CN112861929B - An Image Classification Method Based on Semi-Supervised Weighted Transfer Discriminant Analysis - Google Patents

Abstract

The invention discloses an image classification method based on semi-supervised weighted migration discriminant analysis, and belongs to the technical field of machine learning. The method introduces the difference weight of a sample on the basis of the traditional feature migration method, constructs a feature migration classification model and solves the problem of image cross-domain classification. The invention firstly designs a cross-domain mean value approximation weight. And secondly, introducing cross-domain mean value approximation weight into the MMD, and improving and modifying the JDA. Then, adding a semi-supervised discriminant analysis SDA, fully mining the original spatial structure information of the label information and the data, and improving the class separability of the algorithm. The method can effectively extract high-quality shared features among fields, improve the transfer efficiency of knowledge among the fields and obtain higher classification precision.

Description

An Image Classification Method Based on Semi-Supervised Weighted Transfer Discriminant Analysis

technical field

The invention relates to the technical field of machine learning, in particular to an image classification method based on semi-supervised weighted migration discriminant analysis.

Background technique

In the prior art, transfer learning using machine learning methods has been extensively studied. In the face of the rapid development of big data technology and the promotion and application of mobile Internet, 5G network and high-definition cameras and other equipment, human beings receive high-dimensional visual data showing exponential growth. How to quickly and efficiently mine the valuable information of such data has become an important challenge. . Feature extraction converts the high-dimensional feature space into the corresponding low-dimensional representation space through transformation, and maintains the discriminative information of the original space as much as possible in the low-dimensional space. It can avoid the disaster of dimensionality while making full use of the useful information of the data. It has become a research hotspot in data mining, machine learning, pattern recognition and other fields.

At present, scholars have proposed many feature extraction algorithms, such as principal component analysis (Principal Component Analysis, PCA), linear discriminant analysis (Linear Discriminant Analysis, LDA), maximum boundary criterion and so on. The above algorithms are all global algorithms and cannot extract the local manifold structure information in the image. For this reason, many feature extraction algorithms based on local manifold structure have appeared, such as: local linear embedding, isometric feature map, Laplacian feature map, locality preserving projection (Locality Preserving Projection, LPP) and neighborhood preserving embedding, etc. . Although they can extract the local structure information of the dataset, they cannot solve the learning problem of out-of-sample. In addition, there are feature extraction algorithms derived from other non-graph-theoretic models, such as non-negative matrix factorization and dictionary learning sparse representation, etc. However, none of them unify label information and geometric structure into one objective function to exploit simultaneously. To this end, the prior art has designed a semi-supervised discriminant analysis (Semi-supervised Discriminant Analysis, SDA), which in a semi-supervised situation, simultaneously integrates Fisher's discriminant criterion, local preservation regularization and Tikhonov regularization. Feature extraction is achieved by maximizing the inter-class scatter for labeled data and maintaining the intrinsic spatial structure of both labeled and unlabeled data. Other semi-supervised feature extraction methods, such as semi-supervised maximum margin criterion and semi-supervised manifold-preserving embedding, also use unlabeled samples to improve algorithm performance.

However, it can be seen from the analysis that none of the above feature extraction algorithms can be applied in the transfer learning environment. Migration learning breaks through the limitation that the labeled data set of the traditional machine learning training model follows the same distribution as the unlabeled data set to be tested, and uses the training data in the source domain that is different from the target domain data distribution but related to help the task in the target domain. study. In order to carry out effective feature extraction in the transfer learning environment, the Transfer Component Analysis (TCA) algorithm is also proposed, which combines PCA with Maximum Mean Discrepancy (MMD) to achieve The extraction of shared feature space and the cross-domain transfer of knowledge have been widely used in the field of transfer learning. In order to further improve the performance of the algorithm, on the basis of TCA, with the help of the source domain data label and iterative refinement mechanism, a new feature extraction algorithm is designed in the scene where the target domain has no labeled data: Joint Distribution Adaptation (Joint Distribution Adaptation, JDA). JDA combines MMD to adjust the marginal distribution difference and conditional distribution difference between domains in the iterative process, and integrate it into principal component analysis to construct a new feature subspace, in which the source domain The marginal distribution difference and conditional distribution difference between the data and the target domain are further reduced.

The image classification technology based on semi-supervised weighted transfer discriminant analysis, by adding the cross-domain mean approximation weight into the maximum mean difference measure, to transform the joint distribution adjustment, and combined with semi-supervised discriminant analysis, the algorithm makes the algorithm in the process of label iterative refinement, Fully mine labeled information and original structure information to improve the efficiency of cross-domain image classification tasks. The image classification technology based on semi-supervised weighted transfer discriminant analysis proposes cross-domain mean approximation weights, and introduces feature transfer learning technology, which is a new technology to realize the reuse of shared features in different fields.

Contents of the invention

The object of the present invention is to provide an image classification method based on semi-supervised weighted transfer discriminant analysis, which solves the problem that when the training and test samples come from different distributions, the traditional feature transfer method ignores the sample difference when measuring the distribution difference between fields, and the sample Insufficient mining of label information and original structure information seriously affects classification performance.

The present invention proposes a kind of image classification method based on semi-supervised weighted migration discriminant analysis, comprising the following steps:

S1: Preprocess the image samples of the source domain and the target domain respectively, and obtain the data sets D _S and D _T of the source domain and the target domain;

S2: Obtain the cross-domain mean approximation weights w _S and w _T of the source domain and target domain samples using the source domain and target domain data sets D _S and D _T respectively;

S3: By substituting w _S and w _T into the maximum mean difference measure MMD, and substituting into the joint distribution adjustment JDA, the weighted joint distribution adjustment method WJDA is constructed, and the optimal feature subspace is found by simultaneously reducing the marginal distribution and conditional distribution between fields, Ensure that the image features between the source domain and the target domain remain unchanged during the cross-domain knowledge transfer process;

At the same time, the semi-supervised discriminant analysis SDA and WJDA are combined to construct the objective function of the semi-supervised weighted transfer discriminant analysis model;

Use the generalized eigendecomposition method to learn the feature subspace projection matrix P ^* , and obtain the shared feature expression Z ^* = {Z _S , Z _T } of samples in different fields;

S4: Use the subspace feature expression Z _S of the source domain sample set D _S and its label set Y _S to train the k-nearest neighbor classifier, and perform label prediction on the subspace feature expression Z _T corresponding to the target domain data set D _T to obtain the prediction As a result Y _T , go to step S2 until the maximum number of iterations is reached or Y _T no longer changes.

Further, in the step S1, the preprocessing of the image samples in the source domain and the target domain includes the following steps:

S11: Scaling and scaling the image samples D _S1 and D _T1 in the source domain and the target domain respectively to obtain D _S2 and D _T2 ;

S12: Normalize D _S2 and D _T2 respectively to obtain D _S3 and D _T3 ;

S13: Perform PCA dimensionality reduction processing on D _S3 and D _T3 respectively to obtain D _S and D _T .

Further, in the step S2, the cross-domain mean value approximation weight of the design sample is expressed as follows:

μ_T(S)为目标(源)领域样本的均值。in,

μT _(S) is the mean value of samples in the target (source) domain.

Further, the weighted joint distribution adjustment objective function construction process in the step S3 is:

和目标域

两个高维数据集共享标签集合

S31: Given a high-dimensional dataset source domain from two related domains

and the target domain

Two high-dimensional datasets share a set of labels

Among them, n _S and n _T are the number of samples of the two data sets respectively, d is the dimension of the feature space, the samples in D _T do not contain labeled samples, y _Si ∈ Y, and C is the number of categories;

The objective function of Joint Distribution Adjustment (JDA) is:

为中心矩阵，q∈Rⁿ为元素为1的列向量，n＝n_S+n_T；M₀为(n_S+n_T)阶边缘分布差异矩阵，其元素为：Among them, X＝{D _S ∪D _T }, P is the projection matrix,

is the center matrix, q∈R ⁿ is a column vector with an element of 1, n=n _S +n _T ; M ₀ is a (n _S +n _T ) order marginal distribution difference matrix, and its elements are:

M _c is the conditional distribution difference weight matrix, which is:

和

为源域和目标域中标签类别为c的样本子集，

和

分别为

和

中的样本，

分别为

和

中的样本个数；in,

and

is the sample subset of the label category c in the source domain and the target domain,

and

respectively

and

in the sample,

respectively

and

The number of samples in ;

S32: Introduce the cross-domain mean approximation weight of the source domain and target domain data set samples into formula (2), and construct a cross-domain shared feature extraction algorithm: weighted joint distribution adjustment WJDA, and its objective function is:

In the formula: W ₀ and W _c are marginal distribution and conditional difference matrix, whose elements are respectively:

和

分别为

和

中样本的跨领域均值逼近判别权重，其表达式为：in,

and

respectively

and

The cross-domain mean value of the sample in approximates the discriminant weight, and its expression is:

为目标(源)领域中标签为c类样本集合的均值。in,

is the mean value of the sample set labeled c in the target (source) domain.

Further, in the step S3, the semi-supervised weighted migration discriminant analysis objective function construction process is:

S33: Given a sample set X=X _S ∪X _T , the objective function of semi-supervised discriminant analysis (SDA) is as follows:

G是由X构成的图近邻相似矩阵。S_b和S_t分别表示类间离散度和总散度矩阵：Among them, P ^{T X} L ^{X T} P is the graph regularization item, the parameter α is the balance parameter between the graph regularization item and the inter-class divergence, and the Laplacian matrix of the graph regularization item is L=DP,

G is the graph neighbor similarity matrix composed of X. S _b and S _t represent the between-class scatter and the total scatter matrix, respectively:

S34: Combining WJDA method with SDA, that is, merging formulas (6) and (10), constructing semi-supervised weighted migration discriminant analysis, and its objective function is:

Further deriving the formula (13), we get:

stP ^T X H X ^T P = I

和平衡参数β，为了减小参数β的搜索范围，设定

则公式(14)变为：Among them, θ, λ are balance parameters; among them, in order to control the sparsity of the projection matrix, add in the objective function

and balance parameter β, in order to reduce the search range of parameter β, set

Then formula (14) becomes:

数据集X对应的核矩阵为

则目标函数式(15)在非线性空间内，可以表达为：S35: When the data is non-linear, convert it to a high-dimensional space through kernel mapping, ie

The kernel matrix corresponding to the data set X is

Then the objective function (15) in the nonlinear space can be expressed as:

Further, the solution process of the semi-supervised weighted migration discriminant analysis objective function in the step S3 is:

S36: Using the Lagrange multiplier method, the optimization problem of formula (15) is converted into the generalized eigenvalue solution of the characteristic equation:

Among them, Φ=diag(φ ₁ ,...,φ _k )∈R ^k×k is a diagonal matrix composed of the first k largest eigenvalues, and its corresponding eigenvector matrix is the projection matrix P;

S37: When the data set X is non-linear, the Lagrange multiplier method is used to convert the optimization problem of formula (16) into the generalized eigenvalue solution of the characteristic equation:

分别为S_t、S_b在核映射下的非线性形式。in,

are the nonlinear forms of S _t and S _b under kernel mapping, respectively.

Further, the classification process based on the semi-supervised weighted transfer discriminant analysis in the step S4 is as follows:

The sample features Z _S of the source domain image training set and the sample features Z _T of the target domain test set are extracted by the semi-supervised weighted transfer discriminant analysis model. Choose a linear k-nearest neighbor classifier, and use {Z _S , Y _S } to train the classifier to predict Z _T.

Compared with the prior art, the present invention has the following significant advantages:

(1) Design a cross-domain mean approximation weight by calculating the distance from each sample to the mean point of the other field to reflect the difference between samples;

(2) Introduce the cross-domain mean approximation weight into MMD, transform the Joint Adjusted Distribution (JDA), and design a feature migration method: Weighted Joint Distribution Adaptation (Weighed Joint Distribution Adaptation, WJDA), to improve the cross-domain transfer ability of JDA knowledge ;

(3) Introduce semi-supervised discriminant score (SDA) into WJDA, so that the algorithm can fully mine label information and original structure information in the iterative process of label refinement, so as to improve the extraction of high-quality shared features between domains and the cross-domain transfer of knowledge , which is more conducive to the efficiency of cross-domain image classification tasks.

Description of drawings

Fig. 1 is the flow chart of the image classification method based on semi-supervised weighted transfer discriminant analysis provided by the embodiment of the present invention;

Fig. 2 is the partial image of the experimental dataset provided by the embodiment of the present invention;

Fig. 3 is a curve diagram of cross-domain image classification accuracy of the Office+Caltech256 data set provided by the embodiment of the present invention;

Fig. 4 is a curve diagram of cross-domain image classification accuracy of the PIE data set provided by the embodiment of the present invention;

Fig. 5 is a histogram of cross-domain image classification accuracy of the MNIST+USPS data set provided by the embodiment of the present invention;

Fig. 6 is a histogram of cross-domain image classification accuracy of the COIL data set provided by the embodiment of the present invention;

Fig. 7 is a feature visualization scatter diagram provided by an embodiment of the present invention;

Fig. 8 is a graph showing the influence of each parameter provided by the embodiment of the present invention on the classification accuracy of the algorithm;

Fig. 9 is an MMD distance map provided by an embodiment of the present invention.

Detailed ways

The technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

The present invention proposes an image classification method based on semi-supervised weighted transfer discriminant analysis. Firstly, the image samples in the source domain and the target domain are preprocessed respectively; secondly, the source domain and target domain data are respectively used to obtain the source domain and the target domain. The cross-domain mean approximation weight of domain samples; then, by substituting the cross-domain mean approximation weight into the joint distribution adjustment (JDA), the weighted joint distribution adjustment method (WJDA) is constructed, and by simultaneously reducing the marginal distribution and conditional distribution between domains, to Find the optimal feature subspace; then, combine semi-supervised discriminant analysis (SDA) with WJDA to build a semi-supervised weighted transfer discriminant analysis model to extract high-quality shared features between domains; finally, use the k-nearest neighbor classifier Combined methods to predict the sample labels of the target domain.

With reference to Fig. 1-9, the present invention provides a kind of image classification method based on semi-supervised weighted migration discriminant analysis, comprises the following steps:

S1: Preprocess the image samples in the source domain and the target domain respectively, and obtain the image data sets D _S and D _T in the source domain and the target domain. The preprocessing of image samples in the source and target domains includes the following steps:

(1) Perform resolution-consistent scaling on the image samples in the source and target domains;

(2) Normalize the scaled images uniformly;

(3) The normalized image is subjected to PCA dimensionality reduction processing (retaining 98% of the largest eigenvectors).

S2: Using the source domain and target domain image datasets D _S and D _T to design the cross-domain mean approximation weight of the sample, which is expressed as follows:

μ_T(S)为目标(源)领域样本的均值；in,

μT _(S) is the mean value of samples in the target (source) field;

S3: By substituting w _S and w _T into the maximum mean difference measure MMD, and substituting into the joint distribution adjustment JDA, the weighted joint distribution adjustment method WJDA is constructed, and the optimal feature subspace is found by simultaneously reducing the marginal distribution and conditional distribution between fields, Ensure that the image features between the source domain and the target domain remain unchanged during the cross-domain knowledge transfer process;

At the same time, the semi-supervised discriminant analysis SDA and WJDA are combined to construct the objective function of the semi-supervised weighted transfer discriminant analysis model;

Use the generalized eigendecomposition method to learn the feature subspace projection matrix P ^* , and obtain the shared feature expression Z ^* = {Z _S , Z _T } of samples in different fields;

S4: Use the subspace feature expression Z _S of the source domain sample set D _S and its label set Y _S to train the k-nearest neighbor classifier, and perform label prediction on the subspace feature expression Z _T corresponding to the target domain data set D _T to obtain the prediction As a result Y _T , go to step S2 until the maximum number of iterations is reached or Y _T no longer changes.

Among them, constructing the weighted joint distribution adjustment objective function, the process is as follows:

目标域

它们共享标签集合

其中，n_S和n_T分别为两个数据集的样本个数，d为特征空间维数，D_T中样本未含标记样本，y_Si∈Y，C为类别个数。联合分布调整(JDA)的目标函数为：(1) Given high-dimensional datasets from two related domains, the source domain

target domain

They share a collection of tags

Among them, n _S and n _T are the number of samples of the two data sets respectively, d is the dimension of the feature space, the samples in D _T do not contain labeled samples, y _Si ∈ Y, and C is the number of categories. The objective function of Joint Distribution Adjustment (JDA) is:

为中心矩阵，q∈Rⁿ为元素为1的列向量，n＝n_S+n_T；M₀为(n_S+n_T)阶边缘分布差异矩阵，其元素为：Among them, X＝{D _S ∪D _T }, P is the projection matrix,

is the center matrix, q∈R ⁿ is a column vector with an element of 1, n=n _S +n _T ; M ₀ is a (n _S +n _T ) order marginal distribution difference matrix, and its elements are:

M _c is the conditional distribution difference weight matrix, which is:

和

为源域和目标域中标签类别为c的样本子集，

和

分别为

和

中的样本，

分别为

和

中的样本个数；in,

and

is the sample subset of the label category c in the source domain and the target domain,

and

respectively

and

in the sample,

respectively

and

The number of samples in ;

(2) Introduce the cross-domain mean approximation weights of the source domain and target domain data set samples into formula (2), and construct a cross-domain shared feature extraction algorithm: Weighted Joint Distribution Adjustment (WJDA), whose objective function is:

In the formula: W ₀ and W _c are marginal distribution and conditional difference matrix, whose elements are respectively:

和

分别为

和

中样本的跨领域均值逼近判别权重，其表达式为：in,

and

respectively

and

The cross-domain mean value of the sample in approximates the discriminant weight, and its expression is:

为目标(源)领域中标签为c类样本集合的均值；in,

is the mean value of the sample set labeled c in the target (source) field;

Among them, the semi-supervised weighted migration discriminant analysis objective function is constructed, and the process is as follows:

(1) Given a sample set X=X _S ∪X _T , the objective function of semi-supervised discriminant analysis (SDA) is as follows:

G是由X构成的图近邻相似矩阵。S_b和S_t分别表示类间离散度和总散度矩阵：Among them, P ^{T X} L ^{X T} P is the graph regularization item, the parameter α is the balance parameter between the graph regularization item and the inter-class divergence, and the Laplacian matrix of the graph regularization item is L=DP,

G is the graph neighbor similarity matrix composed of X. S _b and S _t represent the between-class scatter and the total scatter matrix, respectively:

(2) Combining the WJDA method with SDA, that is, merging formulas (6) and (10), constructing a semi-supervised weighted transfer discriminant analysis, and its objective function is:

Further deriving the formula (13), we get:

和平衡参数β，为了减小参数β的搜索范围，设定

则公式(14)变为：Among them, θ, λ are balance parameters; among them, in order to control the sparsity of the projection matrix, add in the objective function

and balance parameter β, in order to reduce the search range of parameter β, set

Then formula (14) becomes:

数据集X对应的核矩阵为

则目标函数式(15)在非线性空间内，可以表达为：(3) When the data is non-linear, convert it to a high-dimensional space through kernel mapping, that is,

The kernel matrix corresponding to the data set X is

Then the objective function (15) in the nonlinear space can be expressed as:

Among them, the process of solving the semi-supervised weighted transfer discriminant analysis objective function is as follows:

(1) Using the Lagrange multiplier method, the optimization problem of formula (15) is converted into the generalized eigenvalue solution of the characteristic equation:

Among them, Φ=diag(φ ₁ ,...,φ _k )∈R ^k×k is a diagonal matrix composed of the first k largest eigenvalues, and its corresponding eigenvector matrix is the projection matrix P;

(2) When the data set X is nonlinear, the Lagrange multiplier method is used to convert the optimization problem of formula (16) into the generalized eigenvalue solution of the characteristic equation:

分别为S_t、S_b在核映射下的非线性形式；in,

are the nonlinear forms of S _t and S _b under kernel mapping, respectively;

Among them, the sample features Z _S of the image training set in the source domain and the sample features Z _T of the test set in the target domain are respectively extracted through the semi-supervised weighted transfer discriminant analysis model. Choose a linear k-nearest neighbor classifier, and use {Z _S , Y _S } to train the classifier to predict Z _T.

Example 1

In order to reflect the credibility and classification performance of the algorithm, three types of benchmark datasets were selected in the experiment: USPS+MNIST handwritten digit dataset, COIL20 object recognition dataset and Office+Caltech256 object recognition dataset, and a total of 36 sets of cross-domain classification tasks were constructed. . The statistical information of each data set is shown in Table 1, and the images of some data sets are shown in Figure 1.

Table 1 Explanation of the experimental image dataset

dataset name type Number of categories Subset (number of samples × sample dimension) USPS number 10 USPS (1800×256) MNIST number 10 MNIST (2000×256) COIL20 object 20 COIL1(1024×720), COIL2(1024×720) office object 10 A(985×800), D(157×800), W(295×800) Caltech256 object 10 C(1123×800)

Object recognition dataset Office+Caltech256 constructs cross-domain classification tasks: Office dataset contains three sub-datasets of Amazon(A), DLSR(D) and Webcam(W), plus Caltech256(C) item recognition dataset, from A, D, W, and C data sets respectively select 958, 157, 295, and 1123 images, each image is represented by an 800-dimensional feature vector, and the four data sets share 10 object categories. Randomly select two of the four data sets as the source domain and target domain data sets, and a total of 12 sets of cross-domain classification experiments can be constructed: C→A(1), C→W(2)0, C→D(3) ,..., D → W (12).

Handwritten font dataset USPS+MNIST constructs a cross-domain classification task: As can be seen from Figure 1, USPS and MNIST images follow different distributions, but share 10 font categories. 1800 and 2000 images were randomly selected from the USPS and MNIST datasets, and the size of all images was linearly scaled to 16×16. Each image was represented by a 256-dimensional feature vector. The two datasets shared 10 font categories. Using USPS and MNIST as the source and target domains respectively, two sets of cross-domain classification experiments can be constructed: U vs M and Mvs U.

PIE is a standard face dataset, which contains images describing the pose, lighting and expression of faces. In the experiment, in order to verify the performance of the algorithm in the cross-domain learning method, 5 subsets of PIE are selected, and each subset corresponds to a different pose. Select PIE1 (C05, left pose), PIE2 (C07, up pose), PIE3 (C09, down pose), PIE4 (C27, front face pose), PIE5 (C29, right pose). In each subset (pose), all faces are under different lighting, illumination and expression conditions. By randomly selecting two subsets as the source domain dataset and the target domain dataset, 5×4=20 cross-domain face datasets can be constructed, PIE1 vs PIE2(1), PIE1 vs PIE3(2),…, PIE5 vsPIE4(20). The source and target domain datasets constructed from face datasets of different poses meet the requirement of following different distributions.

The computer hardware configuration used in the experiment is: Intel Core(TM) i5-3470HQ CPU main frequency 3.2GHz, memory 8GB, using Matlab2017b software programming simulation. In order to reduce the influence of errors on the experimental results, the average value of 20 classification results in each group of experiments was taken. The experimental results are shown in Figure 3-6.

In order to investigate the influence of subspace dimension, iteration number and parameter value on classification performance in the algorithm, the parameters α, θ, μ, λ, and subspace dimension k in the image classification algorithm based on semi-supervised weighted transfer discriminant analysis were respectively analyzed And the number of iterations for sensitivity experiment analysis. Six sets of experiments were conducted on 4 datasets including Avs D, COIL1 vs COIL2, MNISTvs USPS, PIE1 vs PIE4, using 1NN as the benchmark classifier, and each parameter was tested by the fixed variable method in the experiment. The experimental results are shown in Figure 7.

In order to further prove that the shared feature expression learned by the SWJDA algorithm has a better discriminative ability, the group PIE1 vs PIE4 was selected from 36 groups of cross-domain classification tasks for feature visualization analysis experiments, and the source domain was drawn using random nearest neighbor embedding (t-SNE). And target domain original features, JDA and SWJDA algorithm feature scatter plots. t-SNE is an algorithm that maps high-dimensional data to two-dimensional or three-dimensional space through affine transformation for visualization. The experimental results are shown in Figure 8, where each shade of color is represented as a category, and there are 68 categories in total. If the clusters of the same depth are closer together and the clusters of different depths are more scattered, the feature discrimination is stronger.

In order to further prove that the SWJDA algorithm has a good convergence discriminant ability, after each label refinement iteration, the MMD of SWJDA on four data sets including Avs D, MNIST vs USPS, COIL1 vs COIL2, and PIE1 vs PIE4 were calculated. The results are shown in Figure 9. The results show that: 1) The unlabeled MMD distance in the target domain is smaller than the labeled MMD distance due to the difference in calculation methods. 2) As the number of iterations increases, the marginal distribution difference and conditional distribution difference between domains decrease, making the MMD distance gradually smaller and the classification accuracy improved, and this process is synchronous. The results show that SWTDA minimizes the difference of marginal distribution and conditional distribution between domains, which is beneficial to the extraction of shared features and the transfer of knowledge across domains.

The above disclosures are only a few specific embodiments of the present invention, however, the embodiments of the present invention are not limited thereto, and any changes conceivable by those skilled in the art shall fall within the protection scope of the present invention.

Claims (5)

1. An image classification method based on semi-supervised weighted migration discriminant analysis is characterized by comprising the following steps of:

s1: the source domain and target domain image samples are preprocessed separately,obtaining source domain and target domain datasets D _S And D _T ；

S2: using source domain and target domain datasets D, respectively _S And D _T Obtaining cross-domain mean approximation weight w of source domain and target domain samples _S And w _T ；

S3: by mixing w _S And w _T Substituting the MMD into the maximum mean difference measurement and substituting into the JDA to construct a weighted joint distribution adjustment method WJDA, and searching for an optimal feature subspace by simultaneously reducing the edge distribution and the condition distribution between the domains to ensure that the image features between the source domain and the target domain are unchanged in the cross-domain knowledge migration process;

meanwhile, combining semi-Supervised Discriminant Analysis (SDA) with WJDA to construct a target function of a semi-supervised weighted migration discriminant analysis model;

learning a feature subspace projection matrix P by adopting a generalized feature decomposition method ^* Obtaining shared feature expression Z of samples among different fields ^* ＝{Z _S ,Z _T }；

S4: using a source domain sample set D _S By a subspace feature of Z _S And its label set Y _S Training k nearest neighbor classifier to the target domain data set D _T Corresponding subspace feature expression Z _T Performing label prediction to obtain prediction result Y _T Go to step S2 until the maximum number of iterations or Y is reached _T No longer changed;

the cross-domain mean approximation weight of the sample is designed in the step S2, and the expression is as follows:

wherein,

μ _T(S) mean of target (source) domain samples;

the weighted joint distribution adjustment objective function construction process in the step S3 is as follows:

s31: given a high-dimensional dataset source domain from two related domains

And a target domain

Two high-dimensional datasets sharing a labelset

Wherein n is _S And n _T The number of samples of two data sets, D is the characteristic space dimension, D _T Middle sample containing no labeled sample, y _Si E is Y, and C is the number of categories;

the objective function of joint distribution adaptation JDA is:

wherein, X = { D = _S ∪D _T -P is a projection matrix,

as a central matrix, q ∈ R ⁿ For a column vector with element 1, n = n _S +n _T ；M ₀ Is (n) _S +n _T ) The order edge distribution difference matrix has the following elements:

M _c for the conditional distribution disparity matrix, there are:

wherein，

And

for the sample subset with label class c in the source domain and the target domain,

and

are respectively as

And

the sample of (1) is selected from,

are respectively as

And

the number of samples in (1);

s32: introducing cross-domain mean value approximation weights of the source domain and target domain data set samples into a formula (2), and constructing a cross-domain shared feature extraction algorithm: the weighted joint distribution adjustment WJDA has the objective function of:

s.t.P ^T XHX ^T P＝I

(5)

in the formula: w is a group of ₀ And W _c Is an edgeThe elements of the edge distribution difference weight matrix and the condition difference weight matrix are respectively as follows:

wherein,

and

are respectively as

And

the cross-domain mean value of the middle sample approaches to the discrimination weight, and the expression is as follows:

wherein,

is the mean value of the sample set labeled as class c in the target (source) domain.

2. The image classification method based on semi-supervised weighted migration discriminant analysis according to claim 1, wherein in the step S1, the preprocessing of the image samples in the source domain and the target domain includes the following steps:

s11: for image samples D in the source domain and the target domain _S1 And D _T1 Respectively carrying out the scaling treatment with consistent resolution ratio to obtain D _S2 And D _T2 ；

S12: will D _S2 And D _T2 Respectively carrying out normalization treatment to obtain D _S3 And D _T3 ；

S13: will D _S3 And D _T3 Performing PCA dimension reduction treatment respectively to obtain D _S And D _T 。

3. The image classification method based on semi-supervised weighted migration discriminant analysis according to claim 1, wherein the semi-supervised weighted migration discriminant analysis target function constructing process in the step S3 is as follows:

s33: given sample set X = X _S ∪X _T The objective function of the semi-supervised discriminant analysis SDA is as follows:

wherein, P ^T XLX ^T P is a graph regularization term, the parameter α is a balance parameter between the graph regularization term and the interspecies divergence, the Laplace matrix of the graph regularization term is L = D-P,

g is a graph neighborhood similarity matrix composed of X; s. the _b And S _t The inter-class dispersion and total dispersion matrices are represented, respectively:

s34: combining the WJDA method with the SDA, namely combining the formulas (5) and (9), constructing semi-supervised weighted migration discriminant analysis, wherein the objective function is as follows:

s.t.P ^T XHX ^T P＝I (13)

further derivation of equation (13) yields:

wherein θ, λ are balance parameters; wherein, in order to control the sparsity of the projection matrix, an objective function is added

And a balance parameter beta, which is set to reduce the search range of the parameter beta

Mu is a balance parameter, and has the same meaning as beta, and controls the distribution difference weight matrix W ₀ ，W _c For non-weighted distribution difference matrix M ₀ ，M _c The degree of influence of (c); equation (14) becomes:

s35: when the data is non-linear, it is transformed into a high-dimensional space by kernel mapping, i.e.

The kernel matrix for dataset X is

Then the objective function (15) is in a non-linear space, expressed as:

4. the image classification method based on semi-supervised weighted migration discriminant analysis according to claim 1, wherein the solving process of the semi-supervised weighted migration discriminant analysis objective function in the step S3 is as follows:

s36: and (3) converting the optimization problem of the formula (15) into a generalized eigenvalue solution of a characteristic equation by adopting a Lagrange multiplier method:

wherein Φ = diag (Φ) ₁ ,…,φ _k )∈R ^k×k The matrix is a diagonal matrix formed by the first k maximum eigenvalues, and the corresponding eigenvector matrix is a projection matrix P;

s37: when the data set X is nonlinear, the optimization problem of the formula (16) is converted into a generalized eigenvalue solution of a characteristic equation by adopting a Lagrange multiplier method:

wherein,

are respectively S _t 、S _b Non-linear form under kernel mapping.

5. The image classification method based on semi-supervised weighted migration discriminant analysis according to claim 1, wherein the classification process based on semi-supervised weighted migration discriminant analysis in step S4 is as follows:

respectively extracting source field image training set sample characteristics Z through semi-supervised weighted migration discriminant analysis model _S And target Domain test set sample characteristics Z _T (ii) a Selecting a linear k nearest neighbor classifier and using { Z _S ,Y _S Training classifier pair Z _T And (6) predicting.

Images