122] Based on Co, select the k-th gene g k The genes with the highest positive covariance values ​​(ranked Bth) among the genes are considered as the kth gene g. k Neighboring genes, denoted as {g k，1 g k，2 , ..., g k，b , ..., g k，B}, g k，b Represents the k-th gene g k The b-th neighboring gene; the k-th gene g kEach of its neighboring genes constitutes a gene pair {(g k g k，1 ), (g k g k，2 ), ..., (g k g k，b ), ..., (g k g k，B )};

[0123] The c-th gene g c and the kth gene g k Each of them constitutes a gene pair {(g)} with itself c g c ), (g k g k )};

[0124] From {(g c g c ), (g k g k ), (g c g c，1 ), (g c g c，2 ..., (g c g c，B ), (g k g k，1 ), (g k g k，2 ), ..., (g k g k，B )} constitutes the c-th gene g c and the kth gene g k Gene pairs between (g) c g k The set of neighboring gene pairs;

[0125] The neighborhood image method is used because, in gene regulation relationships, transitive interactions between genes can lead to false positives, thus affecting the accuracy of the final gene regulation relationship prediction. Transitive interactions refer to interactions within a gene regulation relationship where even if gene g... c and gene g k There is no direct regulatory relationship between them, but gene g c Regulatory gene g d Gene g d It also regulates gene g k This indirect regulatory relationship may lead to incorrect inferences about gene g. c Directly regulates gene g kThis deviates from the original conditions. By using neighborhood images, we can more accurately capture and analyze the direct regulatory relationships between genes, thereby reducing false positives and improving the accuracy and reliability of gene relationship prediction.

[0126] Step 7, as follows Figure 3 As shown, the c-th gene g is generated. c With the k-th gene g k Histogram Mg′ between c，k ;

[0127] Generate the c-th gene g c and the kth gene g k The set of neighborhood gene pairs between them corresponds to the set of neighborhood histograms Mg″. c，k ;

[0128] From Mg′ c，k and Mg″ c，k Gene pairs (g) c g k ) total histogram Mg c，k Thus, the total histogram set of each gene pair, Mg = {Mg 1，1 Mg 1，2 , ..., Mg c，k , ..., Mg N，N};

[0129] For any pair of genes (g c g k ), and the c-th gene g k The expression range of the M expression values ​​is divided into several equal parts; the expression range of the k-th gene g is divided into several equal parts. k The expression ranges of the M expression values ​​are divided into equal parts;

[0130] The c-th gene g c The x-axis is divided into several equal parts, and the k-th gene g is used as the x-axis value. k The y-axis is divided into several equal parts, thus establishing a two-dimensional coordinate system;

[0131] Statistical analysis of the c-th gene g c and the kth gene g k The number of values ​​whose expression values ​​fall within the same equally divided range in a two-dimensional coordinate system is obtained, and the set of numbers H is obtained. c，k The final histogram Mg′ is obtained using equation (12). c，k :

[0132]

[0133] Step 8: Based on the c-th gene g cThe set consisting of the regulatory probabilities among all genes {MEadj} c，1 MEadj c，2 , ..., MEadj c，N} and the kth gene g k The set consisting of the probabilities of regulation among all genes {MEadj k，1 MEadj k，2 , ..., MEadj k，N Generate the c-th gene g c With the k-th gene g k Enhanced histogram Ma′ between c，k ;

[0134] Generate the c-th gene g c and the kth gene g k The set of enhanced neighborhood histograms Ma″ corresponding to the set of neighboring gene pairs between them c，k , by Ma′ c，k and Ma" c，k Gene pairs (g) c g k The total enhanced histogram Ma c，k Thus, the total enhancement histogram set Ma = {Ma} for each gene pair is obtained. 1，1 Ma 1，2 ,...,Ma c，k ,...,Ma N，N}

[0135] Step 9: Construct the CNN network, including: convolutional pooling layers, fully connected layers, fusion layers, and output layers;

[0136] The convolutional pooling layer processes Mg and Ma to obtain the gene expression feature tensor u. Mg and the enhanced adjacency matrix feature tensor u Ma After being processed by a fully connected layer, a one-dimensional gene feature v is obtained. Mg and one-dimensional enhanced gene features v Ma ;

[0137] The fusion layer will u Mg and u Ma After fusion, a one-dimensional fusion feature V is obtained;

[0138] The specific method for fusion in the fusion layer is to... Mg and u Ma After multiplying corresponding elements, we get the initial fused feature U. We then perform convolutional pooling on U to get the local fused feature U'. We then flatten U to get the flattened feature U'". Finally, we concatenate U' and U' and input them into another fully connected layer to obtain the fused feature.

[0139] Output layer for gene features v Mg Enhance gene characteristics v Ma After splicing the fusion feature V and processing it through another fully connected layer and the sigmoid function, the probability of regulatory relationships between gene pairs is obtained.

[0140] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0141] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0142] To evaluate the model's performance, the results were compared with individual classifiers and other methods, using the Area Under the Receiver Operating Characteristic (AUROC) as the evaluation metric. AAUROC, or Area Under the Receiver Operating Characteristic, is a value between 0 and 1, providing a direct assessment of the classifier's performance; a higher AUC indicates a better classifier. Ten five-fold cross-validations were used in the experiments, and the average value was calculated as the model's result.

[0143] Figure 4 This paper presents a performance comparison between our model and other classic methods on five different networks of the DREAM4 virtual dataset, a benchmark dataset. Experimental results show that our model outperforms all other methods on all five different networks of DREAM4, validating the effectiveness and superiority of our model.

[0144] Figure 5 This paper presents a performance comparison of our model with other classic methods on three different networks in the real-world E. coli dataset, a benchmark dataset. Experimental results show that our model outperforms all other methods in predicting regulatory relationships on the real-world dataset, demonstrating its superiority and indicating that it can more accurately predict regulatory relationships between genes.

Claims

1. A gene regulatory relationship prediction method based on matrix enhancement and feature fusion, characterized in that, The procedure is as follows: Step 1, Obtain Gene G={ and its regulatory relationship R, and any i-th gene It contains expression values ​​of M genes; ; Step 2: Calculate the directed adjacency matrix Adj={ based on the regulatory relationship R. ,in, Represents the c-th gene Does it regulate the kth gene? If regulation is implemented, then... =1, otherwise, let =0; ; Given that R is directional, the genes are treated as source genes or target genes respectively and processed accordingly; Step 3: After generating and normalizing the source gene similarity matrix, the normalized source gene similarity matrix RS={ ,in, Represents the c-th source gene. Represents the k-th source gene. Represents the c-th source gene With the k-th source gene similarity, ; Step 4: After generating and normalizing the similarity matrix of the target genes, the normalized target gene similarity matrix RT={ , in, Represents the c-th target gene. Represents the k-th target gene. Represents the c-th target gene With the kth target gene Similarity; ; Step 5: Input RS, RT, and Adj into the EASNN method, perform matrix augmentation on Adj, and obtain the augmented adjacency matrix MEAdj={ ,in, Represents the c-th gene Regulating the kth gene The probability, ; Step 6, from The covariance matrix Co of the genes generated by gene G is { ;in, Represents the c-th gene and the kth gene The covariance between them; Based on Co, select the c-th gene. The gene with the highest positive covariance among the C genes is designated as the Cth gene. Neighboring genes, denoted as , Represents the c-th gene The b-th neighboring gene; the c-th gene Each of them forms a gene pair with its neighboring genes. ; Based on Co, select the k-th gene. The gene with the highest positive covariance among the genes is the kth gene. Neighboring genes, denoted as , Represents the k-th gene The b-th neighboring gene; the k-th gene Each of its neighboring genes constitutes a gene pair. ; The c-th gene and the kth gene Each of them constitutes a gene pair with itself ; Depend on Constitutes the c-th gene and the kth gene Gene pairs The set of neighboring gene pairs; Step 7: Generate the c-th gene With the kth gene Histogram between ; Generate the c-th gene and the kth gene The set of neighborhood histograms corresponding to the set of neighboring gene pairs. ;Depend on and Gene pairs Total Histogram This yields the total histogram set for each gene pair. ; Step 8: Based on the c-th gene The set consisting of the probability of regulation of all genes. and the kth gene The set consisting of the probability of regulation of all genes. Generate the c-th gene With the kth gene Enhanced histogram between ; Generate the c-th gene and the kth gene The set of enhanced neighborhood histograms corresponding to the set of neighboring gene pairs between them ,Depend on and Gene pairs Total Enhanced Histogram This yields the set of total enhancement histograms for each gene pair. ; Step 9: Construct the CNN network, including: convolutional pooling layers, fully connected layers, fusion layers, and output layers; The convolutional pooling layer processes Mg and Ma to obtain gene expression feature tensors. and the enhanced adjacency matrix feature tensor After being processed by a fully connected layer, one-dimensional gene features are obtained. and one-dimensional enhanced gene characteristics ; The fusion layer will and After fusion, a one-dimensional fusion feature V is obtained; The output layer supports gene features. Enhance gene characteristics After splicing the fusion feature V and processing it through another fully connected layer and the sigmoid function, the probability of regulatory relationships between gene pairs is obtained.

2. The gene regulation relationship prediction method according to claim 1, characterized in that, Step 3 involves generating the source gene similarity matrix as follows: The c-th source gene before normalization is obtained using equation (1). With the k-th source gene similarity : (1) In equation (1), This indicates that based on the c-th source gene With the k-th source gene For the first Individual genes The corresponding weights assigned to the regulatory relationship, : when or That is, the c-th source gene With the k-th source gene If a regulatory relationship exists, then let ; when That is, the c-th source gene With the k-th source gene There is no regulatory relationship, and the c-th source gene With the k-th source gene For each of the other l-th genes If the same regulatory relationship exists, then let ; when That is, the c-th source gene With the k-th source gene There is no regulatory relationship, and the c-th source gene With the k-th source gene For each of the other l-th genes Different regulatory relationships exist, which leads to ; And there are: (2) In equation (2), Indicates the confidence level, and >

1.

3. The gene regulation relationship prediction method according to claim 2, characterized in that, The EASNN method in step 5 is performed according to the following steps: Step 5.1: Transfer the c-th source gene The one-dimensional matrix formed by the similarity to all other source genes is denoted as . ,right After sorting in descending order, the resulting one-dimensional matrix is ​​denoted as . Find the position that satisfies equation (3). : (3) In equation (3), Indicates the step size. Represents the sorted one-dimensional matrix The sum of the similarities of the first a positions, and ,in Represents the sorted one-dimensional matrix The similarity ranking A in the data; Step 5.2: Use equation (4) to obtain the c-th source gene after filtering. With the k-th source gene Similarity between : (4) In equation (4), Represents the sorted one-dimensional matrix In the context, the set consisting of the first a largest similarities; Represents the c-th source gene With the k-th source gene The similarity between them; Step 5.3: Target the c-th gene The one-dimensional matrix formed by the similarity to all other target genes is denoted as . ,right The sorted one-dimensional matrix obtained by performing a descending sort is denoted as Find the position that satisfies equation (3). : (5) In equation (5), Indicates the step size. Represents the sorted one-dimensional matrix Center front The sum of the similarity of the positions, and ,in, Represents the sorted one-dimensional matrix The similarity ranking A in the data; Step 5.4: Use equation (6) to obtain the c-th target gene after filtering. With the kth target gene Similarity between : (6) In equation (6), Represents the sorted one-dimensional matrix Center front The set consisting of the largest similarity values; Indicates the c-th target gene With the kth target gene Similarity; Step 5.5: Construct the source gene using equation (7) Interaction spectrum : (7) In equation (8), Indicates the relationship with the source gene The weighting factor of the source gene ranked nth in similarity, and , Indicates control weight The attenuation factor, and , Indicates source gene The normalization term, and ; Step 5.6: Construct the target gene using equation (9) Interaction profile of target genes : (9) In equation (9), Indicates the relationship with target genes Similarity ranking The weighting factor of the target gene at each position, and , Indicates control weight The attenuation factor, and , Indicates target gene The normalization term, and ; Step 5.7: Obtain the new interaction spectrum using equation (10). : (10) In equation (10), and These represent the control factors for the fusion rate of the source gene and the fusion rate of the target gene, respectively. Step 5.8: Use equation (11) to process the original adjacency matrix. The enhancement is performed, resulting in the enhanced adjacency matrix MEAdj: (11)。 4. The gene regulation relationship prediction method according to claim 3, characterized in that, In step 7, the histogram is generated according to the following process: For any pair of genes ( , ), the c-th gene The expression range of the M expression values ​​is divided into several equal parts; the k-th gene is... The expression ranges of the M expression values ​​are divided into equal parts; The c-th gene The x-axis is divided into several equal parts, and the k-th gene is used as the x-axis value. The y-axis is divided into several equal parts, thus establishing a two-dimensional coordinate system; Count the c-th gene and the kth gene The number of values ​​whose expression values ​​fall within the same equally divided range in a two-dimensional coordinate system is obtained, resulting in a set of quantities. The final histogram is obtained using equation (12). : (12)。 5. The gene regulation relationship prediction method according to claim 4, characterized in that, The fusion layer in step 9 is to... and After multiplying corresponding elements, the initial fusion feature is obtained. Local fusion features are obtained by performing convolutional pooling on U. Simultaneously, the flattened feature is obtained by flattening the U. Finally, the pieces will be assembled. and The input is then processed in another fully connected layer to obtain the fused feature V.

6. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the gene regulatory relationship prediction method according to any one of claims 1-5, and the processor is configured to execute the programs stored in the memory.

7. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it performs the steps of the gene regulatory relationship prediction method according to any one of claims 1-5.

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