Sparse site selection method and device and storage medium
By incorporating the maximum entropy criterion and local geometry preservation term into the sparse location model, the location matrix and reconstruction matrix are optimized, solving the problem of noise impact in ocean observation, achieving stable sparse location and high-precision data reconstruction, and reducing sensor deployment costs.
Patent Information
- Application Number
- CN202410793066.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-06-19
- Publication Date
- 2025-12-19
AI Technical Summary
Existing sparse site selection methods do not fully consider the impact of noise in ocean observation, resulting in unstable solution results and high sensor deployment costs.
An error measurement function based on the maximum entropy criterion is adopted, and local geometric structure preservation terms, sparsity of the addressing matrix, and noise influence are added as regularization terms. By iteratively updating the sparse addressing model, the addressing matrix and reconstruction matrix are gradually optimized to reduce the influence of noise.
It achieves stable sparse site selection under noisy conditions, reduces sensor deployment costs, and improves data reconstruction accuracy and robustness.
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Figure CN121167972A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of monitoring and site selection technology, and in particular to a sparse site selection method, apparatus and storage medium. Background Technology
[0002] For general monitoring systems, the ability to effectively monitor the state of a target is crucial. This is especially true in the field of ocean observation, where the location of sensors used to monitor the physical environment directly impacts the deployment cost of the ocean observation system, as well as the effectiveness and accuracy of the monitoring. Due to the vastness of the ocean, conducting full-state monitoring of ocean physical quantities globally is impractical because the cost of deploying a large number of sensors worldwide is prohibitively high. In particular, sensors used for monitoring the marine environment are often deployed on buoys, moorings, or engineering vessels, resulting in high deployment and data acquisition costs.
[0003] Therefore, it is necessary to determine the optimal observation location in an ocean observation system through site selection optimization, so that the ocean observation system can be reconstructed from the ocean physical quantity data at a finite number of locations by deploying sensors at those locations. This generally involves data dimensionality reduction and reconstruction techniques.
[0004] However, existing methods for sensor location by mapping low-dimensional data to high-dimensional data do not fully consider the impact of noise in the original data when performing data dimensionality reduction and reconstruction. Furthermore, the basis used for reconstruction in these methods typically employs a random matrix conforming to a standard normal distribution, which introduces a degree of randomness. Summary of the Invention
[0005] The purpose of this invention is to overcome the defects of existing sparse addressing schemes, such as unstable solution results, and to provide a sparse addressing method, device and storage medium.
[0006] The objective of this invention can be achieved through the following technical solutions:
[0007] As a first aspect of the present invention, a sparse addressing method is provided, comprising the steps of:
[0008] Input historical data and the number of site selections into the sparse site selection model;
[0009] The sparse addressing model adopts an error measurement function based on the maximum entropy criterion, and adds a local geometry preservation term, the sparsity of the addressing matrix and the influence of noise as regularization terms, and an entropy term corresponding to the noise weight.
[0010] The location matrix, reconstruction matrix, and noise matrix of the sparse location model are iteratively updated step by step to estimate the data;
[0011] After iterating until the preset termination condition is met, the final set of location selections is the sparse location selection result.
[0012] As a preferred technical solution, the sparse addressing model is expressed as follows:
[0013]
[0014] Where A is the reconstruction matrix; C is the addressing matrix; and W is the first noise weight representing the smaller noise level. To characterize the second noise weight for larger noise, α, β, and γ are preset coefficients; X represents historical data, including m samples and n candidate locations. Let X be the i-th sample; σ be the kernel bandwidth of the Gaussian kernel function used in the maximum entropy criterion; μ be the coefficient of the local geometry retention term; (·) T α represents the transpose operation; L is the graph Laplacian matrix, used to describe the local geometric structure of historical data X; α is the coefficient of the sparse regularization term; This indicates the magnitude of the influence of larger noise, where β is the regularization coefficient of the influence of larger noise.
[0015] As a preferred technical solution, the method employs block coordinate updates for iterative model solving and approximates the optimal solution using semi-quadratic optimization techniques. The sparse addressing model is simplified into several sub-problems. In each iteration, the addressing matrix C, reconstruction matrix A, noise weights, and transformation variable q are updated respectively. When updating one matrix, the remaining variables are fixed. The decomposition sub-functions of the sparse addressing optimization model are as follows:
[0016]
[0017] In the k-th iteration, update each variable individually:
[0018]
[0019]
[0020] in, for Lipschitz constant relative to C; Let be the estimated location matrix for the k-th iteration;
[0021]
[0022] Where, ω k ∈[0,1] represents the preset weight;
[0023]
[0024] Where, δ ω <1 is the preset value; And t0 = 1,
[0025] As a preferred technical solution, the sub-functions corresponding to the addressing matrix C are solved using the block near-end gradient method:
[0026] The address matrix C subproblem is transformed into:
[0027]
[0028] in, For coefficients;
[0029] The transformed matrix is decomposed into subproblems corresponding to n variables according to the dimension of the number of positions:
[0030]
[0031] Where s represents the i-th row of matrix S, corresponding to the i-th position;
[0032] Update each row c of the addressing matrix C according to the following formula to obtain the new addressing matrix:
[0033]
[0034] Where Ω represents the index set of the positive elements of s, ||s Ω ||2>0.
[0035] As a preferred technical solution, in the sparse addressing model, when iteratively solving the subproblem of reconstructing matrix A, reconstructing matrix A is updated according to the following formula:
[0036]
[0037] As a preferred technical solution, the first noise weight W and the second noise weight The corresponding sub-functions complete the first noise weight W and the second noise weight using the following two equations. Update:
[0038]
[0039] As a preferred technical solution, the sub-function corresponding to the transformation variable q is updated as follows:
[0040]
[0041] As a preferred technical solution, the sparse addressing model undergoes a progressive iterative update process as follows:
[0042] Input historical data X and the number of locations p;
[0043] Determine whether the convergence condition is met in the k-th iteration;
[0044] Calculate the Lipschitz constant based on the updated addressing matrix C, the reconstruction matrix A, the noise weight matrix, the variable q, and the matrix X;
[0045] Determine whether the updated objective function value is greater than the previous value;
[0046] If so, then: If not, calculate the preset weight ω. k And update
[0047] Let k ← k+1;
[0048] Repeat the above steps until the preset convergence condition is met, then end the iteration process.
[0049] The obtained location matrix C is normalized column by column, and the 2-norm of the normalized location matrix C is calculated column by column. The indices of the p columns with the largest 2-norm values are stored in the location set.
[0050] Output the location matrix C, the reconstruction matrix A, and the set of location positions obtained through iteration.
[0051] As a second aspect of the present invention, a sparse addressing apparatus is provided, including a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the sparse addressing method as described above.
[0052] As a third aspect of the present invention, a storage medium is provided having a program stored thereon, characterized in that the program, when executed, implements the sparse addressing method as described above.
[0053] Compared with the prior art, the present invention has the following beneficial effects:
[0054] 1) The method of the present invention achieves sparse addressing by establishing an optimization model and iteratively solving it step by step. This method can make the objective function value gradually converge to the optimal solution stably. Even if there are many different kinds of noise, high-precision reconstruction can still be achieved based on the addressing matrix and reconstruction matrix in the obtained optimal solution and the addressing data.
[0055] 2) This invention improves the original error measurement method based on Euclidean distance to an error measurement method based on the maximum entropy criterion, making the location method less susceptible to the influence of non-Gaussian noise and outliers.
[0056] 3) In order to improve the reconstruction accuracy, the present invention adds a local geometry preservation term, as well as a sparse addressing regularization term and a noise term to the model, so as to achieve sparse addressing while having good robustness.
[0057] 4) This invention uses a subspace learning method to iteratively update the addressing matrix and the reconstruction matrix simultaneously to obtain the estimated reconstruction data, thereby minimizing the difference between the original historical data X and the estimated data. Attached Figure Description
[0058] Figure 1 This is a flowchart illustrating the sparse addressing method for sensors according to the present invention. Detailed Implementation
[0059] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.
[0060] Example 1
[0061] This invention proposes a sparse sensor location method, constructing an optimization model for sparse sensor location based on the maximum entropy criterion. Entropy is used to measure the similarity between the original data and the estimated data. Noise weights are added to the optimization model to indicate noise, further reducing the impact of noise. The location matrix, reconstruction matrix, and noise matrix are updated iteratively to achieve sparse sensor location, resulting in good location performance and significantly higher accuracy of the estimated data compared to related methods. A large noise regularization term and the entropy of all noise weights are added to the optimization model to obtain better estimated data even under severe noise conditions. A sparse regularization term is added to the optimization model to achieve sparse location while ensuring the reconstruction accuracy of the estimated data, thereby reducing deployment costs. The establishment and solution of the sparse location model are detailed below:
[0062] 1. Establishment of sparse location model
[0063] Traditional subspace learning uses Euclidean distance to measure the error between the original data and the reconstructed data, as shown below:
[0064]
[0065] in, The original data, To reconstruct the data, Let p be the addressing matrix containing p unit vectors. Let n be the corresponding reconstruction matrix, n be the candidate position summary, and m be the number of samples.
[0066] To mitigate the sensitivity of Euclidean distance to non-Gaussian noise and outliers, this invention employs an error measurement function based on the maximum entropy criterion (i.e., a sensor selection model based on the maximum entropy criterion):
[0067]
[0068] Where σ is the kernel bandwidth of the Gaussian kernel function used in the maximum entropy criterion. Let X be the i-th sample of historical data X.
[0069] To improve reconstruction accuracy, a local geometry preservation term is added, and the sparsity of the addressing matrix (its rank should be less than or equal to p, i.e., r(C)≤p) is added as a regularization term to equation (2). Simultaneously, the above equation is transformed into:
[0070]
[0071] in,(·) T Let L denote the transpose operation, where L is an m*m dimensional graph Laplacian matrix used to describe the local geometry of data X. μ represents the coefficients of the local geometry retention term, and α represents the coefficients of the sparse regularization term.
[0072] To further improve robustness, a first noise weight is established. and the second noise weight These are used to characterize lower noise and higher noise, respectively. The sparse addressing problem model is then redefined as:
[0073]
[0074] Where ⊙ represents the dot product, w ij ∈W. The data is historical, consisting of m samples and n candidate locations. For estimated data.
[0075] When the number of locations is p, combining equations (3) and (4), the optimization model for the sparse location problem is:
[0076]
[0077] Due to multiple constraints, the optimization function in equation (5) is difficult to solve. Therefore, it is necessary to limit the influence of large noise on the objective function and the magnitude of the influence of large noise. It is also added as a regularization term to equation (5). Then we have:
[0078]
[0079] Where α and β are preset coefficients. The noise weights can be further relaxed as follows: In addition, the corresponding entropy term is added: A larger entropy term indicates that the term corresponding to the noise weight better represents the distribution of the system's state variables. Therefore, a sparse addressing optimization model with good robustness is obtained:
[0080]
[0081] 2. Solving the sparse location model
[0082] 2.1 The model is simplified into various sub-problems.
[0083] When calculating the maximum value of cross-entropy using a Gaussian kernel function, the result can be viewed as a Weltch M-estimation, and therefore can be approximated using semi-quadratic optimization techniques. Let... Then we have:
[0084]
[0085] Here, φ(x) = exp(-x), where, q i To transform the variables, we can obtain:
[0086]
[0087] make:
[0088]
[0089] The model is solved iteratively using block coordinate updates. In each iteration, C, A, and W are updated separately, while the others are fixed during the update of one of them. Therefore, to simplify:
[0090] First, decompose equation (7) into three sub-functions, as follows:
[0091]
[0092] G α (C)=α||C|| 2，1 (12)
[0093]
[0094] The overall objective function can then be expressed as: O(C,A,W,q)=F(C,A,W,q)+G α (C)+H(W). In the k-th iteration, update each variable according to the following formula:
[0095]
[0096] in, for The Lipschitz constant relative to C. And:
[0097]
[0098] Where, ω k ∈[0,1] represents the preset weight.
[0099] Secondly, give Value:
[0100] Through derivation, we can obtain:
[0101]
[0102] For any have:
[0103]
[0104] The inequality part of equation (17) is derived using the Cauchy-Schwarz inequality: ||UV|| F ≤||U||2||V|| F The law is transformed. According to the definition of the Lipschitz constant, we know that:
[0105]
[0106] Finally, the weights in equation (15) are:
[0107]
[0108] Where, δ ω <1 is the default value. And t0 = 1,
[0109] 2.2 Solving C-subproblems
[0110] The addressing matrix C is a matrix consisting of 0s and 1s, where 0 indicates that the corresponding position is not selected and 1 indicates that the corresponding position is selected. This matrix is difficult to solve for function (14a) using the gradient method; therefore, the block near-end gradient method is used for the solution.
[0111] Function (14a) is transformed into:
[0112]
[0113] in, Let be the coefficients. The matrix of equation (20) is decomposed into n subproblems corresponding to n variables according to the dimension of the number of positions, as follows:
[0114]
[0115] Here, s represents the i-th row of matrix S, corresponding to the i-th position. Let Ω denote the index set of the positive elements of s, and ||s Ω When ||2>0, we have:
[0116]
[0117] Then, by updating each row c of matrix C according to equation (22), the entire new addressing matrix C can be obtained.
[0118] 2.3A - Solving Subproblems
[0119] From equation (14b), we can obtain:
[0120]
[0121] make:
[0122]
[0123] The above expression is equivalent to solving:
[0124]
[0125] Taking the first derivative of A with respect to this expression and setting the result to 0, we get:
[0126]
[0127] in, It is a pseudo-inverse. The reconstructed matrix A can be updated according to equation (26).
[0128] 2.4 Solving Subproblems
[0129] Taking the (i,j) term as an example, The solution to the subproblem first involves the expression in equation (13) regarding... The function of the terms is proposed and transformed using the Lagrange multiplier method as follows:
[0130]
[0131] Where, ρ i For Lagrange multipliers, q is received here. i The impact is X. k Find the distribution with respect to w. ij , ρ i Taking the partial derivative and setting the result to 0, we have:
[0132]
[0133] Then we can deduce that:
[0134]
[0135] corresponding
[0136] Then W and W can be completed through equation (29). Update.
[0137] Solving the 2.5q-subproblem
[0138] Equation (8) Please find the answer to q. i If we take the partial derivative of q and set it to 0, then we have: i = -exp(-x). Therefore, we can obtain:
[0139]
[0140] Execution process of the method of the present invention Figure 1 As shown, the data used is ocean surface temperature data. By inputting the data and a preset value 'p', the optimal site selection location can be obtained. The overall implementation process of this method is as follows:
[0141] Step 1) Input historical data X and the number of locations p.
[0142] Step 2) Determine whether the convergence condition has been met for the kth iteration.
[0143] Step 3) Calculate the Lipschitz constant according to equation (18), update the addressing matrix C according to equation (20), update the reconstruction matrix A according to equation (23), and update the weight matrix W according to equation (29). Update variable q according to equation (30), and update matrix X according to equation (24).
[0144] Step 4) Determine whether the updated objective function value is greater than the previous value, i.e., O(C k+1 A k+1 W k+1 ,q k )≥O(C k A k W k ,q k ).
[0145] If so, then: If not, then calculate ω according to equation (19). k Update according to formula (15)
[0146] Step 5) Let k ← k+1.
[0147] Step 6) Repeat steps 2) to 5) until the preset convergence condition is met, then end the iteration process;
[0148] Step 7) Normalize the obtained location matrix C column by column, and calculate the 2-norm of the normalized matrix column by column. Store the indices of the p columns with the largest 2-norm values into the location set.
[0149] Step 8) Output the location matrix C, reconstruction matrix A, and location set obtained from the iteration.
[0150] The final set of location selections is the sparse location selection result obtained by this invention.
[0151] The convergence condition refers to one of the following: the maximum number of iterations when the method is executed as needed, whether the difference of the objective function in the last few iterations is less than the preset difference, and the maximum execution time of the method as a whole.
[0152] This invention constructs an optimization model for sparse sensor location based on the maximum entropy criterion, using entropy to measure the similarity between the original and estimated data. Noise weights are added to the optimization model to indicate noise levels, further reducing the impact of noise. Sparse sensor location is achieved by iteratively updating the location matrix, reconstruction matrix, and noise matrix, resulting in better location performance and significantly higher accuracy in the estimated data compared to related methods. Incorporating a large noise regularization term and the entropy of all noise weights into the optimization model enables better estimation even under severe noise conditions. The addition of a sparsity regularization term to the optimization model achieves sparse location while maintaining the accuracy of the estimated data reconstruction, thereby reducing deployment costs.
[0153] Example 2
[0154] As a second aspect of the present invention, this application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the sensor sparse addressing method described above. In addition to the processors, memory, and interfaces described above, any data processing device in the embodiments may also include other hardware depending on the actual function of the data processing device, which will not be elaborated further.
[0155] Example 3
[0156] As a third aspect of the present invention, this application also provides a computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the sensor sparse addressing method described above. The computer-readable storage medium can be an internal storage unit of any data processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.
[0157] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.
Claims
1. A sparse location method, characterized in that the steps include... include: Input historical data and the number of site selections into the sparse site selection model; The sparse addressing model adopts an error measurement function based on the maximum entropy criterion, and adds a local geometry preservation term, the sparsity of the addressing matrix and the influence of noise as regularization terms, and an entropy term corresponding to the noise weight. The location matrix, reconstruction matrix, and noise matrix of the sparse location model are iteratively updated step by step to estimate the data; After iterating until the preset termination condition is met, the final set of location selections is the sparse location selection result.
2. The sparse location method according to claim 1, characterized in that, The sparse addressing model is expressed as follows: Where A is the reconstruction matrix; C is the addressing matrix; W is the first noise weight representing the smaller noise, w ij ∈W w ij ∈W; To characterize the second noise weight for larger noise, α, β, and γ are preset coefficients; X represents historical data, including m samples and n candidate locations. Let X be the i-th sample; σ be the kernel bandwidth of the Gaussian kernel function used in the maximum entropy criterion; μ be the coefficient of the local geometry retention term; (·) T α represents the transpose operation; L is the graph Laplacian matrix, used to describe the local geometric structure of historical data X; α is the coefficient of the sparse regularization term; This indicates the magnitude of the influence of larger noise, where β is the regularization coefficient of the influence of larger noise.
3. The sparse location method according to claim 2, characterized in that, The method employs block coordinate updates for iterative model solving and approximates the optimal solution using semi-quadratic optimization techniques. The sparse addressing model is simplified into several sub-problems. In each iteration, the addressing matrix C, reconstruction matrix A, noise weights, and transformation variable q are updated separately. When updating one matrix, the remaining variables are fixed. The decomposition sub-functions of the sparse addressing optimization model are as follows: G α (C)=α||C|| 2，1 In the k-th iteration, update each variable individually: in, for Lipschitz constant relative to C; Let be the estimated location matrix for the k-th iteration; Where, ω k ∈[0,1] represents the preset weight; Where, δ ω <1 is the preset value; And t0 = 1, 4. The sparse location method according to claim 3, characterized in that, The sub-functions corresponding to the addressing matrix C are solved using the block near-end gradient method: The address matrix C subproblem is transformed into: in, For coefficients; The transformed matrix is decomposed into subproblems corresponding to n variables according to the dimension of the number of positions: Where s represents the i-th row of matrix S, corresponding to the i-th position; Update each row c of the addressing matrix C according to the following formula to obtain the new addressing matrix: Where Ω represents the index set of the positive elements of s, ||s Ω ||2>0.
5. The sparse location method according to claim 1, characterized in that, In the sparse addressing model, when iteratively solving the subproblem of reconstructing matrix A, reconstructing matrix A is updated according to the following formula:
6. The sparse location method according to claim 3, characterized in that, The first noise weight W and the second noise weight The corresponding sub-functions complete the first noise weight W and the second noise weight using the following two equations. Update:
7. The sparse location method according to claim 3, characterized in that, The sub-function corresponding to the transformation variable q is updated as follows:
8. A sparse addressing method according to any one of claims 3-7, characterized in that, The sparse addressing model undergoes a step-by-step iterative update process as follows: Input historical data X and the number of locations p; Determine whether the convergence condition is met in the k-th iteration; Calculate the Lipschitz constant based on the updated addressing matrix C, the reconstruction matrix A, the noise weight matrix, the variable q, and the matrix X; Determine whether the updated objective function value is greater than the previous value; If so, then: If not, calculate the preset weight ω. k And update Let k ← k+1; Repeat the above steps until the preset convergence condition is met, then end the iteration process. The obtained location matrix C is normalized column by column, and the 2-norm of the normalized location matrix C is calculated column by column. The indices of the p columns with the largest 2-norm values are stored in the location set. Output the location matrix C, the reconstruction matrix A, and the set of location positions obtained through iteration.
9. A sparse addressing device, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the sparse addressing method as described in any one of claims 1-8.
10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the sparse addressing method as described in any one of claims 1-8.