Weight matrix design method and device, equipment and storage medium

Abstract

The invention relates to a weight matrix design method and device, equipment and a storage medium, and is applied to the field of distributed systems, and the method comprises the steps: determining a random matrix according to a to-be-solved actual problem, a preset distributed model and a preset hypothesis condition; constructing a minimum problem of the spectral radius of the random matrix, and generating a first weight matrix design problem according to the minimum problem of the spectral radius of the random matrix; according to a preset matrix, constructing a minimum problem of the spectral radius of the preset matrix, and according to the minimum problem of the spectral radius of the preset matrix, generating a second weight matrix design problem; converting the first weight matrix design problem and the second weight matrix design problem into a first semi-definite programming problem and a second semi-definite programming problem; and carrying out joint solution on the first semi-definite programming problem and the second semi-definite programming problem, and generating an optimal weight matrix. The method has the technical effects that the node information updating and processing frequency is reduced, and the communication burden and the calculation overhead are reduced.

Description

Technical Field

[0001] The present application relates to the technical field of distributed systems, and in particular to a weight matrix design method, apparatus, device and storage medium. Background Art

[0002] In large-scale distributed systems, such as wireless sensor networks, the Internet of Things, and cloud computing, nodes share and exchange data across the network to achieve distributed data processing. These systems are becoming increasingly popular, ranging from real-time monitoring in smart cities to data collection and processing in automated industries. In these environments, the way data is transmitted and processed between network nodes is crucial to the performance of the entire system.

[0003] Centralized estimation methods, which collect and process all data at a central node, can provide high estimation accuracy. However, as the network scales, this approach's efficiency and scalability decrease significantly. This is primarily due to the large amount of data transmission required, which increases bandwidth requirements. Furthermore, the data processing burden on the central node also increases rapidly with network size. Furthermore, if the central node fails, the functionality of the entire network will be affected, or even completely paralyzed. Therefore, centralized methods have clear limitations in modern large-scale systems.

[0004] To overcome these challenges, distributed estimation has gradually become a research hotspot. In distributed estimation algorithms, each node not only collects and processes its own data, but also obtains more global information by exchanging information with neighboring nodes. This approach reduces dependence on a single central node and improves the robustness and scalability of the system. Under this architecture, each node can work in parallel, thereby improving the computational efficiency of the entire system. However, the performance of distributed estimation depends largely on the information transmission mechanism between nodes, which is determined by the weight matrix W(t). The weight matrix W(t) describes the information sharing and transmission rules between nodes, that is, the way each node assigns different weights when receiving and processing information from its neighboring nodes.

[0005] In existing distributed estimation algorithms, weight matrices are typically generated using simple adjacency matrices or fixed rules. However, while computationally simple, this approach often performs poorly in complex, dynamic network environments. When the network structure changes frequently or communication quality is unstable, algorithms using fixed weight matrices can experience slow convergence, leading to system issues that cannot be resolved within the processing time. This, in turn, limits the widespread adoption of distributed estimation algorithms in practical applications, particularly in scenarios requiring high-frequency updates and real-time processing. Summary of the Invention

[0006] In order to accelerate the convergence speed of a distributed estimation algorithm or reduce its sampling quantity, the present application provides a weight matrix design method, apparatus, device and storage medium.

[0007] In a first aspect, the present application provides a weight matrix design method, which adopts the following technical solution: the method includes:

[0008] Determine the random matrix based on the actual problem to be solved, the preset distribution model and the preset assumptions;

[0009] Constructing a minimum value problem of the spectral radius of the random matrix, and generating a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix;

[0010] Constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix;

[0011] Converting the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem;

[0012] The first semidefinite programming problem and the second semidefinite programming problem are jointly solved to generate an optimal weight matrix.

[0013] In a specific possible implementation scheme, the preset distributed model includes a network model and a measurement model;

[0014] The network model includes:

[0015]

[0016] in, Represents a collection of nodes, represents the edge set, Represents a network model;

[0017] The measurement model includes:

[0018] y n (t) = H n θ+v n (t),

[0019] Where θ∈R d represents the deterministic parameter vector to be estimated, represents the observation matrix, v n (t) represents Gaussian noise, y n (t) represents the measurement model, d n and d represents the dimension of the data.

[0020] In a specific implementation scheme, the preset assumptions include:

[0021] In the network model, the edge set ε(t) is independent and identically distributed;

[0022] In the measurement model, the Gaussian noise v n The components of (t) are independently normally distributed;

[0023] In the measurement model, the observation matrix H n is a column-full rank matrix;

[0024] The random matrix is ​​a non-negative symmetric matrix, the diagonal elements of the random matrix are positive numbers and the rows are random.

[0025] In a specific implementation method, constructing the minimum value problem of the spectral radius of the random matrix and generating the first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix includes:

[0026] Calculating the probability of the random matrix taking values, and constructing a minimum value problem of the spectral radius of the random matrix according to the probability of the random matrix taking values;

[0027] generating a first weight matrix design problem according to a minimum value problem of the spectral radius of the random matrix;

[0028] The calculation method of the value probability of the random matrix includes:

[0029] π k =P(ε(t)=ε k ),k=1,..,K,

[0030] Among them, ε(t) represents the edge set, ε K represents the kth edge in the edge set, P represents the value probability calculation function, π k represents the probability of taking a value, and K represents the number of edges in the edge set;

[0031] The calculation method of the spectral radius of the random matrix includes:

[0032]

[0033] Wherein, M(t) represents the random matrix, M k represents the value in the random matrix, π k represents the probability of taking values, I represents the identity matrix, N represents the number of nodes, and ρ() represents the spectrum radius calculation function;

[0034] The first weight matrix design problem includes:

[0035]

[0036] Among them, S k represents the set of solutions defined by:

[0037]

[0038] In a specific implementation scheme, constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix includes:

[0039] Constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, wherein the preset matrix is ​​a set of preset weight matrices that meet the preset assumption condition;

[0040] Generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix;

[0041] The calculation method of the spectral radius of the preset matrix includes:

[0042]

[0043] Among them, W(t) represents the preset weight matrix set, W k represents the preset weight matrix in the preset weight matrix set, I represents the identity matrix, ρ() represents the spectrum radius calculation function, x k Indicates the probability of the value corresponding to the preset weight matrix;

[0044] The second weight matrix design problem includes:

[0045]

[0046] In a specific embodiment, it is characterized in that:

[0047] The first semidefinite programming problem includes:

[0048]

[0049] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and π k represents the probability of taking a value, X k Represents the preset semidefinite matrix, M k represents the value in the random matrix, S k represents the set of defined solutions, and N represents the number of nodes;

[0050] The second semidefinite programming problem includes:

[0051]

[0052] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and x k It represents the probability of the value corresponding to the preset weight matrix, and N represents the number of nodes.

[0053] In a specific implementation scheme, the first semidefinite programming problem and the second semidefinite programming problem are jointly solved to generate the optimal weight matrix.

[0054] Solving the first semidefinite programming problem to obtain a matrix solution, and calculating a first spectral radius of a random matrix corresponding to the matrix solution;

[0055] Solving the second semidefinite programming problem to obtain a probabilistic solution, and calculating a second spectral radius of a preset matrix corresponding to the probabilistic solution;

[0056] cyclically solving the matrix solution and the probability solution, and calculating a radius difference between the first spectrum radius and the second spectrum radius obtained from each solution;

[0057] When the radius difference is less than a preset threshold, an optimal matrix solution and an optimal probability solution are obtained;

[0058] The optimal matrix solution and the optimal probability solution are set as the optimal weight matrix.

[0059] In a second aspect, the present application provides a weight matrix design device, which adopts the following technical solution: the device includes:

[0060] A constraint condition acquisition module is used to determine a random matrix based on the actual problem to be solved, a preset distributed model, and preset assumptions;

[0061] a first problem design module, configured to construct a minimum value problem of the spectral radius of the random matrix, and generate a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix;

[0062] a second problem design module, configured to construct a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generate a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix;

[0063] a weight problem conversion module, configured to convert the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem;

[0064] A weight problem solving module is used to jointly solve the first semidefinite programming problem and the second semidefinite programming problem and generate an optimal weight matrix.

[0065] In a third aspect, the present application provides a computer device that adopts the following technical solution: it includes a memory and a processor, and the memory stores a computer program that can be loaded by the processor and execute any of the weight matrix design methods described above.

[0066] In a fourth aspect, the present application provides a computer-readable storage medium, which adopts the following technical solution: storing a computer program that can be loaded by a processor and execute any of the above-mentioned weight matrix design methods.

[0067] In summary, this application has the following beneficial technical effects:

[0068] The weight matrix design method reduces the number of iterations in the distributed algorithm, thereby conserving resources. For nodes in resource-limited distributed networks, optimizing communication and computing resources is crucial. By accelerating the algorithm's convergence process, the frequency of node information updates and processing is reduced, thereby reducing the communication burden and computational overhead. This feature is particularly important in practical applications, such as wireless sensor nodes with limited battery life or IoT devices that rely on energy conservation. Reducing communication frequency not only extends the node's lifespan but also improves the overall system's operational efficiency and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the weight matrix design method in an embodiment of the present application;

[0070] Figure 2 Schematic diagram of simulation results of a C5 dynamic network with 20 nodes in an embodiment of the present application;

[0071] Figure 3 Schematic diagram of simulation results of a C5 dynamic network with 30 nodes in an embodiment of the present application;

[0072] Figure 4 is a schematic diagram of a weight matrix design device in an embodiment of the present application;

[0073] Figure 5 It is a schematic diagram used to embody a computer device in an embodiment of the present application.

[0074] Reference numerals: 401, constraint condition acquisition module; 402, first problem design module; 403, second problem design module; 404, weight problem conversion module; 405, weight problem solving module. DETAILED DESCRIPTION

[0075] The following combination Figure 1-Figure 5 This application is described in further detail.

[0076] The embodiments of the present application disclose a weight matrix design method, which can reduce the number of iterations of distributed algorithms and save resources. In large-scale distributed systems, such as wireless sensor networks, the Internet of Things, and cloud computing environments, nodes share and exchange data through the network to achieve distributed data processing. The application of such systems is becoming more and more extensive, from real-time monitoring of smart cities to data collection and processing in automated industries, which are inseparable from distributed systems. Therefore, the way data is transmitted and processed between network nodes is crucial to the performance of the entire system.

[0077] Centralized estimation methods, which collect and process all data at a central node, can provide high estimation accuracy. However, as the network scales, this approach's efficiency and scalability decrease significantly. This is primarily due to the large amount of data transmission required, which increases bandwidth requirements. Furthermore, the data processing burden on the central node also increases rapidly with network size. Furthermore, if the central node fails, the functionality of the entire network will be affected, or even completely paralyzed. Therefore, centralized methods have clear limitations in modern large-scale systems.

[0078] To overcome the limitations of centralized estimation methods, distributed estimation has gradually become a research hotspot. In distributed estimation algorithms, each node not only collects and processes its own data but also obtains more global information by exchanging information with neighboring nodes. This approach reduces reliance on a single central node and improves the robustness and scalability of the system. Under this architecture, each node can work in parallel, thereby improving the computational efficiency of the entire system. However, the performance of distributed estimation depends largely on the information transmission mechanism between nodes, which is determined by the weight matrix W(t). The weight matrix W(t) describes the information sharing and transmission rules between nodes, that is, the way each node assigns different weights when receiving and processing information from its neighboring nodes.

[0079] In existing distributed estimation algorithms, the weight matrix is ​​usually generated using a simple adjacency matrix or fixed rules. However, although this method is simple to calculate, its performance is often not ideal in a complex dynamic network environment. When the network structure changes frequently or the communication quality is unstable, the algorithm using a fixed weight matrix may converge slowly, which will cause the system problem to be unable to be solved within the processing time, thereby limiting the widespread application of distributed estimation algorithms in practical applications, especially in scenarios that require high-frequency updates and real-time processing, such as wireless sensor nodes with limited battery life or IoT devices that rely on energy saving. The communication quality is unstable and the distributed structure may cause the algorithm to converge slower, thereby affecting the efficiency of the system. In order to help improve the operating efficiency and stability of the system, the present application provides a weight matrix design method.

[0080] Reference Figure 1 , the method comprises the following steps:

[0081] S10, determining a random matrix according to the actual problem to be solved, the preset distributed model and the preset assumptions.

[0082] Specifically, the actual problem to be solved is abstracted into a random matrix for optimization calculation according to preset constraints. It can also be understood that the abstracted random matrix is ​​a given known matrix.

[0083] In the embodiment of the present application, the given preset distributed model includes a network model and a measurement model. For the communication model of the distributed network, a graph that changes over time is usually used for simulation. The graph of the distributed network at time t, that is, the network model, can be expressed as:

[0084]

[0085] in, Represents a collection of nodes, Represents the network model, represents an edge set, which includes all node pairs that are connected by a channel at time t. When the node pair (i, j) belongs to the edge set ε(t), it indicates that there is a communication path from node j to node i at time t. In the embodiment of this application, an undirected graph is considered, that is, when the point pair (i, j)∈ε(t), the node pair (j, i) is also in the edge set ε(t).

[0086] In actual scenarios, the communication connections of nodes in the network change dynamically over time. Therefore, {ε(t): t=1,2,...} is a random sequence that changes over time. Given the number of nodes N, the network has at most N nodes. 2 The node pairs are connected, so the edge set ε(t) takes values ​​in a finite set. In the embodiment of this application, the same distributed network is considered, so the edge set sequence {ε(t): t=1,2,...} is independent and identically distributed. In addition, in the embodiment of this application, it is assumed that ε(t) has a set of K edge sets ε={ε1,...,ε K}, where ε is the set of edge sets that have a positive probability of appearing in the current scene. For the edge set ε={ε1,...,ε K}, the average connection set can be constructed

[0087] Consider a distributed network with N sensors, θ∈R d is the deterministic parameter vector to be estimated. The nodes in the distributed network observe the parameter vector θ to be estimated through an observation model with additive noise. At time t, the measurement model observed by node n can be expressed as:

[0088] y n (t) = H n θ+v n (t),

[0089] Where θ∈R d represents the deterministic parameter vector to be estimated, represents the observation matrix, v n (t) represents Gaussian noise, y n (t) represents the measurement model, d n and d represent the dimensions of the data.

[0090] The given preset assumptions include the following four:

[0091] Assumption 1: In the network model, the edge set ε(t) is independent and identically distributed. The edge set ε(t) is in the set ε={ε1,...,ε K} and take the element ε k The probability is π k =P(ε(t)=ε h )>0, In addition, Figure The average connection set of If the nodes are connected, any node in the distributed network can transmit information through the channels between them or the paths passing through them.

[0092] Assumption 2: In the measurement model, Gaussian noise v n The components of (t) are independently normally distributed. And the random variable v n (t) and random variable v m (s) independent and identically distributed, n≠m or s≠t.

[0093] Assumption 3: In the measurement model, the observation matrix H n is a column-full rank matrix. The ranks are full.

[0094] Assumption 4: The random matrix is ​​a non-negative symmetric matrix, the diagonal elements of the random matrix are positive and the rows are random. For the random matrix W(t), , so W(t) is in the matrix set {W1, ..., W K}, W k For the picture The weight matrix, k = 1, 2, ..., K. W(t) takes the element W k The probability is π k (π k =P(ε(t)=ε k)), the sequence {W(t):t=1,2,...} is independent and identically distributed.

[0095] In a distributed system, the working mode of the node and the information transmission mechanism of the network can be calculated through a distributed algorithm (FADE algorithm). The FADE algorithm can be expressed as:

[0096]

[0097] in, W(t) is a given satisfying W ij (t)≠0, if and only if the weight matrix of (i, j)∈ε(t) is the local estimate of the parameter vector θ by node n.

[0098] S20: constructing a minimum value problem of the spectral radius of the random matrix, and generating a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix.

[0099] Specifically, based on a given random matrix, the spectral radius of the given random matrix is ​​calculated, and an optimization problem is constructed by minimizing the spectral radius of the random matrix. Based on the problem of minimizing the spectral radius, the corresponding first weight matrix design problem is generated. The matrix solution can be solved through the first weight matrix design problem. The weight matrix problem design is based on the following three lemmas:

[0100] Lemma 1: When the above assumptions 1 to 4 hold, the sequence generated by the FDAE algorithm converges to the true parameter vector almost everywhere.

[0101]

[0102] Lemma 2: When Assumptions 1-4 hold, the matrix The spectral radius is less than 1, and the mean square error of the sequence generated by the FDAE algorithm decays to 0.

[0103] Lemma 3: The expectations are the same and is a semidefinite matrix.

[0104] S30 , constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix.

[0105] Specifically, based on the above three lemmas, according to the preset matrix, the spectral radius of the preset matrix is ​​calculated, the optimization problem is constructed by minimizing the spectral radius of the matrix, and the corresponding second weight matrix design problem is generated according to the problem of minimizing the spectral radius. The probabilistic solution can be solved through the first weight matrix design problem.

[0106] S40, converting the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem.

[0107] Specifically, since the constructed weight matrix problem is not easy to solve, the two weight matrix problems are converted into corresponding semidefinite programming problems, which makes it easier to solve the optimal matrix solution or the optimal probability solution.

[0108] S50: jointly solve the first semidefinite programming problem and the second semidefinite programming problem, and generate an optimal weight matrix.

[0109] Specifically, the two transformed semidefinite programming problems are solved separately, and then jointly solved through multiple iterations to obtain the optimal weight matrix. The joint solution method can be specifically implemented as follows: first, the matrix solution is obtained by solving the first semidefinite programming problem, and the first spectral radius of the random matrix corresponding to the matrix solution is calculated; the probability solution is obtained by solving the second semidefinite programming problem, and the second spectral radius of the preset matrix corresponding to the probability solution is calculated; wherein solving one matrix solution and one probability solution can be regarded as one iteration. Afterwards, the matrix solution and the probability solution are solved cyclically, and the radius difference between the first spectral radius and the second spectral radius obtained by each solution is calculated; through multiple iterative loops, the radius difference calculated in each iteration is calculated. When the radius difference is less than a preset threshold, the optimal matrix solution and the optimal probability solution are obtained; after obtaining the optimal solution, the iterative calculation is stopped, and the optimal matrix solution and the optimal probability solution are set as the optimal weight matrix.

[0110] In the present application, the weight matrix design method reduces the number of iterations of the distributed algorithm, thereby saving resources. For nodes in a distributed network with limited resources, the optimization of communication and computing resources is very important. By accelerating the convergence process of the algorithm, the frequency of node information updates and processing is reduced, thereby reducing the communication burden and computing overhead. This feature is particularly important in practical application scenarios, such as in wireless sensor nodes with limited battery life or IoT device scenarios that rely on energy conservation. Reducing the communication frequency not only extends the service life of the node, but also improves the operating efficiency and stability of the overall system.

[0111] In one embodiment, constructing a minimum value problem of the spectral radius of a random matrix and generating a first weight matrix design problem based on the minimum value problem of the spectral radius of the random matrix can be specifically performed as follows:

[0112] First, the probability of the random matrix taking values ​​is calculated, and the minimum value problem of the spectral radius of the random matrix is ​​constructed based on the probability of the random matrix taking values; then, the first weight matrix design problem is generated based on the minimum value problem of the spectral radius of the random matrix.

[0113] Specifically, for a given random matrix M(t), by minimizing the spectral radius of the matrix, that is, The spectral radius of the random matrix is ​​determined by the value set {M1, ..., M K}, where the constraints are given by Assumption 4, π k is the value given in Assumption 3. From Lemmas 1 and 2, we can see that the estimation sequence obtained based on the weight matrix design method (WMD) converges to the true parameter vector and its mean square error decays to 0.

[0114] First, calculate π based on assumption 3 k , the calculation method can be expressed as:

[0115] π k =P(ε(t)=ε k ),k=1,...,K,

[0116] Among them, ε(t) represents the edge set, ε K represents the kth edge in the edge set, P represents the value probability calculation function, π k represents the probability of taking a value, and K represents the number of edges in the edge set;

[0117] Define the function:

[0118]

[0119] Then the matrix variables {M1, ..., M K} can be expressed as:

[0120]

[0121] According to the definition, the A function is equal to the expected matrix of the random matrix, that is:

[0122]

[0123] Then the calculation of minimizing the spectral radius of a random matrix can be expressed as minimizing the definition function,

[0124]

[0125] Among them, M(t) represents a random matrix, M k represents the value in the random matrix, π k represents the probability of taking values, I represents the identity matrix, N represents the number of nodes, and ρ() represents the spectrum radius calculation function;

[0126] Define the set S k , S k Contains the matrix under assumption 4 corresponding to the network model, defining the set S k It can be expressed as:

[0127]

[0128] Then, the first weight matrix design problem can be expressed as:

[0129]

[0130] Considering that the original weight matrix design problem is not easy to solve, the first weight matrix design problem can be converted into a semidefinite programming problem:

[0131]

[0132] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and π k represents the probability of taking a value, X k Represents the preset semidefinite matrix, M k represents the value in the random matrix, S k represents the set of defined solutions, and N represents the number of nodes.

[0133] Given Assumptions 1 to 3, the matrix obtained by the WMD method satisfies Assumption 4. Lemmas 1 and 2 show that the estimated sequence generated by the FADE algorithm based on the WMD method converges to the true parameter vector and its mean square error decays to 0. Furthermore, the matrices in the WMD method can be calculated offline, making them easy to use in distributed algorithms.

[0134] In one embodiment, constructing a minimum value problem of the spectral radius of a preset matrix according to a preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of a random matrix can be specifically performed as follows:

[0135] First, a minimum value problem of the spectral radius of a preset matrix is ​​constructed based on a preset matrix, where the preset matrix is ​​a set of preset weight matrices that meet preset assumptions; and a second weight matrix design problem is generated based on the minimum value problem of the spectral radius of the preset matrix.

[0136] Specifically, based on Lemma 1 and Lemma 2, when Assumptions 1 to 4 hold, the estimated sequence generated by the FADE algorithm converges to the true parameter vector and its mean square error decays to 0. Given a set of edge sets that satisfy Assumption 3 and a set of weight matrices that satisfy Assumption 4, where probability π k Unknown. The Probabilistic Method (PM) method minimizes the matrix The spectral radius determines the probability, constrained to be

[0137] Based on the given edge set ε={ε1,...,ε k} and the weight matrix set {W1, ..., W K};

[0138] Define the function:

[0139]

[0140] Then the weight matrix set {W1, ..., W K} can be expressed as:

[0141]

[0142] According to the definition, the C function is equal to the expected matrix of the random matrix, that is:

[0143]

[0144] Then the calculation of minimizing the preset weight matrix spectral radius can be expressed as minimizing the defined C function,

[0145]

[0146] Among them, W(t) represents the preset weight matrix set, W k represents the preset weight matrix in the preset weight matrix set, I represents the identity matrix, ρ() represents the spectrum radius calculation function, x k Indicates the probability of the value corresponding to the preset weight matrix;

[0147] Then the second weight matrix design problem can be expressed as:

[0148]

[0149] Considering that the original weight matrix design problem is not easy to solve, the second weight matrix design problem can be converted into a semidefinite programming problem:

[0150]

[0151] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and x k It represents the probability of the value corresponding to the preset weight matrix, and N represents the number of nodes.

[0152] In this application, two methods are used to optimize the weight matrix. The estimated sequences obtained based on the weight matrix design method and the probability method can converge to the true parameter vector, and their mean square error decays to 0. The mean square error (MSE) can measure the estimation accuracy of the algorithm at different iteration steps. A lower MSE indicates higher estimation accuracy and algorithm convergence effect. This can effectively solve the slow convergence problem that may occur in the existing weight matrix design method (Metropolis rules, MR method).

[0153] It should be noted that in the embodiments of the present application, the optimization method based on weight matrix design and the optimization method based on probability can be used separately or jointly for optimization solution, which are two independent weight matrix design optimization methods. In order to verify the effect in practical applications, simulation experiments were carried out in the embodiments of the present application, and the results of the weight matrix design (WMD) method and the joint probability solution (WPM) method were compared with the existing MR method.

[0154] For experiments with the WMD method, two representative dynamic network models were selected: the C3 network and the C4 network. The C3 network consists of 24 nodes divided into three clusters, with nodes within each cluster communicating via stable communication links. Communication between clusters occurs via a single connection with a 50% probability of failure to simulate the instability that can exist in real networks. The C4 network consists of 16 nodes divided into four clusters, each with a similar connection structure. One hundred independent simulations were performed, with the measurement data received by the nodes containing random Gaussian noise in each simulation.

[0155] Experiments have shown that, in a C3 network, a distributed estimation algorithm using the WMD method achieved an MSE of 0.01 within 210 iterations. In comparison, the traditional MR method required approximately 430 iterations to achieve the same error level. This demonstrates that the WMD method more efficiently utilizes inter-node communication resources during information transmission, enabling each node to more quickly integrate information from its neighbors, thereby accelerating the convergence of the entire system. Furthermore, the WMD method demonstrated excellent stability in the experiments, maintaining a fast convergence rate and low error even when the network topology changes. This is because the WMD method optimizes the weight matrix design, allowing each node to adaptively adjust the weights used for information processing and transmission under varying communication conditions. This flexible weight distribution reduces estimation bias caused by unstable communication links and changes in network structure.

[0156] In the C4 network, the results show that the WMD method continues to outperform the traditional MR method. Specifically, the WMD method reduces the MSE to 0.01 within approximately 110 steps, while the traditional method requires approximately 210 steps to reach the same error level. As the number of iterations increases, the WMD method's MSE continues to decrease, ultimately achieving a reduction of approximately 30%, while the traditional method's MSE stagnates at a higher level.

[0157] This result highlights the adaptive capabilities of the WMD method in dynamic networks. When the network structure or communication links frequently change, traditional methods often struggle to quickly adjust weight distribution, hindering the estimation process. However, the WMD method can optimize the weight matrix based on the real-time network state, making information flow more efficient and significantly improving both the algorithm's convergence speed and estimation accuracy.

[0158] For the experiment of WPM method, the network model is Take the parameter vector Node n observes model y n (t) = H n θ+v n (t) Obtain observation of parameter vector θ, where the noise v n (t) obeys the standard Gaussian distribution. The measurement matrix where A, B∈R 3×2 , the elements of A and B are independently generated from standard Gaussian distribution.

[0159] At this time, the block random model with m clusters is connected in the form of a chain, that is, node 1 is connected to node node Connect to the node ..., the last node Connect to the node Eliminating the edge set of all clusters connected, the network has K = 2 m-1 -1 possible connection graph, ε={ε1,...ε K}To satisfy the edge set of Assumption 3, the WPM method assumes that the initial probability is The optimal weight matrix set and probability can be obtained offline, and the results of the WPM method are compared. Estimation series using the WMD method and the estimated sequence of the MR method The probabilities in the WMD method and the MR method are

[0160] Through experiments, in the C5 dynamic network, the possible edge sets are ε1,...,ε 15 When N=20, the simulation results of C5 dynamic network refer to Figure 2 The threshold of the WPM method is ∈=1e-5, that is, when the sequence MSE is less than 0.001, the iteration is terminated. The MSE of the sequence converged to an accuracy of 0.001 at 330 steps, followed by the sequence obtained by the WMD method. , and the sequence obtained by the MR method is 1110 steps are required; when N=30, the simulation results of C5 network refer to Figure 3The threshold of the WPM method is ∈=1e-5, that is, when the sequence MSE is less than 0.005, the iteration is terminated. The sequence obtained by the WPM method is The MSE of the sequence first converges to an accuracy of 0.005 in 392 steps, followed by the sequence obtained by the WMD method. Sequences obtained by MR method 1650 steps are required.

[0161] Figure 2 and Figure 3 It can be seen that when the number of simulation nodes of the C5 clustered dynamic network is 20 and 30, the performance of the WPM method is better than the WMD method, and both methods are better than the existing Metropolis rules (MR).

[0162] Figure 1 FIG. 1 is a flow chart of a weight matrix design method in one embodiment. It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows; unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps may be executed in other orders; and Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0163] Based on the above method, an embodiment of the present application also discloses a weight matrix design device.

[0164] Reference Figure 4 , the device includes the following modules:

[0165] The constraint condition acquisition module 401 is used to determine the random matrix according to the actual problem to be solved, the preset distributed model and the preset assumptions;

[0166] A first problem design module 402 is used to construct a minimum value problem of the spectral radius of the random matrix, and generate a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix;

[0167] A second problem design module 403 is configured to construct a minimum value problem of a spectral radius of a preset matrix according to a preset matrix, and generate a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix;

[0168] A weight problem conversion module 404 is used to convert the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem;

[0169] The weight problem solving module 405 is used to jointly solve the first semidefinite programming problem and the second semidefinite programming problem and generate an optimal weight matrix.

[0170] In one embodiment, the distributed model preset in the constraint condition acquisition module 401 includes a network model and a measurement model; the network model includes:

[0171]

[0172] in, Represents a collection of nodes, represents the edge set, Represents a network model;

[0173] The measurement model includes:

[0174] y n (t) = H n θ+v n (t),

[0175] Where θ∈R d represents the deterministic parameter vector to be estimated, represents the observation matrix, v n (t) represents Gaussian noise, y n (t) represents the measurement model, d n and d represents the dimension of the data.

[0176] In one embodiment, the assumptions preset in the constraint condition acquisition module 401 include: in the network model, the edge set ε(t) is independent and identically distributed; in the measurement model, the Gaussian noise v n The components of (t) are independently normally distributed; in the measurement model, the observation matrix H n is a column-full rank matrix; a random matrix is ​​a non-negative symmetric matrix, the diagonal elements of the random matrix are positive and the rows are random.

[0177] In one embodiment, the first problem design module 402 is specifically used to calculate the probability of a random matrix taking a value, construct a minimum value problem of the spectral radius of the random matrix based on the probability of the random matrix taking a value, and generate a first weight matrix design problem based on the minimum value problem of the spectral radius of the random matrix. The calculation method of the probability of a random matrix taking a value includes:

[0178] π k =P(ε(t)=ε k ),k=1,...,K,

[0179] Among them, ε(t) represents the edge set, ε K represents the kth edge in the edge set, P represents the value probability calculation function, π k represents the probability of taking a value, and K represents the number of edges in the edge set;

[0180] The calculation method of the spectral radius of a random matrix includes:

[0181]

[0182]

[0183] Among them, M(t) represents a random matrix, M k represents the value in the random matrix, π k represents the probability of taking values, I represents the identity matrix, N represents the number of nodes, and ρ() represents the spectrum radius calculation function;

[0184] The first weight matrix design problem includes:

[0185]

[0186] Among them, S k represents the set of solutions defined by:

[0187]

[0188] In one embodiment, the second problem design module 403 is specifically configured to construct a minimum value problem of the spectral radius of a preset matrix based on a preset matrix, where the preset matrix is ​​a set of preset weight matrices that satisfy preset assumptions; generate a second weight matrix design problem based on the minimum value problem of the spectral radius of the preset matrix; and calculate the spectral radius of the preset matrix in the following manner:

[0189]

[0190] Among them, W(t) represents the preset weight matrix set, W k represents the preset weight matrix in the preset weight matrix set, I represents the identity matrix, ρ() represents the spectrum radius calculation function, x k Indicates the probability of the value corresponding to the preset weight matrix;

[0191] The second weight matrix design problem includes:

[0192]

[0193] In one embodiment, in the weight problem conversion module 404, the first semidefinite programming problem includes:

[0194]

[0195] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and π k represents the probability of taking a value, X k Represents the preset semidefinite matrix, M k represents the value in the random matrix, S k represents the set of defined solutions, and N represents the number of nodes;

[0196] The second semidefinite programming problem includes:

[0197]

[0198]

[0199]

[0200] Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and x k It represents the probability of the value corresponding to the preset weight matrix, and N represents the number of nodes.

[0201] In one embodiment, the weight problem solving module 405 is specifically used to solve the first semidefinite programming problem to obtain a matrix solution, and calculate the first spectral radius of the random matrix corresponding to the matrix solution; solve the second semidefinite programming problem to obtain a probabilistic solution, and calculate the second spectral radius of a preset matrix corresponding to the probabilistic solution; cyclically solve the matrix solution and the probabilistic solution, and calculate the radius difference between the first spectral radius and the second spectral radius obtained in each solution; when the radius difference is less than a preset threshold, obtain the optimal matrix solution and the optimal probability solution; and set the optimal matrix solution and the optimal probability solution as the optimal weight matrix.

[0202] The weight matrix design device provided in the embodiment of the present application can be applied to the weight matrix design method provided in the above embodiment. For relevant details, please refer to the above method embodiment. Its implementation principle and technical effects are similar and will not be repeated here.

[0203] It should be noted that: when the weight matrix design device provided in the embodiment of the present application performs weight matrix design, only the division of the above-mentioned functional modules / functional units is used as an example. In actual applications, the above-mentioned functions can be assigned to different functional modules / functional units as needed, that is, the internal structure of the weight matrix design device is divided into different functional modules / functional units to complete all or part of the functions described above. In addition, the implementation method of the weight matrix design method provided in the above method embodiment and the implementation method of the weight matrix design device provided in this embodiment belong to the same concept. The specific implementation process of the weight matrix design device provided in this embodiment is detailed in the above method embodiment and will not be repeated here.

[0204] The embodiment of the present application also discloses a computer device.

[0205] Specifically, if Figure 5 As shown, the computer device can be a computer device such as a desktop computer, a laptop computer, a handheld computer, and a cloud server. The computer device may include, but is not limited to, a processor and a memory. The processor and the memory may be connected via a bus or other means. The processor may be a central processing unit (CPU). The processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, graphics processing units (GPU), embedded neural network processors (NPU) or other dedicated deep learning coprocessors, discrete gate or transistor logic devices, discrete hardware components and other chips, or a combination of the above-mentioned chips.

[0206] As a non-transient computer-readable storage medium, the memory can be used to store non-transient software programs, non-transient computer executable programs and modules, such as program instructions / modules corresponding to the methods in the above-mentioned embodiments of the present application. The processor executes various functional applications and data processing of the processor by running the non-transient software programs, instructions and modules stored in the memory, that is, the method in the above-mentioned method embodiment is implemented. The memory may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function; the data storage area may store data created by the processor, etc. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network and a combination thereof.

[0207] The embodiment of the present application also discloses a computer-readable storage medium.

[0208] Specifically, a computer-readable storage medium is used to store a computer program, and when the computer program is executed by a processor, the method in the above-mentioned method implementation is implemented. Those skilled in the art will understand that all or part of the processes in the above-mentioned implementation method of the present application can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it may include the processes of the implementation methods of the above-mentioned methods. Among them, the storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory (Flash Memory), a hard disk (Hard Disk Drive, abbreviated as: HDD) or a solid-state drive (SSD), etc.; the storage medium may also include a combination of the above-mentioned types of memories.

[0209] This specific embodiment is merely an explanation of the present invention and is not intended to limit the present invention. After reading this specification, those skilled in the art may make non-creative modifications to this embodiment as needed. However, as long as such modifications are within the scope of the claims of the present invention, they are protected by patent law.

Claims

1. A weight matrix design method, characterized in that: The method comprises: Determine the random matrix based on the actual problem to be solved, the preset distribution model and the preset assumptions; Constructing a minimum value problem of the spectral radius of the random matrix, and generating a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix; Constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix; Converting the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem; The first semidefinite programming problem and the second semidefinite programming problem are jointly solved to generate an optimal weight matrix.

2. The method according to claim 1, wherein: The preset distributed model includes a network model and a measurement model; The network model includes: in, Represents a collection of nodes, represents the edge set, Represents a network model; The measurement model includes: y n (t)=H n θ+v n (t), Where θ∈R d represents the deterministic parameter vector to be estimated, represents the observation matrix, v n (t) represents Gaussian noise, y n (t) represents the measurement model, d n and d represents the dimension of the data.

3. The method according to claim 2, wherein: The preset assumptions include: In the network model, the edge set ε(t) is independent and identically distributed; In the measurement model, the Gaussian noise v n The components of (t) are independently normally distributed; In the measurement model, the observation matrix H n is a column-full rank matrix; The random matrix is ​​a non-negative symmetric matrix, the diagonal elements of the random matrix are positive numbers and the rows are random.

4. The method according to claim 1, wherein: The constructing of the minimum value problem of the spectral radius of the random matrix and generating the first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix includes: Calculating the probability of the random matrix taking values, and constructing a minimum value problem of the spectral radius of the random matrix according to the probability of the random matrix taking values; generating a first weight matrix design problem according to a minimum value problem of the spectral radius of the random matrix; The calculation method of the value probability of the random matrix includes: p k =P(ε(t)=ε k ),k=1,...,K, Among them, ε(t) represents the edge set, ε K represents the kth edge in the edge set, P represents the value probability calculation function, π k represents the probability of taking a value, and K represents the number of edges in the edge set; The calculation method of the spectral radius of the random matrix includes: Wherein, M(t) represents the random matrix, M k represents the value in the random matrix, π k represents the probability of taking values, I represents the identity matrix, N represents the number of nodes, and ρ( ) represents the spectrum radius calculation function; The first weight matrix design problem includes: Among them, S k represents the set of solutions defined by: When (i,j)∈ε k Or i=j,M ij =0, when 5. The method according to claim 1, wherein: The step of constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix includes: Constructing a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, wherein the preset matrix is ​​a set of preset weight matrices that meet the preset assumption condition; Generating a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix; The calculation method of the spectral radius of the preset matrix includes: Among them, W(t) represents the preset weight matrix set, W k represents the preset weight matrix in the preset weight matrix set, I represents the identity matrix, ρ( ) represents the spectrum radius calculation function, x k Indicates the probability of the value corresponding to the preset weight matrix; The second weight matrix design problem includes:

6. The method according to claim 1, wherein: The first semidefinite programming problem includes: Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and π k represents the probability of taking a value, X k Represents the preset semidefinite matrix, M k represents the value in the random matrix, S k represents the set of defined solutions, and N represents the number of nodes; The second semidefinite programming problem includes: Where t represents the target optimization variable in the random matrix, I represents the identity matrix, and x k It represents the probability of the value corresponding to the preset weight matrix, and N represents the number of nodes.

7. The method according to claim 1, wherein: The joint solution of the first semidefinite programming problem and the second semidefinite programming problem and the generation of the optimal weight matrix include Solving the first semidefinite programming problem to obtain a matrix solution, and calculating a first spectral radius of a random matrix corresponding to the matrix solution; Solving the second semidefinite programming problem to obtain a probabilistic solution, and calculating a second spectral radius of a preset matrix corresponding to the probabilistic solution; cyclically solving the matrix solution and the probability solution, and calculating a radius difference between the first spectrum radius and the second spectrum radius obtained from each solution; When the radius difference is less than a preset threshold, an optimal matrix solution and an optimal probability solution are obtained; The optimal matrix solution and the optimal probability solution are set as the optimal weight matrix.

8. A weight matrix design device, characterized in that: The device comprises: A constraint condition acquisition module (401) is used to determine a random matrix based on the actual problem to be solved, a preset distributed model and preset assumptions; A first problem design module (402) is used to construct a minimum value problem of the spectral radius of the random matrix, and generate a first weight matrix design problem according to the minimum value problem of the spectral radius of the random matrix; A second problem design module (403) is used to construct a minimum value problem of the spectral radius of the preset matrix according to the preset matrix, and generate a second weight matrix design problem according to the minimum value problem of the spectral radius of the preset matrix; A weight problem conversion module (404) is used to convert the first weight matrix design problem and the second weight matrix design problem into a first semidefinite programming problem and a second semidefinite programming problem; The weight problem solving module (405) is used to jointly solve the first semidefinite programming problem and the second semidefinite programming problem and generate an optimal weight matrix.

9. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that A computer program is stored which can be loaded by a processor and execute the method according to any one of claims 1 to 7.

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