CN107392230A - A kind of semi-supervision image classification method for possessing maximization knowledge utilization ability - Google Patents

Abstract

The invention discloses a semi-supervised image classification method capable of maximizing knowledge utilization. This method focuses on image data preprocessing and feature selection in general image classification technology, but has not made breakthroughs in classification methods, and proposes a semi-supervised image classification method with the ability to maximize knowledge utilization. The image classification method first considers the problem of high cost of image labeling in reality, starts from the semi-supervised method, and then maximizes the mining of labeled image data, and mines image data from two aspects of labeled images and unlabeled images At the same time, in the preprocessing and feature selection of image data, the applicable normalization and principal component analysis dimensionality reduction methods are adopted to process image data in advance to fully ensure the integrity of image data information.

Description

A semi-supervised image classification method with the ability to maximize knowledge utilization

technical field

The invention belongs to the field of image processing and application, in particular to a semi-supervised image classification method capable of maximizing knowledge utilization.

Background technique

Support Vector Machine (Support Vector Machine, SVM) is a machine learning method based on statistical learning theory developed gradually after the 1990s. Disaster" and "overfitting" problems, and has good generalization ability, has shown good application prospects in many practical engineering fields. However, as a supervised learning method, the traditional SVM can only learn on a small number of labeled samples, which leads to insufficient learning to a certain extent, and affects the recognition of specific patterns by this method to a certain extent. Ability. If the idea of semi-supervised learning can be introduced into the support vector machine, it will make up for the defects of the standard support vector machine and obtain better classification results.

Traditional machine learning techniques are divided into two categories, one is unsupervised learning and the other is supervised learning. Unsupervised learning uses only unlabeled sample sets, while supervised learning uses only labeled sample sets for learning. But in many practical problems, there is only a small amount of labeled data, because it often takes a lot of manpower and material resources to label samples, and the cost is sometimes high, while a large amount of unlabeled data is easy to obtain. This has prompted the rapid development of semi-supervised learning techniques that can utilize both labeled and unlabeled samples. The semi-supervised support vector machine algorithm based on support vector machine extension has a better effect.

Image classification is to divide images into different preset categories. It is difficult for computers to identify and classify. The reason is twofold. One is the image data. The image is full of a large number of complex and diverse objects that are difficult to describe. There are various data processing and feature selection methods from the original image to the specific data in the pattern recognition method; the second is the specific classification. The selection of methods and classification methods are varied, each with its own advantages and disadvantages. For image classification, the general approach is to start from the first aspect, find out the appropriate feature selection method as much as possible in the process of data preprocessing and feature selection, and then use some classic classification methods such as SVM for image classification, but The premise of this method is that it often needs as much labeled data as possible, which is required for training classifiers, is clearly divided, and the feature selection is appropriate, and this cost is often high. Then starting from the selection of classification methods, semi-supervised support vector machines often have better classification results.

Contents of the invention

The purpose of the present invention is to improve the machine's image classification ability by mining marked and unmarked image sample data more effectively and deeply.

According to the technical solution provided by the present invention, the semi-supervised image classification method with the ability to maximize knowledge utilization includes the following definitions and steps:

definition:

Definition 1: Dataset Indicates the set of samples used for classifier training, d is the data dimension, l is the number of labeled samples and u is the number of unlabeled samples;

Definition 2: y _i ∈{+1,-1}(i=1,...,l) represents the sample label corresponding to l labeled samples of data set X;

Definition 3: Represents a classification decision function, where α _i ≥ 0 is a support vector indicator element, b is a constant, K() is a kernel function, usually a radial basis kernel function: K( _xi ,x _j )=exp(-| |x _i -x _j || ² /2σ ² ), i∈[1,l], j∈[1,l+u], σ is the core broadband;

Definition 4: f=[f ₁ ,...,f _l ,f _l+1 ,...,f _l+u ] ^T is the data set The predicted value obtained according to the classification decision function;

Definition 5: Pairwise constraint sets MS (Must-Link Set, must be connected set) and CS (Cannot-Link Set, cannot be connected set) are converted from the sample labels provided here, and the conversion form is shown in Figure 2;

Definition 6: L=DW is a graph Laplacian matrix, where W=[W _ij ] _(u+l)×(u+l) is the adjacency matrix of data set X, and

D becomes a diagonal matrix, and

Definition 7: Define the matrix Z=HQ, where Q=[Q _ij ] _(u+l)×(u+l) represents the pairwise constraint relationship matrix between marked samples, and the calculation of the matrix element Q _ij is as formula (2) , H is a diagonal matrix, H=diag(Q·1 _(l+u)×1 ), 1 _(l+u)×1 is a vector of (l+u)×1 and all elements are 1;

Among them, |MS| indicates the record capacity of the set that must be connected, and |CS| indicates the record capacity of the set that cannot be connected;

Definition 8: Define the form of Manifold Regularization as

Definition 9: Pairwise constrained regularization form:

In the formula, i, j, p, q are the sample numbers in the data set X, i, j, p, q ∈ [1, l+u], <i, j> represents any pair in the MS set, <p, q> represents any pair in the CS set, and |MS| and |CS| represent the number of elements in the MS set and CS set, respectively. The corresponding formula (4) can be rewritten as:

Definition 10: The specific form of matrix P is

A semi-supervised image classification method with the ability to maximize knowledge utilization, including the following steps:

Step 1: Unify the size of all original images into the same format, and use all the pixels of each image as a feature of a sample, so as to obtain a preliminary image data;

Step 2: Perform data normalization and feature dimensionality reduction (principal component analysis method) processing on the data obtained in step 1 to obtain corresponding image data;

Step 3: Generate a semi-supervised classification model with the ability to maximize knowledge utilization, as shown in formula (6):

In the above formula,

Among them, the data set Represents l labeled samples and u unlabeled samples required for classifier training, the sample dimension is d, y _i ∈ {+1,-1}(i=1,...,l) is this l The sample label of a labeled sample, f(.) represents the classification decision function, H _K is the Reproducing Kernel Hilbert Space (RKHS), K is the kernel matrix calculated by the kernel function K, f=[ f ₁ ,...,f _l ,f _l+1 ,...,f _l+u ] ^T is the data set According to the predicted value obtained by the classification decision function f(.), f _i (i=1,...,l+u), the classification decision function is as in formula (7), γ _A ＞0, γ _I ＞0, γ _D >0 is three regularization coefficients, L and Z are graph Laplacian matrix and pairwise constraint matrix respectively;

Equation (6), that is, the semi-supervised classification model with the ability to maximize knowledge utilization, can be divided into three parts. The first part, namely Equation (6-1), controls empirical risk and is expressed as a hinge loss function. The purpose of the second part, namely formula (6-2), is to avoid overfitting, and the last item of the third part, namely formula (6), represents the joint regularization framework of manifold and pairwise constraints, which is reasonable through the adjustment of parameters γ _I and γ _D Arranging the influence of manifold regularization and pairwise constraint regularization on the whole;

Substituting formula (6-1)-(6-2) into formula (6) can get a specific semi-supervised classification method model with the ability to maximize knowledge utilization:

Step 4: Solve according to the classification model in step 3, obtain the final solutions α ^* and b ^* required in the classification decision function f(.), form the classifier required for image classification, and combine the predictions processed in the data preprocessing process The image data is imported into the classifier model to obtain the classification result of the predicted image.

Further, the optimal solution steps for obtaining the optimal solutions α ^* and b ^* required in the classification decision function f(.) described in step 4 include:

(1) Transform the semi-supervised classification model with the ability to maximize knowledge utilization, that is, formula (8), into a quadratic programming problem solution form. The specific process is to introduce the Lagrangian coefficient β=(β ₁ ,β ₂ ,.. .,β _l ) and γ=(γ ₁ ,γ ₂ ,...,γ _l ), the corresponding Lagrangian function L(α,b,ξ,β,γ) can be obtained:

According to the Karush-Kuhn-Tucker (KKT) condition (Karush-Kuhn-Tucker, KKT), using the classic mathematical method - Lagrange condition extreme value law The following formula can be obtained:

Substituting equations (10)-(12) into equation (9), the corresponding quadratic programming problem can be obtained,

In formula (13), S=P ^T (γ _A K+K(γ _I L+γ _D Z)K) ^-1 P;

(2) Solve the quadratic programming problem of formula (13) to obtain the optimal solution β ^* , and substitute β ^* into the solution form of α in formula (10) to get the final solution α ^* , namely formula (14):

(3) Substituting the final solution α ^* obtained in (2) into formula (15) to obtain the final solution b ^* of b.

The advantages of the present invention are: firstly, the present invention has better learning ability compared with the traditional classification method SVM in the selection of classifiers, and the construction of the joint regularization framework of manifold and pairwise constraints includes a small number of labeled The further mining of sample knowledge (through the mining of MS and CS sets) also includes the knowledge exploration of a large number of unlabeled samples (through the manifold regularization method); secondly, in the data preprocessing of image data, a more widely applicable The feature normalization and feature dimensionality reduction (principal component analysis method) fully guarantee the integrity of data information.

Description of drawings

Fig. 1 is a flow chart of the semi-supervised image classification method with the capability of maximizing knowledge utilization according to the present invention.

Figure 2 is a schematic diagram of the process of converting sample labels into pairwise constraint sets and MS and CS.

Figure 3 is the second-class images required for classifier training and prediction, and a part of them is extracted for display.

Figure 4 is a trend graph of the prediction accuracy values of the classifier under different labels.

detailed description

The present invention will be further described below in conjunction with drawings and embodiments.

For convenience of description, the terms involved in the method of the present invention are defined as follows:

Definition 1: Dataset Represents l labeled samples and u unlabeled samples required for classifier training, y _i ∈ {+1,-1}(i=1,...,l) is the sample of these l labeled samples Label;

Definition 2: f(.) represents the classification decision function, H _K is the Reproducing Kernel Hilbert Space (RKHS), and K is the kernel function. The radial basis kernel function is used here, and the calculation method is σ is the core broadband;

Definition 3: f=[f ₁ ,...,f _l ,f _l+1 ,...,f _l+u ] ^T is the data set The predicted value obtained according to the classification decision function f(.), f _i (i=1,...,l+u),;

Definition 4: The pairwise constraint sets MS and CS are converted from the sample labels provided here, and the conversion form is shown in Figure 2;

Definition 5: W _ij ∈ W(i,j=1,...,u+l) is the edge weight of the adjacency matrix of the data set X, L=DW is the graph Laplacian matrix, D is the diagonal matrix,

Definition 6: Q _ij ∈ Q(i,j=1,...,u+l) represents the pairwise constraint relationship between labeled samples, and the calculation of its matrix element Q _ij is as in formula (2), and Z=HQ is similar In the Laplacian matrix form, H is a diagonal matrix, H=diag(Q 1 _(l+u)×1 ), where 1 _(l+u)×1 is (l+u)×1 Matrix and the matrix elements are all 1;

Definition 7: Manifold Regularization form:

Definition 8: Pairwise constrained regularization form:

In the formula, i, j, p, q are the sample numbers in X, i, j, p, q ∈ [1, l+u], <i, j> represents any pair in the MS set, <p, q> represents any pair in the CS set, and |MS| and |CS| represent the number of elements in the MS set and CS set respectively, and the corresponding formula (4) can be rewritten as:

Definition 9: The concrete form of matrix P is

As shown in Figure 1, the semi-supervised image classification method with the ability to maximize knowledge utilization is implemented according to the following steps based on the aforementioned definition:

Step 1: Unify the size of all original images into the same format, and use all the pixels of each image as a feature of a sample, so as to obtain a preliminary image data;

Step 2: Perform data normalization and feature dimensionality reduction (principal component analysis method) processing on the data obtained in step 1 to obtain corresponding image data;

Step 3: Generate a semi-supervised classification model with the ability to maximize knowledge utilization, as shown in formula (6):

In the above formula,

Among them, the data set Represents l labeled samples and u unlabeled samples required for classifier training, the sample dimension is d, y _i ∈ {+1,-1}(i=1,...,l) is this l The sample label of a labeled sample, f(.) represents the classification decision function, H _K is the Reproducing Kernel Hilbert Space (RKHS), K is the kernel matrix calculated by the kernel function K, where the kernel function K uses the radial basis kernel function here, and the calculation method is σ is the core broadband, f=[f ₁ ,...,f _l ,f _l+1 ,...,f _l+u ] ^T is the data set According to the predicted value obtained by the classification decision function f(.), f _i (i=1,...,l+u), the classification decision function is as in formula (7), γ _A ＞0, γ _I ＞0, γ _D >0 is three regularization coefficients, L and Z are graph Laplacian matrix and pairwise constraint matrix respectively;

Equation (6), that is, the semi-supervised classification model with the ability to maximize knowledge utilization, can be divided into three parts. The first part, namely Equation (6-1), controls empirical risk and is expressed as a hinge loss function. The purpose of the second part, namely formula (6-2), is to avoid overfitting, and the last item in the third part, namely formula (6), represents the joint regularization framework of manifold and pairwise constraints, through the adjustment of parameters γ _I , γ _D Reasonably arrange the influence of manifold regularization and pairwise constraint regularization on the whole;

Substituting formula (6-1)-(6-2) into formula (6) can get a specific semi-supervised classification method model with the ability to maximize knowledge utilization:

Step 4: Solve according to the classification model in step 3, obtain the final solutions α ^* and b ^* required in the classification decision function f(.), form the classifier required for image classification, and combine the predictions processed in the data preprocessing process The image data is imported into the classifier model to obtain the classification result of the predicted image.

Further, the optimal solution steps for obtaining the optimal solutions α ^* and b ^* required in the classification decision function f(.) described in step 4 include:

(1) Transform the semi-supervised classification model with the ability to maximize knowledge utilization, that is, formula (8), into a quadratic programming problem solution form. The specific process is to introduce the Lagrangian coefficient β=(β ₁ ,β ₂ ,.. .,β _l ) and γ=(γ ₁ ,γ ₂ ,...,γ _l ), the corresponding Lagrangian function L(α,b,ξ,β,γ) can be obtained:

According to the Karush-Kuhn-Tucker (KKT) condition (Karush-Kuhn-Tucker, KKT), using the classic mathematical method - Lagrange condition extreme value law The following formula can be obtained:

Substituting equations (10)-(12) into equation (9), the corresponding quadratic programming problem can be obtained,

In formula (13), S=P ^T (γ _A K+K(γ _I L+γ _D Z)K) ^-1 P;

(2) Solve the quadratic programming problem of formula (13) to obtain the optimal solution β ^* , and substitute β ^* into the solution form of α in formula (10) to get the final solution α ^* , namely formula (14):

(3) According to the obtained final solution α ^* , that is, formula (14), substitute it into formula (15) to obtain the final solution b ^* of b.

The following is a detailed implementation process.

1. Raw image data preprocessing process:

1) Unify the size of all original images (including all images for training and testing) into a phase format, with a specific resolution of 256*256, and use all pixels of each image as a feature of a sample, so as to obtain a preliminary image dataset;

2) normalize the preliminary image data set obtained in 1) and obtain a normalized image data set;

3) The principal component analysis method is used to perform feature dimensionality reduction on the normalized image data set obtained in 2), and the first 1000 dimensions with the largest feature value are selected (the cumulative contribution rate at this time reaches 94%, ensuring the integrity of the data information Integrity), complete feature extraction;

2. Classifier training and prediction stage:

1) Generate the MS set CS set according to the training data and data labels obtained by data preprocessing, and obtain the graph Laplacian matrix L and the pairwise constraint matrix Z;

2) Carry out high-dimensional mapping on the given training data set according to the radial basis kernel function, obtain the kernel matrix K required for training the classifier, and calculate the matrix P and S;

3) Utilize the quadratic programming toolbox to find the quadratic programming problem formula (15), and obtain the optimal solution β ^* ;

4) Substituting β ^* into the solution form of α in formula (12) to get the final solution α ^* , and substituting the solved α ^* into formula (17) to get the final solution b ^* of b, so that the image classification can be obtained The required classifier model, namely formula (9);

5) Import the predicted data obtained by data preprocessing into formula (9), and divide the image category according to the positive or negative of the predicted value, the positive value corresponds to the positive category, and the negative value corresponds to the negative category. Through the above two stages, the optimal image classification accuracy of the semi-supervised image classification method with the ability to maximize knowledge utilization is finally obtained.

Example 1

Figures 3(a)-3(d) show that various images are some samples of images used for training and testing. Among them, 400 images are used for training and 220 images are used for testing. Figure 4 shows the classification of images under different labeled sample points Accuracy trend graph, the parameter selection method in this embodiment is cross-validation, and the respective ranges of parameters γ _A , γ _I , and γ _D are set to {10 ^-5 , 10 ^-4 , 10 ^-3 , 10 ^-2 , 10 ^-1 , 10 ¹ , 10 ² }, the classification accuracy in the embodiment is the result of cross-validation to obtain the optimal parameters, and the present invention should not be limited to the content disclosed in the embodiment and the accompanying drawings. Therefore, all equivalents or modifications that do not deviate from the spirit disclosed in the present invention fall within the protection scope of the present invention.

The above are preferred embodiments of the present invention, and those skilled in the art to which the present invention pertains can also make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments described above, and any obvious improvement, replacement or modification made by those skilled in the art on the basis of the present invention falls within the protection scope of the present invention.

Claims (3)

1. a kind of semi-supervision image classification method for possessing maximization knowledge utilization ability, is characterized in, according to being defined as below and Step is implemented：

Define 1：Data setThe l samples and u for having label needed for the training of presentation class device Individual unlabeled exemplars, y_i∈ {+1, -1 } (i=1 ..., l) it is this l sample labels for having exemplar；

Define 2：F () presentation class decision function,H_KFor reproducing kernel Hilbert space (Reproducing Kernel Hilbert Space, RKHS), K is kernel function, here be Radial basis kernel function, calculate Mode isσ is core broadband；

Define 3：F=[f₁,...,f_l,f_l+1,...,f_l+u]^TFor data setDetermined according to classification The predicted value that plan function f () is obtained, f_i(i=1 ..., l+u)；

Define 4：Paired constraint set MS and CS here by the sample label provided it is converted Lai；

Define 5：W_ij∈ W (i, j=1 ..., u+l) are the side right of data set X adjacency matrix, and L=D-W is figure Laplce's square Battle array, D is diagonal matrix,

Define 6：Q_ij∈ Q (i, j=1 ..., u+l) illustrate the paired restriction relation between marker samples, its matrix element Q_ij's Calculate such as formula (2), Z=H-Q is similar to figure Laplce's matrix form, and H is diagonal matrix, H=diag (Q1_(l+u)×1), its In, 1_(l+u)×11 is all for the matrix and matrix element of (l+u) × 1；

Define 7：Popular regularization (Manifold Regularization) form：

<mrow> <mo>|</mo> <mo>|</mo> <mi>f</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mi>I</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mi>u</mi> <mo>+</mo> <mi>l</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mi>f</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>f</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mi>u</mi> <mo>+</mo> <mi>l</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msup> <mi>f</mi> <mi>T</mi> </msup> <mi>L</mi> <mi>f</mi> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Define 8：Constraint regularization form in pairs：

<mrow> <munder> <mi>min</mi> <mi>f</mi> </munder> <mrow> <mo>(</mo> <mfrac> <mrow> <munder> <mi>&amp;Sigma;</mi> <mrow> <mo>&lt;</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>&gt;</mo> <mo>&amp;Element;</mo> <mi>M</mi> <mi>S</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>f</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mo>|</mo> <mi>M</mi> <mi>S</mi> <mo>|</mo> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <munder> <mi>&amp;Sigma;</mi> <mrow> <mo>&lt;</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>&gt;</mo> <mo>&amp;Element;</mo> <mi>C</mi> <mi>S</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>p</mi> </msub> <mo>-</mo> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mo>|</mo> <mi>C</mi> <mi>S</mi> <mo>|</mo> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

In formula, i, j, p, q be X in sample sequence number, i, j, p, q ∈ [1, l+u],<i,j>Represent in MS set any pair,<p,q >Represent in CS set any pair, | MS | and | CS | the element number of MS set and CS set, corresponding formula (4) are represented respectively It can be rewritten as：

<mrow> <munder> <mi>min</mi> <mi>f</mi> </munder> <mrow> <mo>(</mo> <msup> <mi>f</mi> <mi>T</mi> </msup> <mi>Z</mi> <mi>f</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> 1

Define 9：Matrix P concrete form is

Step 1：The size of all original images is unified for same format, and using all pixels o'clock of every image as one The feature of sample, so obtain a preliminary view data；

Step 2：Data normalization and Feature Dimension Reduction (principal component analytical method) processing are carried out to the data that obtain in step 1, obtained To corresponding view data；

Step 3：Generation possesses the semisupervised classification model of maximization knowledge utilization ability, as shown in formula (6)：

<mrow> <munder> <mi>min</mi> <mrow> <mi>f</mi> <mo>&amp;Element;</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> </mrow> </munder> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>A</mi> </msub> <mo>|</mo> <mo>|</mo> <mi>f</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mi>K</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>f</mi> <mi>T</mi> </msup> <mo>(</mo> <mrow> <msub> <mi>&amp;gamma;</mi> <mi>I</mi> </msub> <mi>L</mi> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <mi>Z</mi> </mrow> <mo>)</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

In above formula,

<mrow> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mi>f</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mo>+</mo> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mo>|</mo> <mo>|</mo> <mi>f</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mi>K</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mi>&amp;alpha;</mi> <mi>T</mi> </msup> <mi>K</mi> <mi>&amp;alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

Wherein, data setThe l samples and u for having label needed for the training of presentation class device Individual unlabeled exemplars, sample dimension are d, y_i∈ {+1, -1 } (i=1 ..., l) is the sample labels that this l has exemplar, f () presentation class decision function, H_KFor reproducing kernel Hilbert space (Reproducing Kernel Hilbert Space, RKHS), K is the nuclear matrix that is calculated by kernel function K, f=[f₁,...,f_l,f_l+1,...,f_l+u]^TFor data setThe predicted value obtained according to categorised decision function f (), f_i(i=1 ..., l+u), classification Decision function such as formula (7), γ_A＞ 0, γ_I＞ 0, γ_D＞ 0 is three regularization coefficients, and L and Z are respectively figure Laplacian Matrix With paired constraint matrix；

<mrow> <msup> <mi>f</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </munderover> <msubsup> <mi>&amp;alpha;</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mi>K</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>b</mi> <mo>*</mo> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Formula (6-1)-(6-2) is updated into formula (6) can specifically be possessed semi-supervised point of maximization knowledge utilization ability Class method model：

<mrow> <mtable> <mtr> <mtd> <munder> <mi>min</mi> <mrow> <mi>&amp;alpha;</mi> <mo>&amp;Element;</mo> <msup> <mi>R</mi> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </msup> <mo>,</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>R</mi> </mrow> </munder> </mtd> <mtd> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>A</mi> </msub> <msup> <mi>&amp;alpha;</mi> <mi>T</mi> </msup> <mi>K</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msup> <mi>&amp;alpha;</mi> <mi>T</mi> </msup> <mi>K</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;gamma;</mi> <mi>I</mi> </msub> <mi>L</mi> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <mi>Z</mi> </mrow> <mo>)</mo> <mi>K</mi> <mi>&amp;alpha;</mi> <mo>)</mo> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </munderover> <msub> <mi>&amp;alpha;</mi> <mi>j</mi> </msub> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>l</mi> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>&amp;GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>l</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

Step 4：Utilize the last solution obtained by step 1 needed for categorised decision function and point needed for composition image classification Class device, and the predicted image data handled in process of data preprocessing is imported into sorter model, obtain prognostic chart picture Classification results.

2. possessing the semi-supervision image classification method of maximization knowledge utilization ability as claimed in claim 1, it is characterized in, it is described Obtain the optimal solution α needed for categorised decision function f ()^*And b^*Optimization Solution step include：

(1) the semisupervised classification model i.e. formula (8) that will be provided with maximization knowledge utilization ability is changed into quadratic programming problem solution Form, detailed process are introducing Lagrange coefficient β=(β₁,β₂,...,β_l) and γ=(γ₁,γ₂,...,γ_l), it can obtain To corresponding LagrangianL (α, b, ξ, β, γ)：

<mrow> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>&amp;xi;</mi> <mo>,</mo> <mi>&amp;beta;</mi> <mo>,</mo> <mi>&amp;gamma;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>+</mo> <msup> <mi>a</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>&amp;gamma;</mi> <mi>A</mi> <mi>K</mi> <mo>+</mo> <mi>K</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;gamma;</mi> <mi>I</mi> </msub> <mi>L</mi> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <mi>Z</mi> </mrow> <mo>)</mo> <mi>K</mi> <mo>)</mo> </mrow> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </munderover> <mrow> <msub> <mi>&amp;alpha;</mi> <mi>j</mi> </msub> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> </mrow> </mrow> <mo>)</mo> <mo>-</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

According to Caro need-Kuhn-Tucker condition (Karush-Kuhn-Tucker, KKT), mathematical method-glug of classics is utilized Bright day conditional extremum decreeIt can obtain following formula：

Wushu (10)-(12) substitute into formula (9) and can obtain corresponding quadratic programming problem,

<mrow> <mtable> <mtr> <mtd> <munder> <mi>max</mi> <mrow> <mi>&amp;beta;</mi> <mo>&amp;Element;</mo> <msup> <mi>R</mi> <mi>l</mi> </msup> </mrow> </munder> </mtd> <mtd> <mrow> <mo>(</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msup> <mi>&amp;beta;</mi> <mi>T</mi> </msup> <mi>S</mi> <mi>&amp;beta;</mi> <mo>)</mo> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&amp;le;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mi>1</mi> <mi>l</mi> </mfrac> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>l</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

S=P in formula (13)^T(γ_AK+K(γ_IL+γ_DZ)K)^-1P；

(2) quadratic programming problem solution is carried out to formula (13), obtains optimal solution β^*, and β^*α solution form in substitution formula (10) In go to obtain last solution α^*, i.e. formula (14)：

<mrow> <msup> <mi>&amp;alpha;</mi> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mi>A</mi> </msub> <mi>K</mi> <mo>+</mo> <mi>K</mi> <mo>(</mo> <mrow> <msub> <mi>&amp;gamma;</mi> <mi>I</mi> </msub> <mi>L</mi> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <mi>Z</mi> </mrow> <mo>)</mo> <mi>K</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>P&amp;beta;</mi> <mo>*</mo> </msup> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

(3) according to the last solution α obtained in (2)^*, it is updated in formula (15) and obtains b last solution b^*。

<mrow> <msup> <mi>b</mi> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>l</mi> <mo>+</mo> <mi>u</mi> </mrow> </munderover> <msubsup> <mi>&amp;alpha;</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mi>K</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

3. possess the semisupervised classification method of maximization knowledge utilization ability as claimed in claim 1, it is characterized in that, possess greatly The semisupervised classification model for changing knowledge utilization ability is that formula (6) can be divided into three parts, and Part I is that formula (6-1) controls Empiric risk is expressed as hinge loss function (hinge loss function), and Part II is that formula (6-2) purpose is to avoid Fitting, Part III are that last in formula (6) represents manifold and constraint joint regularization framework in pairs, pass through parameter γ_I,γ_D Regulation come reasonable arrangement manifold regularization and in pairs constraint regularization each to entirety influence.