Small-sample target recognition method based on forward feature compatibility

Abstract

The embodiments of the present application relate to the field of image processing technology, and in particular to a small-sample target recognition method based on forward feature compatibility, comprising: constructing a learning task for a generalized small-sample learning algorithm; constructing a forward-category-compatible prototype vector that maximizes the robustness of a linear discriminant classifier based on Mahalanobis distance; constructing a deep neural network that can map samples to latent features that conform to a distribution that maximizes Mahalanobis distance; training a classification subnetwork; and recognizing target images. The embodiments of the present application provide a small-sample target recognition method based on forward feature compatibility, which addresses the problems of weak classifier robustness due to limited labeled samples in the test phase, low classification accuracy when samples are unbalanced, and inability to classify newly added categories, which exist in automatic target recognition methods.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of image processing technology, and in particular to a small sample target recognition method based on forward feature compatibility. Background Art

[0002] In object recognition tasks, most objects are complex, making them challenging and inefficient for the human eye to recognize. Therefore, automatic object recognition has received widespread attention in recent years, and various methods have been proposed to address this problem.

[0003] Currently, the main idea behind automatic target recognition is to extract features from target images by building deep neural networks, and then classify these features through various methods to achieve automatic target recognition. For example, multi-view deep learning frameworks are used to train pose-sensitive images; complex convolutional neural networks (CNNs) are used to train image models with the help of phase information; calibrated autoencoders and mean contour regularization are used to extract target features from high-resolution range profiles (HRRPs); and convolutional neural networks and recurrent neural networks are used to model spatial and temporal correlations, respectively.

[0004] However, existing automatic target recognition methods often suffer from the problem of overfitting due to limited labeled samples. Traditional small-sample learning algorithms also have problems such as inability to classify basic classes during the testing phase, weak classifier robustness, and low classification accuracy when sample categories are unbalanced. Summary of the Invention

[0005] An embodiment of the present application provides a small sample target recognition method based on forward feature compatibility, which solves the problems existing in automatic target recognition methods, such as weak classifier robustness caused by limited labeled samples in the test phase, low classification accuracy when samples are unbalanced, and inability to classify newly added categories.

[0006] To solve the above technical problems, an embodiment of the present application provides a small-sample target recognition method based on forward feature compatibility, including: constructing a learning task of a generalized small-sample learning algorithm; constructing a limit of a forward category-compatible prototype vector for classifier robustness; constructing a deep neural network for mapping samples into latent features that conform to a maximized Mahalanobis distance distribution; training a classification subnetwork; and identifying target image data based on the deep neural network and the trained classification subnetwork.

[0007] In some exemplary embodiments, the construction of the limit of the forward category-compatible prototype vector of the classifier robustness includes: proposing an assumption about a p-dimensional random variable and its label distribution; regularizing the p-dimensional random variable, and proposing an assumption about the processed p-dimensional random variable and its label distribution for the processed p-dimensional random variable; defining adversarial samples of ordinary samples of different categories on the decision boundary, using Mahalanobis distance to describe the expectation of the distance between ordinary samples and adversarial samples, and using the expectation to measure the local robustness of the classifier; defining an approximate value of the local robustness; calculating the upper bound of the approximate value of the local robustness; constructing a forward compatible class-level prototype vector that meets the upper bound, and obtaining the limit of the forward category-compatible prototype vector of the classifier robustness.

[0008] In some exemplary embodiments, the adversarial samples of ordinary samples of different categories on the decision boundary are defined as follows:

[0009] y(x (i) )=i,y(x * (i,j) )=j

[0010] Among them, x (i) is a normal sample, x * (i,j) is an adversarial sample on the decision boundary, y(.) represents the prediction result of the predictor, and i and j are the two set Gaussian components.

[0011] In some exemplary embodiments, the adversarial samples of ordinary samples of different categories on the decision boundary are defined as follows:

[0012] y(x (i) )=j,y(x * (i,j) )=i

[0013] Among them, x (i) is a normal sample, x * (i,j) is an adversarial sample on the decision boundary, y(.) represents the prediction result of the predictor, and i and j are the two set Gaussian components.

[0014] In some exemplary embodiments, the hypothesis about the p-dimensional random variable and its label distribution is as shown in the following formula:

[0015]

[0016] Assume i∈[L] in formula (1), And each Gaussian distribution has the same covariance matrix Σ;

[0017] The hypothesis about the processed p-dimensional random variable and its label distribution is proposed for the processed p-dimensional random variable, as shown in the following formula:

[0018]

[0019] Assume i∈[L] in formula (2), and

[0020] In some exemplary embodiments, the Mahalanobis distance is used to describe the expectation of the distance between the common sample and the adversarial sample, as shown in the following formula:

[0021]

[0022] in, Φ(.) is the normal cumulative distribution function.

[0023] In some exemplary embodiments, before adopting the expectation to measure the local robustness of the classifier, the method includes: obtaining a partial derivative of the expectation with respect to the Mahalanobis distance;

[0024] The partial derivative of the expectation with respect to the Mahalanobis distance is shown below:

[0025]

[0026] The local robustness of the classifier is measured by the expectation, as shown in the following formula:

[0027]

[0028] Among them, LB is the local robustness of the classifier, is the expectation of the distance between normal samples and adversarial samples,

[0029] Φ(.) is the normal cumulative distribution function.

[0030] In some exemplary embodiments, the learning task of constructing a generalized small sample learning algorithm includes: sampling samples in a support set in a test task; wherein the support set in each test task includes K categories, and each category contains N samples; sampling samples in a query set in the test task; wherein the query set in each test task includes K categories, and each category of samples in the query set can be sampled according to a uniform distribution sampling procedure or a Dirichlet distribution sampling procedure.

[0031] In some exemplary embodiments, the construction is used to map samples into a deep neural network with latent features that conform to the maximized Mahalanobis distance distribution, including: defining a loss function of the deep neural network; minimizing the loss function on the training data of the deep neural network to obtain the optimal parameters of the deep neural network model.

[0032] In some exemplary embodiments, the training of the classification subnetwork includes: defining a loss function in a test phase; and minimizing the loss function in the test phase on test data in the test phase to obtain optimal parameters of the classification subnetwork.

[0033] The technical solution provided by the embodiments of the present application has at least the following advantages:

[0034] The embodiments of the present application aim at the problems existing in traditional automatic target recognition methods, such as limited labeled samples, inability to classify basic class samples in the test phase, weak classifier robustness, and low classification accuracy when sample categories are unbalanced. The embodiments of the present application provide a small sample target recognition method based on forward feature compatibility. The present application can solve the problem of limited labeled samples and avoid the possible overfitting problem. The present application belongs to a generalized small sample learning algorithm. By constructing a forward compatible class-level prototype vector, the present application solves the problem that traditional small sample learning algorithms cannot classify basic classes in the test phase. The present application is the first method to use an adversarial perspective to achieve forward compatible training, and makes a theoretical guarantee for the maximum robustness of the MM-LDA classifier, ensuring that the MM-LDA classifier has the maximum robustness. The present application introduces the maximum mutual information loss expanded by α divergence. It can solve the problem of low classification accuracy of the classifier when the test data query set distribution is non-uniform. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] One or more embodiments are exemplarily described by the pictures in the corresponding drawings. These exemplifications do not constitute limitations on the embodiments. Unless otherwise stated, the pictures in the drawings do not constitute proportional limitations.

[0036] Figure 1 A flowchart of a small sample target recognition method based on forward feature compatibility provided in one embodiment of the present application;

[0037] Figure 2 A schematic diagram of a process for constructing a generalized small sample learning algorithm learning task provided in one embodiment of the present application;

[0038] Figure 3 A flowchart of constructing a forward-compatible prototype vector that satisfies the maximum robustness of the MM-LDA classifier is provided in one embodiment of the present application. DETAILED DESCRIPTION

[0039] As can be seen from the background technology, the current existing automatic target recognition methods usually have the problem of overfitting due to limited labeled samples, and traditional small sample learning algorithms also have the problems of being unable to classify basic classes during the testing phase, weak classifier robustness, and low classification accuracy when the sample categories are unbalanced.

[0040] As mentioned earlier, automatic target recognition can currently be achieved by using methods such as convolutional neural networks and recurrent neural networks to model spatial and temporal correlations, respectively. Many of these methods utilize transfer learning, which transfers source domain knowledge acquired through training models to the target domain, thereby reducing the number of target domain SAR samples required. For example, these methods utilize bottom convolutional layers in SAR image classification to leverage transferable knowledge; leverage the transfer capabilities of CNN networks across simulated datasets and real SAR image sets; learn domain-independent embedding spaces from the electro-optical (EO) domain to the SAR domain; and learn connection-independent attention modules to selectively transfer features shared by EO and SAR domain samples.

[0041] Meta-learning methods have also been applied to small-shot SAR image recognition. These include hybrid inference networks combining inductive and transductive methods; methods using the bulldozer distance instead of Euclidean space; and attribute-guided multi-scale prototype networks combined with subband decomposition. However, these methods, which build deep neural networks to extract image features and then classify them using various methods, often suffer from overfitting due to the lack of a large number of labeled target samples. Transfer learning and meta-learning have primarily focused on small-shot learning for target recognition. The test phase uses samples from new classes, not the base class, making them impractical in real-world recognition scenarios. Furthermore, while the traditional backward-compatible small-shot learning training paradigm is compatible with older models and prevents forgetting, it shifts the burden of overcoming forgetting to the next generation model. If the previous generation model performs poorly, the next generation model's performance will be weakened.

[0042] In order to solve the above technical problems, the embodiment of the present application provides a small sample target recognition method based on forward feature compatibility, including: constructing a learning task of a generalized small sample learning algorithm; constructing a limit of a forward category-compatible prototype vector for classifier robustness; constructing a deep neural network for mapping samples to latent features that conform to the maximized Mahalanobis distance distribution; training a classification subnetwork; and identifying target image data based on the deep neural network and the trained classification subnetwork. The present application solves the problem that traditional small sample learning algorithms cannot classify basic classes in the test phase by constructing forward compatible class-level prototype vectors; the present application is the first method to use an adversarial perspective to achieve forward compatible training, and makes a theoretical guarantee for the maximum robustness of the MM-LDA classifier, ensuring that the MM-LDA classifier has the maximum robustness; the present application introduces the maximum mutual information loss expanded by α divergence. It can solve the problem of low classification accuracy of the classifier when the test data query set distribution is non-uniform.

[0043] The following detailed description of the various embodiments of the present application is provided in conjunction with the accompanying drawings. However, those skilled in the art will appreciate that many technical details are provided in the various embodiments of the present application to facilitate a better understanding of the present application. However, even without these technical details and the various variations and modifications based on the following embodiments, the technical solutions claimed in the present application can still be implemented.

[0044] refer to Figure 1 The present invention provides a small sample target recognition method based on forward feature compatibility, including the following steps:

[0045] Step S1: Construct a learning task for a generalized small sample learning algorithm.

[0046] Step S2: Construct the limit of the classifier robustness forward category compatible prototype vector.

[0047] Step S3: construct a deep neural network for mapping samples into latent features that conform to the maximized Mahalanobis distance distribution.

[0048] Step S4: training the classification sub-network.

[0049] Step S5: Identify target image data based on the deep neural network and the trained classification subnetwork.

[0050] It should be noted that the limit value of the forward category compatible prototype vector for classifier robustness constructed in step S2 is specifically the forward category compatible prototype vector with the maximum robustness of the MM-LDA classifier.

[0051] The small sample target recognition method based on forward feature compatibility provided by the embodiment of the present application first constructs a learning task of the generalized small sample learning algorithm (GFSL) for target recognition. Reconstruct the forward class compatible prototype vector that satisfies the maximum classification robustness of Mahalanobis distance based linear discriminant classifier (MM-LDA) Retraining can map the samples into a deep neural network (MM-LDA Network) θ that conforms to the latent feature z of the maximized Mahalanobis distance distribution, and then use the knowledge preservation technology to maximize the mutual information loss after α divergence expansion. The classification subnetwork φ is trained on the network θ, and finally the target image is classified on the network θ and the classification subnetwork φ.

[0052] The embodiment of the present application provides a small sample target recognition method based on forward feature compatibility, which can solve the problem of limited labeled samples and avoid the possible overfitting problem. In addition, the present application belongs to a generalized small sample learning algorithm. By constructing a forward compatible class-level prototype vector, it solves the problem that the traditional small sample learning algorithm cannot classify the basic class in the test phase. Moreover, the present application is the first method to use an adversarial perspective to achieve forward compatible training, and makes a theoretical guarantee for the maximum robustness of the MM-LDA classifier, ensuring that the MM-LDA classifier has the greatest robustness. Finally, the present application introduces the maximum mutual information loss expanded by α divergence. It can solve the problem of low classification accuracy of the classifier when the test data query set distribution is non-uniform.

[0053] In some embodiments, in step S1, a learning task of a generalized small sample learning algorithm is constructed, and the learning task (test task) is The specific steps include:

[0054] Step S101: Sampling test task The samples in the support set S in each task contain K categories, and each category contains N samples. test In the algorithm, K categories are randomly selected first, and then N samples are randomly selected under each category.

[0055] As an example, in the test data D test In the first step, we select K categories that are the same as the support set S, and let n k =1, The number of samples under each category K is Take the closest p k |Q| integer, and finally randomly select a sample.

[0056] Step S102: Sampling test task The samples in the query set Q in each task contain K categories, and each category of samples in the query set can be sampled according to the uniform distribution procedure ζ Uniform or the Dirichlet distribution sampling procedure ζ Dirichlet Take samples.

[0057] As an example, given the parameters of the Dirichlet distribution a = (a1, ..., a K ), N1,...,N K are K independent Gamma-distributed random variables, where the parameter of the Gamma distribution is a k , that is, N k *Gamma(a k ), and then sample K samples (n1,...,n K ), then calculate The number of samples under each category k is Take the closest p k |Q| integer, and finally randomly select a sample.

[0058] In step S2, the forward category compatible prototype vector with the maximum robustness of the MM-LDA classifier is constructed The specific steps include:

[0059] Step S201: Propose a hypothesis about the distribution of a p-dimensional random variable x and its label y.

[0060] Step S202: normalize the p-dimensional random variable x to Re-propose and its label y distribution assumptions. To simplify the expression without introducing ambiguity, this step will be replaced by the symbol x.

[0061] Step S203: Define common samples x of category i (i) Adversarial example x on the decision boundary * (i,j) , and then use the Mahalanobis distance Δ i,j Description x (i) and x * (i,j) Distance d (i,j) Expectations use Measures the local robustness LB of the LDA classifier.

[0062] Step S204: Define the approximate value of LB

[0063] Step S205: Calculate The upper bound of .

[0064] Step S206: Construct The upper bound of the forward-compatible class-level prototype vector

[0065] As an example, the specific implementation process of step S2 is:

[0066] Step S201: Propose a hypothesis about the distribution of the p-dimensional random variable x and its label y, as shown in the following formula (1).

[0067]

[0068] Assume that i∈[L], L is the total number of categories. And each Gaussian distribution has the same covariance matrix Σ.

[0069] Step S202: normalize the p-dimensional random variable x to Q is a lower triangular matrix, Σ=QQ T , and Σ is assumed to be a non-singular matrix with no generalization loss, and then The assumption of its label y distribution is shown in the following formula (2):

[0070]

[0071] Assume that i∈[L], L is the total number of categories, and From this standard form, the Mahalanobis distance between two Gaussian components i, j can be defined as In the next step, we assume that the input pair (x, y) satisfies the assumption (2). For simplicity of representation and to avoid ambiguity, we use x instead of x in the following steps and use μ i Replace μ i .

[0072] In step S203, the common sample x of category i is defined (i) Adversarial example x on the decision boundary * (i,j) ,Right now or Represents the prediction results of the LDA predictor.

[0073] In some embodiments, the Mahalanobis distance Δ i,j Description x (i) and x * (i,j) Distance d (i,j) Expectations As shown in the following formula (3):

[0074]

[0075] In formula (3), Φ(.) is the normal cumulative distribution function.

[0076] Furthermore, it can be proved that Is with Δ i,j Monotonically increasing.

[0077] In some embodiments, About Δ i,j The partial derivative of is shown in formula (4):

[0078]

[0079] Reuse The local robustness LB of the LDA classifier is measured as shown in the following formula (5):

[0080]

[0081] Step S204: Define the approximate value of LB

[0082] From formula (4), we can see that when Δ i,j >10 o'clock, Then the local robustness can be approximated as:

[0083]

[0084] Step S205: Calculate The upper bound of .

[0085] Specifically, assuming and Then the robustness of the approximation The upper bound of is:

[0086]

[0087] The inequality holds if and only if:

[0088]

[0089] Step S206: Generate a forward-compatible class prototype vector using the constant C, the dimension p of the vector, and the total number of classes L (L≤p+1). Construct a prototype vector that satisfies formula (8).

[0090] initialization Other prototype vectors Here e1 and 0 p are the unit basis vector and zero vector of the p-dimensional space respectively. Assign values ​​to each vector The first j digits (j≤i-1) are Assignment, the i-th position is Assign. Then for each vector according to Assignment. At this point, the best prototype vector is completed 's construction.

[0091] Define the joint probability distribution:

[0092]

[0093] It is the maximum Mahalanobis distance distribution (MMD), because for a given |μ|2, any two Gaussian components have the maximum Mahalanobis distance, that is, when the input distribution is MMD, the LDA classifier has the greatest robustness.

[0094] In step S3, a deep neural network (MM-LDA Network) θ is constructed to map the sample into a latent feature z that conforms to the maximized Mahalanobis distance distribution, specifically including the following steps:

[0095] Step S301: Define the loss function of MM-LDA Network

[0096] Step S302: Minimize the loss on the training data Get the optimal parameters θ of the model * ,φ * .

[0097] Specifically, the loss function of the MM-LDA Network defined in step S01 is:

[0098]

[0099] The loss function is the one-hot label 1 of the training data. y and the predicted value F (θ,φ) The cross entropy of (x).

[0100] In step S302, the loss is minimized on the training set. Get the optimal parameters θ of the model * ,φ * , the training set is (The training set only contains basic classes, and each basic class has enough labeled samples.) Initialize the number of training steps s = 0, and the feature extraction network parameter θ is θ s , the classifier φ on the base class is φ s , p is the dimension of the hidden feature z output by the feature extraction network, input (C, p, L) and use step S2 to generate the prototype vector β is the learning rate,

[0101] For each from the training set Mini-batch Calculate the objective function value Then The parameters are updated in this way. After the parameters are updated, the number of training steps s is increased by 1. After the number of training steps s reaches the specified number of iterations, the optimal model parameters are obtained, as shown in the following formula (11):

[0102]

[0103] In step S4, the classification subnetwork is trained, and the classification subnetwork is set to φ. Specifically, the following steps are included:

[0104] Step S401: Define the loss function for the test phase

[0105] Step S402: Minimize the loss on the test data Get the optimal parameter φ of the classification subnetwork.

[0106] In some embodiments, step S4 utilizes knowledge preservation technology to maximize mutual information loss after α divergence expansion. The classification subnetwork φ is trained on it.

[0107] In step S401, the loss function of the test phase is defined As shown in the following formula:

[0108]

[0109]

[0110] Among them, in formula (13) is the modified transductive mutual information maximization (MTIM) loss, It is to rewrite the MTIM loss using α divergence, is the explicit weight constraint (EWC) loss. δ is equal to 1 when the test task query set is balanced, and 0 otherwise. γ is a parameter used to control the degree of knowledge preservation.

[0111] In the MTIM loss term, here is the cross entropy defined on the support set S. is the query set sample X Q and their corresponding hidden labels Y QThe first term in the mutual information is an empirical estimate of the marginal entropy of the query set prediction labels, which can be marked as The second term is the empirical estimate of the conditional entropy of the predicted label given the query set features, which can be written as λ is a non-negative hyperparameter. When λ=1, It is the standard form of mutual information.

[0112] p i,k =P(Y=k|X=x i ;μ * ,θ);p i,k is the posterior probability of the i-th feature in the query set on category k. k =P(Y Q =k;μ*,θ),P k is the marginal distribution of class k. * is the class prototype vector generated by step S2, θ is the parameter of the network trained by step S3, z i It is the latent feature of the network θ that is fitted to maximize the Mahalanobis distance distribution.

[0113] In rewriting the MTIM loss term using α divergence, is an empirical estimate of the marginal entropy of predicted labels for the query set rewritten using α divergence, It is an empirical estimate of the conditional entropy of the predicted labels given the query set features rewritten using α-divergence. The loss after α-divergence rewriting can be used in the transductive approach to extend the query set samples from a uniform distribution to a non-uniform distribution during the training phase of the test.

[0114] Explicit weight constraints In the term, where φ old is the trained classification sub-network parameter, φ new The knowledge preservation technology uses the parameters of the classification sub-network updated in the testing phase to further improve the generalization ability of the model.

[0115] In step S402, the loss is minimized on the test data Get the optimal parameter φ of the classification sub-network. This step uses the loss function Train the transductive or inductive classification subnetwork φ. The specific training method is:

[0116] For each training data Mission Calculate the objective function value at each epoch Then After training on all epochs, the optimal model parameter φ is obtained.

[0117] Step S5, identifying the target image, specifically includes the following steps:

[0118] Step S501: Construct target image data for testing

[0119] Step S502: Use the deep neural network θ and the classification sub-network φ to identify the target data

[0120] In step S501, construct target data for testing

[0121] First, select L categories, which include both the training set category base category and the test set category novel category. In , the base class is sampled from the validation set of the training data, and the novel class is sampled from the test data. Let n k =1, The number of samples under each category k is Take the closest Finally, randomly select an integer under each category. sample.

[0122] Target image data After the construction is completed, step S502 is executed to use the deep neural network θ and the classification sub-network φ to identify the target image data

[0123] For each target dataset The latent features z are first extracted through the feature extraction network of the deep neural network θ, and then the latent features are classified through the classification sub-network φ, thus completing the recognition of the target image.

[0124] Based on the above technical solutions, the embodiments of the present application aim at the problems existing in traditional automatic target recognition methods, such as limited labeled samples, inability to classify basic class samples in the test phase, weak classifier robustness, and low classification accuracy when sample categories are unbalanced. The embodiments of the present application provide a small sample target recognition method based on forward feature compatibility. The present application can solve the problem of limited labeled samples and avoid the possible overfitting problem. The present application belongs to a generalized small sample learning algorithm. By constructing a forward compatible class-level prototype vector, the present application solves the problem that the traditional small sample learning algorithm cannot classify the basic class in the test phase. The present application is the first method to use an adversarial perspective to achieve forward compatible training, and makes a theoretical guarantee for the maximum robustness of the MM-LDA classifier, ensuring that the MM-LDA classifier has the maximum robustness. The present application introduces the maximum mutual information loss expanded by α divergence. It can solve the problem of low classification accuracy of the classifier when the test data query set distribution is non-uniform.

[0125] Those skilled in the art will appreciate that the above-described embodiments are specific examples for implementing the present application, and that in actual applications, various changes in form and detail may be made thereto without departing from the spirit and scope of the present application. Any person skilled in the art may make changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be subject to the scope defined in the claims.

Claims

1. A small sample target recognition method based on forward feature compatibility, characterized in that: include: Constructing learning tasks for generalized few-shot learning algorithms; Constructing the limit of the prototype vector compatible with the forward category of the classifier robustness; Construct a deep neural network for mapping samples into latent features that conform to the distribution that maximizes the Mahalanobis distance; Train the classification subnetwork; Identifying target image data based on the deep neural network and the trained classification subnetwork; The limit of the prototype vector compatible with the forward category of the constructed classifier robustness includes: Make assumptions about the p-dimensional random variables and their label distributions; performing normalization processing on the p-dimensional random variable, and proposing an assumption about the processed p-dimensional random variable and its label distribution; Define adversarial samples of different categories of common samples on the decision boundary, use Mahalanobis distance to describe the expectation of the distance between common samples and adversarial samples, and use the expectation to measure the local robustness of the classifier; defining an approximate value of said local robustness; Calculating an upper bound on an approximate value of the local robustness; A forward-compatible class-level prototype vector that meets the upper bound is constructed, and a limit value of the forward-class-compatible prototype vector of the classifier robustness is obtained.

2. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The definition of adversarial samples of different categories of ordinary samples on the decision boundary is as follows: in, For ordinary samples, is an adversarial example on the decision boundary, represents the prediction result of the predictor, are the two Gaussian components set respectively.

3. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The definition of adversarial samples of different categories of ordinary samples on the decision boundary is as follows: in, For ordinary samples, is an adversarial example on the decision boundary, represents the prediction result of the predictor, are the two Gaussian components set respectively.

4. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The hypothesis about the p-dimensional random variable and its label distribution is as shown in the following formula: Assume that in formula (1) , and each Gaussian distribution has the same covariance matrix ; The hypothesis about the processed p-dimensional random variable and its label distribution is proposed for the processed p-dimensional random variable, as shown in the following formula: Assume that in formula (2) ,and .

5. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The Mahalanobis distance is used to describe the expectation of the distance between common samples and adversarial samples, as shown in the following formula: in, , is the normal cumulative distribution function.

6. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: Before adopting the expectation to measure the local robustness of the classifier, the method includes: obtaining the partial derivative of the expectation with respect to the Mahalanobis distance; The partial derivative of the expectation with respect to the Mahalanobis distance is shown below: The local robustness of the classifier is measured by the expectation, as shown in the following formula: in, is the local robustness of the classifier, is the expectation of the distance between normal samples and adversarial samples, is the normal cumulative distribution function.

7. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The learning tasks for constructing the generalized small sample learning algorithm include: Sampling samples from the support set of the test task; where the support set of each test task includes K categories, and each category contains N samples; Sampling samples from the query set in the test task; wherein the query set in each test task includes K categories, and each category of samples in the query set can be sampled according to a uniform distribution sampling procedure or a Dirichlet distribution sampling procedure.

8. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The method comprises the following steps: Defining a loss function for the deep neural network; The loss function is minimized on the training data of the deep neural network to obtain optimal parameters of the deep neural network model.

9. The small sample target recognition method based on forward feature compatibility according to claim 1 is characterized in that: The training classification sub-network includes: Define the loss function for the test phase; The loss function of the test phase is minimized on the test data of the test phase to obtain the optimal parameters of the classification subnetwork.

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