CN117671704B - A method, device and computer storage medium for handwritten digit recognition - Google Patents

Abstract

The present invention discloses a method for handwritten digit recognition, including the steps of normalizing the collected samples to obtain training data, the training data including label data and unlabeled data; calculating the intra-class scatter matrix and the inter-class scatter matrix from the label data; constructing a neighbor graph from the label data and the unlabeled data to calculate the manifold regularization term; using the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method, and using the iterative optimization method to solve the optimization problem to obtain the optimal projection matrix, normalizing the samples to be recognized, and then obtaining the projected data through the optimal projection matrix, and then using the nearest neighbor classifier to obtain the recognition label. The present invention also discloses a device based on the method and a computer storage medium. The present invention effectively solves the problem of multiple classifications with less label data, improves the utilization rate of data, and enhances the classification performance.

Description

A method, device and computer storage medium for handwritten digit recognition

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 away as possible. This method can be used to solve image classification problems, such as handwritten digit recognition. Linear discriminant analysis can improve classification accuracy by projecting data onto the optimal linear discriminant direction. However, for multi-classification problems, LDA is not the best choice. Under the assumption of homoscedastic Gaussian, the projection of LDA is obtained by maximizing the weighted arithmetic mean of the Kullback-Leibler (KL) divergence between different categories. The projection direction is dominated by class pairs with large KL divergence, which leads to the overlap of class pairs with small KL divergence in the projection space, which significantly degrades the 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 the KL divergence between different class pairs and assign different weights to class pairs with different KL divergences; the other is to focus on the separation of similar class pairs and emphasize class pairs with small KL divergence. However, these methods are supervised and 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 the performance of existing algorithms has become a current research hotspot. Semi-supervised learning is to use 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 ability. 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.

Summary of the invention

In view of the above-mentioned defects of the prior art, the present invention provides a handwritten digit recognition method, which extends the supervised discriminant analysis method to semi-supervised learning, and solves the problem of class separation in multi-classification tasks with little label data and the use of traditional discriminant analysis methods. 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 method for handwritten digit recognition comprises the following steps:

Step S1, the collected samples are normalized to obtain training data, wherein the training data includes labeled data and unlabeled data;

Step S2, calculating the intra-class scatter matrix and the inter-class scatter matrix based on the label data in the training data;

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

Step S4, using the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method, including setting the optimization target of the Laplace adaptive weighted discriminant analysis method to

,

,

in is the intra-class scatter matrix, /> is the inter-class scatter matrix, /> is the projection matrix/> The L _2,1 norm of , m is the number of features, d is the dimension of the projection space, /> is the manifold regularization term, To weigh the parameters, /> is the identity matrix, /> is the number of categories of label information in the training data; the projection matrix is solved by iterative optimization method/> 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 present invention also provides a handwritten digit recognition device, comprising:

Preprocessing module: normalize the collected samples to obtain training data, which includes labeled data and unlabeled data;

The first calculation module: calculates the intra-class scatter matrix and the inter-class scatter matrix based on 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 the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method, including setting the optimization target of the Laplace adaptive weighted discriminant analysis method to

,

,

in is the intra-class scatter matrix, /> is the inter-class scatter matrix, /> is the projection matrix/> The L _2,1 norm of , m is the number of features, d is the dimension of the projection space, /> is the manifold regularization term, To weigh the parameters, /> is the identity matrix, /> is the number of categories of label information in the training data; the projection matrix is solved by iterative optimization method/> and weight vector/> , get the optimal projection matrix;

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

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

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

,

in Expressed as/> /> Neighbor set;

Step S3.2: Calculate the Laplace matrix in the manifold regularization term , where/> is a diagonal matrix, with diagonal elements/> , the manifold regularization term in the projection space is

,

in is the _L2 norm,/> Expressed as/> The image in the low-dimensional projected space, /> , .

Furthermore, the projection matrix is solved by using an iterative optimization method. and weight vector/> , get the optimal projection matrix, including the steps:

Step S4.1: Initialize weights , solve 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

,

Apply the Lagrange multiplier method to transform the optimization problem into a eigendecomposition problem:

,

in is a diagonal matrix, with diagonal elements/> ,/> For/> The first/> Row vector, /> is the eigenvalue, the optimal projection matrix/> It is from the previous/> The maximum eigenvalue corresponds to /> feature vectors, where /> ;

Step S4.2: Fix the projection matrix , solve for the weight vector/> , then the objective function of LapAWDA becomes

,

,

According to the Cauchy 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, the next round of alternating iteration is performed, that is, /> , fixed projection matrix/> , update the weight vector according to step S4.2/> , repeat step S4.3 until the stop condition is met to obtain the optimal projection matrix/> .

Since the optimization problem of the Laplace adaptive weighted 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 proved to be convergent.

Furthermore, the stopping condition in step S4.3 is .

Furthermore, the intra-class scatter matrix The calculation is as follows:

,

in Indicates the first/> The first in the category/> samples, /> Indicates the first/> The mean vector of the class;

The between-class scatter 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-mentioned handwritten digit recognition method is implemented.

Compared with the prior art, the advantages of the technical solution provided by the present invention are:

The present invention introduces the structural information of unlabeled data through the manifold regularization term, and uses an adaptive weight method to balance the KL divergence between each class pair, so as to avoid the disappearance of class pairs with small KL divergence in the projection space. In addition, an _L2,1 norm constraint is imposed on the projection matrix to obtain a sparse discriminant projection matrix, further improve the classification accuracy, and thus be more suitable for multi-classification tasks. The optimal solution to the LapAWDA optimization problem can extract useful information that is beneficial to subsequent classification tasks.

By combining the discriminant analysis method with 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 little labeled data, improve data utilization, and enhance classification performance.

BRIEF DESCRIPTION OF THE DRAWINGS

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

FIG. 2 is a flow chart of the Laplace adaptive weighted discriminant analysis method.

Figure 3 shows a sample from the MNIST dataset.

Figure 4 shows the average accuracy of 10 methods on the MNIST dataset as the dimension changes when there are 10 labeled data.

Figure 5 shows the average accuracy of 10 methods on the MNIST dataset as the dimension changes when there are 20 labeled data.

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

Detailed ways

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

The handwritten digit recognition device involved in this embodiment includes:

Preprocessing module: normalize the collected samples to obtain training data, which includes labeled data and unlabeled data;

The first calculation module: calculates the intra-class scatter matrix and the inter-class scatter matrix based on 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 the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method;

Recognition module: Normalize the samples 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, referring to FIG. 1 and FIG. 2 , the handwritten digit recognition method adopted 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]. The training data includes label data and unlabeled data/> , the training data is /> , where the label vector of the label data is , tag 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, calculating the intra-class scatter matrix and the inter-class scatter matrix based on the label data in the training data;

for Class data, total intra-class scatter matrix/> The calculation method is: ,

in Indicates the first/> The first in the category/> samples, /> Indicates the first/> The mean vector of the classes.

And for The composition between any two classes in the class/> Class pairs get /> The inter-class scatter matrix, that is, the first/> Class and No./> The inter-class scatter matrix of the class/> The calculation method is:

.

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

Step S3.1: Using training data Construct a neighbor graph to get a neighbor matrix , neighbor matrix/> is constructed as follows:

,

in Expressed as/> /> Neighbor set.

Step S3.2: Calculate the Laplace matrix in the manifold regularization term , where/> is a diagonal matrix, with diagonal elements/> , the manifold regularization term in the projection space is

,

in is the _L2 norm,/> Expressed as/> The image in the low-dimensional projected space, /> , d is the dimension of the projection space.

Step S4: From the expression of the manifold regularization term, it can be seen that it is related to the projection vector Therefore, the manifold regularization term is introduced into the Laplace adaptive weighted discriminant analysis method (LapAWDA), which requires solving the projection vector in the optimization process. . Since the weight vector/> It is not predefined, but learned from the low-dimensional projection space. Moreover, the optimization objective of LapAWDA shows that it is non-smooth and cannot directly solve the projection vector at the same time./> and weight vector/> , but the iterative optimization algorithm can get an approximate optimal solution, so the LapAWDA optimization problem adopts 1) fixed weight vector/> , update the projection vector/> ; 2) Fixed projection vector/> , update the weight vector/> These two steps are solved alternately and iteratively until the stopping condition is met and an approximate optimal solution is obtained.

Specifically, the optimization objective of the Laplace adaptive weighted discriminant analysis method is set as

,

,

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

The iterative optimization steps are as follows:

Step S4.1: Initialize weights , solve 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

,

Apply the Lagrange multiplier method to transform the optimization problem into a eigendecomposition problem:

,

in is a diagonal matrix, with diagonal elements/> ,/> For/> The first/> Row vector, /> is the eigenvalue, the optimal projection matrix/> It is from the previous/> The maximum eigenvalue corresponds to /> feature vectors, where /> ;

Step S4.2: Fix the projection matrix , solve for the weight vector/> , then the objective function of LapAWDA becomes

,

,

According to the Cauchy 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, the next round of alternating iteration is performed, 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. The projected image is , and then the nearest neighbor classifier is used to get the identification label.

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

The MNIST dataset is a classic dataset in the field of machine learning, consisting of 60,000 training samples and 10,000 test samples, each of which is a 28 * 28 pixel grayscale handwritten digit picture, as shown in Figure 3. In the experiment, the training set consists of 100 images randomly selected from each type of training set 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 are used for training in the experiment, and the average value of the accuracy of 10 tests on the test set is taken as the evaluation index. The present invention is a method for feature extraction. In order to demonstrate its classification performance on the MNIST dataset, a nearest neighbor classifier is used.

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

In order to verify the effectiveness and superiority of the present invention, five supervised discriminant analysis methods (LDA, LFDA, aPAC, LADA and MDAAWS) and four semi-supervised discriminant analysis methods (SLDA, SMMC, SSDR and SELF) were experimentally compared. Here, the number of nearest neighbors is set to 5, and the regularization term parameters in each method are within the parameter range. Obtained through grid search. Table 1 records the classification accuracy of the present invention and the other 9 comparison methods under different numbers of labels, where the feature dimension 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 the unlabeled data provides favorable information, and with the increase in the number of labeled samples, some supervised discriminant analysis methods lead to a decrease in classification performance due to overfitting, but the semi-supervised discriminant analysis methods do not encounter this phenomenon. Therefore, the introduction of unlabeled data information can improve the generalization ability of the algorithm. The LapAWDA method proposed in the present invention has the highest classification accuracy whether it is on the training data of 10, 20 or 30 labeled data, which is significantly better than other discriminant analysis methods.

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

In order to study the influence 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 with dimensions ranging from 5 to 50. The present invention has achieved the highest accuracy in each dimension, especially when the dimensions are taken as the top 20, the classification performance of the present invention is far superior to other methods. Moreover, with the increase of labeled samples, the classification accuracy of the present invention is also increasing. The above results all show that the present invention can obtain more discriminant information from the training data through the projection matrix in the classification task, while improving the utilization rate of the 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 this application can be stored on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.).

Claims (8)

1. A method for handwritten digit recognition, comprising the following steps: Step S1, the collected samples are normalized to obtain training data, wherein the training data includes labeled data and unlabeled data; Step S2, calculating the intra-class scatter matrix and the inter-class scatter matrix based on the label data in the training data; Step S3, constructing a neighbor graph from the labeled data and the unlabeled data in the training data to calculate the manifold regularization term; Step S4, using the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method, including setting the optimization target of the Laplace adaptive weighted discriminant analysis method to , , in is the intra-class scatter matrix, /> is the inter-class scatter matrix, /> is the projection matrix The L _2,1 norm of , m is the number of features, d is the dimension of the projection space, /> is the manifold regularization term, /> To weigh the parameters, /> is the identity matrix, /> is the number of categories of label information in the training data; the projection matrix is solved by iterative optimization method/> 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 step S3 includes the following steps: Step S3.1: Using training data Construct a neighbor graph to get a neighbor matrix , tag data/> , unlabeled data/> , the number of label data is/> , the number of unlabeled data is/> , neighbor matrix/> is constructed as follows: , in Expressed as/> /> Neighbor set; Step S3.2: Calculate the Laplace matrix in the manifold regularization term , where/> is a diagonal matrix, with diagonal elements/> , the manifold regularization term in the projection space is , in is the _L2 norm,/> Expressed as/> The image in the low-dimensional projected space, /> , . 2. The handwritten digit recognition method according to claim 1, characterized in that the projection matrix is solved by an iterative optimization method and weight vector/> , get the optimal projection matrix, including the steps: Step S4.1: Initialize weights , solve 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 , Apply the Lagrange multiplier method to transform the optimization problem into a eigendecomposition problem: , in is a diagonal matrix, with diagonal elements/> ,/> For/> The first/> Row vector, /> is the eigenvalue, the optimal projection matrix/> It is from the previous/> The maximum eigenvalue corresponds to /> feature vectors, where /> ; Step S4.2: Fix the projection matrix , solve for the weight vector/> , then the objective function of LapAWDA becomes , , According to the Cauchy 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, the next round of alternating iteration is performed, that is, /> , fixed projection matrix/> , update the weight vector according to step S4.2/> , repeat step S4.3 until the stop condition is met to obtain the optimal projection matrix/> . 3. The handwritten digit recognition method according to claim 2, characterized in that the stopping condition in step S4.3 is . 4. The handwritten digit recognition method according to claim 1, characterized in that the intra-class scatter matrix The calculation is as follows: , in Indicates the first/> The first in the category/> samples, /> Indicates the first/> The mean vector of the class; The between-class scatter matrix The calculation is as follows: . 5. A handwritten digit recognition device, comprising: Preprocessing module: normalize the collected samples to obtain training data, which includes labeled data and unlabeled data; The first calculation module: calculates the intra-class scatter matrix and the inter-class scatter matrix based on the label data in the training data; The second computing 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 the training data to learn the optimal projection matrix through the Laplace adaptive weighted discriminant analysis method, including setting the optimization target of the Laplace adaptive weighted discriminant analysis method to , , in is the intra-class scatter matrix, /> is the inter-class scatter matrix, /> is the projection matrix The L _2,1 norm of , m is the number of features, d is the dimension of the projection space, /> is the manifold regularization term, /> To weigh the parameters, /> is the identity matrix, /> is the number of categories of label information in the training data; the projection matrix is solved by iterative optimization method/> and weight vector/> , get the optimal projection matrix; Recognition module: normalize the samples 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 second calculation module calculates the manifold regularization term including: Using training data Construct the neighbor graph to get the neighbor matrix/> , tag data/> , unlabeled data/> , the number of label data is/> , the number of unlabeled data is/> , neighbor matrix/> is constructed as follows: , in Expressed as/> /> Neighbor set; Compute the Laplacian matrix in the manifold regularization term , where/> is a diagonal matrix with diagonal elements , the manifold regularization term in the projection space is , in is the _L2 norm,/> Expressed as/> The image in the low-dimensional projected space, /> , . 6. The handwritten digit recognition device according to claim 5, characterized in that the optimal projection matrix solving module uses an iterative optimization method to solve the projection matrix and weight vector/> , get the optimal projection matrix, including the steps: Initialize weights , solve 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 , Apply the Lagrange multiplier method to transform the optimization problem into a eigendecomposition problem: , in is a diagonal matrix, with diagonal elements/> ,/> For/> The first/> Row vector, /> is the eigenvalue, the optimal projection matrix/> It is from the previous/> The maximum eigenvalue corresponds to /> feature vectors, where /> ; Fixed projection matrix , solve for the weight vector/> , then the objective function of LapAWDA becomes , , According to the Cauchy inequality, the solution of the weight vector is ; Update the weight vector , continue to solve the projection matrix/> ; After obtaining the optimal projection matrix of this round, the next round of alternating iteration is performed, that is, /> , fixed projection matrix/> , and then update the weight vector/> , repeatedly solve the projection matrix/> Until the stop condition is met to obtain the optimal projection matrix/> . 7. The handwritten digit recognition device according to claim 6, characterized in that the stopping condition is . 8. A computer storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for handwritten digit recognition according to any one of claims 1 to 4 is implemented.