A domain-adaptive image classification method with periodic reconstruction subspace learning

Abstract

This invention relates to a domain-adaptive image classification method with periodic reconstruction subspace learning, belonging to the field of computer vision. It addresses the problem that existing image classification methods generally assume that training and test samples follow the same distribution, but in practical applications, their distributions are often different due to various factors (such as illumination and resolution). By using an iterative strategy, the data matrix is ​​reconstructed cyclically in both the source and target domains using reconstruction matrices, and the common subspace is updated. This approach not only learns the invariant features of the common subspace but also preserves the global and local structures of the source and target domains. Furthermore, additional discriminative constraints are implemented on the transformed features to ensure class discriminability between the two domains. To avoid overfitting, a graph regularization constraint is added. By reducing the distribution difference between the two domains, cross-domain recognition is achieved, improving image classification performance.

Description

Technical Field

[0001] This invention belongs to the field of computer vision and relates to a domain-adaptive image classification method with periodic reconstruction subspace learning. Background Technology

[0002] Machine learning and data mining methods have achieved remarkable success in pattern recognition. However, a major assumption of many machine learning and data mining algorithms is that training and test data must have the same feature distribution in the same feature space. But in many practical applications, this assumption may not be correct due to variations in lighting intensity, camera equipment, environment, viewpoint, and resolution. In such cases, most statistical models need to be reconstructed using newly collected training data, which is expensive and time-consuming. In this situation, if knowledge can be successfully transferred, expensive data annotation can be avoided, and learning performance can be greatly improved. At this point, domain adaptation solves the problem of cross-domain classification by extracting useful information from data in the relevant domain and transferring it to the target domain. Domain adaptation is generally divided into two categories: semi-supervised domain adaptation and unsupervised domain adaptation. Semi-supervised domain adaptation means that a subset of samples in the target domain have labels, while unsupervised domain adaptation means that samples in the target domain do not have available labels. This invention mainly studies the more challenging unsupervised domain adaptation.

[0003] Existing domain adaptation methods aim to find a useful transformation matrix that projects data from two domains into a common subspace with reduced divergence. To preserve useful properties in the resulting common subspace, existing work introduces a matrix called the reconstruction matrix, which connects the source and target domains after the transformation. In this way, each data point from the target domain can be linearly reconstructed from the source data in the common subspace, rather than simply reducing the differences in domain distribution. However, this will cause some damage to the basic structure of the source domain in order to better represent the target data in a single direction. The data in the target domain representing the source data will, to some extent, compromise the structure of the target domain (i.e., some basic data information is lost). Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a domain-adaptive image classification method with periodic reconstruction subspace learning. This method uses an iterative strategy to cyclically reconstruct the data matrix using two reconstruction matrices and update the common subspace, learning invariant features in the common subspace. This better preserves the global and local structures of the two original domains. Additional discriminative constraints, such as intra-class aggregation and inter-class diffusion, are applied to the transformed features to ensure class discriminability of the data from the two domains and improve the performance of image classification.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A domain-adaptive image classification method with periodic reconstruction subspace learning includes the following steps:

[0007] S1: For the image to be classified, first find a suitable projection matrix P to project the source domain and the target domain onto a common subspace to reduce the difference in domain distribution.

[0008] S2: Use a classifier to classify the transformation results of the target domain.

[0009] Furthermore, step S1 specifically includes the following steps:

[0010] S11: Use two reconstruction matrices to reconstruct the common subspace in a loop, so that the subspace and reconstruction matrices are modified according to the feedback of the loop iteration;

[0011] S12: Apply different constraints to different reconstruction matrices to preserve different structural information of the original domain;

[0012] S13: After mapping the original domain to the common subspace P using reliable labels of the source domain, iterative reconstruction is performed to learn the discriminative subspace, and a label relaxation matrix is ​​introduced to obtain a more flexible common subspace.

[0013] S14: By using the improved linear discriminant analysis (LDA) method, the distance between samples of different classes is increased, the distance between samples of the same class is reduced, and the class discriminant ability is increased.

[0014] S15: Introduce graph regularization terms to preserve the data structure.

[0015] Furthermore, step S11 specifically includes:

[0016] Given source domain data m is the feature dimension label, n s The number of source data items is [number], and the target domain data is [number]. n t Let P ∈ R be the number of target data points. m×C For the projection matrix, Let P be the source reconstruction coefficient matrix. T X s P represents the transformed source sample. T X t The transformed target sample is represented by data from the source domain reconstructed into the target domain as follows:

[0017] P T X s Z s =P T X t

[0018] Using the target reconstruction matrix in the target domain The reconstructed features in the source domain are represented as follows:

[0019] (P T X s ) T =Z t (P T X t ) T

[0020] The two equations are combined to establish a cyclic subspace. The source data is projected onto the target domain, and the target domain data is used to reconstruct the source data in turn until convergence.

[0021] Furthermore, step S12 specifically includes:

[0022] Given the source reconstruction coefficient matrix Z s Add sparse constraints:

[0023]

[0024] Reconstruct the target matrix Z t Apply low-rank constraints:

[0025]

[0026] Among them, ||·|| * It is the nuclear norm of the matrix.

[0027] Furthermore, in step S13, after mapping the original domain to the common subspace P using reliable labels from the source domain, iterative reconstruction is performed to learn the discriminative subspace, as shown below:

[0028]

[0029] Introducing a nonnegative label relaxation matrix M relaxes the strict binary label matrix into a relaxation variable matrix, providing P with greater degrees of freedom:

[0030]

[0031] Among them, matrix Let C be the label matrix, where C is the number of classes. For unsupervised domain adaptation, the labels only apply to the source domain; for sample x... i Its label is y i ∈R C If x i If it is the kth class, then only y i The k-th element is 1, and all other elements are 0; ⊙ is the Hadamard product operator, and B is a constant matrix where each element... Geometrically speaking, B ijCorresponding to the drag direction, "+1" indicates dragging towards the positive axis, and "-1" indicates dragging towards the negative axis; the drag size of each element on Y is the corresponding element in M; assuming three samples x1, x2, and x3 belong to the third, first, and second classes respectively, their traditional label matrix is... When x1 and x2 are projected into the label space, their distance is... Their label relaxation matrices are When x1 and x2 are projected into the label space, their distance is...

[0032] Furthermore, step S14 specifically includes:

[0033] Introducing intra-class and inter-class scattering matrices, where S w S is the intraclass scattering matrix. b The inter-class scattering matrix is ​​calculated using the following methods:

[0034]

[0035]

[0036] Among them, u c Let and u represent the sample mean of class c and all classes, respectively;

[0037] The "average margin" between two categories is used to measure how well the transformed samples resemble samples from the same class, while separating them from samples from different classes. The expression is:

[0038]

[0039] Furthermore, step S15 specifically includes:

[0040] Introduce the adaptive graph Laplace constraint, defined as:

[0041]

[0042] Where A∈R n×n This is a diagram to be studied;

[0043] Introducing a graph smoothing term based on manifold sorting:

[0044]

[0045] Where, Q∈R n×n This represents an initial graph pre-constructed from the data, where each element represents the similarity between two corresponding samples; a Gaussian kernel function is used. Calculate sample x i and x j The similarity between them, the diagonal matrix D∈R n ×nDepend on get;

[0046] Combining the above formula, it can be expressed as:

[0047]

[0048] st0≤A≤1,dig(A=0,A T =A,Ae n =e n

[0049] Where {0≤A≤1, dig(A)=0, A T =A,Ae n =e n} represents the boundary constraints, and the minimization steps are used to achieve this. Simultaneously acquire the local geometric structure and representation structure of the data;

[0050] The objective function is expressed as:

[0051]

[0052] stP T X s Z s =P T X t , (P T X s ) T =Z t (P T X t ) T ,M≥0,0≤A≤1,dig(A)=0,A T =A,Ae n =e n .

[0053] Furthermore, it also includes the following steps:

[0054] A1: Introduce variables Z1 and Z2, and two constraints Z. t =Z1,Z s =Z2, rewrite the objective function as:

[0055]

[0056] stP T X s Z s =P T X t , (P T X s ) T =Z t (PT X t ) T ,M≥0,0≤A≤1,dig(A)=0,

[0057] A T =A,Ae n =e n Z t =Z1,Z s =Z2

[0058] The above equation is optimized using Lagrange multipliers and transformed into an augmented Lagrange function;

[0059] A2: Input source domain data X s Target domain data X t The source domain label matrix Y, with ρ, μ max ε initialization;

[0060] A3: By fixing other variables, the augmented Lagrangian function is transformed into a function of P, and then its derivative is set to 0. The solution for P is:

[0061] P * =(A1-A2+A3+λI) -1 (A4+A5)

[0062] Where A1=(1+μ)X s X s T +μX s Z s Z s T X s T +2λ1XL A X T ,

[0063]

[0064] A4 = X s (Y s +B⊙M) T -X s Z s Y1 T ,

[0065] A4: By fixing other variables, the augmented Lagrangian function is transformed into a function with respect to Z. t The function is then used, and its derivative is set to 0 to obtain Z. t The solution is:

[0066]

[0067] A5: By fixing other variables, the augmented Lagrangian function is transformed into a function with respect to Z. s The function is then used, and its derivative is set to 0 to obtain Z. s The solution is:

[0068]

[0069] A6: By fixing other variables, the augmented Lagrangian function is transformed into a function of M, and then its derivative is set to 0. The solution for M is:

[0070] M = max(R⊙B, 0)

[0071] A7: By fixing other variables, the augmented Lagrangian function is transformed into a function of Z1, and then its derivative is set to 0. The solution for Z1 is:

[0072]

[0073] A8: By fixing other variables, the augmented Lagrangian function is transformed into a function of Z2, and then its derivative is set to 0. The solution for Z2 is:

[0074]

[0075] A9: By fixing other variables, the augmented Lagrange function is transformed into a function of A:

[0076]

[0077] in, Solving the problem using an alternating update method breaks it down into two simpler problems:

[0078]

[0079] The optimal solution to the two simple problems is expressed as follows:

[0080]

[0081] Where, O=(H+H T ) / 2;

[0082] A10: By fixing other variables, the augmented Lagrangian function is transformed into a function of S:

[0083]

[0084] The solution for S is:

[0085]

[0086] Among them, S (t) This represents the value of variable S at step t. as well as

[0087] A11: Update the Lagrange multipliers:

[0088]

[0089] A12: During the iteration process, determine whether the set termination condition is met. If the iteration condition is met, continue to execute step A2. If the iteration count is completed or the iteration condition is not met, the iteration terminates. The termination conditions set during the iteration process are as follows:

[0090]

[0091] Furthermore, step S2 specifically includes: obtaining the transformation results of the source data and the target data using the transformation matrix P respectively; and classifying the transformation results of the target domain data using a 1-nearest neighbor classifier or a support vector machine.

[0092] The beneficial effects of this invention are as follows: This invention uses an iterative strategy with two reconstruction matrices to cyclically reconstruct the data matrix and update the common space. In this way, invariant features in the common subspace are learned, while better preserving the global and local structures of the two original domains. Furthermore, a margin criterion is added to the transformed features, making the transformed samples closer to samples of the same class and further away from samples of different classes. To avoid overfitting, a graph regularization term is introduced. This invention explores the higher-order structure of the data while capturing its local geometric and representational structures. It effectively reduces the distributional differences between the source and target domains, improving the performance of classification images.

[0093] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0094] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0095] Figure 1 This is a schematic flowchart of the domain-adaptive image classification method with periodic reconstruction subspace learning described in this invention. Detailed Implementation

[0096] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0097] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0098] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0099] Please see Figure 1 This invention provides a domain-adaptive image classification method with periodic reconstruction subspace learning, which specifically includes the following steps:

[0100] Step 1) Find a suitable projection matrix P to project the source and target domains onto a common subspace to reduce the difference in domain distribution.

[0101] Step 1.1) Establish a cyclic reconstruction subspace. Use two reconstruction matrices to cyclically reconstruct the common subspace, allowing the subspace and reconstruction matrices to be modified based on the feedback of the cyclic iteration, reducing the differences between the two domains while retaining more useful information.

[0102] Given source domain data m is the feature dimension label, n s The number of source data items. The target domain data is... n t Let P ∈ R be the number of target data points. m×C For the projection matrix, Let P be the source reconstruction coefficient matrix. T X s P represents the transformed source sample. T X t The transformed target sample, reconstructed using data from the source domain, can be represented as:

[0103] P T X s Z s =P T X t

[0104] Using the target reconstruction matrix in the target domain Reconstruct the features in the source domain. Represented as:

[0105] (P T X s ) T =Z t (P T X t ) T

[0106] By combining the two equations above, a cyclic structure subspace is established. The source data is projected onto the target domain, and the target domain data is used to reconstruct the source data sequentially until convergence. This invention employs a cyclic iterative method to gradually explore the required subspace, which is a process of gradually approximating the optimal solution. This not only does not change the structure of the source domain but also ensures that the domain-invariant features and structural properties that need to be retained are well preserved.

[0107] Step 1.2) Preserving Structure and Information. Since the source and target domains have different feature distributions, they possess unique structures and information. Therefore, this invention applies different constraints to different reconstruction matrices to preserve the different structural information of the original domains.

[0108] Given the source reconstruction coefficient matrix Z s Add sparsity constraints to make Z s It has as few non-zero terms as possible. Therefore, the expression in step 1.1 can be further expressed as:

[0109]

[0110] By analyzing Z s Adding sparsity constraints involves using as little source domain information as possible to represent target domain samples in a given incomplete dictionary, thereby obtaining a more concise feature representation. This makes it easier to obtain local information contained in the source domain during feature learning in the target domain.

[0111] To effectively preserve global structural information and align the two domains, source data of the same class should be represented by target data in the same way as possible, giving the target reconstruction matrix Z. t By applying a low-rank constraint, the expression in step 1.1 can be further expressed as:

[0112]

[0113] Here, rank() represents the rank of the matrix, but since the rank minimization problem is non-convex, it can be further rewritten as...

[0114]

[0115] Among them, ||·|| * It is the nuclear norm of the matrix. The target reconstruction matrix Z t The low-rank feature of the target domain means that the same category in the source domain corresponds to the same linear representation in the target domain, while original samples belonging to different categories correspond to different representations.

[0116] Step 1.3) A more flexible public subspace. After mapping the original domain to the public subspace P using reliable labels of the source domain, iterative reconstruction is performed to learn the discriminative subspace. A label relaxation matrix is ​​introduced to obtain a more flexible public subspace.

[0117] After mapping the original domain to a common subspace P using reliable labels from the source domain, iterative reconstruction is performed to learn the discriminative subspace, denoted as...

[0118]

[0119] Introducing a nonnegative label relaxation matrix M relaxes the strict binary label matrix into a relaxation variable matrix, providing greater degrees of freedom for P. The expression in step 3.1 can be rewritten as follows:

[0120]

[0121] Among them, matrix Let be the label matrix, where C is the number of classes. For unsupervised domain adaptation, the labels are only applicable to the source domain. For sample x... i Its label is y i ∈R C If x i If it is the kth class, then only y i The k-th element is 1, and all other elements are 0. ⊙ represents the Hadamard product operator, and B is a constant matrix where each element... Geometrically speaking, B ijCorresponding to the drag direction, "+1" indicates dragging towards the positive axis, and "-1" indicates dragging towards the negative axis. The dragged size of each element in Y is the corresponding element in M. Assume three samples x1, x2, and x3 belong to the third, first, and second classes respectively, and their traditional label matrix is... When x1 and x2 are projected into the label space, their distance is... Their label relaxation matrices are When x1 and x2 are projected into the label space, their distance is... This shows that a subspace P with greater degrees of freedom can be obtained through the label relaxation matrix, and a larger variation space can reduce the influence of noise.

[0122] Step 1.4) Increase class discriminability. By using an improved LDA (Linear Discriminant Analysis) method, the distance between samples of different classes is increased, while the distance between samples of the same class is decreased. In this way, samples with the same label form a compact cluster, and different class clusters are kept as far apart as possible.

[0123] Introduce intra-class and inter-class scattering matrices. Where S... w S is the intraclass scattering matrix. b The inter-class scattering matrix can be calculated using the following methods:

[0124]

[0125]

[0126] Among them, u c and u represent the sample mean of class c and all classes, respectively.

[0127] This measures the "average margin" between two categories, making the transformed samples approximate samples of the same class, but separate them from samples of different classes. The expression is:

[0128]

[0129] Step 1.5) Introduce a graph regularization term. To avoid overfitting, a graph regularization term is introduced, which can effectively preserve the structure of the data.

[0130] Introducing the adaptive graph Laplacian constraint, it can be defined as:

[0131]

[0132] Where A∈R n×n This is a diagram to be studied.

[0133] By introducing a graph smoothing term based on manifold sorting, which can explore information from the nearest neighbor graph Q, this invention can obtain a more reasonable graph from the data to guide the learning of the regression matrix.

[0134]

[0135] Where, Q∈R n×n This represents an initial graph pre-constructed from the data, where each element represents the similarity between two corresponding samples. Here we use the Gaussian kernel function. Calculate sample x i and x j The similarity between them, the diagonal matrix D∈R n×n Depend on get.

[0136] This proposed novel graph embedding model explores higher-order structural information among four tuples, and can simultaneously explore the local geometry and representational structure of the data. Combining these two steps can be represented as follows:

[0137]

[0138] st0≤A≤1,dig(A=0,A T =A,Ae n =e n

[0139] {0≤A≤1,dig(A=0,A T =A,Ae n =e n} represents the boundary constraints. In this case, we can minimize the steps in the above equation. Simultaneously, the local geometric structure and representation structure of the data are obtained.

[0140] Based on the above steps, the objective function of this invention can be expressed as:

[0141]

[0142] stP T X s Z s =P T X t , (P T X s ) T =Z t (P T X t ) T ,M≥0,0≤A≤1,dig(A)=0,A T =A,Ae n =e n

[0143] Step A1) To ensure that the problem proposed in this invention is solvable, variables Z1 and Z2, as well as two constraint conditions Z1 and Z2, are introduced.t =Z1,Z s =Z2, the objective function of the method proposed in this invention can be rewritten as:

[0144]

[0145] stP T X s Z s =P T X t , (P T X s ) T =Z t (P T X t ) T ,M≥0,0≤A≤1,dig(A)=0,

[0146] A T =A,Ae n =e n Z t =Z1,Z s =Z2

[0147] The above equation is optimized using Lagrange multipliers and transformed into an augmented Lagrange function.

[0148] Step A2) Input source domain data X s Target domain data X t The source domain label matrix Y, with ρ, μ max ε initialization.

[0149] Step A3) By fixing other variables, the augmented Lagrangian function in step A1) is transformed into a function of P, and then its derivative is set to 0. The solution for P is then obtained as follows:

[0150] P * =(A1-A2+A3+λI) -1 (A4+A5)

[0151] Where A1=(1+μ)X s X s T +μX s Z s Z s T X s T +2λ1XL A X T ,

[0152]

[0153] A4 = X s (Y s +B⊙M) T -X s Z s Y1 T ,

[0154] Step A4): By fixing other variables, transform the augmented Lagrangian function in step A1) into a function with respect to Z. t By taking the function and setting its derivative to 0, we can obtain Z. t Solution

[0155]

[0156] Step A5): By fixing other variables, transform the augmented Lagrangian function in step A1) into one with respect to Z. s By taking the function and setting its derivative to 0, we can obtain Z. s Solution

[0157]

[0158] Step A6): By fixing other variables, transform the augmented Lagrangian function from step A1) into a function of M, and then set its derivative to 0, the solution to M can be obtained.

[0159] M = max(R⊙B, 0)

[0160] Step A7): By fixing other variables, transform the augmented Lagrangian function in step A1) into a function of Z1, and then set its derivative to 0, the solution for Z1 can be obtained.

[0161]

[0162] Step A8): By fixing other variables, transform the augmented Lagrangian function from step A1) into a function of Z2, and then set its derivative to 0, the solution for Z2 can be obtained.

[0163]

[0164] Step A9): By fixing other variables, transform the augmented Lagrangian function in step A1) into a function of A:

[0165]

[0166] in, Directly optimizing the above equation is difficult, so we use an alternating update method to solve it, breaking this problem down into two simpler problems:

[0167]

[0168] The optimal solutions to the two simple problems above can be expressed as:

[0169]

[0170] Where, O=(H+H T ) / 2.

[0171] Step A10): By fixing other variables, transform the augmented Lagrangian function in step A1) into a function of S:

[0172]

[0173] The solution for S is:

[0174]

[0175] Among them, S (t) This represents the value of variable S at step t. as well as

[0176] Step A11): Update the Lagrange multipliers

[0177]

[0178] Step A12) During the iteration process, determine whether the set termination condition is met. If the iteration condition is met, continue with step A2). If the iteration count is completed or the iteration condition is not met, the iteration terminates. The termination condition set during the iteration process is as follows:

[0179]

[0180] Step A13) yields the transformation matrix P, and then P is used directly to obtain the transformation results for the source and target data respectively. A 1-Nearest Neighbor (NN) classifier or a Support Vector Machine (SVM) is applied to classify the transformation results of the target domain data.

[0181] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A domain-adaptive image classification method with periodic reconstruction subspace learning, characterized in that: Includes the following steps: S1: For the image to be classified, first find the projection matrix P to project the source and target domains onto a common subspace, reducing the difference in domain distribution; step S1 specifically includes the following steps: S11: Use two reconstruction matrices to reconstruct the common subspace in a loop, so that the subspace and reconstruction matrices are modified according to the feedback of the loop iteration; S12: Apply different constraints to different reconstruction matrices to preserve different structural information of the original domain; S13: After mapping the original domain to the common subspace W using reliable labels of the source domain, iterative reconstruction is performed to learn the discriminative subspace, and a label relaxation matrix is ​​introduced to obtain a more flexible common subspace. S14: By using the improved linear discriminant analysis (LDA) method, the distance between samples of different classes is increased, the distance between samples of the same class is reduced, and the class discriminancy is enhanced; Step S14 specifically includes: Introducing intra-class and inter-class scattering matrices, where S w S is the intraclass scattering matrix. b The inter-class scattering matrix is ​​calculated using the following methods: Among them, u c Let and u represent the sample mean of class c and all classes, respectively; The "average margin" between two categories is used to measure how well the transformed samples resemble samples of the same class, while separating them from samples of different classes. The expression is: S15: Introduce graph regularization terms to preserve the data structure; S2: Use a classifier to classify the transformation results of the target domain.

2. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 1, characterized in that: Step S11 specifically includes: Given source domain data m is the feature dimension label, n s The number of source data items is [number], and the target domain data is [number]. n t Let P ∈ R be the number of target data points. m×C For the projection matrix, Let P be the source reconstruction coefficient matrix. T X s P represents the transformed source sample. T X t The transformed target sample is represented by data from the source domain reconstructed into the target domain as follows: P T X s Z s =P T X t Using the target reconstruction matrix in the target domain The reconstructed features in the source domain are represented as follows: (P T X s ) T =Z t (P T X t ) T The two equations are combined to establish a cyclic subspace. The source data is projected onto the target domain, and the target domain data is used to reconstruct the source data in turn until convergence.

3. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 1, characterized in that: Step S12 specifically includes: Given the source reconstruction coefficient matrix Z s Add sparse constraints: Reconstruct the target matrix Z t Apply low-rank constraints: Among them, ||·|| * It is the nuclear norm of the matrix.

4. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 1, characterized in that: In step S13, after mapping the original domain to the common subspace W using reliable labels from the source domain, iterative reconstruction is performed to learn the discriminative subspace, as shown below: Introducing a nonnegative label relaxation matrix M relaxes the strict binary label matrix into a relaxation variable matrix, providing greater degrees of freedom for W: Among them, matrix Let C be the label matrix, where C is the number of classes. For unsupervised domain adaptation, the labels only apply to the source domain; for sample x... i Its label is y i ∈R C If x i If it is the kth class, then only y i The k-th element is 1, and all other elements are 0; ⊙ is the Hadamard product operator, and B is a constant matrix where each element... Geometrically speaking, B ij Corresponding to the drag direction, "+1" indicates dragging towards the positive axis, and "-1" indicates dragging towards the negative axis; the dragged size of each element in Y is the corresponding element in M; assuming three samples x1, x2, and x3 belong to the third, first, and second classes respectively, their traditional label matrix is... When x1 and x2 are projected into the label space, their distance is... Their label relaxation matrices are When x1 and x2 are projected into the label space, their distance is...

5. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 1, characterized in that: Step S15 specifically includes: Introduce the adaptive graph Laplace constraint, defined as: Where A∈R n×n This is a diagram to be studied; Introducing a graph smoothing term based on manifold sorting: Where, Q∈R n×n This represents an initial graph pre-constructed from the data, where each element represents the similarity between two corresponding samples; a Gaussian kernel function is used. Calculate sample x i and x j The similarity between them, the diagonal matrix D∈R n×n Depend on get; Combining the above formula, it can be expressed as: s.t.0≤A≤1,dig(A)=0,A T =A,Ae n =e n Where {0≤A≤1, dig(A)=0, A T =A,Ae n =e n } represents the boundary constraints, and the minimization steps are used to achieve this. Simultaneously acquire the local geometric structure and representation structure of the data; The objective function is expressed as: s.t.P T X s Z s =P T X t ,(P T X s ) T =Z t (P T X t ) T ,M≥0,0≤A≤1,dig(A)=0,A T =A,Ae n =e n 。 6. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 5, characterized in that: It also includes the following steps: A1: Introduce variables Z1 and Z2, and two constraints Z. t =Z1,Z s =Z2, rewrite the objective function as: s.t.P T X s Z s =P T X t ,(P T X s ) T =Z t (P T X t ) T ,M≥0,0≤A≤1,dig(A)=0, A T =Ah, Yes n =e n ,Z t =Z1,Z s =Z2 The above equation is optimized using Lagrange multipliers and transformed into an augmented Lagrange function; A2: Input source domain data X s Target domain data X t The source domain label matrix Y, with ρ, μ max ε initialization; A3: By fixing other variables, the augmented Lagrangian function is transformed into a function of P, and then its derivative is set to 0. The solution for P is: P * (A1-A2+A3+λI) -1 (A4+A5) Where A1=(1+μ)X s X s T +μX s Z s Z s T X s T +2λ1XL A X T , A4=X s (Y s +B⊙M) T -X s From s Y1 T , A4: By fixing other variables, the augmented Lagrangian function is transformed into a function with respect to Z. t The function is then used, and its derivative is set to 0 to obtain Z. t The solution is: A5: By fixing other variables, the augmented Lagrangian function is transformed into a function with respect to Z. s The function is then used, and its derivative is set to 0 to obtain Z. s The solution is: A6: By fixing other variables, the augmented Lagrangian function is transformed into a function of M, and then its derivative is set to 0. The solution for M is: M = max(R⊙B, 0) A7: By fixing other variables, the augmented Lagrangian function is transformed into a function of Z1, and then its derivative is set to 0. The solution for Z1 is: A8: By fixing other variables, the augmented Lagrangian function is transformed into a function of Z2, and then its derivative is set to 0. The solution for Z2 is: A9: By fixing other variables, the augmented Lagrange function is transformed into a function of A: in, Solving the problem using an alternating update method breaks it down into two simpler problems: The optimal solution to the two simple problems is expressed as follows: Where, O=(H+H T ) / 2; A10: By fixing other variables, the augmented Lagrangian function is transformed into a function of S: The solution for S is: Among them, S (t) This represents the value of variable S at step t. as well as A11: Update the Lagrange multipliers: A12: During the iteration process, determine whether the set termination condition is met. If the iteration condition is met, continue to execute step A2. If the iteration count is completed or the iteration condition is not met, the iteration terminates. The termination conditions set during the iteration process are as follows:

7. The domain-adaptive image classification method with periodic reconstruction subspace learning according to claim 6, characterized in that: Step S2 specifically includes: obtaining the transformation results of the source data and the target data using the projection matrix P respectively; and classifying the transformation results of the target domain data using a 1-nearest neighbor classifier or a support vector machine.

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