Domain adaptation image classification method based on width learning and stochastic sensitivity

Abstract

The application discloses a domain self-adaptive image classification method based on width learning and random sensitivity, comprising the following steps: 1) constructing width model input information; 2) constructing a width network model; 3) introducing an edge distribution alignment loss into the model; 4) introducing a more fine-grained conventional conditional distribution alignment loss into the model; 5) iteratively selecting pseudo labels with high quality, constructing an enhanced conditional distribution alignment loss and introducing the enhanced conditional distribution alignment loss into the model; 6) introducing a popular regularization into the model to explore potential distribution information of samples; 7) introducing random sensitivity into the model to solve the problem of overfitting of the model on source domain samples; and 8) solving model connection weights and obtaining a classification result. The application enables the model to achieve better effects on target domains with different distributions. The application solves the problem of consumption of a large amount of computing resources in a deep domain self-adaptive method to a certain extent, and further realizes more flexible and accurate downstream applications.

Description

Technical Field

[0001] This invention relates to the field of domain adaptation technology, and in particular to a domain-adaptive image classification method based on width learning and random sensitivity. Background Technology

[0002] In machine learning, it's typically assumed that training and test sets are independent and have the same distribution. However, in real-world image classification tasks, the samples used to train and test models often come from different sources, making it difficult to guarantee that the samples have the same distribution. This leads to models that perform well on the training set often performing poorly on the test set. To overcome this problem, the domain adaptation problem in transfer learning has received widespread attention. It is defined as source and target domain samples sharing the same feature space, but with different marginal and conditional distributions. Simultaneously, the labels of the source and target domain samples belong to the same label space, meaning they belong to the same category.

[0003] Furthermore, obtaining labeled training sets is costly for image classification tasks. Therefore, it is desirable to learn sufficient knowledge from richly labeled source domain samples to guide the classification of unlabeled target domain samples with different distributions. Thus, unsupervised domain adaptation has become a key research focus and is also the focus of this method. Unsupervised refers to the fact that only samples are available during target domain training, and their true labels are unavailable. Unsupervised domain adaptation aims to utilize source domain knowledge and existing target domain sample distribution information to train a prediction function that minimizes classification error in the target domain, thereby better performing image classification tasks.

[0004] Existing unsupervised adaptive image classification methods aim to minimize the distributional discrepancy between the source and target domains, thereby enabling better application of knowledge from the source domain to the target domain. With advancements in computer technology, two main types of methods have emerged: 1. Traditional domain adaptive image classification methods. These methods primarily learn a shared feature space to reduce the distributional mismatch between source and target domain samples, for example, by mapping features to a regenerated Hilbert space. 2. Deep learning-based domain adaptive image classification methods. Some of these methods directly minimize the maximum mean error between the source and target domains, while others employ adversarial learning to learn domain-invariant features. Although deep learning-based methods significantly improve accuracy, the large number of parameters in deep learning models necessitates substantial computational resources, requiring improvements in model training and deployment. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings and deficiencies of the prior art and propose a domain-adaptive image classification method based on width learning and stochastic sensitivity. This method can perform domain-adaptive image classification using the special network structure of the width network model. It also introduces various distribution alignment methods and stochastic sensitivity to alleviate the negative transfer that occurs during the domain adaptation process and improve the generalization ability of the width network model. Compared with deep networks, it has fewer parameters, requires less computing resources and training time, and can achieve more flexible and accurate downstream applications.

[0006] To achieve the above objectives, the technical solution provided by this invention is: a domain-adaptive image classification method based on width learning and random sensitivity, comprising the following steps:

[0007] 1) Construct the input data using source domain samples, source domain sample labels, and target domain samples;

[0008] 2) Complete the construction of the feature mapping layer, enhancement layer, and output layer of the wide network model;

[0009] 3) Introduce edge distribution alignment loss into the wide network model to alleviate the decline in model generalization ability caused by the different edge distributions of source domain samples and target domain samples;

[0010] 4) Use an SVM classifier to obtain pseudo-labels for target domain samples, and introduce finer-grained inter-class alignment, i.e., conventional conditional distribution alignment loss, into the wide network model that has already introduced edge distribution alignment loss, thereby further improving its performance in the target domain.

[0011] 5) Considering that the pseudo-labels obtained by SVM are not of high quality, which will reduce the effect of the conditional distribution, high-quality pseudo-labels are selected iteratively to construct an enhanced conditional distribution alignment loss and introduce it into the wide network model that has already introduced the regular conditional distribution alignment loss to alleviate the negative transfer caused by the pseudo-label quality problem.

[0012] 6) After completing the distribution alignment, in order to explore the potential distribution information of the samples and smooth the classification boundary, the popular regularization loss is introduced into the wide network model that has already introduced the enhanced conditional distribution alignment loss, so that the wide network model can better learn the distribution of the samples and improve its accuracy.

[0013] 7) Steps 2) through 6) are all aimed at improving the performance of the wide network model from the perspective of sample distribution. From the perspective of overfitting, in order to solve the problem of overfitting of the wide network model on the source domain samples caused by the unavailability of the true label in the target domain, random sensitivity is introduced into the wide network model that has already introduced manifold regularization loss to improve its generalization ability.

[0014] 8) Based on the losses in steps 2) to 7), use the ridge regression algorithm to solve for the connection weights of the width network model and obtain the classification results.

[0015] Furthermore, in step 1), the input data includes source domain samples, target domain samples, and source domain sample labels, wherein the actual labels of the target domain samples are unavailable;

[0016] Source domain sample set X s Represented as:

[0017]

[0018] In the formula, Represent real numbers, This represents the i-th source domain sample. Each source domain sample has a dimension of 1×d, where d represents the feature dimension of the sample. There are n features in total. s There are n such source domain samples, that is, there are n source domain samples. s indivual;

[0019] Target domain sample set X t Represented as:

[0020]

[0021] In the formula, Let represent the j-th target domain sample. Each target domain sample has a dimension of 1×d, and there are n samples in total. t There are n such target domain samples, that is, there are n target domain samples. t indivual;

[0022] The set of labels corresponding to each source domain sample is the source domain label set Y. s Represented as:

[0023]

[0024] In the formula, C represents the total number of sample categories. This represents the category label corresponding to the i-th source domain sample, and there are n such labels. s One tag;

[0025] The sample X input into the wide network model is represented as:

[0026] X = [X] s ;X t ]

[0027] In the formula,

[0028] The label Y input into the wide network model is represented as:

[0029] Y = [Y s [Zeros]

[0030] In the formula, A matrix of all zeros is used to represent labels indicating that samples in the target domain are unavailable.

[0031] This represents all the labels entered.

[0032] Furthermore, in step 2), the width network model is divided into three layers:

[0033] The first layer is the feature mapping layer, which is responsible for transforming the input samples into feature maps through random weights, biases, and linear activation functions and storing them in the feature nodes.

[0034] The second layer is the enhancement layer, which maps the feature nodes again and stores them in the enhancement nodes through random weights and biases;

[0035] The third layer is the output layer, which merges the feature nodes and enhancement nodes to form full feature nodes that are directly connected to the output layer. Finally, the ridge regression algorithm is used to solve for the connection weights of the width network model.

[0036] The construction process of the width network model is as follows:

[0037] Inputting X into a wide network model, the i'th feature layer node Z, which contains k feature nodes, will then be... i' Represented as:

[0038]

[0039] In the formula, and Let represent the weights and biases of the randomly generated i'-th group of feature layer nodes, where n represents the number of feature node groups, and φ i' Z represents the linear activation function of the i'-th feature layer node, and the combination of all feature nodes. n Represented as:

[0040] Z n =[Z1,Z2,...,Z n ]

[0041] In the formula, n×k represents the total number of feature nodes;

[0042] The j'th group of enhanced nodes H is generated by mapping the feature nodes. j' Represented as:

[0043]

[0044] In the formula, and This represents the weights and biases of the randomly generated j'-th group, where m represents the total number of augmented nodes, and δ... j' Let H represent the nonlinear activation function of the j'-th group of boosting nodes, and let H represent all the boosting nodes. m Represented as:

[0045] H m =[H1,H2,...,H m ]

[0046] In the formula,

[0047] After merging all feature nodes and augmentation nodes, the resulting full feature node A is represented as:

[0048] A = [Z] n |H m ]

[0049] In the formula, n×k+m represents the total number of feature nodes and augmentation nodes;

[0050] The wide network model processes the input labels as one-hot labels and solves for their connection weights by minimizing the sum of prediction errors. After introducing an L2 regularization term, the loss function is expressed as:

[0051]

[0052] In the formula, α represents the penalty coefficient of the L2 regularization term, and W represents the connection weights of the width network model. Let I represent the empirical matrix, and let I represent the identity matrix.

[0053] Furthermore, in step 3), in order to minimize the difference in edge distribution between the source domain samples and the target domain samples, edge distribution alignment is introduced into the constructed width network model, using X... s and X t The difference in the mean of the predicted outputs is used as a standard to measure the difference in marginal distributions;

[0054] Inputting X into a wide network model, after merging the feature nodes and augmentation nodes, the full feature node A of X is expressed as:

[0055]

[0056] In the formula, This represents the transpose of the matrix, where r represents the total number of samples in the source and target domains, i.e., n. s +n t ,a(x r ) represents the full feature layer node corresponding to the r-th sample;

[0057] The predicted output ψ of the r-th sample r Represented as:

[0058] ψ r =a(x r W

[0059] Introducing edge distribution alignment into the wide network model, its loss term Represented as:

[0060]

[0061] This loss item Rewritten as:

[0062]

[0063] In the formula, Tr represents the trace of the matrix, and the matrix... The calculation method is as follows:

[0064]

[0065] In the formula, Represents the source domain set, This represents a set of target domains for which actual labels are unavailable. for For any element x μ and x γ Represents any sample.

[0066] Furthermore, in step 4), in order to improve the conditional distribution alignment effect, a finer-grained conventional conditional distribution alignment is introduced into the wide network model that has already introduced edge distribution alignment loss. To calculate the conventional conditional distribution alignment loss, an SVM classifier is first used to obtain the target domain sample pseudo-label set.

[0067] The set of pseudo-labels corresponding to each target domain sample is the target domain pseudo-label set. Represented as:

[0068]

[0069] In the formula, This represents the category label corresponding to the j-th target domain sample, and there are n categories in total. t One tag;

[0070] The difference in the mean of the predicted outputs of samples belonging to the same category in the source and target domains is used as a measure of conditional distribution difference; therefore, the conventional conditional distribution alignment loss term... Represented as:

[0071]

[0072] In the formula, This represents the sample set in the source domain whose true label is category c. This represents the sample set in the target domain whose pseudo-label is category c. This indicates the number of samples in the source domain that belong to class c. This indicates the number of samples in the target domain that belong to category c. This represents the j-th target domain sample. pseudo-tags;

[0073] This loss item Rewritten as:

[0074]

[0075] In the formula, the matrix The calculation method is as follows:

[0076]

[0077] In the formula, express Any element in the set.

[0078] Furthermore, in step 5), considering that the pseudo-labels obtained by the SVM classifier are not of high quality and will cause the conditional distribution to perform poorly, high-quality pseudo-labels are iteratively selected to construct an enhanced conditional distribution alignment loss and introduced into the wide network model that has already incorporated the regular conditional distribution alignment loss. This mitigates the negative transfer caused by the quality problem of the pseudo-labels, and includes the following steps:

[0079] 5.1) Select pseudo-labels with high confidence through sub-models;

[0080] Set the number of sub-models to N. drop Set the 0% ratio to F%, then randomly generate N. drop A 0-1 mask with a zero-to-1 ratio of F%. N is obtained by multiplying the dot product of different Masks and A. drop Each sub-model will be applied to X. t The mean of the predicted output is used as the final predicted output, and the variance is used as a measure of the quality of the corresponding pseudo-labels. The smaller the variance, the higher the quality.

[0081] X t After being input into the width network model, it will be combined with X t The corresponding feature nodes and enhancement nodes are merged to obtain X. t The full feature node T is represented as:

[0082]

[0083] In the formula, This represents the full feature node corresponding to the j-th target domain sample;

[0084] After obtaining each sub-model, calculate the output vector of the sub-model for the target domain samples. Represented as:

[0085]

[0086] In the formula, This represents the predicted output vector of the ε-th sub-model for the target domain samples;

[0087] The predicted output vectors of each sub-model are summed and averaged to obtain the result. Represented as:

[0088]

[0089] In the formula, This represents the average value of the predicted output vectors for each sample in the sub-model.

[0090] Will Convert them into one-hot tags for output, as pseudo-tags for output. At the same time, it can also obtain the set of output vectors for each target domain sample in each sub-model. Represented as:

[0091]

[0092] In the formula, N represents the j-th target domain sample. drop The set of predicted output vectors This represents the predicted output vector of the ε-th sub-model for the j-th target domain sample;

[0093] The quality of a single sample pseudo-label is calculated as follows:

[0094]

[0095] In the formula, η j The quality of the pseudo-label obtained from the j-th target domain sample is represented by Var, where Var represents the variance. This represents the set of prediction results from all sub-models for class c of j samples;

[0096] 5.2) Iterative integration of pseudo-labels to participate in enhanced conditional distribution alignment;

[0097] Create a collection to store high-quality pseudo-tags The pseudo-labels of the target domain samples calculated in the current round. According to η j Sort the samples from highest to lowest quality, and add the top P% of high-quality samples to set ξ. For the same sample that is selected in multiple iterations, the pseudo-label is... After determining the final classification through majority voting, ξ is updated, and the target domain samples with high-quality pseudo-labels are denoted as... Record the corresponding high-quality pseudo-labels as This indicates the number of target domain samples with high-quality pseudo-labels; the superscript * indicates high-quality labels.

[0098] The conditional distribution alignment for participating in the next round of enhancement can be obtained through ξ. and corresponding Give it a comparison using X t and corresponding The loss term for regular conditional distribution alignment has a higher weight. The reason for retaining the regular conditional distribution alignment loss term is that, although X participates in the regular conditional distribution alignment... t pseudo-tags Although it lacks high quality, it still has positive significance for wide network models;

[0099] In this way, each iteration is correct. Update the distribution for participation in the next round of regular conditional distribution alignment, and integrate. As the number of samples increases, the conditional distribution alignment in the next round of enhancement becomes increasingly better. Further differentiation using weights further improves the conditional distribution alignment, mitigating negative transfer caused by low-quality pseudo-labels. Ultimately, this process is repeated iteratively. The results were obtained after the round;

[0100] Therefore, based on the principle of conditional distribution alignment, the enhanced conditional distribution alignment loss... From source domain sample X s and target domain samples with high-quality pseudo-labels The difference between the mean of the predicted outputs of the same category is summed. However, for target domain samples and source domain samples X that lack high-quality pseudo-labels... s The alignment loss between them is 0;

[0101] According to the above rules, the enhanced conditional distribution alignment loss term Represented as:

[0102]

[0103] In the formula, the matrix The calculation method is as follows:

[0104]

[0105] In the formula, This represents the set of high-quality pseudo-labeled samples with c in the target domain. Indicates the j-th * A target domain sample with high-quality pseudo-labels Indicates the j-th * High-quality pseudo-labels for target domain samples with high-quality pseudo-labels. express Any element in This indicates the number of samples with high-quality pseudo-labels that belong to class c.

[0106] Furthermore, in step 6), in order to explore the potential distribution information of the samples and improve the generalization ability of the wide network model in the target domain, the manifold regularization loss is introduced into the wide network model that has already incorporated the enhanced conditional distribution alignment loss. Its loss term... Represented as:

[0107]

[0108] In the formula, a(x μ ) is the sample x μ The full feature nodes, a(x γ ) is the sample x γ All feature nodes, ω μγ To represent the similarity between any two samples, cosine similarity is used for calculation:

[0109]

[0110] In the formula, Let τ represent the set of τ nearest neighbors of any sample x, which is clustered using the KNN algorithm;

[0111] Loss items Rewritten as:

[0112]

[0113] In the formula, Ω-Δ represents the Laplace matrix. ω is generated by all samples μγ The resulting adjacency matrix, where Ω represents the diagonal matrix, is calculated as follows:

[0114]

[0115] In the formula, Ω μμ Represents the elements in Ω;

[0116] Standardize the Laplace matrix:

[0117]

[0118] In the formula, Represents the standardized Laplace matrix;

[0119] Therefore, the loss item The final form is expressed as:

[0120]

[0121] Furthermore, in step 7), the source domain samples in the input space are divided into two parts, namely each source domain sample and the hidden samples around it Indicates in A set of samples within a specific positive range Q, that is, in each dimension and The distance between each sample is less than Q. A set of hidden samples that meet the following requirements can be found.

[0122]

[0123] In the formula, Δx κ express and The difference vector between any two dimensions, Δx is and The difference vector between the samples is given, where Q is a user-defined value. The value of Q should not be too large, as samples that are too far from the current sample may no longer belong to the current category. The optimal value can be determined based on neighborhood knowledge or repeated experiments. It is also assumed that each hidden sample... They all have the same generation probability, that is, they follow a uniform distribution; in other words, they can be regarded as... yes The surrounding disturbance points, while Δx is the degree of random disturbance;

[0124] Random sensitivity aims to reduce and The mean squared error of the predicted output alleviates the overfitting problem of the wide network model itself, while also enabling it to have better generalization ability for target domain samples that still have distribution differences.

[0125] For each source domain sample, a set of perturbation points are generated. If each group has 0 perturbation points, then the total number of perturbation points is... The perturbation points of all source domain samples are represented as: Disturbance point It only participates in the calculation of random sensitivity and is not involved in the calculation of other loss terms. After inputting into the width network model, The corresponding feature nodes and enhancement nodes are merged to obtain The full feature node U is represented as:

[0126]

[0127] In the formula, This represents the full feature node corresponding to the e-th perturbation point of the i-th source domain sample;

[0128] X s After inputting X into the width network model s The corresponding feature nodes and enhancement nodes are merged to obtain X. s The full feature node S is represented as:

[0129]

[0130] In the formula, This represents the full feature node corresponding to the i-th source domain sample;

[0131] Therefore, the random sensitivity loss term Represented as:

[0132]

[0133] In the formula, This represents the predicted output vector for the perturbation sample. express The result of stacking 0 times is that the stacked values ​​result in UW and The dimensions are consistent and can ensure that each source domain sample and its perturbation point have a one-to-one correspondence in the predicted output vector.

[0134] Furthermore, in step 8), the final loss function of the width network model obtained from steps 2) to 7) is expressed as follows:

[0135]

[0136] In the formula, λ1 is the weight of the edge distribution alignment loss, λ2 is the weight of the regular conditional distribution alignment loss, σ is the weight of the random sensitivity loss term, λ3 is the weight of the manifold regularization loss, and λ4 is the weight of the enhanced conditional distribution alignment loss, where λ4 is higher than λ2.

[0137] The value of W is obtained using the ridge regression algorithm:

[0138]

[0139] Because the ridge regression algorithm is used to solve the wide network model, UW and At least one condition must be known for a solution to be found. Therefore, the first iteration is used as the initialization round for the random sensitivity. No random sensitivity loss term is added in the first iteration. After obtaining the SW, the results are repeated and stacked o times to form the solution. And record it, starting from the second round, adding a random sensitivity loss term, using the result obtained from the first round of iterations. Calculate the random sensitivity, and then use the values ​​calculated in the second round of iterations. Record this information for use in calculating the random sensitivity during the third iteration, and so on, iterating continuously; Meanwhile, because the wide network model generates N in each iteration... drop To reduce the impact of sub-model structure on stochastic sensitivity in different iteration rounds, N used to generate the sub-model will be... drop Each mask is shared across iterations, and the random sensitivity loss term is used by each sub-model when calculating it. All of these are sub-models generated using the same Mask in the previous iteration;

[0140] Iteration of the width network model Next time, use the first Wheel As the final classification result of the model, the classification result of the model is calculated.

[0141] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0142] 1. This invention uses a wide network model for domain-adaptive image classification, which greatly shortens the training time and requires less computational resources compared to other deep domain methods.

[0143] 2. Compared with other unsupervised domain adaptive image classification methods, this invention alleviates the negative transfer problem and the problem of model overfitting on source domain data by further introducing enhanced distribution alignment and random sensitivity, thereby improving the accuracy of the domain adaptive method.

[0144] 3. The method of the present invention has a wide range of applications in computer vision classification tasks. It is simple to operate, highly adaptable, and has broad application prospects.

[0145] In summary, this invention enhances the generalization ability of wide network models through distribution alignment, manifold regularization, and stochastic sensitivity, enabling them to achieve better results in target domains with different distributions. This invention also addresses, to some extent, the long processing time and high computational resource consumption issues commonly found in deep domain adaptive methods, further enabling more flexible and accurate downstream applications. Attached Figure Description

[0146] Figure 1 This is a schematic diagram of the logic flow of the present invention.

[0147] Figure 2 This is a diagram of the architecture of the present invention.

[0148] Figure 3 This is a structural diagram of the width network model.

[0149] Figure 4 This is a diagram illustrating negative migration. Detailed Implementation

[0150] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0151] like Figure 1 and Figure 2 As shown, this embodiment discloses a domain-adaptive image classification method based on width learning and random sensitivity, which includes the following steps:

[0152] 1) Using the Office-31 dataset, with the Amazon domain as the source domain and the Webcam domain as the target domain, and taking AlexNet-FC7 features finely tuned on the source domain as an example, the input to this method includes source domain samples, target domain samples, and labels for the source domain samples, where the true labels for the target domain samples are unavailable.

[0153] 2) The input data includes source domain samples, target domain samples, and source domain sample labels, where the actual labels of the target domain samples are unavailable.

[0154] Source domain sample set X s Represented as:

[0155]

[0156] In the formula, Represent real numbers, This represents the i-th source domain sample. Each source domain sample has a dimension of 1×d, where d represents the feature dimension of the sample. There are n features in total. s There are n such source domain samples, that is, there are n source domain samples. s indivual;

[0157] Target domain sample set X t Represented as:

[0158]

[0159] In the formula, Let represent the j-th target domain sample. Each target domain sample has a dimension of 1×d, and there are n samples in total. t There are n such target domain samples, that is, there are n target domain samples. t indivual;

[0160] The set of labels corresponding to each source domain sample is the source domain label set Y. s Represented as:

[0161]

[0162] In the formula, C represents the total number of sample categories. This represents the category label corresponding to the i-th source domain sample, and there are n such labels. s One tag;

[0163] The sample X input into the wide network model is represented as:

[0164] X = [X] s ;X t ]

[0165] In the formula,

[0166] The label Y input into the wide network model is represented as:

[0167] Y = [Y s [Zeros]

[0168] In the formula, A matrix of all zeros is used to represent labels indicating that samples in the target domain are unavailable.

[0169] This represents all the labels entered;

[0170] At this time, n s =2817, n t =795, d=4096, C=31;

[0171] like Figure 3 As shown, the width network model consists of three layers:

[0172] The first layer is the feature mapping layer, which is responsible for transforming the input samples into feature maps through random weights, biases, and linear activation functions and storing them in the feature nodes.

[0173] The second layer is the enhancement layer, which maps the feature nodes again and stores them in the enhancement nodes through random weights and biases;

[0174] The third layer is the output layer, which merges the feature nodes and enhancement nodes to form full feature nodes that are directly connected to the output layer. Finally, the ridge regression algorithm is used to solve for the connection weights of the width network model.

[0175] The construction process of the width network model is as follows:

[0176] Inputting X into a wide network model, the i'th feature layer node Z, which contains k feature nodes, will then be... i' Represented as:

[0177]

[0178] In the formula, and Let represent the weights and biases of the randomly generated i'-th group of feature layer nodes, where n represents the number of feature node groups, and φ i' Z represents the linear activation function of the i'-th feature layer node, and the combination of all feature nodes. n Represented as:

[0179] Z n =[Z1,Z2,...,Z n ]

[0180] In the formula, n×k represents the total number of feature nodes, where k = 50 and n = 10.

[0181] The j'th group of enhanced nodes H is generated by mapping the feature nodes. j' Represented as:

[0182]

[0183] In the formula, and This represents the weights and biases of the randomly generated j'-th group, where m represents the total number of augmented nodes, and δ... j' Let H represent the nonlinear activation function of the j'-th group of boosting nodes, and let H represent all the boosting nodes. m Represented as:

[0184] H m =[H1,H2,...,H m ]

[0185] In the formula, Here, m is set to 1500;

[0186] After merging all feature nodes and augmentation nodes, the resulting full feature node A is represented as:

[0187] A = [Z] n |H m ]

[0188] In the formula, n×k+m represents the total number of feature nodes and augmentation nodes;

[0189] The wide network model processes the input labels as one-hot labels and solves for their connection weights by minimizing the sum of prediction errors. After introducing an L2 regularization term, the loss function is expressed as:

[0190]

[0191] In the formula, α represents the penalty coefficient of the L2 regularization term, and W represents the connection weights of the width network model. Let α denote the empirical matrix, and I denote the identity matrix. Here, we set α = 1 × 10⁻⁶. -10 .

[0192] 3) To minimize the difference in edge distribution between source and target domain samples, edge distribution alignment is incorporated into the constructed wide network model, using X... s and X t The difference in the mean of the predicted outputs is used as a standard to measure the difference in marginal distributions;

[0193] Inputting X into a wide network model, after merging the feature nodes and augmentation nodes, the full feature node A of X is expressed as:

[0194]

[0195] In the formula, This represents the transpose of the matrix, where r represents the total number of samples in the source and target domains, i.e., n. s +n t ,a(x r ) represents the full feature node corresponding to the r-th sample;

[0196] The predicted output ψ of the r-th sample r Represented as:

[0197] ψ r =a(x r W

[0198] Introducing edge distribution alignment into the wide network model, its loss term Represented as:

[0199]

[0200] This loss item Rewritten as:

[0201]

[0202] In the formula, Tr represents the trace of the matrix, and the matrix... The calculation method is as follows:

[0203]

[0204] In the formula, Represents the source domain set, This represents the target domain set, whose actual labels are not available.

[0205] 4) To improve the conditional distribution alignment effect, a finer-grained conventional conditional distribution alignment is introduced into the wide network model that has already incorporated edge distribution alignment loss. To calculate the conventional conditional distribution alignment loss, an SVM classifier is first used to obtain pseudo-labels for the target domain samples.

[0206] The set of pseudo-labels corresponding to each target domain sample is the target domain pseudo-label set. Represented as:

[0207]

[0208] In the formula, This represents the category label corresponding to the j-th target domain sample, and there are n categories in total. t One tag;

[0209] The difference in the mean of the predicted outputs of samples belonging to the same category in the source and target domains is used as a measure of conditional distribution difference; therefore, the conventional conditional distribution alignment loss term... Represented as:

[0210]

[0211] In the formula, This represents the sample set in the source domain whose true label is category c. This represents the sample set in the target domain whose pseudo-label is category c. This indicates the number of samples in the source domain that belong to class c. This indicates the number of samples in the target domain that belong to category c. This represents the j-th target domain sample. pseudo-tags;

[0212] This loss item Rewritten as:

[0213]

[0214] In the formula, the matrix The calculation method is as follows:

[0215]

[0216] In the formula, express Any element in the set.

[0217] 5) Considering that the pseudo-labels obtained by the SVM classifier are not of high quality and will reduce the effectiveness of the conditional distribution, high-quality pseudo-labels are iteratively selected to construct an enhanced conditional distribution alignment loss. This enhanced loss loss is then introduced into the wide network model that already incorporates the regular conditional distribution alignment loss, thus mitigating the effects of pseudo-label quality issues. Figure 4 The negative migration scenario shown includes the following steps:

[0218] 5.1) Select pseudo-labels with high confidence through sub-models;

[0219] Set the number of sub-models to N. drop Set the 0% ratio to F%, then randomly generate N. drop A 0-1 mask with a zero-to-1 ratio of F%. N is obtained by multiplying the dot product of different Masks and A. drop Each sub-model will be applied to X. t The mean of the predicted outputs is used as the final predicted output, and the variance is used as a measure of the quality of the corresponding pseudo-labels. The smaller the variance, the higher the quality. Here, N is set to... drop =3, F=5;

[0220] X t After being input into the width network model, it will be combined with X t The corresponding feature nodes and enhancement nodes are merged to obtain X. t The full feature node T is represented as:

[0221]

[0222] In the formula, This represents the full feature node corresponding to the j-th target domain sample;

[0223] After obtaining each sub-model, calculate the output vector of the sub-model for the target domain samples. Represented as:

[0224]

[0225] In the formula, This represents the predicted output vector of the ε-th sub-model for the target domain samples;

[0226] The predicted output vectors of each sub-model are summed and averaged to obtain the result. Represented as:

[0227]

[0228] In the formula, This represents the average value of the predicted output vectors for each sample in the sub-model.

[0229] Will Convert them into one-hot tags for output, as pseudo-tags for output. At the same time, it can also obtain the set of output vectors for each target domain sample in each sub-model. Represented as:

[0230]

[0231] In the formula, N represents the j-th target domain sample. drop The set of predicted output vectors This represents the predicted output vector of the ε-th sub-model for the j-th target domain sample;

[0232] The quality of a single sample pseudo-label is calculated as follows:

[0233]

[0234] In the formula, η j The quality of the pseudo-label obtained from the j-th target domain sample is represented by Var, where Var represents the variance. This represents the set of prediction results from all sub-models for class c of j samples;

[0235] 5.2) Iterative integration of pseudo-labels to participate in enhanced conditional distribution alignment;

[0236] Create a collection to store high-quality pseudo-tags The pseudo-labels of the target domain samples calculated in the current round. According to η j Sort the samples from highest to lowest quality, and add the top P% of high-quality samples to set ξ. For the same sample that is selected in multiple iterations, the pseudo-label is... After determining the final classification through majority voting, ξ is updated, and the target domain samples with high-quality pseudo-labels are denoted as... Record the corresponding high-quality pseudo-labels as This represents the number of target domain samples with high-quality pseudo-labels. The superscript * indicates high-quality labeling. Here, P = 20.

[0237] The conditional distribution alignment for participating in the next round of enhancement can be obtained through ξ. and corresponding Give it a comparison using X t and corresponding The loss term for regular conditional distribution alignment has a higher weight. The reason for retaining the regular conditional distribution alignment loss term is that, although X participates in the regular conditional distribution alignment... t pseudo-tags While it lacks high quality, it still has positive implications for wide network models, especially when integrated in the early stages of its iteration. In my youth;

[0238] In this way, each iteration is correct. Update the distribution for participation in the next round of regular conditional distribution alignment, and integrate. As the number of samples increases, the conditional distribution alignment in the next round of enhancement becomes increasingly better. Further differentiation using weights further improves the conditional distribution alignment, mitigating negative transfer caused by low-quality pseudo-labels. Ultimately, this process is repeated iteratively. The result is obtained after the round, and it is set here.

[0239] Therefore, based on the principle of conditional distribution alignment, the enhanced conditional distribution alignment loss... From source domain sample X s and target domain samples with high-quality pseudo-labels The difference between the mean of the predicted outputs of the same category is summed. However, for target domain samples and source domain samples X that lack high-quality pseudo-labels... s The alignment loss between them is 0;

[0240] According to the above rules, the enhanced conditional distribution alignment loss term Represented as:

[0241]

[0242] In the formula, the matrix The calculation method is as follows:

[0243]

[0244] In the formula, This represents the set of high-quality pseudo-labeled samples with c in the target domain. Indicates the j-th * A target domain sample with high-quality pseudo-labels Indicates the j-th * High-quality pseudo-labels for target domain samples with high-quality pseudo-labels. express Any element in This indicates the number of samples with high-quality pseudo-labels that belong to class c.

[0245] 6) To explore the latent distribution information of the samples and improve the generalization ability of the wide network model in the target domain, manifold regularization loss is introduced into the wide network model that has already incorporated enhanced conditional distribution alignment loss. Its loss term... Represented as:

[0246]

[0247] In the formula, a(x μ ) is the sample x μ The corresponding full feature node, a(x γ ) is the sample x γ The corresponding full feature node representation, ω μγ To represent the similarity between any two samples, cosine similarity is used for calculation:

[0248]

[0249] In the formula, Let τ represent the set of τ nearest neighbors of any sample x, which is clustered using the KNN algorithm;

[0250] Loss items Rewritten as:

[0251]

[0252] In the formula, Ω-Δ represents the Laplace matrix. ω is generated by all samples μγ The resulting adjacency matrix, where Ω represents the diagonal matrix, is calculated as follows:

[0253]

[0254] In the formula, Ω μμ This represents an element in Ω.

[0255] Standardize the Laplace matrix:

[0256]

[0257] In the formula, Represents the standardized Laplace matrix;

[0258] Therefore, the loss item The final form is expressed as:

[0259]

[0260] 7) Divide the source domain samples in the input space into two parts, namely each source domain sample and the hidden samples around it Indicates in A set of samples within a specific positive range Q, that is, in each dimension and The distance between each sample is less than Q. A set of hidden samples that meet the following requirements can be found.

[0261]

[0262] In the formula, Δx κ express and The difference vector between any two dimensions, Δx is and The difference vector between the samples is given by Q, which is a user-defined value. The value of Q should not be too large, as samples that are too far from the current sample may no longer belong to the current category. The optimal value can be determined based on neighborhood knowledge or repeated experiments. Here, Q is set to 0.05. It is also assumed that each hidden sample... They all have the same generation probability, that is, they follow a uniform distribution; in other words, they can be regarded as... yes The surrounding disturbance points, while Δx is the degree of random disturbance;

[0263] Random sensitivity aims to reduce and The mean squared error of the predicted output alleviates the overfitting problem of the wide network model itself, while also enabling it to have better generalization ability for target domain samples that still have distribution differences.

[0264] For each source domain sample, a set of perturbation points are generated. If each group has 0 perturbation points, then the total number of perturbation points is... The perturbation points of all source domain samples are represented as: Disturbance point It only participates in the calculation of random sensitivity and does not participate in the calculation of other loss terms. Let o = 20. After inputting into the width network model, The corresponding feature nodes and enhancement nodes are merged to obtain The full feature node U is represented as:

[0265]

[0266] In the formula, This represents the full feature node corresponding to the e-th perturbation point of the i-th source domain sample;

[0267] X s After inputting X into the width network model s The corresponding feature nodes and enhancement nodes are merged to obtain X. s The full feature node S is represented as:

[0268]

[0269] In the formula, This represents the full feature node corresponding to the i-th source domain sample;

[0270] Therefore, the random sensitivity loss term Represented as:

[0271]

[0272] In the formula, This represents the predicted output vector for the perturbation sample. express The result of stacking 0 times is that the stacked values ​​result in UW and The dimensions are consistent and can ensure that each source domain sample and its perturbation point have a one-to-one correspondence in the predicted output vector.

[0273] 8) Based on steps 2) to 7), the final loss function of the width network model is expressed as follows:

[0274]

[0275] In the formula, λ1 is the weight of the edge distribution alignment loss, λ2 is the weight of the regular conditional distribution alignment loss, σ is the weight of the random sensitivity loss term, λ3 is the weight of the manifold regularization loss, and λ4 is the weight of the enhanced conditional distribution alignment loss, where λ4 is higher than λ2. Here, we set λ1 = 10, λ2 = 10, σ = 1, λ3 = 1, and λ4 = 30.

[0276] The value of W is obtained using the ridge regression algorithm:

[0277]

[0278] Because the ridge regression algorithm is used to solve the wide network model, UW and At least one condition must be known for a solution to be found. Therefore, the first iteration is used as the initialization round for the random sensitivity. No random sensitivity loss term is added in the first iteration. After obtaining the SW, the results are repeated and stacked o times to form the solution. And record it, starting from the second round, adding a random sensitivity loss term, using the result obtained from the first round of iterations. Calculate the random sensitivity, and then use the values ​​calculated in the second round of iterations. Record this information for use in calculating the random sensitivity during the third iteration, and so on, iterating continuously; Meanwhile, because the wide network model generates N in each iteration... drop To reduce the impact of sub-model structure on stochastic sensitivity in different iteration rounds, N used to generate the sub-model will be... dropEach mask is shared across iterations, and the random sensitivity loss term is used by each sub-model when calculating it. All of these are sub-models generated using the same Mask in the previous iteration;

[0279] Iteration of the width network model Next time, use the first Wheel As the final classification result of the model, the classification result of the model is calculated.

[0280] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A domain-adaptive image classification method based on width learning and stochastic sensitivity, characterized in that, Includes the following steps: 1) Construct the input data using source domain samples, source domain sample labels, and target domain samples; 2) Complete the construction of the feature mapping layer, enhancement layer, and output layer of the wide network model; 3) Introduce edge distribution alignment loss into the wide network model to alleviate the decline in model generalization ability caused by the different edge distributions of source domain samples and target domain samples; 4) Use an SVM classifier to obtain pseudo-labels for target domain samples, and introduce finer-grained inter-class alignment, i.e., conventional conditional distribution alignment loss, into the wide network model that has already introduced edge distribution alignment loss, thereby further improving its performance in the target domain. 5) Considering that the pseudo-labels obtained by SVM are not of high quality, which will reduce the effect of the conditional distribution, high-quality pseudo-labels are selected iteratively to construct an enhanced conditional distribution alignment loss and introduce it into the wide network model that has already introduced the regular conditional distribution alignment loss to alleviate the negative transfer caused by the pseudo-label quality problem. 6) After completing the distribution alignment, in order to explore the potential distribution information of the samples and smooth the classification boundary, the popular regularization loss is introduced into the wide network model that has already introduced the enhanced conditional distribution alignment loss, so that the wide network model can better learn the distribution of the samples and improve its accuracy. 7) Steps 2) through 6) are all aimed at improving the performance of the wide network model from the perspective of sample distribution. From the perspective of overfitting, in order to solve the problem of overfitting of the wide network model on the source domain samples caused by the unavailability of the true label in the target domain, random sensitivity is introduced into the wide network model that has already introduced manifold regularization loss to improve its generalization ability. 8) Based on the losses in steps 2) to 7), use the ridge regression algorithm to solve for the connection weights of the width network model and obtain the classification results.

2. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 1, characterized in that, In step 1), the input data includes source domain samples, target domain samples, and source domain sample labels, wherein the actual labels of the target domain samples are unavailable; Source domain sample set X s Represented as: In the formula, Represent real numbers, This represents the i-th source domain sample. Each source domain sample has a dimension of 1×d, where d represents the feature dimension of the sample. There are n features in total. s There are n such source domain samples, that is, there are n source domain samples. s indivual; Target domain sample set X t Represented as: In the formula, Let represent the j-th target domain sample. Each target domain sample has a dimension of 1×d, and there are n samples in total. t There are n such target domain samples, that is, there are n target domain samples. t indivual; The set of labels corresponding to each source domain sample is the source domain label set Y. s Represented as: In the formula, C represents the total number of sample categories. This represents the category label corresponding to the i-th source domain sample, and there are n such labels. s One tag; The sample X input into the wide network model is represented as: X=[X s ;X t ] In the formula, The label Y input into the wide network model is represented as: And=[And s [Zeros] In the formula, A matrix of all zeros is used to represent labels indicating that samples in the target domain are unavailable. This represents all the labels entered.

3. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 2, characterized in that, In step 2), the width network model consists of three layers: The first layer is the feature mapping layer, which is responsible for transforming the input samples into feature maps through random weights, biases, and linear activation functions and storing them in the feature nodes. The second layer is the enhancement layer, which maps the feature nodes again and stores them in the enhancement nodes through random weights and biases; The third layer is the output layer, which merges the feature nodes and enhancement nodes to form full feature nodes that are directly connected to the output layer. Finally, the ridge regression algorithm is used to solve for the connection weights of the width network model. The construction process of the width network model is as follows: Inputting X into a wide network model, the i'th feature layer node Z, which contains k feature nodes, will then be... i' Represented as: In the formula, and Let represent the weights and biases of the randomly generated i'-th group of feature layer nodes, where n represents the number of feature node groups, and φ i' Z represents the linear activation function of the i'-th feature layer node, and the combination of all feature nodes Z n Represented as: WITH n =[Z1,Z2,...,Z n ] In the formula, n×k represents the total number of feature nodes; The j'th group of enhanced nodes H is generated by mapping the feature nodes. j' Represented as: In the formula, and This represents the weights and biases of the randomly generated j'-th group, where m represents the total number of augmented nodes, and δ... j' Let H represent the nonlinear activation function of the j'-th group of boosting nodes, and let H represent all the boosting nodes. m Represented as: H m =[H1,H2,...,H m ] In the formula, After merging all feature nodes and augmentation nodes, the resulting full feature node A is represented as: A=[Z n |H m ] In the formula, n×k+m represents the total number of feature nodes and augmentation nodes; The wide network model processes the input labels as one-hot labels and solves for their connection weights by minimizing the sum of prediction errors. After introducing an L2 regularization term, the loss function is expressed as: In the formula, α represents the penalty coefficient of the L2 regularization term, and W represents the connection weights of the width network model. Let I represent the empirical matrix, and let I represent the identity matrix.

4. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 3, characterized in that, In step 3), in order to minimize the difference in edge distribution between the source domain samples and the target domain samples, edge distribution alignment is introduced into the constructed width network model, using X. s and X t The difference in the mean of the predicted outputs is used as a standard to measure the difference in marginal distributions; Inputting X into a wide network model, after merging the feature nodes and augmentation nodes, the full feature node A of X is expressed as: In the formula, T represents the transpose of the matrix, and r represents the total number of samples in the source and target domains, i.e., n. s +n t ,a(x r ) represents the full feature layer node corresponding to the r-th sample; The predicted output ψ of the r-th sample r Represented as: ψ r =a(x r )W Introducing edge distribution alignment into the wide network model, its loss term Represented as: This loss item Rewritten as: In the formula, Tr represents the trace of the matrix, and the matrix... The calculation method is as follows: In the formula, Represents the source domain set, This represents a set of target domains for which actual labels are unavailable. for For any element x μ and x γ Represents any sample.

5. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 4, characterized in that, In step 4), in order to improve the conditional distribution alignment effect, a finer-grained conventional conditional distribution alignment is introduced into the wide network model that has already incorporated edge distribution alignment loss. To calculate the conventional conditional distribution alignment loss, an SVM classifier is first used to obtain the pseudo-label set of target domain samples. The set of pseudo-labels corresponding to each target domain sample is the target domain pseudo-label set. Represented as: In the formula, This represents the category label corresponding to the j-th target domain sample, and there are n categories in total. t One tag; The difference in the mean of the predicted outputs of samples belonging to the same category in the source and target domains is used as a measure of conditional distribution difference; therefore, the conventional conditional distribution alignment loss term... Represented as: In the formula, This represents the sample set in the source domain whose true label is category c. This represents the sample set in the target domain whose pseudo-label is category c. This indicates the number of samples in the source domain that belong to class c. This indicates the number of samples in the target domain that belong to category c. This represents the j-th target domain sample. pseudo-tags; This loss item Rewritten as: In the formula, the matrix The calculation method is as follows: In the formula, express Any element in the set.

6. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 5, characterized in that, In step 5), considering that the pseudo-labels obtained by the SVM classifier are not of high quality and will reduce the effectiveness of the conditional distribution, high-quality pseudo-labels are selected iteratively to construct an enhanced conditional distribution alignment loss and introduce it into the wide network model that has already incorporated the regular conditional distribution alignment loss. This mitigates the negative transfer caused by the quality of the pseudo-labels. The steps include: 5.1) Select pseudo-labels with high confidence through sub-models; Set the number of sub-models to N. drop Set the 0% ratio to F%, then randomly generate N. drop A 0-1 mask with a zero-to-1 ratio of F%. N is obtained by multiplying the dot product of different Masks and A. drop Each sub-model will be applied to X. t The mean of the predicted output is used as the final predicted output, and the variance is used as a measure of the quality of the corresponding pseudo-labels. The smaller the variance, the higher the quality. X t After being input into the width network model, it will be combined with X t The corresponding feature nodes and enhancement nodes are merged to obtain X. t The full feature node T is represented as: In the formula, This represents the full feature node corresponding to the j-th target domain sample; After obtaining each sub-model, calculate the output vector of the sub-model for the target domain samples. Represented as: In the formula, This represents the predicted output vector of the ε-th sub-model for the target domain samples; The predicted output vectors of each sub-model are summed and averaged to obtain the result. Represented as: In the formula, This represents the average value of the predicted output vectors for each sample in the sub-model. Will Convert them into one-hot tags for output, as pseudo-tags for output. At the same time, it can also obtain the set of output vectors for each target domain sample in each sub-model. Represented as: In the formula, N represents the j-th target domain sample. drop The set of predicted output vectors This represents the predicted output vector of the ε-th sub-model for the j-th target domain sample; The quality of a single sample pseudo-label is calculated as follows: In the formula, η j The quality of the pseudo-label obtained from the j-th target domain sample is represented by Var, where Var represents the variance. This represents the set of prediction results from all sub-models for class c of j samples; 5.2) Iterative integration of pseudo-labels to participate in enhanced conditional distribution alignment; Create a collection to store high-quality pseudo-tags The pseudo-labels of the target domain samples calculated in the current round. According to η j Sort the samples from highest to lowest quality, and add the top P% of high-quality samples to set ξ. For the same sample that is selected in multiple iterations, the pseudo-label is... After determining the final classification through majority voting, ξ is updated, and the target domain samples with high-quality pseudo-labels are denoted as... Record the corresponding high-quality pseudo-labels as This indicates the number of target domain samples with high-quality pseudo-labels; the superscript * indicates high-quality labels. The conditional distribution alignment for participating in the next round of enhancement can be obtained through ξ. and corresponding Give it a comparison using X t and corresponding The loss term for regular conditional distribution alignment has a higher weight. The reason for retaining the regular conditional distribution alignment loss term is that, although X participates in the regular conditional distribution alignment... t pseudo-tags Although it lacks high quality, it still has positive significance for wide network models; In this way, each iteration is correct. Update the distribution for participation in the next round of regular conditional distribution alignment, and integrate. As the number of samples increases, the conditional distribution alignment in the next round of enhancement becomes increasingly better. Further differentiation using weights further improves the conditional distribution alignment, mitigating negative transfer caused by low-quality pseudo-labels. Ultimately, this process is repeated iteratively. The results were obtained after the round; Therefore, based on the principle of conditional distribution alignment, the enhanced conditional distribution alignment loss... From source domain sample X s and target domain samples with high-quality pseudo-labels The difference between the mean of the predicted outputs of the same category is summed. However, for target domain samples and source domain samples X that lack high-quality pseudo-labels... s The alignment loss between them is 0; According to the above rules, the enhanced conditional distribution alignment loss term Represented as: In the formula, the matrix The calculation method is as follows: In the formula, This represents the set of high-quality pseudo-labeled samples with c in the target domain. Indicates the j-th * A target domain sample with high-quality pseudo-labels Indicates the j-th * High-quality pseudo-labels for target domain samples with high-quality pseudo-labels. express Any element in This indicates the number of samples with high-quality pseudo-labels that belong to class c.

7. The domain-adaptive image classification method based on width learning and stochastic sensitivity according to claim 6, characterized in that, In step 6), to explore the latent distribution information of the samples and improve the generalization ability of the wide network model in the target domain, the manifold regularization loss is introduced into the wide network model that has already incorporated the enhanced conditional distribution alignment loss. The loss term... Represented as: In the formula, a(x μ ) is the sample x μ The full feature nodes, a(x γ ) is the sample x γ All feature nodes, ω μγ To represent the similarity between any two samples, cosine similarity is used for calculation: In the formula, Let τ represent the set of τ nearest neighbors of any sample x, which is clustered using the KNN algorithm; Loss items Rewritten as: In the formula, Ω-Δ represents the Laplace matrix. ω is generated by all samples μγ The resulting adjacency matrix, where Ω represents the diagonal matrix, is calculated as follows: In the formula, Ω μμ Represents the elements in Ω; Standardize the Laplace matrix: In the formula, Represents the standardized Laplace matrix; Therefore, the loss item The final form is expressed as:

8. The domain-adaptive image classification method based on width learning and stochastic sensitivity according to claim 7, characterized in that, In step 7), the source domain samples in the input space are divided into two parts, namely each source domain sample. and the hidden samples around it Indicates in A set of samples within a specific positive range Q, that is, in each dimension and The distance between each sample is less than Q. A set of hidden samples that meet the following requirements can be found. In the formula, Δx κ express and The difference vector between any two dimensions, Δx is and The difference vector between the samples is given, where Q is a user-defined value. The value of Q should not be too large, as samples that are too far from the current sample may no longer belong to the current category. The optimal value can be determined based on neighborhood knowledge or repeated experiments. It is also assumed that each hidden sample... They all have the same generation probability, that is, they follow a uniform distribution; in other words, they can be regarded as... yes The surrounding disturbance points, while Δx is the degree of random disturbance; Random sensitivity aims to reduce and The mean squared error of the predicted output alleviates the overfitting problem of the wide network model itself, while also enabling it to have better generalization ability for target domain samples that still have distribution differences. For each source domain sample, a set of perturbation points are generated. If each group has 0 perturbation points, then the total number of perturbation points is... The perturbation points of all source domain samples are represented as: Disturbance point It only participates in the calculation of random sensitivity and is not involved in the calculation of other loss terms. After inputting into the width network model, The corresponding feature nodes and enhancement nodes are merged to obtain The full feature node U is represented as: In the formula, This represents the full feature node corresponding to the e-th perturbation point of the i-th source domain sample; X s After inputting X into the width network model s The corresponding feature nodes and enhancement nodes are merged to obtain X. s The full feature node S is represented as: In the formula, This represents the full feature node corresponding to the i-th source domain sample; Therefore, the random sensitivity loss term Represented as: In the formula, This represents the predicted output vector for the perturbation sample. express The result of stacking 0 times is that the stacked values ​​result in UW and The dimensions are consistent and can ensure that each source domain sample and its perturbation point have a one-to-one correspondence in the predicted output vector.

9. The domain-adaptive image classification method based on width learning and random sensitivity according to claim 8, characterized in that, In step 8), the final loss function of the width network model obtained from steps 2) to 7) is expressed as follows: In the formula, λ1 is the weight of the edge distribution alignment loss, λ2 is the weight of the regular conditional distribution alignment loss, σ is the weight of the random sensitivity loss term, λ3 is the weight of the manifold regularization loss, and λ4 is the weight of the enhanced conditional distribution alignment loss, where λ4 is higher than λ2. The value of W is obtained using the ridge regression algorithm: Because the ridge regression algorithm is used to solve the wide network model, UW and At least one condition must be known for a solution to be found. Therefore, the first iteration is used as the initialization round for the random sensitivity. No random sensitivity loss term is added in the first iteration. After obtaining the SW, the results are repeated and stacked o times to form the solution. And record it, starting from the second round, adding a random sensitivity loss term, using the result obtained from the first round of iterations. Calculate the random sensitivity, and then use the values ​​calculated in the second round of iterations. Record this information for use in calculating the random sensitivity during the third iteration, and so on, iterating continuously; Meanwhile, because the wide network model generates N in each iteration... drop To reduce the impact of sub-model structure on stochastic sensitivity in different iteration rounds, N used to generate the sub-model will be... drop Each mask is shared across iterations, and the random sensitivity loss term is used by each sub-model when calculating it. All of these are sub-models generated using the same Mask in the previous iteration; Iteration of the width network model Next time, use the first Wheel As the final classification result of the model, the classification result of the model is calculated.

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