CN112037849A - Device and method for predicting protein-protein interaction based on alternative direction multiplier method - Google Patents

Abstract

The invention discloses a device and a method for predicting protein-protein interaction based on an alternative direction multiplier method, which comprises the following steps of S1: inputting initial protein interaction data and constructing a symmetric sparse matrix W; s2: constructing an augmented Lagrange function and initializing parameters; s3: performing iterative optimization on the augmented Lagrangian function to obtain an optimized hidden feature matrix; s4: and calculating the predicted value of the interaction between the deleted proteins. According to the invention, the symmetrical non-negative implicit characteristic decomposition method by using the alternative direction multiplier method can provide high-precision protein interaction data prediction with smaller time and space complexity, so that the prediction precision of the interaction between the missing proteins considering the non-negative symmetry of the data is improved, and the method plays an important role in scientific research.

Description

Apparatus and method for protein-protein interaction prediction based on alternating direction multiplier method

technical field

The present invention relates to the technical field of data processing, in particular to a device and method for predicting the interaction between proteins based on the alternating direction multiplier method.

Background technique

There are a variety of proteins in species, and people's understanding of life activities is often inseparable from the interaction between proteins. It is difficult to completely determine the interaction between all proteins of a species through traditional biological experimental methods. However, it is possible to analyze species through computer design. full prediction of all protein-protein interactions. Therefore, how to efficiently and accurately predict the missing interactions between proteins by computer design has become a growing concern in the industry.

Generally speaking, since there are many different kinds of proteins contained in a species, and we can only determine part of the interaction information between proteins in reality, the network formed by the interactions between proteins of a species is an undirected network. High-dimensional sparse networks. In recent years, many scholars have proposed algorithms for predicting missing protein-protein interactions, among which the singular value decomposition method can be used for effective prediction of missing values. However, this method not only cannot handle high-dimensional data, but also does not take into account the non-negative symmetry of the data, that is, the modeling of the algorithm is not designed for the undirected network of protein-protein interactions. On the other hand, some scholars use symmetric non-negative matrix factorization methods to predict missing values for other symmetric data problems. However, symmetric non-negative matrix factorization is not efficient for large high-dimensional networks. For the undirected high-dimensional sparse network constructed from the protein-protein interaction data, how to accurately and efficiently predict the missing protein-protein interaction under the premise of considering the non-negative symmetry of the data has become a popular but difficult problem in academic research. The problem.

SUMMARY OF THE INVENTION

Aiming at the problem that the prediction accuracy of the missing protein interaction in the prior art is low, the present invention proposes a protein interaction prediction device and method based on the alternating direction multiplier method. The feature decomposition method can provide high-precision protein interaction data prediction with less time and space complexity, and improve the prediction accuracy of missing protein interactions.

In order to achieve the above object, the present invention provides the following technical solutions:

The protein-protein interaction prediction device based on the alternate direction multiplier method includes a data conversion module, a data initialization module, an alternate direction multiplier training module and a prediction data generation module connected in sequence; wherein,

The data conversion module is used to construct the received initial protein-protein interaction data into a corresponding symmetric sparse matrix, and store all non-missing values in the symmetric sparse matrix;

The data initialization module is used to generate the initial latent feature matrix, linear deviation vector, multiplier matrix and multiplier vector, and then constructs according to the non-missing value, latent feature matrix, linear deviation vector, multiplier matrix and multiplier vector The corresponding augmented Lagrangian function, and initialize the function;

The alternating direction multiplier training module is used to first slice the hidden feature matrix according to the hidden feature dimension, and then perform iterative optimization and updating of the iterative parameters, non-negative parameters and multiplier parameters in sequence, so that the convergent hidden feature can be obtained. feature matrix;

The predicted data generation module is used to calculate the predicted value of the interaction between missing proteins according to the converged latent feature matrix.

Preferably, the data conversion module includes a symmetric sparse matrix generation unit and a protein-protein interaction data storage unit; wherein,

The symmetric sparse matrix generation unit is used to construct the received initial protein-protein interaction data into a symmetric sparse matrix W;

The protein-protein interaction data storage unit is used to store all non-missing values in the constructed symmetric sparse matrix W.

Preferably, the data initialization module includes a linear deviation data generation unit, an augmented Lagrangian function construction unit and an initialization unit; wherein,

The linear deviation data generation unit is used to generate an initial linear deviation vector of protein-protein interaction;

The augmented Lagrangian function building unit is configured to construct a corresponding augmented Lagrangian function according to the initial inter-protein interaction linear deviation vector and the non-missing value;

The initialization unit is used to initialize the parameters involved in the prediction process of protein-protein interaction.

The present invention also provides a protein-protein interaction prediction method based on the alternating direction multiplier method, which specifically includes the following steps:

S1: Input the initial protein-protein interaction data and construct a symmetric sparse matrix W;

S2: Build an augmented Lagrangian function and initialize parameters;

S3: Iteratively optimize the augmented Lagrangian function to obtain the optimized latent feature matrix;

S4: Calculate the predicted value of missing protein-protein interactions.

Preferably, the S1 includes:

S1-1: Construct a symmetric sparse matrix W;

For the received initial protein-protein interaction data, it is stored as a triple entry, and the triple entry is represented as (pi , p _j , v _ij ), where pi represents the _ith protein, _and p _j represents the j-th protein, and v _ij represents the interaction value between the i-th protein and the j-th protein; the symmetric entry corresponding to each triple entry is generated to construct a symmetric sparse matrix W.

Preferably, the S2 includes:

S2-1: Construct the target loss function Q;

According to the symmetric sparse matrix W, all the non-missing value sets Γ are obtained. Combined with the set Γ and the generated linear deviation vectors H and G, the Euclidean distance is used as the optimization goal to construct the corresponding objective loss function Q:

s.t.E=F, E≥0; G=H, G≥0; (1)

In formula (1), E and F are latent feature matrices with M rows and D columns; the capacity of linear deviation vectors H and G is M; Γ represents the set of non-missing values in the symmetric sparse matrix W corresponding to the protein-protein interaction data ; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; e _i,d ∈ E, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix F; g _i ∈ G, represents the ith element of the linear deviation vector G; h _i ∈ H, represents the linear The i-th element of the deviation vector H; h _j ∈ H, represents the j-th element of the linear deviation vector H;

S2-2: Construct an augmented Lagrangian function.

According to the principle of the alternating direction multiplier method, the corresponding augmented Lagrangian function ε can be obtained, which is expressed by the following formula:

In formula (2), Γ represents the set of non-missing values in the symmetric sparse matrix W corresponding to the protein-protein interaction data; M represents the number of proteins, D represents the latent feature dimension; w _i,j represents protein i and protein The interaction value between j; e _i,d ∈ E, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, represents the ith protein in the latent feature matrix F The d-th element of the corresponding latent feature; f _j,d ∈ F, represents the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, represents the i-th element of the linear deviation vector G h _i ∈ H, represents the i-th element of the linear deviation vector H; h _j ∈ H, represents the j-th element of the linear deviation vector H; κ _{i,d ∈} K, represents the i-th element in the multiplier matrix K The d-th element of the latent feature corresponding to each protein; δ _i ∈ Z, represents the ith element of the multiplier vector Z; ρ _i and _ui are the penalty parameters, which are non-negative integers;

S2-3: Initialize relevant parameters for prediction;

Initialize the relevant parameters for prediction, the parameters include the latent feature matrix F, the latent feature matrix E, the multiplier matrix K, the linear deviation vector H, the linear deviation vector G, the multiplier vector Z, the hidden feature dimension D, the maximum training Iterative round number T, iteration round number control variable t, convergence termination threshold τ, learning rate η, penalty parameters ρ _i and _ui .

Preferably, the S3 includes:

S3-1: Iteratively update the iterative parameters, non-negative parameters and multiplier parameters in turn. The update strategy is as follows:

for d=1D

表示为第t+1轮迭代中由隐特征矩阵F中第1～第(d-1)个列向量所组成的M行(d-1)列的隐特征子矩阵；

表示为第t轮迭代中由隐特征矩阵F中第(d+1)～第D个列向量所组成的M行(D-d)列的隐特征子矩阵；

表示为第t轮迭代中由隐特征矩阵F中第d～第D个列向量所组成的M行(D-d+1)列的隐特征子矩阵；

表示为第t+1轮迭代中由线性偏差向量H中第1～第(d-1)个元素所组成的大小为(d-1)的线性偏差子向量；

表示为第t轮迭代中由线性偏差向量H中第d～第D个元素所组成的大小为(D-d+1)的线性偏差子向量；

表示为第t轮迭代中由线性偏差向量H中第(d+1)～第D个元素所组成的大小为(D-d)的线性偏差子向量；F^t+1表示为第t+1轮迭代中隐特征矩阵F；H^t+1表示为第t+1轮迭代中线性偏差向量H；G^t+1表示为第t+1轮迭代中线性偏差向量G；G^t表示为第t轮迭代中线性偏差向量G；E^t+1表示为第t+1轮迭代中隐特征矩阵E；E^t表示为第t轮迭代中隐特征矩阵E；K^t+1表示为第t+1轮迭代中乘子矩阵K；K^t表示为第t轮迭代中乘子矩阵K；Z^t+1表示为第t+1轮迭代中乘子向量Z；Z^t表示为第t轮迭代中乘子向量Z；η用于控制每次参数迭代优化过程中所走的步长；

表示增广拉格朗日函数ε对乘子矩阵K求偏导数；

表示增广拉格朗日函数ε对乘子向量Z求偏导数；In formula (3), F _{(1～M), d} represents the d-th column vector in the latent feature matrix F, wherein the column vector contains M elements, and H _d represents the d-th element in the linear deviation vector H;

It is expressed as a latent feature sub-matrix of M rows (d-1) columns composed of the 1st to (d-1)th column vectors in the latent feature matrix F in the t+1th iteration;

is represented as a latent feature sub-matrix of M rows (Dd) columns composed of (d+1) to D-th column vectors in the latent feature matrix F in the t-th iteration;

is represented as a latent feature sub-matrix of M rows (D-d+1) columns composed of the dth to Dth column vectors in the latent feature matrix F in the t-th iteration;

is expressed as a linear deviation sub-vector of size (d-1) composed of the 1st to (d-1)th elements in the linear deviation vector H in the t+1th iteration;

is expressed as a linear deviation sub-vector of size (D-d+1) composed of the d-th elements in the linear deviation vector H in the t-th iteration;

It is expressed as the linear deviation sub-vector of size (Dd) composed of the (d+1)~Dth elements in the linear deviation vector H in the t-th iteration; F ^t+1 is expressed as the t+1-th iteration Implicit feature matrix F; H ^t+1 represents the linear deviation vector H in the t+1 round of iteration; G ^t+1 represents the linear deviation vector G in the t+1 round of iteration; G ^t represents the t-th round iteration Medium linear deviation vector G; E ^t+1 represents the latent feature matrix E in the t+1 round of iteration; E ^t represents the latent feature matrix E in the t-th round of iteration; K ^t+1 represents the t+1 round of iteration Middle multiplier matrix K; K ^t is the multiplier matrix K in the t-th iteration; Z ^t+1 is the multiplier vector Z in the t+1-th iteration; Z ^t is the multiplier vector in the t-th iteration Z; η is used to control the step size taken in each parameter iterative optimization process;

represents the partial derivative of the augmented Lagrangian function ε with respect to the multiplier matrix K;

represents the partial derivative of the augmented Lagrangian function ε with respect to the multiplier vector Z;

S3-2: Iteratively optimize the augmented Lagrangian objective loss function ε;

The training iteration formulas are as follows:

In formula (4), Γ(i) represents all the non-missing value sets related to protein i in the non-missing value set Γ; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix F d elements; f _j,d ∈ F, is the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, is the i-th element of the linear deviation vector G; h _j ∈ H, is the jth element of the linear deviation vector H; h _i ∈ H, is the ith element of the linear deviation vector H; κ _{i,d ∈} K, is the latent feature corresponding to the ith protein in the multiplier matrix K The d-th element of ; δ _i ∈ Z is the i-th element of the multiplier vector Z; ρ _i and u _i are the penalty parameters;

S3-3: Determine whether the iterative process of the augmented Lagrangian objective loss function ε is terminated:

The judgment condition is that for each iteration of the augmented Lagrangian objective loss function ε, the value of the control variable t for the number of training iterations increases by 1. When the value of t reaches the maximum number of training iterations T, ε stops training; or augmentation During the training process of the Lagrangian objective loss function ε, when the absolute value of the difference between the ε value calculated after the current iteration and the previous round ε value has become smaller than the convergence termination threshold τ, ε stops training.

Preferably, in the S4, the calculation formula of the predicted value of the missing protein-protein interaction is:

表示计算得到的蛋白质间相互作用估计值；g_i∈G，为线性偏差向量G的第i个元素；g_j∈G，为线性偏差向量G的第j个元素；e_i,d∈E，为隐特征矩阵E中第i个蛋白质所对应隐特征的第d个元素；e_j,d∈E，为隐特征矩阵E中第i个蛋白质所对应隐特征的第d个元素；D表示隐特征维数。In formula (5),

represents the calculated estimated value of protein-protein interaction; g _i ∈ G, is the i-th element of the linear deviation vector G; g _j ∈ G, is the j-th element of the linear deviation vector G; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; e _j,d ∈ E is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; D represents the hidden feature feature dimension.

To sum up, due to the adoption of the above technical solutions, compared with the prior art, the present invention has at least the following beneficial effects:

By using the symmetrical non-negative latent feature decomposition method of the alternating direction multiplier method, the present invention can provide high-precision protein interaction data prediction with less time and space complexity, so as to improve the missing protein considering the non-negative symmetry of the data. Interaction prediction accuracy plays an important role in scientific research.

Description of drawings:

FIG. 1 is a schematic diagram of a protein-protein interaction prediction device based on the alternating direction multiplier method according to an exemplary embodiment of the present invention.

FIG. 2 is a schematic diagram of a protein-protein interaction prediction method based on the alternating direction multiplier method according to an exemplary embodiment of the present invention.

Detailed ways

The present invention will be further described in detail below with reference to the examples and specific implementation manners. However, it should not be construed that the scope of the above-mentioned subject matter of the present invention is limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

In the description of the present invention, it should be understood that the terms "portrait", "horizontal", "upper", "lower", "front", "rear", "left", "right", "vertical", The orientations or positional relationships indicated by "horizontal", "top", "bottom", "inside", "outside", etc. are based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than An indication or implication that the referred device or element must have a particular orientation, be constructed and operate in a particular orientation, is not to be construed as a limitation of the invention.

As shown in FIG. 1 , the present invention proposes a protein-protein interaction prediction device based on the alternate direction multiplier method, including a data conversion module 10, a data initialization module 20, an alternate direction multiplier training module 30 and a prediction data generation module 40; The input terminal of the data conversion module 10 inputs the initial protein interaction data, the output terminal of the data conversion module 10 is connected to the input terminal of the data initialization module 20, and the output terminal of the data initialization module 20 is connected to the input terminal of the alternating direction multiplier training module 30. The output terminal of the alternating direction multiplier training module 30 is connected with the input terminal of the prediction data generation module 40, and the output terminal of the prediction data generation module 40 outputs the prediction data of protein-protein interaction.

The data conversion module 10 is configured to construct the received initial protein-protein interaction data into a corresponding symmetric sparse matrix W, and store all non-missing values in the symmetric sparse matrix W.

The data initialization module 20 is used to generate an initial protein-protein interaction linear deviation vector Z, and then construct a corresponding augmented Lagrangian function according to all non-missing values and linear deviation data in the generated symmetric sparse matrix, and Initialize the relevant parameters involved in the function.

The alternating direction multiplier training module 30 is used for firstly slicing the hidden feature matrix according to the hidden feature dimension, and then performing iterative optimization and updating of the iterative parameters, non-negative parameters and dual parameters in sequence, so that the converged hidden feature matrix can be obtained. .

The predicted data generation module 40 is configured to calculate the predicted value of the missing protein interaction according to the latent feature matrix of the protein interaction trained by the alternating direction multiplier.

In this embodiment, the data conversion module 10 includes a symmetric sparse matrix generation unit 101 and an inter-protein interaction data storage unit 102 . The output end of the symmetric sparse matrix generation unit 101 is connected to the input end of the inter-protein interaction data storage unit 102 .

The symmetric sparse matrix generation unit 101 is configured to construct the received initial protein-protein interaction data into a symmetric sparse matrix W. Among them, for the received initial protein-protein interaction data, each protein-protein interaction is stored in the form of triples, and the representation of the triples is ppi ₌ (pi , p _j , v _ij ) , where pi represents the _ith protein, p _j represents the jth protein, and v _ij represents the interaction value between the ith protein and the jth protein. The received initial protein-protein interaction data is not really all the protein-protein interaction data. In the initially received protein-protein interaction data, taking the interaction between protein i and protein j as an example, in the initial data set only There are only (pi , p _j , v _ij ) entries, and no corresponding (p _j , p _i , _{v ij )} . Therefore, before doing other data processing, the symmetric entry corresponding to each entry in the initially received protein-protein interaction data is generated to construct a symmetric matrix W. The rows and columns of matrix W correspond to the same protein sequence. Since there are many proteins, the known interaction data between proteins must be far less than the total number of elements of matrix W, so matrix W is a symmetric sparse matrix.

The protein-protein interaction data storage unit 102 is used to store all the non-missing values in the constructed symmetric sparse matrix W, wherein each non-missing value is also stored in the form of triples.

The data initialization module 20 includes a linear deviation data generation unit 201 , an augmented Lagrangian function construction unit 202 , and an initialization unit 203 .

The linear deviation data generating unit 201 is used for generating initial linear deviation data of protein-protein interaction.

The augmented Lagrangian function constructing unit 202 is configured to construct a corresponding target loss function according to the initial protein-protein interaction linear deviation data and the non-missing values extracted from the symmetric sparse matrix W.

The initialization unit 203 is used to initialize the parameters involved in the prediction process of protein-protein interaction, wherein the parameters include the initialization of the latent feature matrix F responsible for iteration, the latent feature matrix E responsible for non-negative control, the dual matrix K, and the linear deviation responsible for iteration vector H, linear deviation vector G responsible for non-negative control, dual vector Z, latent feature dimension D, maximum number of training iterations T, control variable t for the number of iterations in the training process, convergence termination threshold τ, learning rate η, penalty Parameters ρ _i and _ui . The latent feature dimension D determines the latent feature space dimension of the latent feature matrices E and F, and is initialized to a positive integer; the structure size of the latent feature matrices E and F is determined by the received initial protein-protein interaction data. The number of proteins M and the hidden feature dimension D are determined, that is, E and F are latent feature matrices with M rows and D columns. Initialization; the maximum number of training iteration rounds T is a variable that controls the upper limit of the iteration process and is initialized to a large positive integer; the iteration round number control variable t is initialized to 0; the convergence termination threshold τ is a parameter used to judge whether the iteration process is converged, Initialize with a very small positive number; the learning rate η is used to control the step size taken in each iteration of the optimization process, initialized with a very small positive number; the penalty parameters ρ _i and _ui are used to control the Lagrangian The effect of the augmentation term in the function, initialized with a positive number.

The alternating direction multiplier training module 30 is used for slicing the matrices F, E, K according to the hidden feature dimension D, and iteratively updates the iterative parameters, non-negative parameters and dual parameters in sequence according to the slicing.

In this embodiment, the prediction data generation module 40 includes a prediction data storage unit for storing the predicted missing protein interaction values, wherein each missing protein interaction prediction value is also stored in the form of triples.

The device can be deployed in an existing server, or can be deployed in a separate server dedicated to predicting interactions between proteins.

Based on the above device, the present invention also proposes a method for predicting the interaction between proteins based on the alternating direction multiplier method, which acts on the prediction of the interaction between missing proteins and can perform efficient and high-accuracy prediction of the interaction between missing proteins, such as As shown in Figure 2, it specifically includes the following steps:

S1: Input initial protein-protein interaction data and construct a symmetric sparse matrix W.

In this embodiment, the server sends an instruction for predicting the protein-protein interaction and initial protein-protein interaction data to the device, and the instruction includes periodicity, notification from the device, notification from the server, and the like.

S1-1: Construct a symmetric sparse matrix W.

In this embodiment, the received initial protein-protein interaction data are all stored in the form of triples, and the representation of the triples is ppi _{=(pi , p j , v ij ) ,} where _pi represents the ith protein, p _j represents the jth protein, and v _ij represents the interaction value between the ith protein and the jth protein.

The initial protein-protein interaction data received at this time is not really all the protein-protein interaction data. In the received initial protein-protein interaction data, taking the interaction between protein i and protein j as an example, in the initial data There are only (p _i , p _j , v _ij ) entries in the set, and there is no corresponding (p _j , p _i , v _ij ), because the matrix formed by the protein interaction data is a symmetric matrix, so there is v _ij = v _ji . Therefore, in order to save space for storing data, only (pi , p _j , v _ij ) entries are required in the initial _dataset . Therefore, before doing other data processing, the symmetric entry corresponding to each entry in the received initial protein-protein interaction data is generated to construct a symmetric sparse matrix W. The rows and columns of the symmetric sparse matrix W correspond to the same protein sequence. Since there are many proteins, the known interaction data between proteins must be far less than the total number of elements in the symmetric sparse matrix W.

S2: Build the augmented Lagrangian function and initialize the parameters.

S2-1: Construct the target loss function Q.

In this step, according to the generated symmetric sparse matrix W, the non-missing value elements in the upper triangle of the matrix W are traversed. In each traversal, for the traversed upper triangle non-missing value elements, according to the characteristics of the symmetric matrix, Generate the non-missing value element corresponding to the lower triangle, and then add these two elements to the non-missing value set. When the traversal is completed, the set Γ of all non-missing values can be obtained. Decompose the symmetric sparse matrix W to obtain the latent feature matrix F and the deviation vector H, where the structural size of F is determined by the number M of proteins involved in the received initial protein-protein interaction data and the latent feature dimension D. , that is, F is the latent feature matrix with M rows and D columns, and the latent feature matrix F is initialized with a random positive number in the open interval (0, 0.004); the structure size of H is determined by the received initial protein-protein interaction data. The number M of proteins received is determined, that is, H is a vector containing M elements, and the deviation vector H is initialized with a random positive number in the open interval (0, 0.004). The structure size of the latent feature E is the same as that of F, and the structure size of the bias vector G is the same as that of H. Then let the initial value of each element in E equal the initial value of the corresponding element in F, and the initial value of each element in G is equal to the initial value of the corresponding element in H. Combining the set Γ and the generated latent feature matrices E and F and the deviation vectors G and H, the Euclidean distance is used as the optimization goal to construct the corresponding objective loss function Q, which is expressed by the following formula:

s.t.E=F, E≥0; G=H, G≥0; (1)

In formula (1), E, F are latent feature matrices with M rows and D columns; linear deviation vectors H, G are vectors containing M elements; Γ represents the non-symmetric sparse matrix W corresponding to the protein-protein interaction data. The set of missing values; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; f _i,d ∈ F, represents the d-th hidden feature corresponding to the ith protein in the latent feature matrix F g _i ∈ G, represents the ith element of the linear deviation vector G; h _i ∈ H, represents the ith element of the linear deviation vector H; h _j ∈ H, represents the j th element of the linear deviation vector H .

S2-2: Construct an augmented Lagrangian function.

First, construct a multiplier matrix K with M rows and D columns and a multiplier vector Z containing M elements, where M represents the number of proteins, D represents the latent feature dimension, and the multiplier matrix K is initialized to a zero matrix, and The multiplier vector Z is initialized to a zero vector. Then, according to the principle of the alternating direction multiplier method, the corresponding augmented Lagrangian function ε can be obtained, which is expressed by the following formula:

In formula (2), Γ represents the set of non-missing values in the symmetric sparse matrix W corresponding to the protein-protein interaction data; M represents the number of proteins, D represents the latent feature dimension; w _i,j represents protein i and protein The interaction value between j; e _i,d ∈ E, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, represents the ith protein in the latent feature matrix F The d-th element of the corresponding latent feature; f _j,d ∈ F, represents the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, represents the i-th element of the linear deviation vector G h _i ∈ H, represents the i-th element of the linear deviation vector H; h _j ∈ H, represents the j-th element of the linear deviation vector H; κ _{i,d ∈} K, represents the i-th element in the multiplier matrix K The d-th element of the latent feature corresponding to each protein; δ _i ∈ Z, represents the i-th element of the multiplier vector Z; ρ _i and _ui are the penalty parameters, which are non-negative integers.

S2-3: Initialize relevant parameters for prediction.

In this step, initialize the relevant parameters for prediction, the parameters include initializing the latent feature matrix F responsible for iteration; initializing the latent feature matrix E responsible for non-negative control; initializing the multiplier matrix K; initializing the linear deviation vector H responsible for the iteration; Initialize the linear deviation vector G responsible for non-negative control; initialize the multiplier matrix Z; initialize the latent feature dimension D; initialize the maximum number of training iterations T; Learning rate η; initialization penalty parameters ρ _i and _ui .

in,

The latent feature dimension D determines the latent feature space dimension of the latent feature matrices E and F, and is initialized to a positive integer;

The structure size of the latent feature matrices E and F is determined by the number M of proteins involved in the initially received protein-protein interaction data and the latent feature dimension D, that is, E and F are latent feature matrices with M rows and D columns. , initialize the latent feature matrices E and F and the linear deviation vectors G and H with small random positive numbers respectively;

The multiplier matrix K is initialized to a zero matrix and the multiplier vector Z is initialized to a zero vector;

The maximum number of training iterations T is a variable that controls the upper limit of the iteration process, and is initialized to a larger positive integer;

The iteration round number control variable t is initialized to 0;

The convergence termination threshold τ is a parameter used to judge whether the iterative process is converged, initialized with a very small positive number;

The learning rate η is used to control the step size taken in each iteration of the optimization process, and is initialized with a very small positive number;

Penalty parameters ρ _i and u _i are used to control the effect of the augmentation term in the Lagrangian function and are initialized with positive numbers.

S3: Iteratively optimize the augmented Lagrangian function to obtain the optimized latent feature matrix.

S3-1: Fragment and update the augmented Lagrangian function.

In this step, the augmented Lagrangian function ε is sharded according to the hidden feature dimension D, and then the iterative parameters, non-negative parameters and multiplier parameters are iteratively updated according to the sharding.

The specific update strategy is as follows:

for d=1 D

表示为第t+1轮迭代中由隐特征矩阵F中第1～第(d-1)个列向量所组成的M行(d-1)列的隐特征子矩阵；

表示为第t轮迭代中由隐特征矩阵F中第(d+1)～第D个列向量所组成的M行(D-d)列的隐特征子矩阵；

表示为第t轮迭代中由隐特征矩阵F中第d～第D个列向量所组成的M行(D-d+1)列的隐特征子矩阵；

表示为第t+1轮迭代中由线性偏差向量H中第1～第(d-1)个元素所组成的大小为(d-1)的线性偏差子向量；

表示为第t轮迭代中由线性偏差向量H中第d～第D个元素所组成的大小为(D-d+1)的线性偏差子向量；

表示为第t轮迭代中由线性偏差向量H中第(d+1)～第D个元素所组成的大小为(D-d)的线性偏差子向量；F^t+1表示为第t+1轮迭代中隐特征矩阵F；H^t+1表示为第t+1轮迭代中线性偏差向量H；G^t+1表示为第t+1轮迭代中线性偏差向量G；G^t表示为第t轮迭代中线性偏差向量G；E^t+1表示为第t+1轮迭代中隐特征矩阵E；E^t表示为第t轮迭代中隐特征矩阵E；K^t+1表示为第t+1轮迭代中乘子矩阵K；K^t表示为第t轮迭代中乘子矩阵K；Z^t+1表示为第t+1轮迭代中乘子向量Z；Z^t表示为第t轮迭代中乘子向量Z；η用于控制每次参数迭代优化过程中所走的步长；

表示增广拉格朗日函数ε对乘子矩阵K求偏导数；

表示增广拉格朗日函数ε对乘子向量Z求偏导数。In formula (3), F _{(1～M), d} represents the d-th column vector in the latent feature matrix F, wherein the column vector contains M elements, and H _d represents the d-th element in the linear deviation vector H;

It is expressed as a latent feature sub-matrix of M rows (d-1) columns composed of the 1st to (d-1)th column vectors in the latent feature matrix F in the t+1th iteration;

is represented as a latent feature sub-matrix of M rows (Dd) columns composed of (d+1) to D-th column vectors in the latent feature matrix F in the t-th iteration;

is represented as a latent feature sub-matrix of M rows (D-d+1) columns composed of the dth to Dth column vectors in the latent feature matrix F in the t-th iteration;

is expressed as a linear deviation sub-vector of size (d-1) composed of the 1st to (d-1)th elements in the linear deviation vector H in the t+1th iteration;

is expressed as a linear deviation sub-vector of size (D-d+1) composed of the d-th elements in the linear deviation vector H in the t-th iteration;

It is expressed as the linear deviation sub-vector of size (Dd) composed of the (d+1)~Dth elements in the linear deviation vector H in the t-th iteration; F ^t+1 is expressed as the t+1-th iteration Implicit feature matrix F; H ^t+1 represents the linear deviation vector H in the t+1 round of iteration; G ^t+1 represents the linear deviation vector G in the t+1 round of iteration; G ^t represents the t-th round iteration Medium linear deviation vector G; E ^t+1 represents the latent feature matrix E in the t+1 round of iteration; E ^t represents the latent feature matrix E in the t-th round of iteration; K ^t+1 represents the t+1 round of iteration Middle multiplier matrix K; K ^t is the multiplier matrix K in the t-th iteration; Z ^t+1 is the multiplier vector Z in the t+1-th iteration; Z ^t is the multiplier vector in the t-th iteration Z; η is used to control the step size in the iterative optimization process of each parameter;

represents the partial derivative of the augmented Lagrangian function ε with respect to the multiplier matrix K;

Represents the partial derivative of the augmented Lagrangian function ε with respect to the multiplier vector Z.

It can be seen from the above update strategy that the decision parameters of the corresponding dimension of the latent feature matrix F and the linear deviation vector H are updated according to the slicing; then the decision parameters and the linear deviation vector G of the corresponding dimension of the latent feature matrix E are updated; Finally, the decision parameters of the corresponding dimension of the multiplier matrix K and the multiplier vector Z are updated.

S3-2: Iteratively optimize the augmented Lagrangian objective loss function ε.

According to the sharding update strategy, based on the obtained set of non-missing values Γ, the objective loss function Q, namely the augmented Lagrangian objective loss function ε, is iteratively optimized.

In this step, according to the shard update strategy and the obtained set of non-missing values Γ, for shard d, the training iteration formulas for the iteration parameters, non-negative parameters and multiplier parameters are as follows:

In formula (4), Γ(i) represents all the non-missing value sets related to protein i in the non-missing value set Γ; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix F d elements; f _j,d ∈ F, is the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, is the i-th element of the linear deviation vector G; h _i ∈ H, is the i-th element of the linear deviation vector H; h _j ∈ H, is the j-th element of the linear deviation vector H; κ _{i,d ∈} K, is the latent feature corresponding to the i-th protein in the multiplier matrix K The d-th element of ; δ _i ∈ Z is the i-th element of the multiplier vector Z; ρ _i and _ui are the penalty parameters.

In this step, according to the sharding and update strategy, since the hidden feature dimension is D, each round of iterative update contains D sub-updates in total. After each round of iterative optimization is completed, we can obtain the generated The latent feature matrix E, F, linear deviation vector G, H, multiplier matrix K and multiplier vector Z.

S3-3: Determine whether the training iteration process of the augmented Lagrangian objective loss function ε on Γ reaches the termination condition.

In this step, the augmented Lagrangian objective loss function ε has two cases when the training iterative process on Γ reaches the termination condition. The first is that for each iteration of Q, the value of the control variable t for the number of training iterations is increased by 1. When the value of t reaches the maximum number of training iterations T, Q stops training; the second is that during the Q training process, the current iteration After the end, when the absolute value of the difference between the calculated Q value and the previous round Q value has become smaller than the convergence termination threshold τ, Q stops training.

S4: Calculate the predicted value of missing protein-protein interactions.

其中i,j∈M，M表示蛋白质个数,计算公式为：In this step, when the target loss function Q, that is, the augmented Lagrangian target loss function ε, converges on the upper Γ pair, take the latent feature matrix E and the linear deviation vector G obtained by training that minimize Q, and use its value to calculate the predicted value of the interaction between protein i and protein j

where i, j∈M, M represents the number of proteins, and the calculation formula is:

表示计算得到的蛋白质间相互作用估计值；g_i∈G，为线性偏差向量G的第i个元素；g_j∈G，为线性偏差向量G的第j个元素；e_i,d∈E，为隐特征矩阵E中第i个蛋白质所对应隐特征的第d个元素；e_j,d∈E，为隐特征矩阵E中第i个蛋白质所对应隐特征的第d个元素；D表示隐特征维数。In formula (5),

represents the calculated estimated value of protein-protein interaction; g _i ∈ G, is the i-th element of the linear deviation vector G; g _j ∈ G, is the j-th element of the linear deviation vector G; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; e _j,d ∈ E is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; D represents the hidden feature feature dimension.

It can be seen from the above technical solutions that the embodiment of the present invention provides a method for predicting missing protein interactions by symmetric non-negative latent feature analysis using the alternating direction multiplier method, which specifically acts on the interaction data between missing proteins and can be used with a small amount of data. It provides high-precision protein interaction data prediction to solve the problem of missing protein-protein interaction prediction for non-negative symmetry of the data.

Those of ordinary skill in the art can understand that the above-mentioned embodiments are specific examples for realizing the present invention, and in practical applications, various changes in form and details can be made without departing from the spirit and the spirit of the present invention. scope.

Claims (8)

1. the inter-protein interaction prediction device based on the alternate direction multiplier method, is characterized in that, comprises data conversion module, data initialization module, alternate direction multiplier training module and prediction data generation module; Wherein, The data conversion module is used to construct the received initial protein-protein interaction data into a corresponding symmetric sparse matrix, and store all non-missing values in the symmetric sparse matrix; The data initialization module is used to generate the initial latent feature matrix, linear deviation vector, multiplier matrix and multiplier vector, and then constructs according to the non-missing value, latent feature matrix, linear deviation vector, multiplier matrix and multiplier vector The corresponding augmented Lagrangian function, and initialize the function; The alternating direction multiplier training module is used to first slice the hidden feature matrix according to the hidden feature dimension, and then perform iterative optimization and updating of the iterative parameters, non-negative parameters and multiplier parameters in sequence, so that the convergent hidden feature can be obtained. feature matrix; The predicted data generation module is used to calculate the predicted value of the interaction between missing proteins according to the converged latent feature matrix. 2. The protein-protein interaction prediction device based on the alternating direction multiplier method according to claim 1, wherein the data conversion module comprises a symmetric sparse matrix generation unit and a protein-protein interaction data storage unit; wherein, The symmetric sparse matrix generation unit is used to construct the received initial protein-protein interaction data into a symmetric sparse matrix W; The protein-protein interaction data storage unit is used to store all non-missing values in the constructed symmetric sparse matrix W. 3. The protein-protein interaction prediction device based on the alternating direction multiplier method according to claim 1, wherein the data initialization module comprises a linear deviation data generation unit, an augmented Lagrangian function construction unit and an initialization unit. unit; of which, The linear deviation data generation unit is used to generate an initial linear deviation vector of protein-protein interaction; The augmented Lagrangian function building unit is configured to construct a corresponding augmented Lagrangian function according to the initial inter-protein interaction linear deviation vector and the non-missing value; The initialization unit is used to initialize the parameters involved in the prediction process of protein-protein interaction. 4. A protein-protein interaction prediction method based on the alternating direction multiplier method, characterized in that it specifically comprises the following steps: S1: Input the initial protein-protein interaction data and construct a symmetric sparse matrix W; S2: Build an augmented Lagrangian function and initialize parameters; S3: Iteratively optimize the augmented Lagrangian function to obtain the optimized latent feature matrix; S4: Calculate the predicted value of missing protein-protein interactions. 5. The protein-protein interaction prediction method based on the alternating direction multiplier method as claimed in claim 4, wherein the S1 comprises: S1-1: Construct a symmetric sparse matrix W; For the received initial protein-protein interaction data, it is stored as a triple entry, and the triple entry is represented as (pi , p _j , v _ij ), where pi represents the _ith protein, _and p _j represents the j-th protein, and v _ij represents the interaction value between the i-th protein and the j-th protein; the symmetric entry corresponding to each triple entry is generated to construct a symmetric sparse matrix W. 6. The protein-protein interaction prediction method based on the alternating direction multiplier method as claimed in claim 4, wherein the S2 comprises: S2-1: Construct the target loss function Q; According to the symmetric sparse matrix W, all the non-missing value sets Γ are obtained. Combined with the set Γ and the generated linear deviation vectors H and G, the Euclidean distance is used as the optimization goal to construct the corresponding objective loss function Q:

s.t.E=F, E≥0; G=H, G≥0; (1) In formula (1), E and F are latent feature matrices with M rows and D columns; the capacity of linear deviation vectors H and G is M; Γ represents the set of non-missing values in the symmetric sparse matrix W corresponding to the protein-protein interaction data ; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; e _i,d ∈ E, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix F; g _i ∈ G, represents the ith element of the linear deviation vector G; h _i ∈ H, represents the linear The i-th element of the deviation vector H; h _j ∈ H, represents the j-th element of the linear deviation vector H; S2-2: Construct an augmented Lagrangian function. According to the principle of the alternating direction multiplier method, the corresponding augmented Lagrangian function ε can be obtained, which is expressed by the following formula:

In formula (2), Γ represents the set of non-missing values in the symmetric sparse matrix W corresponding to the protein-protein interaction data; M represents the number of proteins, D represents the latent feature dimension; w _i,j represents protein i and protein The interaction value between j; e _i,d ∈ E, represents the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, represents the ith protein in the latent feature matrix F The d-th element of the corresponding latent feature; f _j,d ∈ F, represents the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, represents the i-th element of the linear deviation vector G h _i ∈ H, represents the i-th element of the linear deviation vector H; h _j ∈ H, represents the j-th element of the linear deviation vector H; κ _{i,d ∈} K, represents the i-th element in the multiplier matrix K The d-th element of the latent feature corresponding to each protein; δ _i ∈ Z, represents the ith element of the multiplier vector Z; ρ _i and _ui are the penalty parameters, which are non-negative integers; S2-3: Initialize relevant parameters for prediction; Initialize the relevant parameters for prediction, the parameters include the latent feature matrix F, the latent feature matrix E, the multiplier matrix K, the linear deviation vector H, the linear deviation vector G, the multiplier vector Z, the hidden feature dimension D, the maximum training Iterative round number T, iteration round number control variable t, convergence termination threshold τ, learning rate η, penalty parameters ρ _i and _ui . 7. The protein-protein interaction prediction method based on the alternating direction multiplier method as claimed in claim 4, wherein the S3 comprises: S3-1: Iteratively update the iterative parameters, non-negative parameters and multiplier parameters in turn. The update strategy is as follows: for d=1 D

In formula (3), F _{(1～M), d} represents the d-th column vector in the latent feature matrix F, wherein the column vector contains M elements, and H _d represents the d-th element in the linear deviation vector H;

It is expressed as a latent feature sub-matrix of M rows (d-1) columns composed of the 1st to (d-1)th column vectors in the latent feature matrix F in the t+1th iteration;

is represented as a latent feature sub-matrix of M rows (Dd) columns composed of (d+1) to D-th column vectors in the latent feature matrix F in the t-th iteration;

is represented as a latent feature sub-matrix of M rows (D-d+1) columns composed of the dth to Dth column vectors in the latent feature matrix F in the t-th iteration;

is expressed as a linear deviation sub-vector of size (d-1) composed of the 1st to (d-1)th elements in the linear deviation vector H in the t+1th iteration;

is expressed as a linear deviation sub-vector of size (D-d+1) composed of the d-th elements in the linear deviation vector H in the t-th iteration;

It is expressed as the linear deviation sub-vector of size (Dd) composed of the (d+1)~Dth elements in the linear deviation vector H in the t-th iteration; F ^t+1 is expressed as the t+1-th iteration Implicit feature matrix F; H ^t+1 represents the linear deviation vector H in the t+1 round of iteration; G ^t+1 represents the linear deviation vector G in the t+1 round of iteration; G ^t represents the t-th round iteration Medium linear deviation vector G; E ^t+1 represents the latent feature matrix E in the t+1 round of iteration; E ^t represents the latent feature matrix E in the t-th round of iteration; K ^t+1 represents the t+1 round of iteration Middle multiplier matrix K; K ^t is the multiplier matrix K in the t-th iteration; Z ^t+1 is the multiplier vector Z in the t+1-th iteration; Z ^t is the multiplier vector in the t-th iteration Z; η is used to control the step size in the iterative optimization process of each parameter; ▽ _K ε(E ^t+1 , G ^t+1 , F ^t+1 , H ^t+1 , K, Z ^t ) represents the increase The generalized Lagrangian function ε finds the partial derivative of the multiplier matrix K; ▽ _Z ε(E ^t+1 ,G ^t+1 ,F ^t+1 ,H ^t+1 ,K ^t ,Z) represents the augmented Lag The Rangian function ε finds the partial derivative with respect to the multiplier vector Z; S3-2: Iteratively optimize the augmented Lagrangian objective loss function ε; The training iteration formulas are as follows:

κ _i,d ←κ _i,d +ηρ _i (f _i,d -e _i,d )

δ _i ←δ _i +ηu _i (h _i -g _i ) In formula (4), Γ(i) represents all the non-missing value sets related to protein i in the non-missing value set Γ; D represents the latent feature dimension; w _i,j represents the interaction value between protein i and protein j; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; f _i,d ∈ F, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix F d elements; f _j,d ∈ F, is the d-th element of the latent feature corresponding to the j-th protein in the latent feature matrix F; g _i ∈ G, is the i-th element of the linear deviation vector G; h _j ∈ H, is the jth element of the linear deviation vector H; h _i ∈ H, is the ith element of the linear deviation vector H; κ _{i,d ∈} K, is the latent feature corresponding to the ith protein in the multiplier matrix K The d-th element of ; δ _i ∈ Z is the i-th element of the multiplier vector Z; ρ _i and u _i are the penalty parameters; S3-3: Determine whether the iterative process of the augmented Lagrangian objective loss function ε is terminated: The judgment condition is that for each iteration of the augmented Lagrangian objective loss function ε, the value of the control variable t for the number of training iterations increases by 1. When the value of t reaches the maximum number of training iterations T, ε stops training; or augmentation During the training process of the Lagrangian objective loss function ε, when the absolute value of the difference between the ε value calculated after the current iteration and the previous round ε value has become smaller than the convergence termination threshold τ, ε stops training. 8. The protein-protein interaction prediction method based on the alternating direction multiplier method as claimed in claim 4, wherein in the S4, the calculation formula of the missing protein-protein interaction prediction value is:

In formula (5),

represents the calculated estimated value of protein-protein interaction; g _i ∈ G, is the i-th element of the linear deviation vector G; g _j ∈ G, is the j-th element of the linear deviation vector G; e _i,d ∈ E, is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; e _j,d ∈ E is the d-th element of the latent feature corresponding to the ith protein in the latent feature matrix E; D represents the hidden feature feature dimension.

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