CN100585617C - Face Recognition System and Method Based on Classifier Ensemble - Google Patents

Abstract

The invention discloses a face recognition system and method based on classifier integration, the purpose of which is to integrate the outputs of multiple sub-classifiers by solving the weight coefficients of multiple sub-classifiers to obtain a better recognition rate for the face recognition system . The whole system includes two parts, the training system and the classification system. The training system is completed: feature extraction of face images, selection of multiple sub-classifiers with posterior probability output, input of different training samples to the sub-classifiers for training, and obtaining The posterior probability of the original training samples is obtained by linear programming optimization to obtain the weighting coefficients of each sub-classifier; the classification system is completed: input the samples to be classified after feature extraction into the trained sub-classifiers, and obtain the posterior probability of the samples to be classified Probability, and design classification rules through the posterior probability and sub-classifier weighting coefficients, and output classification results. The invention has the advantage of high recognition rate and can be used for face recognition in the fields of machine learning and pattern recognition.

Description

Face Recognition System and Method Based on Classifier Ensemble

technical field

The invention belongs to the technical field of image processing, and in particular relates to face recognition, which can be used for supervision and protection of public safety, information safety and financial safety.

Background technique

Face recognition is a non-invasive recognition method that is relatively easy to be accepted by people, so it has become a hot issue that has attracted much attention in the fields of computer vision and pattern recognition. The purpose of face recognition technology is to give computers the ability to identify people based on their faces. As a scientific problem, face recognition is a typical computer problem of image pattern analysis, understanding and classification, which involves pattern recognition, computer vision, intelligent human-computer interaction, graphics, cognitive science and other disciplines. As one of the key technologies of biometric identification, face recognition technology has potential application prospects in public security, information security, finance and other fields. In face recognition technology, the high-precision core recognition algorithm is the key to the problem, and the ultimate goal of designing a recognition system is to obtain a good recognition rate. The traditional method is to design different classifiers to achieve the purpose of face recognition. The role of the classifier in the recognition system is to assign a class mark to a tested sample according to the feature vector obtained by the feature extractor, so as to achieve classification. the goal of. Since the misclassified samples of different classifiers are not necessarily the same, the classifiers can be fused to produce better performance. A large number of studies have shown that integrating multiple sub-classifiers is an effective means to improve the recognition rate. In this way, face recognition can be realized.

The existing classifier output integration methods mainly include: J.Kittler et al. from the United Kingdom summarized the method of classifier output integration in their 1998 paper. This method proposes that if the output of a single classifier can be expressed in the form of posterior probability, the results of multiple sub-classifiers can be integrated by using the product rule, sum rule, maximum rule, minimum rule and median rule. It is a nonlinear integration method, which is more complicated in application. In practical applications, the linear integration method is the most common, and the simple voting rule is one of the commonly used linear integration methods. For this reason, Italian G. Fumera et al. compared simple voting and weighted voting methods in 2005. Point out that simple average voting is the optimal rule if the individual classifiers have the same performance and have the same correlation to the estimation error. Otherwise, the weighted voting rule is superior to the simple average voting rule. Regarding how to find the weight coefficients, J.A.Benediktsson et al. in 1997 and M.P.Perrone et al. in 1993 proposed to use regression estimation to solve the weight coefficients, but these methods are not suitable for classification problems. N. Ueda designed a linear weighting method based on the principle of minimum classification error for classification problems in 2000. The objective function of this method is nonlinear, and there are local extremum points in theory, and the gradient descent method used to solve the objective function depends to a large extent on the selection of initial weights. If the initial weights are not well selected, It will reduce the recognition rate of the classifier, leading to the deterioration of the performance of the face recognition system.

content of the invention

The purpose of the present invention is to overcome above-mentioned deficiencies in prior art, has proposed a kind of face recognition system and its method based on classifier integration, to improve the recognition rate of integrated classifier, improve the performance of face recognition system.

For realizing the above object, technical scheme of the present invention is:

1. A face recognition system based on classifier integration, including:

The original face image feature extraction module is used to extract features from the original face image input into the computer, and obtain c class original training sample sets with identification;

The face image feature extraction module to be classified is used for feature extraction of the face image to be classified input into the computer, and obtains samples x∈R ⁿ to be classified;

The training module is used to select N sub-classifiers with posterior probability output, and train them according to the original training sample set to obtain the posterior probability R _j (ω _k |xi ₎ , _xi of the original training sample set Represents the i-th training sample, ω _k represents the k-th category;

The sub-classifier weight coefficient calculation module is used to solve the weight coefficient α _j of each sub-classifier through linear programming according to the posterior probability P _j (ω _k |xi ₎ , and output it to the integration module;

The sub-classifier classification module is used to input the sample to be classified into the N sub-classifiers trained in the training process to obtain the posterior probability P _j (ω _k |x) of the sample to be classified;

The integration module is used to design a classification rule according to the weight coefficient α _j obtained in the training process and the posterior probability P _j (ω _k |x) to be classified, and obtain the classification result according to the classification rule;

The classification result output module is used for outputting the classification result of the sample to be classified in the form of category identification and displaying it on the computer display screen.

2. A face recognition training method based on classifier integration, including the following process:

Extract the features of the original face image input into the computer, and obtain c-type labeled original training sample sets: {( _xi , y _i )| _xi ∈ R ⁿ , y _i ∈ {1, 2, ..., c }, i=1,..., l}, wherein: x _i represents a sample in the n-dimensional real number space, and y _i is its mark, takes a value in a positive integer between 1 and c, if y _i =k, Then it means x _i ∈ ω _k class, l is the number of samples;

Select N sub-classifiers with posterior probability output, and train them according to the original training sample set to obtain the posterior probability P _j (ω _k | _xi ) of the original training sample set. This formula represents the jth sub-classification The device is the posterior probability that the x _i sample belongs to the class ω _k , where j=1,...,N, k=1,...,c, i=1,...,l;

According to the posterior probability P _j (ω _k | _xi ), the weighting coefficient α _j of each sub-classifier is solved by linear programming, and the solution formula is:

$\underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$

subject to $\left[\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j(P_j\left({\mathrm{\&omega;}}_m\right|x_i)-P_j\left({\mathrm{\&omega;}}_k\right|x_i))\right]1(x_i\&Element;{\mathrm{\&omega;}}_m)\&Greater\; Equal;-{\mathrm{\&xi;}}_q$

ξ _q ≥ 0, α _j ≥ 0, i=1,..., l, j=1,..., N, k≠m, k=1,..., c

q=1, 2, ..., l(c-1)

C是折中系数，ξ_q是松弛变量，

是容量控制项，

是经验风险项；In the formula, j=1,...,N;

C is the compromise coefficient, ξ _q is the slack variable,

is the capacity control item,

is the empirical risk item;

Output the weighting coefficient α _j of each sub-classifier to the classification system.

3. A face recognition classification method based on classifier integration, including the following process:

Extracting the feature of the face image to be classified inputted into the computer, and obtaining the sample x∈R ⁿ to be classified;

Input the sample to be classified into the N sub-classifiers trained in the training process, and obtain the posterior probability P _j (ω _k |x) of the sample to be classified, j=1,...,N, k=1,...,c ;

According to the weight coefficient α _j obtained in the training process and the posterior probability P _j (ω _k |x) to be classified, the classification rules are designed. The classification rules set by this module are:

if $\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_m\right|x)=\underset{k=\mathrm{1,2},\&CenterDot;\&Center\; Dot;\&Center\; Dot;,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_k\right|x),$ Then x ∈ ω _m class, m ∈ {1, 2, ..., c} represent different categories, and its category identification is y=m.

The classification results of the samples to be classified are output in the form of category identification and displayed on the computer display screen.

In the present invention, the weight coefficient of the sub-classifier obtained through the weight coefficient calculation module of the sub-classifier in the training system is globally optimal, thereby ensuring a higher recognition rate of the whole classification system for the face image to be divided. Simulation results show that under the condition of repeating 30 times of training and classification on 360 images, the average recognition rate of the present invention is 3.54% higher than that of the existing Ueda linear weighting method.

Description of drawings

Fig. 1 is a virtual system block diagram of the present invention;

Fig. 2 is the training process flowchart of the present invention;

Fig. 3 is a flow chart of the classification process of the present invention.

Detailed ways

With reference to Fig. 1, face recognition system of the present invention comprises two parts of training system and classification system, and wherein training system is made up of original face image feature extraction module, training module, sub-classifier weight coefficient calculation module and training result output module. The classification system consists of a face image feature extraction module to be classified, a sub-classifier classification module, an integration module and a classification result output module. Its working principle is:

The original face image feature extraction module extracts features from the original face image input into the computer, and obtains c-type original training sample sets with labels: {( _xi , y _i )| _xi ∈ R ⁿ , y _i ∈ {1, 2, ..., c}, i=1, ..., l}, wherein: x _i represents a sample in the n-dimensional real number space, y _i is its identity, and it is selected from positive integers between 1 and c value, if y _i =k, it means x _i ∈ ω _k class, l is the number of samples, the original training sample set is sent to the training module. The training module first selects N sub-classifiers with posterior probability output, and then trains these sub-classifiers according to the original training sample set to obtain the posterior probability P _j (ω _k | _xi ) of the original training sample set, In the formula, x _i represents the i-th training sample, ω _k represents the k-th category, j=1,...,N, k=1,...,c, i=1,...,l, the training of each sub-classifier The samples are generated by randomly sampling the features of the original training sample set, and the number of features of each sub-classifier is the same. The sub-classifier weight coefficient calculation module, according to the posterior probability P _j (ω _k | _xi ), solves the weight coefficient α _j of each sub-classifier through linear programming, and its solution formula is:

$\underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$

subject to $\left[\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j(P_j\left({\mathrm{\&omega;}}_m\right|x_i)-P_j\left({\mathrm{\&omega;}}_k\right|x_i))\right]1(x_i\&Element;{\mathrm{\&omega;}}_m)\&Greater\; Equal;-{\mathrm{\&xi;}}_q$

ξ _q ≥ 0, α _j ≥ 0, i=1,..., l, j=1,..., N, k≠m, k=1,..., c

q=1, 2, ..., l(c-1)

是容量控制项，

是经验风险项。该加权系数α_j的具体计算可以调用已有的工具包来实现，比如调用Matlab中的线性规划函数，即可求得线性规划问题的最优解α_j。得到各个子分类器的加权系数α_j后，输出到分类系统中的集成模块作为后续分类的一个输入参数。In the formula, j=1,...,N; C is the compromise coefficient, ξ _q is the slack variable,

is the capacity control item,

is the empirical risk term. The specific calculation of the weighting coefficient α _j can be realized by calling the existing toolkit, for example, calling the linear programming function in Matlab, and the optimal solution α _j of the linear programming problem can be obtained. After getting the weighted coefficient α _j of each sub-classifier, it is output to the integration module in the classification system as an input parameter for subsequent classification.

The feature extraction module of the face image to be classified in the classification system extracts the feature of the face image to be classified input into the computer, obtains the sample x∈R ⁿ to be classified, and outputs it to the sub-classifier classification module, wherein the sample to be classified cannot appear in the training sample set. The sub-classifier classification module inputs the sample to be classified into the N sub-classifiers that have been trained in the training module, obtains the posterior probability P _j (ω _k |x) of the sample to be classified, and outputs it to the integration module. The integration module, according to the weight coefficient α _j obtained by the training system and the posterior probability P _j (ω _k |x) to be classified, designs classification rules and obtains classification results. The classification rules set by this module are: if $\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_m\right|x)=\underset{k=\mathrm{1,2},\&Center\; Dot;\&CenterDot;\&Center\; Dot;,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_k\right|x),$ Then x ∈ ω _m class, m ∈ {1, 2, ..., c} represent different categories, the classification result can be represented by the class identification y=m, and displayed on the computer screen through the classification result output module.

Each module in the above-mentioned entire face recognition system realizes its function through a computer program, and completes the recognition of the face image.

With reference to Fig. 2, the training implementation process that the present invention realizes face recognition is described in detail as follows:

This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

The embodiment adopts a public face database——UMIST database. There are 574 images of 20 different faces in this database. This image library is a multi-view database with different poses from the side to the front. The training process is:

Step 1, perform feature extraction on the original face image, and obtain the original training sample set with class c identification: {( _xi , y _i )| _xi ∈ R ⁿ , yi ∈ {1, 2, ..., c}, i=1,...,l}, wherein: x _i represents a sample in the n-dimensional real number space, y _i is its identifier, and takes a value in a positive integer between 1 and c, if y _i =k, then represents x _i ∈ω _k category, l is the number of samples; feature extraction refers to principal component analysis or downsampling or various transformations on the image.

The size of the original face image is 112×92. Here, the feature extraction method adopts the next four sampling method, and the size of each image after sampling is n=28×23.

Since each category has more or less samples, the minimum is 19. 18 samples are randomly drawn for each category, so the size of the entire dataset is 360 images. During the simulation, 5 samples are randomly selected from 18 for each type of face as training samples, and the remaining 13 are used as test samples. This forms a set of training-testing samples. Here, the values of the parameters n, c and l of the training samples are n=644, c=20 and l=100 respectively.

Step 2, select a classifier with posterior probability output, and set the number N of sub-classifiers, and design a sub-classifier; the choice of classifier can be neural network or support vector machine or K nearest neighbor or discriminant method or decision tree Or a Bayesian decision classifier. Designing sub-classifiers refers to designing different training sets for sub-classifiers. The method uses direct random sampling of the original training set or random sampling of the features of the original training set, so that the sub-classifiers have diversity.

In the implementation process, the K-nearest neighbor classifier is selected, which is a non-parametric learning model, and since the K-nearest neighbor classifier itself does not have a probability output, its output must be processed to obtain a form of probability output. The specific processing process is: for a certain training or to-be-classified sample x′, find its K neighbors in the training sample, if the training sample belonging to the ω _k class among the K neighbors is K _k , then $K={\mathrm{\&Sigma;}}_{k=1}^c{K}_k.$ Use P(ω _k |x')=K _k /K to represent the posterior probability of the K nearest neighbor classifier about x'. Here, the number of classifiers is set to N=100, and the number of neighbors K is regarded as a variable parameter. The variation range of K in the experiment is {3, 4, 5}. The training samples of each sub-classifier are randomly sampled from the features of the original training set, and the number of features of each sub-classifier is the same. Here, the characteristic number is also regarded as a variable parameter, and the range of variation is {2 ³ , 2 ⁴ , 2 ⁵ , 2 ⁶ }.

Step 3, train N sub-classifiers, and obtain the posterior probability P _j (ω _k | _xi ) of each sub-classifier on the original training sample, where x _i represents the i-th sample, and ω _k represents the k-th category, j=1,...,N,k=1,...,c,i=1,...,l;

Step 4, obtain the weighting coefficient α _j of each sub-classifier through linear programming, j=1,...,N.

The form of linear programming is:

$\underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$

subject to $\left[\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j(P_j\left({\mathrm{\&omega;}}_m\right|x_i)-P_j\left({\mathrm{\&omega;}}_k\right|x_i))\right]1(x_i\&Element;{\mathrm{\&omega;}}_m)\&Greater\; Equal;-{\mathrm{\&xi;}}_q$

ξ _q ≥ 0, α _j ≥ 0, i=1,..., l, j=1,..., N, k≠m, k=1,..., c

q=1, 2, ..., l(c-1)

in C is the compromise coefficient, _ξq is the slack variable and _αj is the weighting coefficient of the jth classifier.

中，第一项是容量控制项，第二项是经验风险项，该目标函数的最小化体现了结构风险最小化原则。线性规划的求解可以调用已有的工具包来实现，比如调用Matlab中的线性规划函数，即可求得线性规划问题的最优解α_j。in the objective function

Among them, the first item is the capacity control item, and the second item is the empirical risk item. The minimization of the objective function embodies the principle of structural risk minimization. The solution of linear programming can be realized by calling the existing toolkit, for example, calling the linear programming function in Matlab to obtain the optimal solution α _j of the linear programming problem.

With reference to Fig. 3, the classification implementation process that the present invention realizes face recognition is described in detail as follows:

Step A, perform feature extraction on the face image to be classified, obtain the sample x∈R ⁿ to be classified, and input it into the N sub-classifiers trained during the training process; here, the feature extraction and the feature extraction during the training process the way is consistent;

In this embodiment, the samples to be classified are also referred to as test samples, which cannot appear in the training sample set.

Step B, using the same method as the training process to obtain the posterior probability P _j (ω _k |x) of the sample to be classified, j=1,..., N, k=1,..., c;

Step C, output the classification result of the sample to be classified; the classification rule is:

if $\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_m\right|x)=\underset{k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_k\right|x),$ Then x∈ω _k class, that is, its identification is y=m.

Effect of the present invention can be further illustrated by the following simulation data:

1. Simulation conditions and content

The UMIST data set is simulated by obtaining the training-classification sample set according to the above-mentioned specific implementation process, generating 30 sets of random training-classification sample sets, repeating the above training and classification process 30 times, and calculating the average recognition rate. The simulations of several methods are carried out under the same experimental environment.

2. Simulation results

In repeating the above training and classification process 30 times, record the recognition rate obtained by each simulation, and calculate the average recognition rate, as shown in Table 1. The "K nearest neighbor method" in Table 1 is a classifier that does not use integration; in the integration method, 100 sub-classifiers are used, "simple voting" means that the weights are all taken as 1/100, and "Ueda linear weighted "Used is the simulation of the optimal linear weighting method designed by N. Ueda in 2000 for classification problems.

Table 1. Recognition performance comparison

As can be seen from the simulation results in Table 1, the recognition rate of the integrated method is higher than that of the method without integration, and in these integrated methods, the average recognition rate of the method of the present invention is higher than the optimal linearity proposed by simple voting and Ueda et al. weighting method.

Claims (2)

1. A face recognition system based on classifier integration, comprising: The original face image feature extraction module is used to extract features from the original face image input into the computer, and obtain c original training sample sets with identification; The face image feature extraction module to be classified is used to extract the feature of the face image to be classified input into the computer, and obtain the sample x to be classified in the n-dimensional real number space; The training module is used to select N sub-classifiers with posterior probability output, and train them according to the original training sample set. The expression of the original training sample set is: {( _xi , y _i )| _xi ∈ R ⁿ , y _i ∈ {1, 2, ..., c}, i=1, ..., l}, where: x _i represents the ith sample in the n-dimensional real number space, y _i is its identity, between 1 and The value is taken from positive integers between c, if y _i =k, it means x _i ∈ ω _k category, ω _k means the kth category, l is the number of samples; through training to obtain the original training sample set after Posterior probability P _j (ω _k | _xi ), which expresses the posterior probability of the j-th sub-classifier about the x _i sample belonging to ω _k class, where j=1,...,N, k=1,...,c, i=1,...,l; The sub-classifier weight coefficient calculation module is used to solve the weight coefficient α _j of each sub-classifier through linear programming according to the posterior probability P _j (ω _k |xi ₎ , and output it to the integration module. The formula for solving the weight coefficient for: $\underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$ $\mathrm{<span\; class="notranslate">\; subject\; to</span>}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$ ξ _q ≥ 0, α _j ≥ 0, i=1,..., l, j=1,..., N, k≠m, k=1,..., c, q=1, 2, ..., l(c-1) In the formula,

C is the compromise coefficient, _ξq is the slack variable and _αj is the weighting coefficient of the jth classifier,

is the capacity control item,

is the empirical risk item; The sub-classifier classification module is used to input the sample to be classified into the N sub-classifiers trained in the training process to obtain the posterior probability P _j (ω _k |x) of the sample to be classified; The integration module is used to design a classification rule according to the weight coefficient α _j obtained in the training process and the posterior probability P _j (ω _k |x) to be classified, and obtain the classification result according to the classification rule. The classification rule is: if $\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_m\right|x)=\underset{k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_k\right|x),$ Then x ∈ ω _m class, m ∈ {1, 2, ..., c} represent different categories, and the classification result can be represented by the category identifier y=m; The classification result output module is used for outputting the classification result of the sample to be classified in the form of category identification and displaying it on the computer display screen. 2. A face recognition method based on classifier integration, comprising: (1) Face recognition training process: Extract the original face image features input into the computer, and obtain c original training sample sets with labels: {( _xi , y _i )| _xi ∈ R ⁿ , y _i ∈ {1, 2, ..., c}, i=1,...,l}, wherein: x _i represents the i-th sample in the n-dimensional real number space, and y _i is its identification, taking a value in a positive integer between 1 and c, if y _i =k, It means x _i ∈ ω _k class, ω _k represents the kth category, l is the number of samples; Select N sub-classifiers with posterior probability output, and train them according to the original training sample set to obtain the posterior probability P _j (ω _k | _xi ) of the original training sample set. This formula represents the jth sub-classification The device is the posterior probability that the x _i sample belongs to the class ω _k , where j=1,...,N, k=1,...,c, i=1,...,l; According to the posterior probability P _j (ω _k | _xi ), the weighting coefficient α _j of each sub-classifier is solved by linear programming, and the solution formula is: $\underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$ $\mathrm{<span\; class="notranslate">\; subject\; to</span>}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Greater\; Equal;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}$ ξ _q ≥ 0, α _j ≥ 0, i=1,..., l, j=1,..., N, k≠m, k=1,..., c, q=1, 2, ..., l(c-1) In the formula, j=1,...,N;

C is the compromise coefficient, ξ _q is the slack variable,

is the capacity control item,

is the empirical risk item; Output the weighting coefficient α _j of each sub-classifier to the classification system; (2) Face recognition classification process: Extracting the feature of the face image to be classified inputted into the computer, and obtaining the sample x∈R ⁿ to be classified; Input the sample to be classified into the N sub-classifiers trained in the training process, and obtain the posterior probability P _j (ω _k |x) of the sample to be classified, j=1,...,N, k=1,...,c ; According to the weight coefficient α _j obtained in the training process and the posterior probability P _j (ω _k |x) of the sample to be classified, the classification rule is designed as: if $\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_m\right|x)=\underset{k=\mathrm{1,2},\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{P}_j\left({\mathrm{\&omega;}}_k\right|x),$ Then x ∈ ω _m class, m ∈ {1, 2, ..., c} represent different categories, and its category identification is y=m; The classification results of the samples to be classified are output in the form of category identification and displayed on the computer display screen.

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