End-to-end anchor multi-view image clustering method guided by global principal components

Abstract

This application discloses an end-to-end anchor multi-view image clustering method guided by global principal components, specifically relating to the field of image processing. The method comprises: obtaining a sub-view sample matrix for each view and determining a feature mapping matrix; obtaining a global anchor matrix and an anchor graph matrix; obtaining an anchor fuzzy label matrix from the anchor graph matrix, and obtaining a sample fuzzy label matrix based on the anchor fuzzy label matrix; establishing an objective function based on the sub-view sample matrix, feature mapping matrix, global anchor matrix, anchor graph matrix, anchor fuzzy label matrix, and sample fuzzy label matrix; re-determining the feature mapping matrix, and re-transforming the sub-view sample matrices of all views into a unified latent space using the feature mapping matrix until the objective function converges, and outputting the final sample fuzzy label matrix. This method can achieve a unified objective function to facilitate model optimization, learn a global optimal solution, and improve clustering accuracy.

Description

Technical Field

[0001] The present application relates to a field, and in particular to an end-to-end anchor multi-view image clustering method guided by global principal components. Background Art

[0002] The development of multimedia technology can effectively expand the sources of sample features, thereby providing more three-dimensional and detailed data for image analysis. Multi-view clustering, a key research topic in multimedia data mining, aims to extract consistent features from each subview and learn labels based on the cluster distribution of the underlying common representation. Generally speaking, classic multi-view clustering algorithms consist of three independent modules: sub-view feature extraction, common representation fusion, and discrete label learning. Specifically, these algorithms enhance the diversity of representations in smooth multi-view subspaces to normalize view commonality and further analyze the low-rank correlation structure of consensus features to achieve clustering. They introduce anchors to address the high spatial complexity and slow computational speed of traditional multi-view clustering algorithms, and adaptively learn anchor weights to enhance anchor quality. Furthermore, they integrate dictionary learning to integrate intra-view self-representation updates and cross-view graph structure mining into a unified framework, and post-process the unified graph structure to extract final sample labels. Although these modular multi-view clustering algorithms can effectively extract global consensus features, the independence of sub-view feature extraction, common representation fusion, and discrete label learning in these methods makes it difficult to achieve a global optimal solution for the objective function optimization, resulting in reduced clustering accuracy. Summary of the Invention

[0003] The main purpose of this application is to provide an end-to-end anchor multi-view image clustering method guided by global principal components, aiming to solve the problem of low clustering accuracy of existing clustering methods.

[0004] To achieve the above objectives, the present application provides an end-to-end anchor multi-view image clustering method guided by a global principal component, comprising: step 1, obtaining a sub-view sample matrix of each view, and randomly generating an initial global anchor matrix and an initial anchor map matrix; step 2, determining a feature mapping matrix according to the sub-view sample matrix of each view, the initial global anchor matrix, and the initial anchor map matrix; step 3, converting the sub-view sample matrices of all views into a unified latent space through the feature mapping matrix; step 4, extracting common anchor points from the sub-view sample matrices of all views in the unified latent space to obtain a global anchor matrix and an anchor map matrix; step 5, obtaining an anchor fuzzy label matrix in the anchor map matrix, And perform fuzzy label propagation based on the anchor fuzzy label matrix to obtain the sample fuzzy label matrix; Step 6, determine the structural loss and structural loss weight of each view based on the sub-view sample matrix, feature mapping matrix, global anchor matrix, and anchor graph matrix; determine the label transfer loss and transfer loss weight based on the anchor graph matrix, anchor fuzzy label matrix and sample fuzzy label matrix; establish the objective function according to the structural loss and structural loss weight of each view, label transfer loss and transfer loss weight; Step 7, determine the feature mapping matrix according to the sub-view sample matrix, global anchor matrix, and anchor graph matrix of each view, and return to step 3 until the objective function converges and outputs the final sample fuzzy label matrix.

[0005] Optionally, the objective function is as follows:

[0006]

[0007]

[0008] Where, represents the subview sample matrix, ||·|| F represents the norm of matrix F, represents the feature mapping matrix under the v-th subview, t represents the number of unified latent space dimensions, represents the global anchor matrix, m represents the number of global anchor points, represents the anchor graph matrix, and Both represent the identity matrix, and are column vectors whose elements are all 1, Indicates that the column vectors of the feature map matrix satisfy the orthogonal constraint, Z T Z=I m Indicates that the column elements of the global anchor matrix satisfy the orthogonal constraint; represents the sample fuzzy label matrix, represents the anchor point fuzzy label matrix, F≥0,F T 1 c =1 nIndicates that any element in the sample fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1, G≥0,G T 1 c =1 m Indicates that any element in the anchor point fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1; α v represents the loss weight of the v-th view, and β represents the loss weight of label propagation.

[0009] Optionally, the feature map matrix in each view is updated as follows:

[0010]

[0011]

[0012] Where W v The optimal solution is expressed as W v =U v V v T , U v and V v Respectively represent X v B T Z T Perform singular value decomposition on the left and right singular values.

[0013] Optionally, the global anchor matrix is ​​obtained as follows:

[0014]

[0015] Among them, the optimal solution of Z is expressed as Z = UV T , U and V represent the Perform singular value decomposition on the left and right singular values.

[0016] Optionally, the i-th column vector of the anchor map matrix is ​​obtained by the following formula:

[0017]

[0018] Among them, b i represents the i-th column vector in the anchor graph matrix, h i Representation matrix The i-th column vector in .

[0019] Optionally, obtain the anchor point fuzzy label matrix from the anchor point map matrix according to the following formula:

[0020]

[0021] In the formula, Q represents the intermediate variable, g jrepresents the jth column vector in the anchor point fuzzy label matrix, η i Representation matrix The jth column vector in .

[0022] Optionally, the sample fuzzy label matrix is ​​obtained by the following formula:

[0023]

[0024] Where, f i represents the i-th column vector in the sample fuzzy label matrix, ξ i Representation matrix The i-th column vector in , P is the intermediate variable, μ represents the regularization coefficient, Σ F represents the Lagrange multiplier matrix.

[0025] Optionally, the formula for the structural loss weight of each view is:

[0026]

[0027] The formula for transferring loss weight is:

[0028]

[0029] Where, Represents the subview sample matrix.

[0030] Optionally, the objective function converges based on whether the objective function reduction value is less than a convergence threshold.

[0031] Optionally, the reduction value of the objective function is determined according to the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] The end-to-end anchor multi-view image clustering method under the guidance of global principal components of the present invention converts samples under each view into a unified latent space through a feature mapping matrix, and reduces the information loss caused by feature mapping by minimizing the mapping loss function; incorporates sub-view feature extraction and public representation into a unified framework, alternately and collaboratively completes public anchor learning under the guidance of principal components and fuzzy label propagation based on topological information, realizes the unification of objective functions to facilitate model optimization to learn the global optimal solution and improve clustering accuracy, and completes end-to-end learning from image input to label output; performs fuzzy label propagation based on the topological information of the anchor graph matrix, and directly learns anchor label information and sample label information from the topological features of the anchor graph, without the need for post-processing to extract sample labels. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the process of the end-to-end anchor multi-view image clustering method guided by global principal components in this application;

[0035] Figure 2 This is a flowchart of Example 1 of the end-to-end anchor point multi-view image clustering method guided by global principal components of this application;

[0036] Figure 3 This is a result diagram of Example 1 of the end-to-end anchor point multi-view image clustering method guided by global principal components of this application.

[0037] The realization of the objectives, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0038] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions of this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0039] The present invention provides an end-to-end anchor multi-view image clustering method guided by global principal components. Figure 1 As shown, the specific steps include:

[0040] Step S1, obtaining the subview sample matrix of each view, randomly generating the initial feature map matrix, the initial global anchor matrix, the initial anchor map matrix, the initial anchor fuzzy label matrix, and the initial sample fuzzy label matrix;

[0041] In this embodiment, the initial feature map matrix and the initial global anchor matrix under each subview can satisfy the orthogonal constraint by randomly generating column vectors and the number of dimensions respectively satisfy and The matrix is ​​completed, the initial anchor map matrix, the initial sample fuzzy label matrix and the initial anchor fuzzy label matrix all meet the probability constraint, and their initialization can be achieved by randomly generating a matrix with a column vector that meets the non-negative constraint and a row sum of 1. The matrix dimensions meet and

[0042] Step S2, determining a feature mapping matrix according to the sub-view sample matrix of each view, the initial global anchor matrix and the initial anchor map matrix;

[0043] Specifically, the feature mapping matrix under each subview is determined as follows:

[0044]

[0045] in, represents the feature map matrix under the vth subview, t represents the number of unified latent space dimensions, and the constraint Indicates that the column vector of the feature map matrix satisfies the orthogonal constraint, that is, the potential space is unified as an orthogonal space, and the feature map matrix W under different subviews v The updates of are independent of each other, and the update function of the feature map matrix under the corresponding view can finally be written as follows:

[0046]

[0047] Among them, in the first iteration, W v is the initial feature mapping matrix, and W can be obtained by the above formula v The optimal solution can be expressed as W v =U v V v T AndU v and V v Respectively represent X v B T Z T Perform singular value decomposition to obtain the left and right singular values. Traverse each view and calculate the optimal solution of the feature mapping matrix to complete the feature mapping matrix under each subview. Updates.

[0048] Step S3, converting the sub-view sample matrices of all views into a unified latent space through the feature mapping matrix;

[0049] Step S4: extract the common anchor points from the sub-view sample matrices of all views in the unified latent space to obtain a global anchor matrix and an anchor map matrix. The global anchor matrix is ​​obtained by the following formula:

[0050]

[0051] Among them, in the first iteration, Z is the initial global anchor matrix, B is the initial anchor map matrix, Z T Z=I m Indicates that the global anchor matrix column elements satisfy the orthogonal constraint, that is, the anchor points are independent of each other, α v represents the loss weight of the v-th view, and the optimal solution of Z is expressed as Z = UV T , U and V represent the Perform singular value decomposition on the left and right singular values.

[0052] The anchor graph matrix is ​​obtained by the following formula:

[0053]

[0054] Among them, in the first iteration, B is the initial anchor graph matrix, G and F are the initial anchor fuzzy label matrix and the initial sample fuzzy label matrix respectively; B ≥ 0 means that all elements in the anchor graph matrix meet the non-negative constraint, Both represent the identity matrix, and Both represent column vectors whose elements are all 1, β represents the loss weight of label propagation, and b i represents the i-th column vector in the anchor graph matrix, h i Representation matrix The i-th column vector in . Since the anchor graph matrix column vectors are independent of each other, the updates of each anchor feature are independent of each other. Therefore, the update of the anchor graph can be completed by traversing and updating the column vectors. Taking the update of the i-th column vector as an example, its update function can be written as follows:

[0055]

[0056] This optimization problem can be solved in closed form using the Lagrange multiplier method, based on the KKT constraints. Therefore, updating B can be accomplished by traversing and updating the n column vectors in the unified anchor graph matrix. The specific solution is as follows.

[0057] When the Lagrange multiplier method is performed according to the KKT constraints, the above optimization problem can be converted into the following form:

[0058]

[0059] Among them, the vector γ≥0 and the parameter λ are both Lagrange multipliers, and there is a constraint b i ≥0 and γ T b i = 0. For vector b i Taking the derivative we get:

[0060]

[0061] b i =h i +λ1 m +γ substitution We can get:

[0062]

[0063] Will We can get:

[0064]

[0065] Among them, the provisions as well as Can further obtain as well as Because b i ,γ≥0 and γ T b i = 0, for any k (1≤k≤m) γ k b ik =0, that is, there is and and(·) + =max(x,0). At this time b ik The optimal solution depends on The value of , and The optimal value solution of can be equivalent to the solution of the zero point of the following function:

[0066]

[0067] in, And the function problem is a linear piecewise convex problem, and the Newton iteration method can be used to obtain The optimal solution and the iterative formula can be written as:

[0068]

[0069] Since then, The optimal solution of can be obtained through iterative calculation, and when The function value does not change more than 1×10 -2 When , the iterative calculation stops. After the optimal value is obtained, Finally, the optimized unified bipartite anchor graph matrix B is obtained.

[0070] Step S4, obtaining the anchor point fuzzy label matrix in the anchor point map matrix, and performing fuzzy label propagation based on the anchor point fuzzy label matrix to obtain the sample fuzzy label matrix;

[0071] The anchor point fuzzy label matrix G is obtained as follows:

[0072]

[0073] Where, at the first iteration, G and F are the initial anchor point fuzzy label matrix and the initial sample fuzzy label matrix respectively; represents the anchor point fuzzy label matrix and the column vector represents the membership probability of the anchor point and each data cluster, G≥0,G T 1 c =1 mIndicates that any element in the anchor point fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1, that is, the probability that the anchor point corresponding to any column vector belongs to each data cluster is 1. To facilitate optimization, the intermediate variable Q is introduced and its matrix elements are made to approximate the anchor point fuzzy label matrix G. Combined with the Lagrange multiplier method to alternately optimize the above formula, the intermediate variable And the above optimization function can be further rewritten as:

[0074]

[0075] Among them, the variables to be optimized include the regularization coefficient υ, the Lagrange multiplier matrix Σ G , intermediate variable Q and anchor point fuzzy label matrix G. Specifically, in the present invention, the value of the regularization coefficient υ is uniformly initialized to 1×10 -2 And update according to υ=υ×1.2; Lagrange multiplier matrix Σ G Initialize the matrix to all zeros and use Σ G =υ(GQ) to update; the update basis of intermediate variables Complete. For the intermediate variable Q, the Lagrange multiplier matrix Σ G After updating the regularization coefficient υ, the optimization function of the anchor point fuzzy label matrix can be finally written as:

[0076]

[0077] Among them, g j represents the jth column vector in the anchor point fuzzy label matrix, η i Representation matrix Since the updates of anchor labels are independent of each other, the optimization of the anchor fuzzy label matrix can be obtained by traversing m column vectors. Taking the update of the jth column vector as an example, its objective function can be written as follows:

[0078]

[0079] The above objective function can be solved by Lagrange multiplier method according to KKT constraints. Therefore, the anchor point fuzzy label matrix can be obtained by traversing and updating the m column vectors in the anchor point fuzzy label matrix.

[0080] The sample fuzzy label matrix F is obtained by the following formula:

[0081]

[0082] In the formula, at the first iteration, G and F are the initial anchor point fuzzy label matrix and the initial sample fuzzy label matrix respectively; the condition F≥0,F T 1 c =1 nIndicates that any element in the sample fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1, that is, the probability that the sample corresponding to any column vector belongs to each data cluster is 1. Represents the sample fuzzy label matrix and the column vector represents the membership probability of the corresponding sample and each data cluster. To facilitate optimization, this embodiment introduces an intermediate variable P and makes its matrix elements approximate the sample fuzzy label matrix F. Combined with the Lagrange multiplier method to alternately optimize the above formula, the intermediate variable And the above optimization function can be further rewritten as:

[0083]

[0084] Among them, the variables to be optimized include the regularization coefficient μ, the Lagrange multiplier matrix Σ F , intermediate variables P and sample fuzzy label matrix F. Specifically, in the present invention, the regularization coefficient μ is uniformly initialized to 1×10 -2 And update according to μ=μ×1.2; Lagrange multiplier matrix Σ F Initialize the matrix to all zeros and use Σ F =μ(FP) to update; the update basis of intermediate variables Complete. For the intermediate variable P, the Lagrange multiplier matrix Σ F After updating the regularization coefficient μ, the optimization function of the sample fuzzy label matrix can be finally written as:

[0085]

[0086] Among them, f i represents the i-th column vector in the sample fuzzy label matrix, ξ i Representation matrix The i-th column vector in . Since the updates of sample labels are independent of each other, the optimization of the sample fuzzy label matrix can be obtained by traversing n column vectors. Taking the update of the i-th column vector as an example, its objective function can be written as follows:

[0087]

[0088] stf i ≥0,f i T 1 c =1

[0089] For the above objective function, a closed-form solution can be obtained by using the Lagrange multiplier method according to the KKT constraints. Therefore, the update of F can be completed by traversing and updating the n column vectors in the sample fuzzy label matrix.

[0090] Step S5: Determine the structural loss and structural loss weight of each view based on the sub-view sample matrix, feature map matrix, global anchor matrix, and anchor graph matrix obtained above. The formula for the structural loss weight of each view is:

[0091]

[0092] Step S6: determine the label transfer loss and transfer loss weight based on the anchor graph matrix, the anchor fuzzy label matrix, and the sample fuzzy label matrix; the formula for the transfer loss weight is:

[0093]

[0094] Step S7, establishing an objective function based on the structural loss weight of each view, the structural loss of all views, the label transfer loss, and the transfer loss weight;

[0095]

[0096]

[0097] Where, represents the subview sample matrix, ||·|| F represents the norm of matrix F, represents the feature mapping matrix under the v-th subview, t represents the number of unified latent space dimensions, Represents the global anchor matrix, m represents the number of global anchors, and the global anchor matrix column vector represents the corresponding anchor feature. Represents the anchor graph matrix, which is used to describe the correlation between samples and anchor points in the unified latent space. Both represent the identity matrix, and are column vectors whose elements are all 1, Indicates that the column vectors of the feature map matrix satisfy the orthogonal constraint, Z T Z=I m Indicates that the column elements of the global anchor matrix satisfy the orthogonal constraint; represents the sample fuzzy label matrix, represents the anchor point fuzzy label matrix, F≥0,F T 1 c =1 n Indicates that any element in the sample fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1, that is, the probability that the sample corresponding to any column vector belongs to each data cluster is 1; G≥0,G T 1 c =1 m Indicates that any element in the anchor point fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1; α vrepresents the loss weight of the v-th view, and β represents the loss weight of label propagation.

[0098] In step S8, the feature mapping matrix is ​​updated using the subview sample matrix of each view, the global anchor matrix and the anchor map matrix obtained in step S4; and the process returns to step S3 until the objective function converges, and the sample fuzzy label matrix is ​​output.

[0099] Specifically, the basis for the convergence of the objective function is that the reduction value of the objective function is less than the convergence threshold. The reduction value of the objective function is determined by the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization, which can be expressed as:

[0100] loss i =|obj i -obj i-1 |

[0101] Among them, loss i Indicates the reduction value of the objective function corresponding to the i-th round of iterative optimization, obj i represents the objective function value after the i-th round of iterative optimization, ||·|| F Represents absolute value operation.

[0102] Example 1

[0103] This embodiment uses the multi-view image dataset Mfeat as a clustering example. The number of samples is 2000, including 6 sub-view data, and the number of feature dimensions of each view is 216, 76, 64, 6, 240 and 47 respectively, and the number of image label types is 10. The convergence threshold is set to 1×10 -2 The specific clustering process is as follows: Figure 2 As shown, according to the final output sample fuzzy label matrix, the sample is assigned to the corresponding data cluster according to the maximum membership probability to obtain the predicted label Y pre By comparing the true label Y and the predicted label Y pre , the results are as follows Figure 3 As shown in the figure, the objective function decreases steadily with the increase of the number of iterations and converges at the 25th iteration. In the Mfeat dataset, the clustering accuracy (ACC) reaches 86.50%, the clustering normalized mutual information (NMI) reaches 87.78%, and the adjusted Rand coefficient (ARI) reaches 81.80%. It can be seen that the method of the present invention significantly improves the clustering accuracy of multi-view image data, can effectively extract consistent representation distribution in the latent space and accurately complete sample label learning.

[0104] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A global principal component guided end-to-end anchor multi-view image clustering method, characterized by: include: Step 1: Obtain the subview sample matrix of each view and randomly generate the initial global anchor matrix and initial anchor map matrix; Step 2: Determine the feature mapping matrix based on the sub-view sample matrix of each view, the initial global anchor matrix, and the initial anchor map matrix; Step 3: Convert the subview sample matrices of all views to a unified latent space through the feature mapping matrix; Step 4: extract the common anchor points from the sub-view sample matrices of all views in the unified latent space to obtain the global anchor matrix and the anchor map matrix; Step 5: Obtain an anchor point fuzzy label matrix from the anchor point graph matrix, and perform fuzzy label propagation based on the anchor point fuzzy label matrix to obtain a sample fuzzy label matrix; Step 6: Determine the structural loss and structural loss weight of each view based on the sub-view sample matrix, feature map matrix, global anchor matrix, and anchor graph matrix; Determine the label transfer loss and transfer loss weight based on the anchor graph matrix, the anchor fuzzy label matrix, and the sample fuzzy label matrix; establish the objective function based on the structure loss and structure loss weight of each view, the label transfer loss, and the transfer loss weight; Step 7: Determine the feature mapping matrix based on the sub-view sample matrix, the global anchor matrix, and the anchor map matrix of each view, and return to step 3 until the objective function converges, and output the final sample fuzzy label matrix; The objective function is as follows: Where, represents the subview sample matrix, represents the norm of matrix F, Indicates the The feature map matrix under each subview, represents the number of unified latent space dimensions, represents the global anchor matrix, represents the number of global anchor points, represents the anchor graph matrix, and Both represent the identity matrix, and are column vectors whose elements are all 1, Indicates that the column vectors of the feature map matrix satisfy the orthogonal constraint, Indicates that the column elements of the global anchor matrix satisfy the orthogonal constraint; represents the sample fuzzy label matrix, represents the anchor point fuzzy label matrix, Indicates that any element in the sample fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1. Indicates that any element in the anchor point fuzzy label matrix satisfies the non-negative constraint and the sum of the column vector elements is 1; Indicates the The loss weight of each view, represents the loss weight for label propagation.

2. The global principal component guided end-to-end anchor multi-view image clustering method according to claim 1, characterized in that: The update method of the feature map matrix under each view is: Where, The optimal solution is expressed as , and Respectively express Perform singular value decomposition on the left and right singular values.

3. The global principal component guided end-to-end anchor multi-view image clustering method according to claim 1, characterized in that: The global anchor matrix is ​​obtained by the following formula: in, The optimal solution is expressed as , and Respectively express Perform singular value decomposition on the left and right singular values.

4. The global principal component guided end-to-end anchor point multi-view image clustering method according to claim 1, characterized in that: The anchor map matrix The column vectors are obtained by the following formula: in, Indicates the anchor point matrix column vectors, Representation matrix Middle column vectors.

5. The global principal component guided end-to-end anchor multi-view image clustering method according to claim 1, characterized in that: Obtain the anchor fuzzy label matrix in the anchor map matrix according to the following formula: Where, represents the intermediate variable, , Indicates the anchor point fuzzy label matrix column vectors, Representation matrix Middle column vectors.

6. The global principal component guided end-to-end anchor point multi-view image clustering method according to claim 1, characterized in that: The sample fuzzy label matrix is ​​obtained by the following formula: Where, Indicates the first column vectors, Representation matrix Middle column vectors, is an intermediate variable, , represents the regularization coefficient, represents the Lagrange multiplier matrix.

7. The global principal component guided end-to-end anchor point multi-view image clustering method according to claim 1, characterized in that: The formula for the structural loss weight of each view is: The formula for transferring loss weight is: Where, Represents the subview sample matrix.

8. The global principal component guided end-to-end anchor multi-view image clustering method according to claim 1, characterized in that: The basis for the objective function to converge is that the reduction value of the objective function is less than the convergence threshold.

9. The global principal component guided end-to-end anchor point multi-view image clustering method according to claim 8, characterized in that: The reduction value of the objective function is determined according to the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization.

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