CN117671704A - Handwriting digital recognition method, handwriting digital recognition device and computer storage medium - Google Patents

Abstract

The invention discloses a handwriting digital recognition method, which comprises the following steps of carrying out normalization processing on samples collected in the steps to obtain training data, wherein the training data comprises label data and label-free data; calculating an intra-class divergence matrix and an inter-class divergence matrix from the tag data; constructing a neighbor graph by using the label data and the label-free data to calculate manifold regular terms; the training data is utilized to learn through a Laplace self-adaptive weight discriminant analysis method to obtain an optimal projection matrix, an iterative optimization method is adopted to solve an optimization problem to obtain the optimal projection matrix, a sample to be identified is subjected to normalization processing, projected data is obtained through the optimal projection matrix, and then a nearest neighbor classifier is adopted to obtain an identification tag. The invention also discloses a device based on the method and a computer storage medium. The method and the device effectively solve the problem of multiple classification with less tag data, improve the utilization rate of the data and improve the classification performance.

Description

Handwritten digit recognition method, device and computer storage medium

Technical field

The present invention relates to the field of image recognition technology, and in particular to a handwritten digit recognition method, device and computer storage medium.

Background technique

Linear discriminant analysis (LDA) is a classic supervised learning algorithm, mainly used for dimensionality reduction and classification. Its main idea is to project data into a new space so that data of the same type are as close as possible and data of different types are as far apart as possible. This method can be used to solve image classification problems, such as handwritten digit recognition. Linear discriminant analysis methods can improve classification accuracy by projecting data into the best linear discriminant direction. But for multi-classification problems, LDA is not an optimal choice. Under the homoscedastic Gaussian assumption, the projection of LDA is obtained by maximizing the weighted arithmetic mean of the Kullback-Leibler (KL) divergence between different classes, and its projection direction is dominated by class pairs with large KL divergence. , which results in overlapping of class pairs with small KL divergence in the projection space, resulting in significant degradation in classification accuracy. In response to the problem of class separation of LDA in multi-classification problems, many researchers have proposed various weight construction schemes to optimize LDA. This type of supervised discriminant analysis method is mainly divided into two categories. One is to replace the arithmetic mean of KL divergence between different class pairs and give different weights to class pairs with different KL divergence; the other is to focus on similar classes. The separation of pairs emphasizes class pairs with small KL divergence. However, these methods are all supervised, require sufficient labeled data to train the model, and are prone to overfitting problems.

With the development of science and technology, the technology and tools for collecting data are constantly improving. A large amount of data can be used, but the labeling of labeled data still requires a lot of manpower and material resources. Therefore, how to use unlabeled data to help improve existing algorithms? Performance has become a current research hotspot. Semi-supervised learning uses a large amount of unlabeled data to assist a small amount of labeled data to improve learning performance, thereby obtaining a learning model with stronger generalization capabilities. How to extend the supervised discriminant analysis method to semi-supervised learning to obtain a more effective classification model has become one of the tasks that need to be solved urgently.

Contents of the invention

In view of the above-mentioned shortcomings of the prior art, the present invention provides a handwritten digit recognition method, which extends the supervised discriminant analysis method to semi-supervised learning, solving the problem of insufficient label data in multi-classification tasks and the class separation that occurs when using traditional discriminant analysis methods. question. Another object of the present invention is to provide a handwritten digit recognition device and a corresponding computer storage medium.

The technical solution of the present invention is as follows: a handwritten digit recognition method, including the following steps:

Step S1. The collected samples are normalized to obtain training data. The training data includes labeled data and unlabeled data;

Step S2: Calculate the intra-class divergence matrix and the inter-class divergence matrix from the label data in the training data;

Step S3: Construct a neighbor graph from the labeled data and unlabeled data in the training data to calculate the manifold regularization term;

Step S4: Use the training data to learn the optimal projection matrix through the Laplacian adaptive weight discriminant analysis method, including setting the optimization goal of the Laplacian adaptive weight discriminant analysis method to

,

,

in is the within-class divergence matrix,/> is the inter-class divergence matrix,/> is the projection matrix/> L _2,1 norm, m is the number of features, d is the dimension of the projection space,/> is the manifold regular term, To weigh parameters,/> is the identity matrix,/> is the number of categories of label information in the training data; an iterative optimization method is used to solve the projection matrix/> and weight vector/> , get the optimal projection matrix;

Step S5: Normalize the sample to be identified, obtain the projected data through the optimal projection matrix, and then use the nearest neighbor classifier to obtain the identification label.

The invention also provides a handwritten digit recognition device, which includes:

Preprocessing module: The collected samples are normalized to obtain training data. The training data includes labeled data and unlabeled data;

The first calculation module: calculates the intra-class divergence matrix and the inter-class divergence matrix from the label data in the training data;

The second calculation module: constructs a neighbor graph from the labeled data and unlabeled data in the training data to calculate the manifold regularization term;

Optimal projection matrix solution module: Use training data to learn the optimal projection matrix through the Laplacian adaptive weight discriminant analysis method, including setting the optimization goal of the Laplacian adaptive weight discriminant analysis method to

,

,

in is the within-class divergence matrix,/> is the inter-class divergence matrix,/> is the projection matrix/> L _2,1 norm, m is the number of features, d is the dimension of the projection space,/> is the manifold regular term, To weigh parameters,/> is the identity matrix,/> is the number of categories of label information in the training data; an iterative optimization method is used to solve the projection matrix/> and weight vector/> , get the optimal projection matrix;

Recognition module: Normalize the sample to be identified, obtain the projected data through the optimal projection matrix, and then use the nearest neighbor classifier to obtain the identification label.

Further, the step S3 and the second calculation module include calculation steps:

Step S3.1, using training data Construct the nearest neighbor graph to obtain the nearest neighbor matrix , label data/> , unlabeled data/> , the number of tag data is/> , the number of unlabeled data is/> ,nearest neighbor matrix/> is constructed as follows:

,

in Expressed as/> of/> neighbor set;

Step S3.2, Calculate the Laplacian matrix in the manifold regularization term , of which/> is a diagonal matrix, diagonal elements/> , the obtained manifold regular term in the projection space is

,

in is the L ₂ norm,/> Expressed as/> Image in low-dimensional projection space,/> , .

Further, the iterative optimization method is used to solve the projection matrix and weight vector/> , to obtain the optimal projection matrix, including steps:

Step S4.1, initialize weights , solve for the projection matrix/> , the optimization function of LapAWDA is transformed into

,

,

in is a constant,/> 0 is the trade-off coefficient, /> ,

First calculate the matrix , the optimization objective is obtained as

,

Apply the Lagrange multiplier method to convert the optimization problem into an eigendecomposition problem:

,

in is a diagonal matrix with diagonal elements/> ,/> for/> of/> row vector, /> is the eigenvalue, the optimal projection matrix/> by former/> corresponding to the largest eigenvalue/> consists of feature vectors, where/> ;

Step S4.2, fixed projection matrix , solve for the weight vector/> , at this time the objective function of LapAWDA becomes

,

,

According to Cauchy's inequality, the solution of the weight vector is

;

Step S4.3, update weight vector , continue to solve the projection matrix according to step S4.1/> ;After obtaining the optimal projection matrix of this round, proceed to the next round of alternating iterative solution, that is/> , fixed projection matrix/> , update the weight vector according to step S4.2/> , repeat step S4.3 until the stopping condition is met to obtain the optimal projection matrix/> .

Since the optimization problem of the Laplacian adaptive weight discriminant analysis method is not a classic quadratic optimization problem, a fast and effective iterative optimization algorithm is used in the solution process, and it can be theoretically proven that it is convergent. .

Further, the stop condition in step S4.3 is .

Further, the intra-class divergence matrix The calculation is as follows:

,

in Indicates the first/> No./> in class samples,/> Indicates the first/> The mean vector of the class;

The inter-class divergence matrix The calculation is as follows:

.

The present invention also provides a computer storage medium on which a computer program is stored. When the computer program is executed by a processor, the above handwritten digit recognition method is implemented.

Compared with the existing technology, the advantages of the technical solution provided by the present invention are:

This invention introduces structural information of unlabeled data through manifold regularization terms, and uses an adaptive weight method to balance the KL divergence between each class pair to prevent class pairs with small KL divergence from disappearing in the projection space. In addition, the L _2,1 norm constraint is imposed on the projection matrix in order to obtain a sparsely discriminative projection matrix to further improve the classification accuracy and thus be more suitable for multi-classification tasks. The optimal solution to the optimization problem of LapAWDA can extract useful information that is beneficial to subsequent classification tasks.

Through the combination of the discriminant analysis method and the manifold regularization term, the semi-supervised feature extraction method of the present invention is combined with the nearest neighbor classification to obtain a multi-classification model, which can be used to solve the semi-supervised multi-classification problem with less label data and improve the utilization of data. , and improve the classification performance.

Description of drawings

Figure 1 is a schematic flow chart of the handwritten digit recognition method.

Figure 2 is a schematic flow chart of using the Laplacian adaptive weight discriminant analysis method.

Figure 3 shows a sample of the MNIST data set.

Figure 4 shows the average accuracy of 10 methods on the MNIST data set with 10 label data as the dimension changes.

Figure 5 shows the average accuracy of 10 methods on the MNIST data set with 20 label data as the dimension changes.

Figure 6 shows the average accuracy of 10 methods on the MNIST data set with 30 label data as the dimension changes.

Detailed ways

The present invention will be further described below in conjunction with the examples. It should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading this description, those skilled in the art will make various equivalent modifications to this description. All fall within the scope defined by the appended claims of this application.

The handwritten digit recognition device involved in this embodiment includes:

Preprocessing module: The collected samples are normalized to obtain training data. The training data includes labeled data and unlabeled data;

The first calculation module: calculates the intra-class divergence matrix and the inter-class divergence matrix from the label data in the training data;

The second calculation module: constructs a neighbor graph from the labeled data and unlabeled data in the training data to calculate the manifold regularization term;

The optimal projection matrix solution module: uses training data to learn the optimal projection matrix through the Laplacian adaptive weight discriminant analysis method;

Recognition module: Normalize the sample to be identified, obtain the projected data through the optimal projection matrix, and then use the nearest neighbor classifier to obtain the identification label.

Specifically, please refer to Figure 1 and Figure 2. The handwritten digit recognition method used by the device includes the following steps:

Step S1: The collected samples are normalized to obtain training data. The normalization process is to divide each pixel value of the image by 255 and map it to the range of [0,1]. Training data includes labeled data and unlabeled data/> , the training data is/> , where the label vector of label data is/> , label information/> ,/> is the number of categories, and the number of label data is/> , the number of unlabeled data is/> , the total number of training data is/> .

Step S2: Calculate the intra-class divergence matrix and the inter-class divergence matrix from the label data in the training data;

for Class data, total within-class divergence matrix/> The calculation method is: ,

in Indicates the first/> No./> in class samples,/> Indicates the first/> The mean vector of the class.

And for Composed between any two categories in the class/> Each class pair is obtained/> Inter-class divergence matrix, that is, the /> Class and No./> Inter-class divergence matrix of classes/> The calculation method is:

.

Step S3: Construct a neighbor graph from the labeled data and unlabeled data in the training data to calculate the manifold regular term; specifically including:

Step S3.1, using training data Construct the nearest neighbor graph to obtain the nearest neighbor matrix ,nearest neighbor matrix/> is constructed as follows:

,

in Expressed as/> of/> Neighbor collection.

Step S3.2, Calculate the Laplacian matrix in the manifold regularization term , of which/> is a diagonal matrix, diagonal elements/> , the obtained manifold regular term in the projection space is

,

in is the L ₂ norm,/> Expressed as/> Image in low-dimensional projection space,/> , d is the dimension of the projection space.

Step S4. From the expression of the manifold regular term, it can be seen that it is related to the projection vector Relevant, so the manifold regularization term is introduced into the Laplacian adaptive weight discriminant analysis method (LapAWDA), which requires solving the projection vector during the optimization process . Since the weight vector/> It is not predefined, but learned from a low-dimensional projection space, and the optimization goal of LapAWDA shows that it is non-smooth and cannot directly solve the projection vector simultaneously/> and weight vector/> , but an approximately optimal solution can be obtained using an iterative optimization algorithm, so the LapAWDA optimization problem uses 1) fixed weight vector/> , update the projection vector/> ;2) Fixed projection vector/> , update the weight vector/> These two steps are solved iteratively and alternately until the stopping condition is met and an approximately optimal solution is obtained.

Specifically, the optimization objective of the Laplacian adaptive weight discriminant analysis method is set to

,

,

in is the within-class divergence matrix,/> is the inter-class divergence matrix,/> is the projection matrix/> L _2,1 norm, m is the number of features,/> ,/> To weigh parameters,/> is the identity matrix.

The iterative optimization steps are as follows:

Step S4.1, initialize weights , solve for the projection matrix/> , the optimization function of LapAWDA is transformed into

,

,

in is a constant,/> 0 is the trade-off coefficient, /> ,

First calculate the matrix , the optimization objective is obtained as

,

Apply the Lagrange multiplier method to convert the optimization problem into an eigendecomposition problem:

,

in is a diagonal matrix with diagonal elements/> ,/> for/> of/> row vector, /> is the eigenvalue, the optimal projection matrix/> by former/> corresponding to the largest eigenvalue/> consists of feature vectors, where/> ;

Step S4.2, fixed projection matrix , solve for the weight vector/> , at this time the objective function of LapAWDA becomes

,

,

According to Cauchy's inequality, the solution of the weight vector is

;

Step S4.3, update weight vector , continue to solve the projection matrix according to step S4.1/> ;After obtaining the optimal projection matrix of this round, proceed to the next round of alternating iterative solution, that is/> , fixed projection matrix/> , update the weight vector according to step S4.2/> , repeat step S4.3 until the stop condition is met/> , get the optimal projection matrix/> .

Step S5: Normalize the sample to be identified, and then obtain the projected data through the optimal projection matrix. For the normalized data of the identified sample The projected image is/> , and then use the nearest neighbor classifier to obtain the identification label.

The data set used in the demonstration experiment of this invention is: MNIST handwritten digital images.

The MNIST data set is a classic data set in the field of machine learning. It consists of 60,000 training samples and 10,000 test samples. Each sample is a 28 * 28 pixel grayscale handwritten digit picture, as shown in Figure 3. In the experiment, the training set consists of 100 randomly selected images from each category of handwritten digits from 0 to 9, with a total of 10 categories, and the test set is 10,000 test samples. In order to verify the effectiveness of the present invention in semi-supervised learning, different amounts of labeled data were used for training in the experiment, and the average accuracy rate of 10 trials on the test set was taken as the evaluation index. The present invention is a feature extraction method. In order to demonstrate its classification performance on the MNIST data set, the nearest neighbor classifier is used.

Experimental hardware environment: Macbook Pro with Intel Core i5 (2.7GHz) processor and 8GB memory. Code running environment: Matlab (R2015b). The experimental results are as follows:

In order to verify the effectiveness and superiority of the present invention, the experiment compared 5 supervised discriminant analysis methods (LDA, LFDA, aPAC, LADA and MDAAWS) and 4 semi-supervised discriminant analysis methods (SLDA, SMMC, SSDR and SELF ), here, the number of nearest neighbors is set to 5, and the regularization parameters in each method are within the parameter range obtained through grid search. Table 1 records the classification accuracy of the present invention and 9 other comparison methods under different number of labels. The feature dimension here is 20. From the table, it can be seen that the classification accuracy of the semi-supervised discriminant analysis method is generally higher than that of the corresponding supervised method, indicating that unlabeled data provides beneficial information, and as the number of labeled samples increases, the partial supervised discriminant Analysis methods reduce classification performance due to overfitting, but semi-supervised discriminant analysis methods have not encountered this phenomenon. Therefore, introducing the information of unlabeled data can improve the generalization ability of the algorithm. The LapAWDA method proposed by the present invention has the highest classification accuracy regardless of the training data of 10, 20 or 30 labeled data, which is obviously superior. to other discriminant analysis methods.

Table 1 Average classification accuracy (%) of 10 methods under different number of labels

In order to study the impact of the number of features and the number of labeled samples on the projection matrix obtained by LapAWDA, 10, 20 and 30 labeled samples were randomly selected from each type of training data, and the remaining training data were regarded as unlabeled samples. Figures 4 to 6 show the accuracy of multiple discriminant classification methods on the MNIST data set when the dimensions change from 5 to 50. The present invention has achieved the highest accuracy in each dimension, especially when the first 20 dimensions are taken. The classification performance of the invention is far better than other methods. Moreover, as the number of labeled samples increases, the classification accuracy of the present invention also increases. The above results show that the present invention can obtain more discriminative information from training data through the projection matrix in classification tasks, and at the same time improve the utilization of label data.

It should be noted that the specific methods of the above embodiments can form a computer program product. Therefore, the computer program product implemented in the present application can be stored in one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical storage, etc.).

Claims (10)

1. A handwriting digital recognition method, characterized by comprising the steps of:

step S1, carrying out normalization processing on collected samples to obtain training data, wherein the training data comprises label data and label-free data;

s2, calculating an intra-class divergence matrix and an inter-class divergence matrix from tag data in training data;

s3, constructing a neighbor graph to calculate manifold regular terms according to the label data and the label-free data in the training data;

s4, learning by using training data through a Laplace adaptive weight discriminant analysis method to obtain an optimal projection matrix, wherein the method comprises the steps of setting an optimization target of the Laplace adaptive weight discriminant analysis method as follows

，

，

Wherein the method comprises the steps ofIs an intra-class divergence matrix +.>Is an inter-class divergence matrix->For projection matrix->L of (2) _2,1 Norm, m is the number of features, d is the dimension of projection space, +.>Is manifold regular term->To weigh the parameters->Is a unitary matrix->The number of categories of tag information in the training data; solving a projection matrix by adopting an iterative optimization method>And weight vector->Obtaining an optimal projection matrix;

and S5, carrying out normalization processing on the sample to be identified, obtaining projected data through an optimal projection matrix, and obtaining the identification tag by adopting a nearest neighbor classifier.

2. The handwriting recognition method according to claim 1, wherein said step S3 comprises the steps of:

step S3.1, training data is utilizedConstructing a neighbor graph to obtain a neighbor matrix>Tag data->Label-free data->The number of tag data is->The number of unlabeled data is->Neighbor matrix->The construction mode of (2) is as follows:

，

wherein the method comprises the steps ofDenoted as->Is->A neighbor set;

step S3.2, calculating Laplacian matrix in manifold regularization termWherein->For diagonal matrix, diagonal element->The obtained manifold regularization term in the projection space is

，

Wherein the method comprises the steps ofIs L ₂ Norms (F/F)>Denoted as->Image in low-dimensional projection space, +.>，。

3. The handwriting digital recognition method of claim 1, wherein said iterative optimization method is used to solve a projection matrixAnd weight vector->Obtaining an optimal projection matrix, comprising the steps of:

step S4.1, initializing weightsSolving the projection matrix +.>Transformation of the optimization function of LapAWDA into

，

，

Wherein the method comprises the steps ofIs constant (I)>0 is a trade-off coefficient>，

First calculate the momentArrayObtaining the optimization target as

，

And converting the optimization problem into a feature decomposition problem by using a Lagrangian multiplier method:

，

wherein the method comprises the steps ofIs a diagonal matrix, diagonal element->，/>Is->Is>Row vector->For eigenvalues, an optimal projection matrix +.>Is made up of->The corresponding +.>A feature vector composition, wherein->；

Step S4.2, fixing the projection matrixSolving for weight vector +.>At this time, the objective function of LapAWDA becomes

，

，

From the Cauchy inequality, a solution of the weight vector is obtained

；

Step S4.3, updating weight vectorContinuing to solve the projection matrix according to step S4.1>The method comprises the steps of carrying out a first treatment on the surface of the After the optimal projection matrix of the round is obtained, the next round of alternate iterative solution is carried out, namely +.>Fixed projection matrix->Updating the weight vector according to step S4.2 +.>RepeatingStep S4.3 until stopping condition is met to obtain optimal projection matrix +.>。

4. A handwriting recognition method according to claim 3 and wherein said stop condition in step S4.3 is。

5. The method of handwriting digital recognition according to claim 1, wherein said intra-class divergence matrixThe calculation method is as follows:

，

wherein the method comprises the steps ofIndicate->Class->Sample number->Indicate->A mean vector of the class;

the inter-class divergence matrixThe calculation method is as follows:

。

6. a handwriting digital recognition device, comprising:

and a pretreatment module: normalizing the collected samples to obtain training data, wherein the training data comprises label data and label-free data;

a first calculation module: calculating an intra-class divergence matrix and an inter-class divergence matrix from tag data in the training data;

a second calculation module: constructing a neighbor graph by using label data and label-free data in the training data to calculate manifold regular terms;

and an optimal projection matrix solving module: the training data is utilized to obtain an optimal projection matrix through learning by a Laplace adaptive weight discriminant analysis method, and the method comprises the steps of setting an optimization target of the Laplace adaptive weight discriminant analysis method as follows

，

，

Wherein the method comprises the steps ofIs an intra-class divergence matrix +.>Is an inter-class divergence matrix->For projection matrixL of (2) _2,1 Norm, m is the number of features, d is the projectionDimension of space->Is manifold regular term->To weigh the parameters->Is a unitary matrix->The number of categories of tag information in the training data; solving a projection matrix by adopting an iterative optimization method>And weight vector->Obtaining an optimal projection matrix;

and an identification module: and carrying out normalization processing on the sample to be identified, obtaining projected data through an optimal projection matrix, and obtaining the identification tag by adopting a nearest neighbor classifier.

7. The handwriting digital recognition device of claim 6, wherein said second calculation module calculates manifold regularization term comprising:

using training dataConstructing a neighbor graph to obtain a neighbor matrix>Tag dataLabel-free data->The number of tag data is->The number of unlabeled data is->Neighbor matrix->The construction mode of (2) is as follows:

，

wherein the method comprises the steps ofDenoted as->Is->A neighbor set;

computing Laplacian matrix in manifold regularization termWherein->As a diagonal matrix, diagonal elementsThe obtained manifold regularization term in the projection space is

，

Wherein the method comprises the steps ofIs L ₂ Norms (F/F)>Denoted as->Image in low-dimensional projection space, +.>，。

8. The handwriting digital recognition device of claim 6, wherein said optimal projection matrix solving module adopts an iterative optimization method to solve a projection matrixAnd weight vector->Obtaining an optimal projection matrix, comprising the steps of:

initializing weightsSolving the projection matrix +.>Transformation of the optimization function of LapAWDA into

，

，

Wherein the method comprises the steps ofIs constant (I)>0 is a trade-off coefficient>，

First calculate the matrixObtaining the optimization target as

，

And converting the optimization problem into a feature decomposition problem by using a Lagrangian multiplier method:

，

wherein the method comprises the steps ofIs a diagonal matrix, diagonal element->，/>Is->Is>Row vector->For eigenvalues, an optimal projection matrix +.>Is made up of->The corresponding +.>A feature vector composition, wherein->；

Fixed projection matrixSolving for weight vector +.>At this time, the objective function of LapAWDA becomes

，

，

From the Cauchy inequality, a solution of the weight vector is obtained

；

Updating weight vectorsContinuing to solve the projection matrix +.>The method comprises the steps of carrying out a first treatment on the surface of the After the optimal projection matrix of the round is obtained, the next round of alternate iterative solution is carried out, namely +.>Fixed projection matrix->Re-updating the weight vector +.>Repeatedly solving the projection matrix +.>Until the stopping condition is met, obtaining the optimal projection matrix +.>。

9. The handwriting recognition device of claim 8, wherein the stop condition is。

10. A computer storage medium having stored thereon a computer program which, when executed by a processor, implements the handwriting digital recognition method of any one of claims 1 to 5.