CN102722713B - Handwritten numeral recognition method based on lie group structure data and system thereof - Google Patents

Abstract

Embodiments of the present invention provide a handwritten digit recognition method and system based on Lie group structure data. The method extracts the corresponding Lie group structure data from the original handwritten digital image data, constructs a matrix Gaussian kernel function, uses the support vector machine algorithm to train a classifier model, and extracts the Lie group structure data corresponding to the handwritten digital image data to be tested , respectively input into the trained classifier model to obtain the corresponding digital category, so as to capture the nonlinear features of the Lie group structure data corresponding to the handwritten digital image data to be tested, and better realize the handwritten digital recognition.

Description

A handwritten digit recognition method and system based on Lie group structure data

technical field

The present invention relates to the technical field of handwritten digit recognition, more specifically, to a handwritten digit recognition method and system based on Lie group structure data.

Background technique

In recent years, with the rapid development of computer technology and digital image processing technology, handwritten digit recognition technology has been widely used in large-scale data statistics, mail sorting, finance, taxation and financial fields. At the same time, with machine learning With the popularization and application of technology, many physicists and chemists have begun to widely use Lie group theory to study data in related fields. Correspondingly, in the field of handwritten digit recognition technology, Lie group structure data has been widely used due to its good mathematical structure.

At present, handwritten digit recognition based on Lie group structure data generally establishes a classifier model through a classification algorithm, so as to classify and process the Lie group structure data of handwritten digital images, obtain the output result of the classifier, and then obtain Recognition results for handwritten digits. The commonly used classification algorithm in the prior art is the Lie group Fisher algorithm. The Lie group Fisher algorithm needs to perform a linear transformation projection on the original Lie group structure data, so that the data of the same type can be projected together as much as possible, and the data of different types can be separated as much as possible. The data has good separability, but the Lie group Fisher algorithm using the linear classification method must not capture the nonlinear characteristics of the Lie group structure data, which causes the Lie group Fisher algorithm to deal with the nonlinear characteristics of the Lie group structure data. There are certain defects.

Contents of the invention

In view of this, the present invention provides a handwritten digit recognition method and system based on Lie group structure data, to solve the defects existing in the existing handwritten digit recognition technology in dealing with the nonlinear characteristics of Lie group structure data, to realize Lie group Nonlinear processing of structured data.

To achieve the above object, the present invention provides the following technical solutions:

A method for recognizing handwritten digits based on Lie group structure data, comprising the steps of:

A. extract corresponding quantity of Lie group structure data from original handwritten digital image data;

B. using the correspondence between the Lie group structure data and the category labels of its corresponding handwritten digital image data as a training sample, obtain a training sample set corresponding to the Lie group structure data of the corresponding quantity, and simultaneously construct and process the Lie group structure data Matrix Gaussian kernel function:

$k(z_a,z_b)=e^{-p\×{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, p>0 is a kernel function, and ‖‖ _F is a matrix norm;

C. Utilize support vector machine algorithm, take described matrix Gaussian kernel function as kernel function, input training sample, train and obtain classifier model;

D. Input the Lie group structure data corresponding to the handwritten digital image data to be tested into the trained classifier model to obtain the corresponding digital category.

The present invention also provides a handwritten digit recognition system based on Lie group structure data, comprising:

Lie group structure data extraction module, for extracting the Lie group structure data of corresponding quantity from original handwritten digital image data;

The preprocessing module is used to use the correspondence between the Lie group structure data and the category labels of the corresponding handwritten digital image data as a training sample to obtain a training sample set corresponding to the Lie group structure data of the corresponding number, and at the same time, construct processing Matrix Gaussian kernel function for Lie group structured data:

$k(z_a,z_b)=e^{-p\×{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, and a≠b, p>0 is a kernel function, and ‖‖ _F is a matrix norm;

The model training module is used to utilize the support vector machine algorithm, take the matrix Gaussian kernel function as the kernel function, input the training samples, and train to obtain the classifier model;

The classification module is used to input the Lie group structure data corresponding to the handwritten digital image data to be tested into the trained classifier model to obtain corresponding digital categories.

Based on the above technical solutions, the embodiment of the present invention realizes the realization of the advantages of the support vector machine algorithm in identifying images in small samples, nonlinear and high-dimensional modes by constructing a matrix Gaussian kernel function and using the support vector machine algorithm to process Lie group structure data. Nonlinear processing of Lie group structured data.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a kind of flowchart of the handwritten numeral recognition method based on Lie group structure data of the present invention;

Fig. 2 is the Lie group mean algorithm, the contrast figure of Lie group Fisher algorithm and the classification performance of the inventive method to numeral 1 and 7;

Fig. 3 is the comparative figure of the classification performance of number 1,7 and 9 for Lie group mean algorithm and the inventive method;

Fig. 4 is the contrast figure of the classification performance of number 1,2,7 and 9 for Lie group mean algorithm and the inventive method;

Fig. 5 is a structural block diagram of a handwritten digit recognition system based on Lie group structure data of the present invention;

Fig. 6 is the structural block diagram of model training module of the present invention;

Fig. 7 is a structural block diagram of the classification module of the present invention.

Detailed ways

The inventor found through research that the support vector machine algorithm has the advantages of minimizing structural risk and good generalization ability. Using the support vector machine algorithm to realize the recognition of handwritten digits based on Lie group structure data can solve the problem of handwritten digits in small samples, nonlinear and The problem of recognition in high-dimensional mode, so as to solve the defects of existing handwritten digit recognition technology in capturing the nonlinear characteristics of Lie group structure data. However, the inventor also found through research that because the Lie group structure data is matrix data rather than vector data, the current standard application of the support vector machine algorithm does not support the processing of matrix data, so the current standard application of the support vector machine method cannot be used for Lie group data. Structured data is processed.

After further research, the inventor found that the purpose of the present invention can be realized by constructing a matrix Gaussian kernel function and using a support vector machine algorithm to establish a corresponding classifier model to classify Lie group structure data.

Combining the ideas of the present invention above, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than Full examples. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Fig. 1 is a flowchart of a method for recognizing handwritten digits based on Lie group structured data in the present invention. Referring to Figure 1, the method may include:

Step S100, extracting a corresponding number of Lie group structure data from the original handwritten digital image data;

For the convenience of description, in the embodiment of the present invention, x represents handwritten digital image data, and z represents Lie group structure data, and the number of original handwritten digital image data x is l (l is an integer, and l≥1), Then the original handwritten digital image data x are respectively x ₁ ,...x _l , and the corresponding number of Lie group structure data are z ₁ ,...z _l ;

Take a handwritten digital image data to extract Lie group structure data as an example, set rv as the reference vector, randomly select k points on the stroke area of the x image data to form k vectors $v_i=\left(\begin{array}{c}{r}_i\\ {\mathrm{no}}_i\end{array}\right),i=1,...,k,$ r _i represents the modulus length of the vector, n _i is the direction of v _i , and ‖n _i ‖=1=M _i ×rv, $m_i=\left(\begin{array}{cc}{e}^{\mathrm{ai}}& e^{-\mathrm{\θ\; i}}\\ e^{\mathrm{\θ\; i}}& e^{\mathrm{ai}}\end{array}\right),$ Where ‖‖ represents the modulus length of the vector, then the Lie group structure data z corresponding to the handwritten digital image data sample x can be obtained as:

Step S200, using the correspondence between the Lie group structure data and the category labels of the corresponding handwritten digital image data as training samples, obtaining a training sample set corresponding to the corresponding number of Lie group structure data, and constructing and processing the Lie group structure data at the same time The matrix Gaussian kernel function;

Suppose y is the category label of handwritten digital image data x, y∈{1,…c}, c is the number of categories of handwritten digital image data x, then the extracted Lie group structure data z ₁ ,…z _l and the corresponding handwritten Combining the category labels y ₁ , ... y _l of the digital image data, a training sample set {(z ₁ ,y ₁ ),...(z _l ,y _l )} containing the corresponding relationship between x and y can be obtained;

The support vector machine algorithm of current standard application does not support the processing of Lie group structure data, so the kernel function of existing support vector machine algorithm is not suitable for the present invention, in order to solve the applicable problem of support vector machine algorithm to Lie group structure data, The matrix Gaussian kernel function of the support vector machine algorithm can be constructed to make the Lie group structure data compatible with the support vector machine algorithm. The specific formula of the matrix Gaussian kernel function is as follows:

$k(z_a,z_b)=e^{-p\×{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, a, b are integers, both ∈ {1,...l}, and a≠b, p>0 is a kernel function, ‖‖ _F is a matrix norm .

Step S300, using the support vector machine algorithm, using the matrix Gaussian kernel function as a kernel function, inputting training samples, and training to obtain a classifier model;

Those skilled in the art can know the conventional method of machine training using the support vector machine algorithm; and what the embodiment of the present invention will provide is a machine training method that supports multi-classification problem processing of Lie group structure data, the training method is specifically : Input each Lie group structure data into the classifier model of the combined number of c to 2 respectively, one Lie group structure data obtains the corresponding output result of the combined number of classifiers with c taken as 2, and counts the output As a result, the Lie group structure data is divided into values of one of the c categories, and the maximum value is found therefrom, and the maximum value is determined as the digital category of the handwritten digital image data corresponding to the Lie group structure data.

In order to facilitate a detailed understanding of the machine training method of the embodiment of the present invention, a specific training process will be provided below.

The number of categories of the training sample set {(z ₁ ,y ₁ ),…(z _l ,y _l )} is c, from which samples corresponding to two types of category labels are randomly selected, that is, the samples taken out only include the two types of labels, And the labels of the samples in the training sample set that have not been taken out are not the two types of labels. Taking the samples corresponding to the two types of category labels as a combination, we can get the number of combinations in which c takes 2. For the convenience of expression, we now use c to take 2 A combination of several combinations of the i, j (i, j ∈ {1,...c}, and i≠j) samples corresponding to the two types of labels as an example, to illustrate the training process of the classifier model, the specific training The process is:

After extracting the i-th and j-type samples from the training sample set {(z ₁ , y ₁ ),...(z _l , y _l )}, the form optimization of the i-th and j-th types of samples can be obtained: make Among them, the superscript ij indicates the data information related to the i and j categories, and the subscript m indicates an index, Represents the i and j related Lie group structure data, l _ij represents the sum of samples of the i and j classes, for The corresponding category label, and when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=i,$ but ${\stackrel{\‾}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=-1,$ when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=j,$ but ${\stackrel{\‾}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=+1;$

The present invention is based on Lie group structure data, uses the support vector machine method to recognize the image data of handwritten digits, then when using the support vector machine method to process the i, j two types of classification of handwritten digits image data, then need to solve following optimization problem:

$\mathrm{<span\; class="notranslate">\; max</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0,0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>$

Among them, m and n both represent an index, for The corresponding category labels, Both m and n are integers, and m and n are both ∈ {1,...l _ij }, The model coefficients are generated for the training of the support vector machine algorithm, and S is the regular parameter required for the training of the support vector machine algorithm. According to the above optimization training, the following classifier model is generated:

$f_{\mathrm{ij}}\left(z\right)=\mathrm{sgn}\{\underset{m=1}{\overset{l_{\mathrm{ij}}}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_m^{\mathrm{ij}}{\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}k(z,z_m^{\mathrm{ij}})+b_{\mathrm{ij}}\},$ i, j=1,...c, and i≠j;

In the above formula, sgn() represents the sign function, and b _ij is the model threshold, which can be calculated by the following formula:

$b_{\mathrm{ij}}=\stackrel{\&OverBar;}{{\mathrm{the\; y}}_{\mathrm{sv}}}-\underset{m=1}{\overset{l_{\mathrm{ij}}}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_m^{\mathrm{ij}}{\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}k(z_{\mathrm{sv}},z_m^{\mathrm{ij}}),$ Among them, the coefficient value corresponding to z _sv is $0<{\mathrm{\&beta;}}_{\mathrm{sv}}<S;$

The classifier model corresponding to the two types of samples i and j is obtained above. If there are other combinations extracted from the training samples, the principle of training the classifier model for the other combinations is the same, which can be compared with each other, and will not be repeated here repeat.

Step S400 , respectively input Lie group structure data corresponding to the handwritten digital image data to be tested into the trained classifier model to obtain corresponding digital categories.

After the classifier model is obtained in step S300, the corresponding Lie group structure data can be extracted from the handwritten digital image data to be tested, so as to classify the handwritten digital image data to obtain the corresponding digital category. It should be noted that the purpose of the original handwritten digital image data in step S100 is to train a classifier model, which can be considered as a huge handwritten digital image database; and the handwritten digital image data to be tested in step S400 is the handwritten digital image of the present invention. The recognition object of the recognition method is image data of handwritten digits that need to be recognized.

The classifier model trained by the embodiment of the present invention can deal with the multi-classification problem of Lie group structure data. In terms of specific classification and recognition, it can be carried out in the following manner: respectively input the Lie group structure data corresponding to the handwritten digital image data to be tested. In the combined number classifier model where c takes 2, a Lie group structure data obtains the corresponding output result of the combined number classifiers where c takes 2, and the Lie group structure data in the output results are divided into c The value of a certain class in the class, and find the maximum value therefrom, and determine the maximum value as the digital category of the handwritten digital image data corresponding to the Lie group structure data;

The output result of the classifier can be represented by the formula f _ij (z), i, j=1,...c, and i≠j, specifically when the Lie group structure data is to be classified into the value of the i class, it can be obtained by The following formula is carried out:

$\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ,</span>$

Through the above formula, it can be obtained that the statistical Lie group structure data is divided into c values of class i, through the formula The maximum value is found from the c values, and the digital category corresponding to the found maximum value is the category of the handwritten digital image data corresponding to the Lie group structure data.

In the embodiment of the present invention, by constructing a matrix Gaussian kernel function, using the support vector machine algorithm to process the Lie group structure data corresponding to the handwritten digital image data, and using the support vector machine algorithm to identify the advantages of images in small samples, nonlinear and high-dimensional modes, it is realized. Nonlinear feature capture of Lie group structured data;

Secondly, by simplifying the multi-classification problem of Lie group structure data into multiple two-classification problems, and performing classification processing according to the support vector machine algorithm, the multi-classification problem processing of Lie group structure data is realized, so as to better realize the handwritten digits. identify.

Verify the beneficial effect that the present invention can bring by following experiment below:

The number of handwritten digital image data that can be stored in the handwritten digital database is generally 10 categories. Now select four of them and get the numbers 1, 2, 7 and 9 to conduct experiments. Each category is selected from the training set and the test set respectively. 200, that is, each class has 200 training samples and test samples. Then use ten-fold cross-validation to select parameters on the training samples, where the value range of the regular factor is: {2 ^-1 ,2 ⁰ ,...2 ⁴ }, and the value range of the matrix Gaussian kernel parameter is {2 ^-10 ,2 ^-9 ,...2 ^-6 }. Then apply the selected parameters to retrain a model, and estimate the performance on the test set to obtain the recognition rate. Further, the influence of the number of point clouds on the recognition rate can be considered. The value set of the number of point clouds is {5, 10, 15, 20, 25, 30, 35, 40, 50}. The point clouds are randomly generated and can be repeated 5 experiments, giving an average result. Figures 2 to 4 show the experimental results obtained by using the Lie group mean algorithm, the Lie group Fisher algorithm and the technical solution of the present invention.

Fig. 2 is a comparison diagram of Lie group mean algorithm, Lie group Fisher algorithm and the method of the present invention to the classification performance of numbers 1 and 7. Referring to Fig. 2, it can be found that the classification effect based on the present invention is significantly better than the Lie group mean algorithm and the Lie group Fisher algorithm, and the recognition rate shows an increasing trend with the increase of the number of points for each sample. Fig. 3 is the comparison diagram of Lie group mean algorithm and the classification performance of the inventive method to numeral 1,7 and 9, and Fig. 4 is the comparison of the classification performance of Lie group mean algorithm and the inventive method to numeral 1,2,7 and 9 Fig. 3 and Fig. 4, it can be seen that the multi-classification effect of the present invention is obviously better than the Lie group mean algorithm.

Fig. 5 is a structural block diagram of a handwritten digit recognition system based on Lie group structured data in the present invention. Referring to Figure 5, the system may include:

Lie group structure data extraction module 100, for extracting the Lie group structure data of corresponding quantity from original handwritten digital image data;

The preprocessing module 200 is used to use the correspondence between the Lie group structure data and the category labels of the corresponding handwritten digital image data as a training sample to obtain a training sample set corresponding to the corresponding number of Lie group structure data, and at the same time, construct Matrix Gaussian kernel function for Lie group structured data:

$k(z_a,z_b)=e^{-p\&times;{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, and a≠b, p>0 is a kernel function, and ‖‖ _F is a matrix norm;

The model training module 300 is used for utilizing the support vector machine algorithm, using the matrix Gaussian kernel function as a kernel function, inputting training samples, and training to obtain a classifier model;

The classification module 400 is used to input the Lie group structure data corresponding to the handwritten digital image data to be tested into the trained classifier model to obtain corresponding digital categories.

Wherein, the structure of the model training module 300 can be shown in Figure 6, including:

The combination acquisition unit 301 is used to arbitrarily get samples corresponding to two types of category labels from the training sample set, and obtain a number of combinations in which c is 2, and c is the category number of handwritten digital image data;

The loop training unit 302 is used to take each combination as a unit, use the support vector machine algorithm respectively, use the matrix Gaussian kernel function as the kernel function, input the samples corresponding to each combination, and train the combination number classifiers in which c is 2 Model.

Further, the cycle training unit 302 may include

The training subunit (not shown) is used to extract the combination of two types of samples including i and j, i, j are all ∈{1,...c}, and i≠j, and execute the process of training the classifier model: Let l represents the number of handwritten digital image data, x represents the handwritten digital image data, z represents the Lie group structure data, y represents the category label of the handwritten digital image data x, y∈{1,...c}, the superscript ij represents the i, j two types of related data information, the subscript m represents an index, Represents the i and j related Lie group structure data, l _ij represents the sum of samples of the i and j classes, for The corresponding category label, and when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=i,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=-1,$ when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=j,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=+1,$ and solve

$\mathrm{<span\; class="notranslate">\; max</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>$

Both m and n represent an index, Both m and n are integers, and m and n are both ∈ {1,...l _ij }, The model coefficients are generated for the support vector machine algorithm training, S is the regular parameter required for the support vector machine algorithm training, and the classifier model is obtained according to the above solution results $f_{\mathrm{ij}}\left(z\right)=\mathrm{sgn}\{\underset{m=1}{\overset{l_{\mathrm{ij}}}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_m^{\mathrm{ij}}{\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}k(z,z_m^{\mathrm{ij}})+b_{\mathrm{ij}}\},$ sgn() represents the sign function, b _ij is the model threshold;

The loop subunit (not shown) is used to extract another combination after the training subunit completes the above-mentioned process of training the classifier model, and then execute the above-mentioned classifier model training process until the number of combinations in which c is 2 is obtained classifier model.

The structure of the classification module 400 can be shown in Figure 7, including:

The calculation unit 401 is used to input the Lie group structure data corresponding to the handwritten digital image data to be tested into the classifier models with the number of combinations where c is 2, and a Lie group structure data corresponding to the number of combinations where c is 2 is obtained. output of a classifier;

Statistical unit 402, used to count the value of the Lie group structure data in the output result being classified into a certain category in the c category, and find the maximum value therefrom;

The determining unit 403 is configured to determine the maximum value found by the statistical unit as the digital category of the handwritten digital image data corresponding to the Lie group structure data.

Further, the statistical unit 402 may include:

Class value statistics subunit (not shown) for formula i∈{1,...c} counts the value of the Lie group structure data in the output result being divided into the i category, and the i category is a certain category in the assumed c category to be counted;

Maximum Find Subunit (not shown), used by the formula:

Find the maximum value among the values counted by the statistical subunit.

The handwritten digit recognition system based on the Lie group structure data of the present invention corresponds to the handwritten digit recognition method based on the Lie group structure data. The specific functions of the system can be realized by referring to the corresponding method, and will not be repeated here.

Professionals can further realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two. In order to clearly illustrate the possible For interchangeability, in the above description, the composition and steps of each example have been generally described according to their functions. Whether these functions are executed by hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art may use different methods to implement the described functions for each specific application, but such implementation should not be regarded as exceeding the scope of the present invention.

The steps of the methods or algorithms described in connection with the embodiments disclosed herein may be directly implemented by hardware, software modules executed by a processor, or a combination of both. Software modules can be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other Any other known storage medium.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. a handwritten numeral recognition method based on Lie group structure data, is characterized in that, comprises steps: A. extract corresponding quantity of Lie group structure data from original handwritten digital image data; B. using the correspondence between the Lie group structure data and the category labels of its corresponding handwritten digital image data as a training sample, obtain a training sample set corresponding to the Lie group structure data of the corresponding quantity, and simultaneously construct and process the Lie group structure data Matrix Gaussian kernel function: $k(z_a,z_b)=e^{-p\&times;{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, p>0 is a kernel function parameter, and |||| _F is a matrix norm; C. Utilize support vector machine algorithm, take described matrix Gaussian kernel function as kernel function, input training sample, train and obtain classifier model; The step C is specifically: randomly select samples corresponding to two types of category labels from the training sample set, and obtain a pairwise combination in which c is 2, and c is the category number of handwritten digital image data, and each combination contains two categories For the samples corresponding to the labels, each combination is used as a unit, and the support vector machine algorithm is used respectively, and the matrix Gaussian kernel function is used as a kernel function, and the samples corresponding to each combination are input, and the training obtains a combination of several classifier models in which c is 2; D. Input the Lie group structure data corresponding to the handwritten digital image data to be tested into the classifier model obtained by training respectively, and obtain the corresponding digital category; The step D is specifically: input the Lie group structure data corresponding to the handwritten digital image data to be tested into the combined several classifier models in which c takes 2, and a Lie group structure data obtains the corresponding combination of c taking 2 Several classifiers output the results, count the values of the Lie group structure data in the output results being classified into a certain class in the c class, and find the maximum value therefrom, and determine the maximum value as the value corresponding to the Lie group structure data Digit category for handwritten digit image data. 2. The method according to claim 1, wherein said step C comprises: C1. Randomly select samples corresponding to two types of category labels from the training sample set, and obtain a pairwise combination in which c is 2; C2. Extract the combination of two types of samples including i and j, i, j are all ∈{1,...c}, and i≠j, c is the number of categories of handwritten digital image data, and execute the process of training the classifier model: make Among them, l represents the number of handwritten digital image data, z represents the Lie group structure data, y is the category label of the handwritten digital image data, y∈{1,...c}, and the superscript ij represents the two types of i and j Relevant data information, the subscript m represents an index, Represents the Lie group structure data related to the i and j types, l _ij represents the sum of the samples of the i and j types, for The corresponding category label, and when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=i,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=-1,$ when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=j,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=+1,$ and solve, $\mathrm{<span\; class="notranslate">\; max</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>$ for The corresponding category label, m, n both represent an index, Both m and n are integers, and m and n are both ∈{1,...l _ij }, The model coefficients are generated for the support vector machine algorithm training, S is the regular parameter required for the support vector machine algorithm training, and the classifier model is obtained according to the above solution results $f_{\mathrm{ij}}\left(z\right)=\mathrm{sgn}\{\underset{m=1}{\overset{l_{\mathrm{ij}}}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_m^{\mathrm{ij}}{\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}k(z,z_m^{\mathrm{ij}})+b_{\mathrm{ij}}\},$ sgn() represents the sign function, b _ij is the model threshold; C3. Extract another combination, and execute the above-mentioned classifier model training process until a combination of classifier models in which c is 2 is obtained. 3. according to the described method of claim 1 or 2, it is characterized in that, this Lie group structure data in the described output result of described statistics is divided into the value of a certain class in c class is specifically: According to the formula i∈{1,...c} counts the value of the Lie group structure data in the output result being classified into the i category; The specific method of finding the maximum value is as follows: According to the formula $f\left(z\right)=\underset{i=1...c}{\max }\underset{i=1,i\&NotEqual;j}{\overset{c}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}\left(z\right)$ Find the maximum value. 4. A handwritten numeral recognition system based on Lie group structure data, is characterized in that, comprises: Lie group structure data extraction module, for extracting the Lie group structure data of corresponding quantity from original handwritten digital image data; The preprocessing module is used to use the correspondence between the Lie group structure data and the category labels of the corresponding handwritten digital image data as a training sample to obtain a training sample set corresponding to the Lie group structure data of the corresponding number, and at the same time, construct processing Matrix Gaussian kernel function for Lie group structured data: $k(z_a,z_b)=e^{-p\&times;{\left|\right|z_a-z_b\left|\right|}_f^2},$ The z _a and z _b represent any two Lie group structure data, and a≠b, p>0 are kernel function parameters, and |||| _F is a matrix norm; The model training module is used to utilize the support vector machine algorithm, take the matrix Gaussian kernel function as the kernel function, input the training samples, and train to obtain the classifier model; The model training module includes: a combination acquisition unit, which is used to arbitrarily get samples corresponding to two types of category labels from the training sample set, and obtain a pairwise combination in which c is 2, and c is the category number of handwritten digital image data; loop The training unit is used to take each combination as a unit, utilize the support vector machine algorithm respectively, use the matrix Gaussian kernel function as the kernel function, input the samples corresponding to each combination, and train to obtain a combined number of classifier models in which c is 2; The classification module is used to input the Lie group structure data corresponding to the handwritten digital image data to be tested into the classifier model obtained by training respectively, so as to obtain the corresponding digital category; The classification module includes: a calculation unit, which is used to input the Lie group structure data corresponding to the handwritten digital image data to be tested into the combined number classifier models in which c is 2, and one Lie group structure data obtains the corresponding c Get 2 combined several classifier output results; Statistical unit is used to count the Lie group structure data in the output result is divided into the value of a certain class in the c class, and finds the maximum value therefrom; Determination unit is used for The maximum value found by the statistical unit is determined as the digital category of the handwritten digital image data corresponding to the Lie group structure data. 5. The system of claim 4, wherein the circuit training unit comprises: The training sub-unit is used to extract a combination of two types of samples including i and j, i, j are all ∈{1,...c}, and i≠j, c is the number of categories of handwritten digital image data, and execute the training classifier The flow of the model: let Among them, l represents the number of handwritten digital image data, z represents the Lie group structure data, y is the category label of the handwritten digital image data, y∈{1,...c}, and the superscript ij represents the two types of i and j Relevant data information, the subscript m represents an index, Represents the i and j related Lie group structure data, l _ij represents the sum of samples of the i and j classes, for The corresponding category label, and when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=i,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=-1,$ when ${\mathrm{the\; y}}_m^{\mathrm{ij}}=j,$ but ${\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}=+1,$ and solve, $\mathrm{<span\; class="notranslate">\; max</span>}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>$ for The corresponding category label, m, n both represent an index, Both m and n are integers, and m and n are both ∈{1,...l _ij }, The model coefficients are generated for the support vector machine algorithm training, S is the regular parameter required for the support vector machine algorithm training, and the classifier model is obtained according to the above solution results $f_{\mathrm{ij}}\left(z\right)=\mathrm{sgn}\{\underset{m=1}{\overset{l_{\mathrm{ij}}}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_m^{\mathrm{ij}}{\stackrel{\&OverBar;}{\mathrm{the\; y}}}_m^{\mathrm{ij}}k(z,z_m^{\mathrm{ij}})+b_{\mathrm{ij}}\},$ sgn() represents the sign function, b _ij is the model threshold; The cyclic subunit is used to extract another combination after the training subunit completes the above-mentioned process of training the classifier model, and then execute the above-mentioned classifier model training process until several classifier models in which c is 2 are obtained. 6. The system according to claim 4 or 5, wherein the statistical unit comprises: Class value statistics subunit, used by formula i∈{1,...c} counts the value of the Lie group structure data in the output result being divided into the i class, and the i class is a certain class in the hypothetical c class to be counted; Maximum value lookup subcell for use by formula $f\left(z\right)=\underset{i=1...c}{\max }\underset{i=1,i\&NotEqual;j}{\overset{c}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}\left(z\right)$ Find the maximum value among the values counted by the statistical subunit.