Dual relaxation image classification method based on a width learning system

Abstract

The application provides a double relaxation image classification method based on a width learning system, and steps are as follows: firstly, a feature data set and a corresponding class label matrix are acquired, and the feature data set generates width conversion features through a standard width learning network; secondly, a double relaxation technique and a graph regularization technique are introduced, and a double relaxation image classification optimization objective function based on the width conversion features is constructed; finally, the double relaxation image classification optimization objective function is solved by using iterative optimization, a classification result is obtained, and the classification result is evaluated. The manifold regularization technique is applied to the width learning network, and a double relaxation method is used to obtain greater freedom, so that the data geometric structure is mined, and the learning of the intra-class similarity realizes the relaxed regression of the target. The application has the characteristics of higher classification precision, relatively less training time, higher model flexibility and the like, and the introduction of the double relaxation method makes the model have stronger discrimination ability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of computer vision, and relates to an image recognition classification method, in particular to a double relaxation image classification method based on a width learning system. BACKGROUND

[0002] Multi-class recognition task is one of the most key applications in the field of artificial intelligence. The processing method of deep neural network is to improve the recognition accuracy by deepening the network layers. However, a network that is too deep needs to rely on the gradient descent of back propagation when training a large number of weight parameters, which consumes a large amount of computing resources and time, and is easy to fall into the trap of local optimal value, resulting in gradient disappearance and affecting the efficiency of the algorithm. Therefore, Chen et al. proposed a lightweight neural network, a width learning network (BLS). The flattened network architecture avoids the above problems caused by excessive increase of network layers in depth. Unlike deep neural networks, BLS is not constructed based on a single hidden layer neural network, but expands the number of nodes horizontally to enhance the feature extraction capability to obtain better features. By increasing the neurons, it can achieve even better performance than deep neural networks.

[0003] However, the width learning network (BLS) as a lightweight neural network, although it realizes the effect of fewer parameters and shorter training time compared with deep neural networks, and avoids the above problems caused by excessive increase of network layers in depth. But the width learning network still has the following shortcomings: (1) The width learning network BLS uses strict binary label annotation, which strictly fixes the distance between different classes as The regression target is not flexible enough, the flexibility of the model is low, and it is difficult to find the best classification interval. (2) The width learning network BLS does not make good use of the geometric properties of data, ignores the underlying structure of data, and thus cannot learn the similarity between classes well. (3) The use of a single transformation matrix in the BLS based on graph regularization limits the recognition ability of the model in capturing the underlying geometric structure information. (4) The projection matrix learned by the width learning network BLS cannot accurately project the image features into the target space, resulting in weak discrimination ability.

[0004] Due to the strict binary label restriction of BLS, the flexibility of the model is seriously hindered, and there is overfitting. Although the addition of graph regularization can explore the potential geometric structure information of data and enhance the performance of the model, the use of a single conversion matrix to preserve the local structure of data is not flexible enough and cannot learn a better margin. SUMMARY

[0005] In view of the deficiencies in the prior art, the present application provides a double relaxation image classification method based on a width learning system, which provides greater freedom for BLS based on graph regularization, solves the problem that a single conversion matrix is difficult to simultaneously project samples into a target space and expand the inter-class distance and reduce the intra-class distance, and improves the performance of the model in the image classification task.

[0006] The technical solution of the present application is implemented as follows:

[0007] A double relaxation image classification method based on a width learning system applies manifold regularization technology to a width learning network and adopts a double relaxation method to obtain greater freedom, thereby realizing the mining of data geometric structure and the learning of intra-class similarity to achieve target relaxation regression.

[0008] Step one: obtain a feature data set and a corresponding class label matrix, and generate width conversion features through a standard width learning network;

[0009] Step two: introduce double relaxation technology and graph regularization technology, and construct a double relaxation image classification optimization objective function based on width conversion features;

[0010] Step three: solve the double relaxation image classification optimization objective function by iterative optimization to obtain a classification result, and evaluate the classification result.

[0011] The generation method of the width conversion features is as follows:

[0012] S1.1, randomly generate weights and biases Use a linear transformation mapping function φ i (·) to generate N g groups of random mapping features from input data X, and the i-th group of mapping features is:

[0013]

[0014] Combine all the mapping features to obtain:

[0015] S1.2, input the mapping features to the enhancement layer, and input randomly generated weights and biases to the enhancement layer through an activation function ξ i = tanh(·) to obtain l groups of enhanced nodes, and the j-th group of enhanced nodes is represented as:

[0016]

[0017] Combine all the enhanced nodes to obtain:

[0018] S1.3, combine all the mapping features and enhanced nodes to obtain the final width conversion feature A:

[0019]

[0020] The double relaxation image classification optimization objective function based on the width conversion feature is:

[0021]

[0022] Wherein, P is a regression index, A represents the width conversion feature matrix of the training sample, λ1, λ2 both represent regularization parameters, Q is an additional introduced transformation matrix, W represents a projection matrix, ||·||F represents the Frobenius norm of the matrix, y F represents the true class index of the i'th sample x i' , i' represents the i'th row y i' column item of P, P i'j' represents the i'th row j'th column item of P, a i' represents the i'th row vector of the conversion feature matrix, a j' represents the j'th column vector of the conversion feature matrix, M i'j' represents the i'th row j'th column item of M, and T represents transposition.

[0023] The method for solving the double relaxation image classification optimization objective function by iterative optimization is:

[0024] Rewrite the double relaxation image classification optimization objective function based on the width conversion feature as the objective function L(W, P, Q, S):

[0025]

[0026] Wherein, tr(·) is a trace operator representing the sum of the diagonal elements of a matrix, D represents a diagonal matrix calculated, and M represents the similarity weight between samples;

[0027] S3.1, fix W, Q, S, and update the label matrix P:

[0028] If W, Q and S are fixed, the learned label matrix P can be solved by the following formula:

[0029]

[0030] Wherein, F' = AW;

[0031] S3.2, fix W, P, Q, and update S: ​

[0032] At this time, the target function L(S) is:

[0033]

[0034] The derivative of L(S) with respect to S is equal to 0, and the following equation is obtained:

[0035]

[0036] Wherein, sigma is a constant greater than 0;

[0037] S3.3, fix W, P, S, update Q:

[0038] At this time, the target function L(Q) is:

[0039]

[0040] The derivative of L(Q) with respect to Q is equal to 0, and the following equation is obtained:

[0041]

[0042] S3.4, fix P, Q, S, update W:

[0043] At this time, the target function L(W) is:

[0044]

[0045] The derivative of L(W) with respect to W is equal to 0, and the following equation is obtained:

[0046]

[0047] S3.5, iterate the above process to obtain the optimal solution of P, S, Q and W.

[0048] The termination condition of the iterative optimization solution is:

[0049] (obj (t-1) -obj (t) )≤ε0;

[0050] Wherein, obj (t-1) represents the target function value of t-1 round iteration, obj (t) represents the target function value of t round iteration, and epsilon0 is a set value.

[0051] Compared with the prior art, the beneficial effects of the present application are:

[0052] 1) The present application takes the width learning network as the main body, needs fewer parameters, the network structure is simpler, enhances the feature extraction ability, and can achieve similar performance with deep neural network in less time.

[0053] 2) The present application adopts double relaxation constraint technology, and simultaneously incorporates two relaxation schemes into graph-based BLS. On the one hand, by learning the label matrix directly from data and imposing interval constraints, higher degrees of freedom are provided. On the other hand, the two matrices in the graph regularization term not only share the responsibility of transformation, but also help to solve the overfitting problem.

[0054] 3) The embedded graph structure adopted by the present application learns more discriminative information by constraining the output weight with graph regularization, further enhances the classification ability, and under the constraint of Frobenius norm, can further impose constraints on the model to prevent model overfitting. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0056] Figure 1 The flowchart of the present application (DRBLS);

[0057] Figure 2 Some picture samples in each database in the experiment: (a) Extended YaleB, (b) CMUPIE, (c) AR, (d) COIL100, (e) Fifteen Scene, (f) MNIST, (g) USPS;

[0058] Figure 3 The data two-dimensional form visualization processing diagram under the t-SNE algorithm: (a) original data, (b) IGBLS transformed data, (c) DRBLS transformed data;

[0059] Figure 4 The visualization of matrix S under different training numbers on different data sets in the experiment: (a) Extended YaleB with 10 train, (b) COIL100 with 10 train, (c) Fifteen Scene with 10 train, (d) USPS with 100 train;

[0060] Figure 5 The recognition rate and target function value of DRBLS on the handwritten digital database and the curve of the iteration process: (a) MNIST with 800 train, (b) USPS with 250 train;

[0061] Figure 6 DRBLS recognition rates for different parameter settings in the handwritten digit database: (a) MNIST, (b) USPS. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort are within the protection scope of the present application.

[0063] Standard width learning network algorithm: the width learning network first generates feature nodes from the original feature dataset through a mapping function, expands the feature nodes to generate enhanced nodes, and finally connects all the feature nodes and enhanced nodes to the output layer through output weights. X represents the original feature dataset, φ i (·) represents the mapping function for generating feature nodes, ξ j (·) represents the activation function for generating enhanced nodes, With represents the randomly generated weights and biases of appropriate dimensions in the generation of feature nodes, With represents the randomly generated weights and biases of appropriate dimensions in the generation of enhanced nodes.

[0064] Generating width conversion features A: randomly generating weights of appropriate dimensions and biases Using a linear transformation mapping function φ i (·) generates N g groups of random mapping features from the input data X, and the i-th group of mapping features is:

[0065]

[0066] Combining all the mapping features, we get:

[0067] Input the mapping features into the enhanced layer, and input randomly generated weights and biases through the activation function ξ j = tanh(·) to obtain l groups of enhanced nodes, and the j-th group of enhanced nodes is represented as:

[0068]

[0069] Combining all the enhanced nodes, we get:

[0070] Combining all the mapping features and enhanced nodes, the final width conversion feature A is obtained:

[0071]

[0072] Connecting the width conversion feature A to the output, the optimization problem is specifically represented as:

[0073]

[0074] The introduction of graph regularization can be used to better learn the geometric structure of the data and better learn the intra-class similarity. By using the graph regularization constraint to learn more discriminative information, the classification ability is further enhanced, and the general form of the GBLS objective function can be described as:

[0075]

[0076] where E G represents the graph regularization term, and λ1, λ2 are regularization parameters. E G Different methods can be introduced to construct it. The graph regularization BLS model can still effectively extract feature nodes and enhanced nodes from large-scale data by establishing features on the basis of the standard BLS, and combine the generated width conversion features to ensure excellent feature extraction ability and maintain data effectiveness.

[0077] In order to provide more degrees of freedom for the label matrix and avoid the problem of overfitting, the regression target is learned directly from the data while constraining the distance between the true class and the false class. Therefore, the objective function of BLS is modified as:

[0078]

[0079] where P represents the learned regression target, y i' represents the true class index of the i'th sample x i' , represents the i'th row and y i' column term of P, and P i'j' represents the i'th row and j'th column term of P. The constraint is introduced to ensure that the distance between the true class and the false class is greater than a fixed constant 1. Therefore, the discriminative ability of the model is satisfied.

[0080] Moreover, the projection matrix W in equation (6) has two important responsibilities. The first is that it should project the samples to the target space. The other is to expand the distance between different classes and make the distance between the same class samples in the target space closer. However, it is difficult for a single transformation matrix to perform both tasks. Therefore, an additional transformation matrix Q is introduced to share part of the responsibility of W, which is obtained as:

[0081]

[0082] M i'j' is defined as:

[0083]

[0084] where σ denotes the thermal parameter, a i' and a j' is the i'th row and j'th column of the transformed feature matrix. Obviously, the structure of the two transformation matrices W and Q should be similar. Therefore, we introduce a matrix to capture such a similar structure, and define W = QS. Subsequently, the new objective function of DRBLS is derived as:

[0085]

[0086] Obviously, if the optimal S is the identity matrix, the proposed method is meaningless. But in fact, the value of S is very large, which indicates the necessity of introducing another transformation matrix. Furthermore, in equation (9), we can find that the first and third terms are convex. The convexity of the second term can be easily proved by the following two steps.

[0087] 1) The k'th term of ||W T a i' -Q T a j' || 2 (W T a i'k -Q T a j'k ) 2 is convex, which can be proved by proving that its Hessian matrix is positive semi-definite.

[0088] 2) Since M i'j' ≥ 0, such a term is also convex. Therefore, equation (9) is convex.

[0089] In most cases, the graph regularization technique can explore the potential geometric structure information of the data and enhance the performance of the model, but the graph-based model usually uses a single transformation matrix to preserve the local structure of the data, but this is not flexible enough to learn better margin. And the standard BLS uses the traditional 0-1 label matrix, which greatly limits the freedom of the model, and the label relaxation strategy can change the regression label matrix from the matrix composed of 0 and 1, which can achieve good results, but such a strategy still provides limitations to the target space, which seriously reduces the recognition result. In addition, since the method pursues a larger margin, the overfitting problem exists. Therefore, the double relaxation strategy is adopted to enhance the flexibility of the model and control the interval between classes to provide more degrees of freedom.

[0090] The double relaxation constraint is from two aspects, one is to learn the label of the sample directly from the data and constrain the distance between different classes, and the other is to introduce an additional matrix Q in the graph embedding process, which shares part of the responsibility of W, so that the freedom of the model is greatly improved, and it is beneficial to learn a more appropriate interval and improve the recognition ability of the model. The objective function is:

[0091]

[0092]

[0093] The application proposes a double relaxation image classification method based on a width learning system, which effectively improves the classification effect by combining the above graph regularization constraint and double relaxation technology; as shown in the figure, Figure 1 The specific steps of the method include:

[0094] Step 1: Obtain the feature data set and the corresponding class label matrix, and the feature data set is generated by a standard width learning network to generate width conversion features;

[0095] Step 2: Introduce double relaxation technology and graph regularization technology, and construct a double relaxation image classification optimization objective function based on width conversion features;

[0096] Step 3: Use iterative optimization to solve the double relaxation image classification optimization objective function to obtain the classification result, and evaluate the classification result.

[0097] Rewrite the double relaxation image classification optimization objective function based on the width conversion features as the objective function L(W, P, Q, S):

[0098]

[0099] Wherein, tr(·) is the trace operator representing the sum of the diagonal elements of the matrix, D represents the diagonal matrix, M represents the similarity weight between samples; D i'i'is the element in the i'th row and i'th column of matrix D, D i'i' =∑ i' M i'j' , the optimization procedure is as follows:

[0100] S3.1, fixing W, Q, S, updating the solution label matrix P:

[0101] If W, Q, S are fixed, the learned label matrix P can be solved by the following formula:

[0102]

[0103] Where F'=AW; since formula (12) is a constrained quadratic programming problem, it can be decomposed into n independent sub-problems. That is, formula (12) can be solved row by row. If the index of the true class of the i'th sample x i' is t, there is:

[0104]

[0105] Where, Introducing a new variable to solve formula (13), the j'th item can be calculated as:

[0106]

[0107] Where r j′ ≤0 indicates that the boundary constraint between class i' and class t is satisfied, r j′ >0 indicates that the boundary constraint between class i' and class t is violated. Further, with the regression result F i't , P i't =F i't +η, where η represents a parameter that can be optimized. And for the false class, formula (14) can be decomposed into the following form one by one:

[0108]

[0109] Formula (15) is a single-variable constrained quadratic programming problem, which is easy to solve. Therefore, the optimal result is: P i′j′ =F i′j′ +min(η-r j′ ,0), for each P i′j′ :

[0110]

[0111] According to formula (16), the vector p i′ in formula (13) can be redefined by the parameter η, and we rewrite formula (14) as:

[0112]

[0113] It can be solved by deriving its first derivative f'(η) and setting f'(η) = 0. Thus, the optimal solution is:

[0114]

[0115] where Π(·) denotes an indicator. If f'(r j′ ) > 0 is satisfied, then Π(·) = 1, otherwise Π(·) = 0. Then, Algorithm 1 lists the detailed steps to obtain the optimal row vector p i′ . The optimal result P in (12) can be obtained by combining p i′ .

[0116] S3.2, fix W, P, Q, update S:

[0117] If the variables W, P, Q are given, the objective function L(S) is:

[0118]

[0119] Setting the derivative of L(S) with respect to S equal to 0 gives:

[0120]

[0121] where σ is a small constant greater than 0 to ensure the stability of the solution.

[0122] S3.3, fix W, P, S, update Q:

[0123] Fixing W, P, and S, the objective function L(Q) is:

[0124]

[0125] Setting the derivative of L(Q) with respect to Q equal to 0 gives:

[0126]

[0127] S3.4, fix P, Q, S, update W:

[0128] Fixing P, Q, S, the objective function L(W) is:

[0129]

[0130] Setting the derivative of L(W) with respect to W equal to 0 gives:

[0131]

[0132] S3.5, iterate the above process until the termination condition of model convergence is reached, and obtain the optimal solution of P, S, Q and W.

[0133] The termination condition of the iterative optimization solution is:

[0134] (obj (t-1) -obj (t) )≤ε0 (25)

[0135] Wherein, obj (t-1) represents the objective function value of t-1 round iteration, obj (t) represents the objective function value of t round iteration, and ε0 is a set value.

[0136] The double relaxation image classification method algorithm based on the width learning system is as follows:

[0137] (1) input the original feature X and the corresponding label Y, the number of features S in each group of mapping features N, the number of groups of mapping features N g , the number of enhanced nodes N e , and parameters λ1 and λ2.

[0138] (2) randomly generate

[0139] (3) calculate Then combine all feature nodes to get

[0140] (4) calculate H k = ξ(ZW e + β e ), and the width feature is represented as

[0141] (5) initialize Q = W = (AA T ) -1 (AY T ).

[0142] (6) calculate M and D according to formula (8).

[0143] (7) when not converging, the following operations are performed.

[0144] (8) update P according to algorithm 1 row by row.

[0145] (9) update S according to formula (20).

[0146] (10) update Q according to formula (22).

[0147] (11) update W according to formula (24).

[0148] (12) end and output the projection matrix W.

[0149] Experiments

[0150] The method provided by the present application is used in multiple experiments on different recognition tasks, and is compared with classical methods such as SVM, DLSR, ReLSR, RLR and BLS, and common classification task comparison methods such as LRDLSR, IDLSR, FDLSR, DRC, RBD-DPL, IGBLS, DGBLS, SN-TSL and MDBLS, to verify the effectiveness of the DRBLS method. The ExtendedYaleB database, the CMUPIE database and the AR database are used for face recognition tasks, the COIL100 database is used for object recognition tasks, the FifteenScene database is used for scene recognition tasks, and the MNIST database and the USPS database are used for handwriting recognition tasks. The statistical data of the involved databases are listed in Table 2.

[0151] Table 2 Summary of the used databases

[0152]

[0153] Details of the databases and experimental settings used in the experiment, experimental results of different methods on different recognition tasks, experimental result analysis, convergence research, parameter sensitivity, etc. are introduced. The experiment is carried out on a notebook computer with an Intel-i5-12500H 2.50GHz CPU and 16GB of memory, and the platform is MATLAB2018a.

[0154] Figure 2 For some database instances, (a) is part of the images of the ExtendedYaleB database, (b) is part of the images of the CMUPIE database, (c) is part of the images of the AR dataset, (d) is part of the images of the COLL100 dataset, (e) is part of the images of the FifteenScene dataset, (f) is part of the images of the MNIST dataset, and (g) is part of the images of the USPS dataset.

[0155] Table 3: Experimental results on the ExtendedYaleB database (AVER ± STD%)

[0156]

[0157] Table 4: Experimental results on the CMUPIE database (AVER ± STD%)

[0158]

[0159] Table 5: Experimental results on the AR database (AVER ± STD%)

[0160]

[0161] Table 6: Experimental results on COIL100 database (AVER ± STD%)

[0162]

[0163] Table 7: Experimental results on FifteenScene database (AVER ± STD%)

[0164]

[0165] Table 8: Experimental results of IGBLS and DRBLS on MNIST database

[0166]

[0167] Table 9: Experimental results of IGBLS and DRBLS on USPS database

[0168]

[0169] Tables 2 to 7 demonstrate the excellent performance of the above-mentioned algorithms on three face datasets and scene category dataset, object recognition dataset, and handwritten digit dataset.

[0170] Except for SVM, BLS and DRC, the rest of the comparison methods all use soft labeling method. These methods achieve competitive results, especially on the face recognition task, which demonstrates the effectiveness of the relaxed labeling strategy. However, compared with the methods using ε-pull technique, one reason why DRBLS can achieve better performance is that a more flexible labeling relaxation mechanism is introduced, and the additional constraint term can also guarantee proper margin, which well handles the overfitting problem. Compared with the most popular BLS-based methods DGBLS and MDBLS, IGBLS can achieve better performance, which is about 2% lower. In the experiments of object and scene recognition tasks, this gap is smaller, which proves that graph embedding method can help improve the recognition ability of the model. DRBLS adds a new matrix Q in the graph embedding process, which shares part of the responsibility of the projection matrix W. This matrix provides the model with more degrees of freedom to help the model learn a better margin. This is another reason why DRBLS can achieve the best results. Figure 3 And Figure 4 It is also verified that it is necessary to introduce another transformation matrix in the graph embedding process to learn a better margin. Therefore, the DRBLS algorithm is effective in image classification tasks and can achieve excellent performance.

[0171] The experimental results of the method (DRBLS) of the present application on three face datasets-Extended YaleB dataset (Table 3), CMU PIE dataset (Table 4), and AR dataset (Table 5) show that DRBLS can achieve the best classification accuracy in most cases, especially in the case of a small amount of training data. The training results on the COIL20 object recognition dataset (Table 6) show that DRBLS can achieve the best classification accuracy in most cases, but the recognition accuracy on this database is difficult to improve greatly with the increase of the number of training samples. However, the performance is good when the training number is 25, which shows that the method of the present application is qualified, and DRBLS can still achieve the best performance in the object recognition task with a small amount of training data. The experimental results on the Fifteen Scene database (Table 7) which is a popular and representative database in the scene recognition task show that DRBLS can achieve the best classification results when the training number is 10 and 20. In other cases, although MDBLS is the most effective method, DRBLS can still achieve impressive performance with a gap of less than 0.1%, which also reflects the strong recognition ability of the method in the case of a small amount of training samples.

[0172] Tables 8 and 9 reflect the results of handwritten digit recognition to explore the performance improvement of DRBLS compared with IGBLS. Tables 8 and 9 show in detail the experimental results of two handwritten digit databases MNIST and USPS under different training sample numbers, including parameter settings, training time, and recognition accuracy. For network parameters, there is little difference in the total number of nodes between the two methods. As for the regularization parameter, the parameter in DRBLS is relatively larger than that in IGBLS, which shows the importance of the two design terms. In terms of training time, the training time of DRBLS is slightly longer than that of IGBLS. The reasons are as follows: first, IGBLS does not have an iterative process, and only one pseudo-inverse solution is needed to obtain the optimal solution; second, DRBLS is an iterative process, and solving the Sylvester equation is a relatively time-consuming process; however, their training times remain in the same order of magnitude, which shows that the designed optimization algorithm in DRBLS is efficient. In terms of recognition accuracy, DRBLS is superior to IGBLS, especially in the case of a small amount of training samples. Therefore, through the above analysis, it can be concluded that DRBLS has made great improvement compared with IGBLS, and the efficiency and effectiveness of DRBLS have been successfully verified.

[0173] Figure 3The raw data and the transformed data of IGBLS and DRBLS are visualized in two dimensions using t-SNE algorithm, which intuitively shows the impressive performance of DRBLS. The Extended Yale B database (containing 15 columns) is used in the experiment and all samples are visualized. As shown in Fig. Figure 3 , we can see that the layout of the raw data is very chaotic and irregular. After the data is processed and transformed by IGBLS, it becomes separable. However, the boundaries of some classes are still very fuzzy. From Figure 3 (c), we can see that the transformed data of DRBLS is highly separable. Compared with the transformed data of IGBLS, the data sharing the same label is closer and the interval between different classes is larger, indicating that it is effective to combine the two relaxation ideas into graph-based BLS.

[0174] DRBLS realizes double relaxation by directly learning the sample labels from the data, constraining the distance between different classes, and introducing an additional matrix Q to share part of the responsibility of W in the graph embedding process. By introducing a new matrix S and S can successfully capture the similar structure between the two matrices W and Q. While Figure 4 Further visualization of S in experiments on several databases can intuitively find that S is not an identity matrix but a block diagonal matrix, indicating that there is a corresponding relationship between the elements in matrices W and Q. Therefore, it can be ensured that the samples belonging to the same class can be as close as possible because of such a corresponding relationship. In other words, part of the responsibility of W can be shared by Q, so that a better boundary can be learned, which proves the effectiveness of such a similar structure without doubt.

[0175] Figure 5 The curves of the recognition rate and the objective function value of DRBLS and the iteration process on two handwritten digit databases (MNIST, USPS) are shown. Obviously, DRBLS has good convergence. The algorithm can converge to a stable value in no more than 30 iterations or even less. The recognition rate can also gradually increase with the increase of the number of iterations until it stabilizes. Therefore, the effectiveness of this method is obvious.

[0176] Figure 6 The recognition rates of DRBLS with various parameter settings on two databases (MNIST and USPS) are shown. In this experiment, it can be noted that there are three network parameters (N s , N g , N e ) and two regularization parameters (λ1, λ2) that need to be adjusted. However, since the network parameters can be determined according to grid search, and it is difficult to demonstrate the sensitivity of the parameters, the focus is on the regularization parameters. The candidate set of the parameters is fixed to {101 ..., 10 -7 , 10 -8}. It can be observed that in achieving the best results, both regularization parameters are chosen in a large range of values, reflecting the importance of both regularization terms. A reasonable candidate set for the two parameters is λ1∈ [10 -5 , 10 -1 ], λ2∈ [10 -5 , 10 1 ]. In other words, the candidate set for λ2is slightly larger than λ1and its values are also larger than λ1in most cases, indicating that the second regularization term plays a more important role in the identification process, from which it can be concluded that it is effective to provide more degrees of freedom for the graph embedding process.

[0177] The above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A dual relaxation image classification method based on a width learning system, characterized by, The manifold regularization technique is applied to the width learning network, and a double relaxation method is used to obtain greater degrees of freedom, so as to mine the geometric structure of data and realize the target relaxation regression of learning of intra-class similarity. The steps are as follows: Step one: obtain a feature data set and a corresponding class label matrix, and the feature data set is generated by a standard width learning network to generate a width conversion feature; Step two: introduce a double relaxation technique and a graph regularization technique, and construct a double relaxation image classification optimization objective function based on the width conversion feature; The double relaxation image classification optimization objective function based on the width conversion feature is: Where P is the regression index, A represents the width-to-feature matrix of the training samples, λ1 and λ2 are both regularization parameters, Q is the additionally introduced transformation matrix, and W represents the projection matrix, ||·|| F Let y denote the Frobenius norm of the matrix. i' Let x represent the i'th sample. i' True class index, This represents the i'th row and yth column of the regression index P. i' Items, P i'j' a represents the i'th row and j'th column of the regression index P. i' Let a represent the i'-th row vector of the transformed feature matrix. j' M represents the j'-th column vector of the transformed feature matrix. i'j' Let M represent the i'th row and j'th column of the similarity weights M between samples, and T denote the transpose; Step three: the double relaxation image classification optimization objective function is solved by iterative optimization, and the classification result is obtained and evaluated; The method for solving the double relaxation image classification optimization objective function by iterative optimization is: Rewrite the double relaxation image classification optimization objective function based on the width conversion feature as an objective function L(W, P, Q, S): Wherein, tr(·) is a trace operator representing the sum of diagonal elements of a matrix, D represents a diagonal matrix obtained by calculation, and M represents the similarity weight between samples; S3.1, fix W, Q and S, and update the label matrix P; S3.2, fix W, P, Q, and update S; S3.3, fix W, P and S, and update Q; S3.4, fix P, Q and S, and update W: S3.5, iterate the above process to obtain the optimal solution of P, S, Q and W.

2. The dual relaxation image classification method based on a width learning system according to claim 1, characterized in that, The generation method of the width conversion feature is: S1.1, randomly generate weights with bias with linear transformation mapping function φ i (·) from input data X, N g group random mapping features, then the i-th group of mapping features is: Combining all the mapping features together, we get: S1.2, input the mapping features into the enhancement layer, in which the input Randomly generate weights With bias Get l groups of enhancement nodes through the activation function ξj=tanh(·), and the jth group of enhancement nodes is represented as: Combining all the enhanced nodes gives: S1.3, combine all the mapping features and enhanced nodes to obtain the final width conversion feature A:

3. The dual relaxation image classification method based on a width learning system according to claim 1 or 2, characterized in that, If W, Q and S are fixed, the learned label matrix P is solved by the following formula: Wherein, F' = AW; In step S3.2, the objective function L(S) for updating S is fixed W, P and Q: The derivative of L(S) with respect to S is equal to 0: Wherein, σ is a constant greater than 0; In step S3.3, the objective function L(Q) for updating Q is fixed W, P and S: The derivative of L(Q) with respect to Q is equal to 0: In step S3.4, the objective function L(W) for updating W is fixed P, Q and S: The derivative of L(W) with respect to W is equal to 0:

4. The dual relaxation image classification method based on a width learning system according to claim 3, characterized in that, The termination condition of the iterative optimization solution is: (obj (t-1) -obj (t) )≤ε0; wherein, obj (t-1) represents the objective function value of the t-1th iteration, obj (t) represents the objective function value of the tth iteration, and ε0is a set value.

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