Privacy-preserving federated transfer learning method and system based on partial optimal transmission

Abstract

The present application relates to the technical field of federal transfer learning, in particular to a privacy protection federal transfer learning method and system based on partial optimal transmission; the method of the present application firstly extracts source end differential privacy class prototypes and target end local clustering, greatly reducing communication overhead while protecting the privacy of source domain original data; then, a relationship cost matrix is constructed based on domain structure signature and partial optimal transmission is solved, and cluster-to-class semantic mapping is solved to generate pseudo-labels and transmission conditions; then, the transmission conditions guide the conditional variational autoencoder to generate source domain style complementary features, and training weights are generated in combination with double-dimensional uncertainty; finally, the outputs of the trained baseline, enhanced and aligned three types of classifiers are weighted and fused to obtain the target domain classification result, improve the classification accuracy, macro F1, macro AUC and probability calibration quality of the target domain, and improve the cross-domain transfer effect under privacy constraints.

Description

Technical Field

[0001] This invention relates to the field of federated transfer learning technology, specifically to a privacy-preserving federated transfer learning method and system based on partially optimal transfer. Background Technology

[0002] With the widespread application of intelligent systems in fields such as industrial manufacturing, healthcare, and financial risk control, data is often scattered across different institutions, devices, or sites, and cannot be directly aggregated for training due to restrictions such as privacy regulations and data ownership. Federated learning alleviates the data silo problem to some extent by exchanging model parameters or statistics to replace the original data transmission. However, standard horizontal federated learning assumes that all parties share the same feature space, which cannot adapt to many real-world scenarios: the source party with labeled data and the target party to be deployed may use different feature collection methods, resulting in heterogeneous or even disjoint feature spaces, and the target party usually lacks labeled data. This problem is known as unsupervised vertical federated transfer learning.

[0003] Current unsupervised federated transfer learning faces three core challenges: First, the statistics transmitted from the source need strict privacy protection to avoid leakage of individual sample information; second, it is difficult to establish a reliable semantic correspondence between the target cluster and the source category in a heterogeneous feature space; third, after alignment, it is necessary to construct complementary features with rich class information for unlabeled target samples to fully utilize the transferred source domain knowledge. Most existing methods address one of these problems individually, making it difficult to simultaneously achieve reliable alignment and feature enhancement under strict privacy constraints.

[0004] Specifically, most existing differential privacy-preserving federated learning methods introduce noise into gradients or model parameters, resulting in high computational and communication overhead. Furthermore, this noise can easily disrupt the class structure signals required for cross-domain alignment. While prototype-based federated learning offers efficient communication, it fails to consider alignment issues in heterogeneous feature spaces, and privacy perturbations in the prototype can easily lead to alignment failure. Existing domain adaptation methods based on optimal transmission rely on direct cross-domain feature distance calculations, which cannot adapt to vertical federated scenarios with different feature dimensions or disjoint subspaces. Although existing conditional generative models can synthesize complementary views, they lack meaningful semantic conditional signals, and the generated features are prone to deviating from the semantic structure of the source domain, failing to effectively support downstream classification tasks. Summary of the Invention

[0005] This invention provides a privacy-preserving federated transfer learning method and system based on partially optimal transmission.

[0006] The technical solution of this invention is as follows: A privacy-preserving federated transfer learning method based on partially optimal transfer is applied to federated transfer learning involving a source and a target. The source holds a labeled source domain dataset, and the target holds an unlabeled target domain dataset. The method includes the following operations: S1. The source calculates class prototype vectors for each category based on the labeled source domain data, applies differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and sends them to the target. The target performs clustering on the unlabeled target domain data to obtain clustering assignment results containing target cluster centers and samples. S2. Based on the noisy class prototype and the target cluster center, the target side constructs the distance matrix in the source domain and the distance matrix in the target domain, respectively, obtains their respective structural signatures, constructs the relation cost matrix, and obtains the optimal transmission plan through partial optimal transmission solution; according to the optimal transmission plan, it solves the bijective mapping from cluster to class, generates pseudo-labels for target samples, and calculates the transmission conditions corresponding to each target sample. S3. The target side trains a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features of the source domain style and retain the original generated features and the generation variance of each dimension. S4. Based on the original generated features, the dimension-wise generated variance, and the corresponding transmission conditions, the target side calculates the reconstruction uncertainty and semantic uncertainty for each target sample, presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier, and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier, and the alignment classifier through a fusion strategy to obtain the target domain classification result.

[0007] A privacy-preserving federated transfer learning system based on partially optimal transmission is provided to implement the aforementioned privacy-preserving federated transfer learning method based on partially optimal transmission, comprising a source node and a target node. Source nodes include: The differential privacy perturbation module is used by the source to calculate class prototype vectors of various categories based on labeled source domain data, apply differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and send them to the target. The target nodes include: The clustering module is used by the target party to cluster unlabeled target domain data and obtain clustering assignment results containing target cluster centers and samples; The partial optimal transmission solution module is used by the target to construct the distance matrix in the source domain and the distance matrix in the target domain based on the noisy class prototype and the target cluster center, respectively, obtain their respective structural signatures, construct the relation cost matrix, and obtain the optimal transmission plan through partial optimal transmission solution; The transmission condition generation module is used to solve the bijective mapping from cluster to class according to the optimal transmission plan, generate pseudo-labels for target samples, and calculate the transmission conditions corresponding to each target sample. The original generated features and the dimension-wise generated variance generation module are used by the target side to train a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features in the style of the source domain, while retaining the original generated features and the dimension-wise generated variance. The target domain classification result generation module is used by the target party to calculate the reconstruction uncertainty and semantic uncertainty for each target sample based on the original generated features, the dimension-wise generated variance and the corresponding transmission conditions. It presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier and the alignment classifier through a fusion strategy to obtain the target domain classification result.

[0008] A privacy-preserving federated transfer learning device based on partially optimal transfer includes a processor and a memory, wherein the processor implements the above-described privacy-preserving federated transfer learning method based on partially optimal transfer when executing a computer program stored in the memory.

[0009] A computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the above-described privacy-preserving federated transfer learning method based on partially optimal transfer.

[0010] The beneficial effects of this invention are as follows: This invention provides a privacy-preserving federated transfer learning method based on partially optimal transmission. First, through source-side differential privacy class prototype extraction and target-side local clustering, cross-domain knowledge sharing can be achieved with only a single round of transmission of desensitized statistics, significantly reducing communication overhead while strictly protecting the privacy of the original source domain data. Then, a relation cost matrix is ​​constructed based on domain-specific structural signatures, and partially optimal transmission is solved. Robust cluster semantic mapping can be established without direct cross-domain feature comparison, effectively adapting to heterogeneous or even disjoint feature spaces, and exhibiting strong resistance to differential privacy noise. Next, the transmission conditions derived from optimal transmission guide a conditional variational autoencoder to generate complementary features of the source domain style. Simultaneously, a two-dimensional uncertainty assessment is used to assign differentiated training weights to samples, supplementing the target domain's discriminative information through generated features and mitigating the negative impact of low-quality generated samples through quality filtering, ensuring the reliability of the generated enhancements. Finally, a weighted fusion of baseline, enhancement, and alignment classifiers in the later stages balances the classification advantages of different feature perspectives, improving the target domain's classification accuracy, macro-F1, macro-AUC, and probability calibration quality, thereby enhancing the cross-domain transfer performance under privacy constraints.

[0011] This invention provides a privacy-preserving federated transfer learning method based on partially optimal transmission, which features strong privacy protection and low communication overhead, requiring only a single round of transmission of K differential privacy class prototypes, with a communication volume of only [missing information]. This is far lower than the original data transmission or multi-round model aggregation; it provides formal differential privacy guarantees through a calibrated Gaussian mechanism, protecting individual sample information in the source domain.

[0012] This invention provides a privacy-preserving federated transfer learning method based on partially optimal transmission. It constructs a relation cost matrix using intra-domain structural signatures, eliminating the need for direct cross-domain feature comparison. This method is suitable for vertical federated scenarios with different feature dimensions and non-overlapping subspaces. Partial optimal transmission allows for partial quality matching, prioritizing the retention of high-confidence correspondences, and exhibits strong robustness against differential privacy noise and target cluster imbalance.

[0013] This invention provides a privacy-preserving federated transfer learning method based on partially optimal transfer. The semantic conditions derived from the optimal transfer guide the generation of a conditional variational autoencoder. The generated distribution is anchored to the source prototype manifold by combining the Sinkhorn optimal transfer loss, thus avoiding the generated features from deviating from the transfer semantics. After generation, the smoothing effectively reduces the variance of random generation and improves the stability of features and the quality of probability calibration. Attached Figure Description

[0014] The solutions and advantages of this application will become clear to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0015] In the attached diagram: Figure 1 As shown in the embodiment, this is a privacy budget sensitivity curve of the method in this embodiment on the CWRU dataset; Figure 2 As shown in the example, this is a privacy budget sensitivity curve of the method in this embodiment on the Office-Home-10 dataset; Figure 3 In this embodiment, the t-SNE distribution of the original target domain features in the CWRU dataset is shown. Figure 4 In this embodiment, the method of this embodiment fuses complementary features in the CWRU dataset to generate a feature t-SNE distribution map; Figure 5 In this embodiment, the t-SNE distribution of the original target domain features in the Office-Home-10 dataset is shown. Figure 6 In this embodiment, the method of this embodiment generates a feature t-SNE distribution map after fusing complementary features in the Office-Home-10 dataset; Figure 7 As shown in the embodiment, the probability calibration reliability map of the method in this embodiment on the CWRU dataset; Figure 8 As shown in this embodiment, the method of this embodiment is used to perform a probability calibration reliability map on the Office-Home-10 dataset; Figure 9 This is a comparison chart of the cross-party communication costs between the method of this embodiment and existing methods in the embodiments. Figure 10 This is a comparison chart showing the number of communication rounds and the amount of data transmitted per round between the method in this embodiment and existing methods, as illustrated in the example. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the exemplary embodiments of this application clearer, the technical solutions in the exemplary embodiments of this application are described clearly and completely below. Obviously, the described exemplary embodiments are only some embodiments of this application, and not all embodiments.

[0017] This embodiment provides a privacy-preserving federated transfer learning method based on partially optimal transfer, applied to federated transfer learning involving a source and a target. The source holds a labeled source domain dataset, and the target holds an unlabeled target domain dataset. The method includes the following operations: S1. The source calculates class prototype vectors for each category based on the labeled source domain data, applies differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and sends them to the target. The target performs clustering on the unlabeled target domain data to obtain clustering assignment results containing target cluster centers and samples. S2. Based on the noisy class prototype and the target cluster center, the target side constructs the distance matrix in the source domain and the distance matrix in the target domain, respectively, obtains their respective structural signatures, constructs the relation cost matrix, and obtains the optimal transmission plan through partial optimal transmission solution; according to the optimal transmission plan, it solves the bijective mapping from cluster to class, generates pseudo-labels for target samples, and calculates the transmission conditions corresponding to each target sample. S3. The target side trains a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features of the source domain style and retain the original generated features and the generation variance of each dimension. S4. Based on the original generated features, the dimension-wise generated variance, and the corresponding transmission conditions, the target side calculates the reconstruction uncertainty and semantic uncertainty for each target sample, presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier, and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier, and the alignment classifier through a fusion strategy to obtain the target domain classification result. The specific steps are detailed below.

[0018] S1. The source calculates class prototype vectors for each category based on the labeled source domain data, applies differential privacy Gaussian perturbation to each class prototype vector to obtain a noisy class prototype that satisfies differential privacy, and sends it to the target. The target performs clustering on the unlabeled target domain data to obtain clustering assignment results containing the target cluster centers and samples.

[0019] First, configure the source side to hold a labeled source domain dataset. ,in Features of the source domain The target party holds an unlabeled target domain dataset; the target party is labeled with category labels. ,in For the target domain features. In the unsupervised longitudinal federated transfer learning setting, the two parties do not share the original data, but only transmit data from the source to the target party that satisfies the requirements. Summary statistics of differential privacy For differential privacy budgeting, The target domain classifier is trained using the relaxation term of differential privacy. The goal is to achieve high-precision, high-caliber target domain classification under these strict constraints.

[0020] The operation of the differential privacy Gaussian perturbation mechanism is as follows: the feature vector of each source domain sample is pruned using the ℓ2 norm, and the source side performs perturbation on each category. k The conditional mean vector of the classes is used as the original class prototype. The calculation formula is as follows: , For category k The number of samples, For the first i Feature vectors of source domain samples For the corresponding labels, Gaussian noise is applied to each original class prototype to obtain the noisy class prototype. Among them, noise scale , The vector is Gaussian noise. This is the upper limit for cropping. For source domain feature dimensions, It is the identity matrix. This is a relaxation term for differential privacy.

[0021] Meanwhile, the target side uses the k-means algorithm to cluster the ℓ2 standardized target domain features. The number of clusters is equal to the number of source domain categories K, resulting in K target cluster centers and the clustering assignment of each target sample.

[0022] S2. Based on the noisy class prototype and the target cluster center, the target side constructs the distance matrix in the source domain and the distance matrix in the target domain respectively, obtains their respective structural signatures, constructs the relation cost matrix, and obtains the optimal transmission plan through partial optimal transmission solution; according to the optimal transmission plan, it solves the bijective mapping from cluster to class, generates pseudo-labels for target samples, and calculates the transmission conditions corresponding to each target sample.

[0023] First, the target constructs distance matrices within the source domain and within the target domain based on the noisy class prototypes and the target cluster centers, respectively. Then, it calculates the pairwise Euclidean distances between all noisy class prototypes in the source domain, forming a matrix to obtain the source domain distance matrix. Calculate the pairwise Euclidean distances between all cluster centers in the target domain, forming a matrix to obtain the target domain distance matrix. C represents the number of clusters.

[0024] Then, the structural signatures of the distance matrices in the source and target domains are obtained respectively, and a relation cost matrix is ​​constructed. Specifically, each row of the distance matrices in the source and target domains is sorted in ascending order to obtain the structural signature of each source class prototype. and the structural signature of each target cluster; , The distance matrix within the source domain The kLine, containing the source class prototype k Pairwise Euclidean distances to all other source class prototypes For ascending order sorting, the distance vector is sorted to eliminate arbitrary ordering dependencies of neighborhood classes. Distance matrix within the target domain The c Line, containing target cluster centers c The pairwise Euclidean distance to all other target cluster centers; the relation cost is calculated based on the structural signature, using the following formula: , The elements of the relation cost matrix represent the target clustering. c With the source class prototype k The structural similarity between two points is such that the smaller the value, the more similar the intra-domain distance structure of the two points is, and the more likely they are to belong to the same semantic category. The squared Euclidean distance between the structural signatures quantifies the degree of difference between the source and target structural signatures in the sorting space. The maximum structural signature distance between all target clusters and source class prototype pairs is used as a normalization factor to compress the relation cost to the [0,1] interval, thereby eliminating the scale effect caused by the difference in feature dimensions. This is a constant term, a very small constant, to avoid the denominator being zero; , The indices for traversing all target clusters and source class prototypes are taken at 1,…,C and 1,…,K respectively, to calculate the global maximum distance for normalization. The relation cost is calculated entirely based on intra-domain distances, making it coordinate-free in the heterogeneous feature space and stable under the perturbation of a moderate Gaussian difference privacy mechanism for transmitting prototypes. The row sorting operation eliminates the dependency on arbitrary ordering of neighboring classes and converts each cluster or prototype into a structural signature. In effect, the cost queries whether the target cluster occupies a similar relative position within the target cluster as the source prototype occupies within the source class. This is weaker than assuming coordinate-level comparability, but stronger than treating all prototypes as commutative.

[0025] Next, the relational cost matrix is ​​solved using a partially optimal transmission method to obtain the optimal transmission plan. In the partially optimal transmission solution, a marginal distribution of the source domain is set. Target domain marginal distribution , , Given two column vectors of length K and C, both consisting entirely of 1s, the partial optimal transport problem is solved using the following formula: , The optimal transmission plan (matrix) represents the optimal matching transmission quality between the target cluster and the source category; For the candidate transmission plan matrix, Let Frobenius inner product represent the total matching cost under the current transmission scheme T, and let T be the optimization objective, seeking the transmission scheme that minimizes the total matching cost; feasible region , As a row constraint, the total mass actually transmitted by each target cluster does not exceed the marginal distribution of the target domain. , As a column constraint, the total quality actually received by each source category does not exceed the marginal distribution of the source domain. , As a total quality constraint, the sum of all transmission quality is equal to the preset proportion of total transmission quality m, ensuring that the total transmission quality meets the requirements. The value of m that maximizes the average row confidence is selected through grid search.

[0026] Subsequently, the bijective mapping from cluster to class is solved according to the optimal transmission plan to generate pseudo-labels for the target samples. (The optimal transmission plan is then used for further analysis.) Perform row normalization to obtain a normalized transmission plan , for Given rows and vectors, solve the linear assignment problem on a normalized transport plan to obtain a bijective mapping from the target cluster to the source class. Assign pseudo-labels to each target sample based on the bijective mapping results. The calculation formula is as follows: , For the first j Pseudo-labels for each target sample For the first j Clustering assignment results for each target sample.

[0027] Finally, based on the pseudo-labels of the target samples, the transmission conditions corresponding to each target sample are calculated. The calculation of the transmission condition vector is divided into two modes, as follows.

[0028] When the source domain and the target domain feature subspace are semantically related, for a target sample j belonging to cluster c, the corresponding transmission condition is the weighted sum of the corresponding row of the normalized transmission plan and the source prototype after bijective rearrangement, calculated as follows: , For the OT-weighted transmission conditions of the j-th target sample, Clustering in normalized transmission plans The corresponding number c A line is a string of length 1000. K The vector whose th k Each element represents a cluster. c To source category k Normalized matching weights, For clusters to bijective-like σ The rearranged source domain noisy prototype sequence, the first one in the sequence k The elements are Source categoryk Through inverse mapping σ -1 Once the target cluster is located, the source prototype corresponding to that cluster is extracted. The length of this sequence is K, and it is sorted by the source category index. It is a set of basis vectors for weighted mixing.

[0029] When the feature subspaces of the source and target domains do not intersect, the cosine similarity between the target sample and each target cluster center is calculated, and after scaling with a temperature coefficient, soft weights are obtained. These weights are then mapped back to the source prototypes via bijective mapping, and the weighted transfer condition calculation formula is as follows: , , For the first j Prototype similarity weighted transmission conditions for each target sample; For the first j The nth target sample pair k The normalized soft weights of the target cluster centers are obtained by normalizing the temperature-scaled cosine similarity using Softmax. For source category k Through inverse mapping σ -1 After locating the corresponding target cluster, the prototype of the noise source corresponding to that cluster is then extracted; For the first j The target domain feature vector of each target sample For the first k One target cluster center, This refers to the temperature parameter.

[0030] S3. The target side trains a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features in the style of the source domain, while retaining the original generated features and the generation variance of each dimension.

[0031] Among them, encoder target domain features Mapped to Gaussian latent distribution The encoder does not accept conditional input; the decoder The latent vector z is concatenated with the transmission condition cond and mapped to the generated complementary feature distribution. .

[0032] During training, a joint loss function is used, which includes reconstruction loss, KL divergence loss, and Sinkhorn divergence optimal transport regularization. The formula for calculating the joint loss function during training is as follows: , , , These are the reconstruction loss, KL divergence loss, and Sinkhorn optimal transmission loss, respectively. As an effective weight for the KL divergence, it is linearly annealed from 0 to a preset value in the first Ewarmup rounds. β To prevent the KL term from dominating in the early stages of training, which could lead to posterior collapse; The weighting coefficients for the optimal transmission loss control the contribution of the Sinkhorn term to the total loss.

[0033] Reconstruction loss To generate a negative log-likelihood of features relative to the reconstructed target, enabling the generated complementary features to correlate with the target samples while preserving sample specificity, the calculation formula is as follows: , To weight the squared error, the reconstruction error is adaptively weighted by the prediction variance, allowing the model to tolerate larger errors in the high uncertainty region and strictly require accuracy in the low uncertainty region. For the first l The reconstruction objective of the dimension is a weighted mixture of target features and transmission conditions, i.e. , For target domain features, These are interpolation coefficients used to reconstruct the target, controlling the mixing ratio of target domain features and transmission conditions in the reconstructed target. For transmission conditions, The first predicted by the decoder l The posterior mean of the reconstructed features is the posterior mean of the generated complementary features. The first output of the decoder l The prediction standard deviation of a feature dimension describes the uncertainty of the model's reconstruction of that dimension. For the expectation operator of the variational posterior distribution of the encoder, by considering the latent variables z Perform sampling to estimate the reconstruction loss.

[0034] KL divergence loss Let KL divergence be the potential posterior distribution and the standard normal prior, used to regularize the latent space to keep the generation process stationary under target-side perturbations. The calculation formula is as follows: , For the dimension-wise contribution of KL divergence, The latent variable of the encoder output r The standard deviation of the dimensionality describes the latent distribution in the dimensionality. r The degree of discreteness of the dimension, The latent variable of the encoder outputr The mean of the dimension describes the latent distribution in the th dimension. r The central position of the dimension.

[0035] Sinkhorn's optimal transmission loss The entropy-regularized Sinkhorn divergence between the batch-generated feature mean and the batch-transfer conditional distribution aligns the batch-level generation distribution with the transfer conditional distribution, anchoring it to the source prototype manifold. The calculation formula is as follows: , This is the set of posterior means of generated features for all samples in the current training batch, i.e., the set of complementary feature means output by the decoder. This is the set of transmission conditions corresponding to all samples in the current training batch; Entropy-regularized Sinkhorn divergence is a differentiable measure of distribution distance. It accelerates optimal transmission calculation through entropy regularization and measures the degree of matching between the mean distribution of generated features and the distribution of transmission conditions. This is the Sinkhorn entropy regularization coefficient, which controls the weight of the transmission plan entropy.

[0036] The three loss terms mentioned above play different roles: the reconstruction term associates the generated view with the target sample; the KL divergence loss regularizes the latent space so that the generation remains stable under target-end perturbations; and the Sinkhorn optimal transmission loss aligns the batch-level generation distribution with the transmission conditional distribution. Removing any of these terms will result in a unique failure mode: training with only reconstruction may ignore the source semantic manifold, excessive KL divergence pressure may destroy discriminative variation, and generation without Sinkhorn optimal transmission loss control may produce confident but poorly ranked class probabilities.

[0037] Simultaneously, during inference, post-generation smoothing is performed on the generated complementary features to obtain the original complementary features. The original complementary features are generated using the latent posterior mean during inference, and then weighted and smoothed with the transmission conditions to obtain the final complementary features. The calculation formula is as follows: , As complementary features, As original complementary features, This is an oversmoothing coefficient used to balance the variance of generated features with semantic bias, reducing the variance introduced by generation randomness. .

[0038] S4. Based on the original generated features, the dimension-wise generated variance, and the corresponding transmission conditions, the target side calculates the reconstruction uncertainty and semantic uncertainty for each target sample, presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier, and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier, and the alignment classifier through a fusion strategy to obtain the target domain classification result.

[0039] First, based on the original generated features, the dimension-wise generated variance, and the corresponding transmission conditions, the target party calculates the reconstruction uncertainty and semantic uncertainty for each target sample. The formula for calculating the reconstruction uncertainty is: , For the first j Uncertainty in the reconstruction of a target sample For source domain feature dimensions, The first output of the decoder j The sample at the th l The prediction variance of dimension. The formula for calculating semantic uncertainty is: , For the first j The semantic uncertainty of a target sample For the original complementary features of the j-th target sample, For the first j The transmission conditions of a target sample, the semantic uncertainty is the complement of the cosine similarity between the original generated features and the transmission conditions before smoothing.

[0040] Then, based on reconstruction uncertainty and semantic uncertainty, thresholds for reconstruction uncertainty and semantic uncertainty are preset respectively, and weights are assigned to each target sample to generate training weights for each target sample. The thresholds for reconstruction uncertainty and semantic uncertainty are respectively... , For satisfying and The j 1 target sample, training weights The remaining target samples are used for training weights. , Minimum retention ratio Ensure at least A proportional sample.

[0041] Finally, based on the training weights of each target sample, a baseline classifier, an augmentation classifier, and an alignment classifier are trained separately. The outputs of the baseline classifier, the augmentation classifier, and the alignment classifier are then weighted and fused using a fusion strategy to obtain the target domain classification result.

[0042] The baseline classifier is trained with the original target domain features as input and pseudo-labels as supervision; the augmentation classifier is trained with the augmented features obtained by concatenating the original target domain features and complementary features as input and the training weights of the target samples as weighted training; the alignment classifier is trained by solving the least squares linear mapping based on the cluster-to-class bijective mapping and the noisy class prototype of the S1 output to map the target domain features to the source domain space and with the mapped alignment features as input.

[0043] Weighted fusion is achieved through the following formula. , For the classification results of the target domain, , , These are the outputs of the baseline classifier, the augmentation classifier, and the alignment classifier, respectively. , These are the first-layer fusion coefficient and the second-layer fusion coefficient, respectively. The weight parameters of the two-layer fusion are optimized on the validation set using a grid search, with the optimization objective being to maximize the weighted standard (…). w 1 Acc + w 2 F1 + w 3 AUC ), w 1 , w 2 , w 3 The respective accuracy in the grid search optimization objective Acc, F1 score F1、 Area under the ROC curve AUC The weighting coefficients.

[0044] To verify the effectiveness of the method in this embodiment, the following experiment was conducted.

[0045] Datasets and Experimental Setup. The datasets include the CWRU dataset and the Office-Home-10 dataset. The CWRU dataset provides vibration signals of rolling bearings under four fault conditions: normal, inner race, ball race, and outer race fault. Experiments segmented the raw signals into 50 windows of 1024 samples each and extracted 64-dimensional time-frequency features. During training, the target domain was treated as completely unlabeled. The Office-Home-10 dataset contains four visual domains: art, clip art, product, and real-world. The experiments used the 10 categories most relevant to the current vertical FTL setting: backpack, bicycle, calculator, keyboard, laptop, monitor, mouse, mug, printer, and webcam. Images were generated using a 2048-dimensional ResNet-50 feature table, with each descriptor split into two non-overlapping 1024-dimensional halves to simulate two sides with complementary feature subspaces. The source side is the product domain, and the target side is the real-world domain. The target domain was unlabeled during training.

[0046] Comparison with existing methods. Experiments are compared with five methods operating under the same joint constraints (no original source features at the target end): NoTransfer in... and Training on the initial pseudo-labels only implies pseudo-labels; FedAvg-FTL shares CORAL covariance statistics to align target features with the source covariance structure; DANN-FTL fits a least-squares linear mapping from target cluster centers to bijective reordered DP source prototypes; SHOT-FTL self-trains using entropy minimization on the top 60 most confident target predictions after initial pseudo-label training; ProtoFTL computes soft target features as temperature-scaled versions of the DP source prototypes. The softmax weighted sum was used, with weights derived from the prototype similarity on the t-side. The experimental results are shown in Table 1.

[0047] Table 1. Summary of the effects of different methods on the CWRU dataset and the Office-Home-10 dataset. .

[0049] As shown in Table 1, in the industrial fault diagnosis scenario of the CWRU dataset, FedPOT (in this embodiment) achieved the best overall performance across all three metrics. Its accuracy was on par with the existing best baseline, DANN-FTL, and its macro AUC was 0.2 percentage points higher, achieving a balanced optimal performance between classification accuracy and probabilistic calibration quality. In the challenging scenario of the Office-Home-10 dataset where feature subspaces are disjoint, FedPOT (in this embodiment) significantly outperformed all comparison baselines across all three metrics. Its accuracy improved by 14.9 percentage points compared to the strongest baseline, and its macro AUC improved by 7.8 percentage points, fully validating the robust alignment and feature enhancement capabilities of this solution in heterogeneous feature spaces. Overall, FedPOT (in this embodiment) demonstrates significant performance advantages in both types of scenarios, with particularly outstanding improvements in scenarios involving heterogeneous feature spaces and high difficulty in unsupervised transfer learning.

[0050] Ablation test results of core components. To verify the independent contribution and synergistic effect of each core technology component, an ablation test was conducted to test the performance changes after removing different components of FedPOT (in this embodiment). The experimental results are shown in Table 2.

[0051] Table 2. Summary of performance changes after removing different components in the ablation experiment. .

[0053] The results in Table 2 show that the optimal transport is the core component. Removing the corresponding processing content of this component causes a sharp drop in the performance of both datasets, proving that the partially optimal transport based on intra-domain relation costs is the core of establishing cross-domain semantic mapping and cannot be replaced by simple prototype averaging. Meanwhile, each component has independent gains and synergistic effects. Removing the Sinkhorn optimal transport loss and transport conditions results in varying degrees of decrease in macro F1 and macro AUC, demonstrating that the Sinkhorn optimal transport loss and transport condition design can independently improve generation quality and calibration performance. The various technical features are not simply superimposed but work together to achieve end-to-end performance improvement. Furthermore, regarding excellent privacy robustness, FedPOT (in this embodiment) maintains stable accuracy on the Office-Home-10 dataset under the strict condition of a privacy budget tightened to ε=0.02, with only a slight decrease in macro AUC, proving that the relational alignment design of FedPOT (in this embodiment) is highly robust to differential privacy noise.

[0054] Privacy sensitivity analysis. The example tested performance variations under different privacy budgets ε∈[0.1,∞) on the CWRU and Office-Home-10 datasets, respectively. The results are as follows: Figure 1 and Figure 2The experimental results show that, within a wide privacy budget, the accuracy, macro F1, and macro AUC of FedPOT (in this embodiment) remain relatively stable, without any sudden performance drop as privacy tightens. The core reason for this is that the relation cost matrix of FedPOT (in this embodiment) is constructed based on the ordered structural signatures of intra-domain distances, relying on the relative geometric structure between classes rather than the absolute coordinates of the prototype. Therefore, the additive noise introduced by differential privacy does not significantly change the order of the structural signatures, and the semantic bijection from cluster to class remains stable. These results verify that FedPOT (in this embodiment) can maintain stable transfer performance under strict privacy constraints, achieving a balance between privacy protection and classification accuracy.

[0055] Feature Representation Visualization Verification. To intuitively verify the improvement effect of complementary features generated by FedPOT (in this embodiment) on the discriminative power of target domain features, the t-SNE algorithm is used to perform two-dimensional dimensionality reduction visualization of the target domain features. The visualization results of the CWRU bearing fault dataset are shown below. Figure 3 and Figure 4 As shown, the visualization results of the Office-Home-10 cross-domain image dataset are as follows: Figure 5 and Figure 6 As shown. For the CWRU dataset, Figure 3 The distribution results using only the original target domain features show that different fault categories have a certain degree of separability, but there is obvious overlap at the category boundaries and the dispersion of samples within the category is high. Figure 4 The distribution results after fusing the complementary features generated by this invention show that the intra-class cohesion of similar samples is significantly enhanced, the inter-class boundaries are clearer, the number of overlapping samples at the boundaries is significantly reduced, and the class separability is further improved. For the Office-Home-10 dataset, Figure 5 The distribution results using only the original target domain features are weak overall class discrimination because the source and target domain feature subspaces do not intersect and there are many categories with severe overlap in most categories. Figure 6 The distribution results after fusing complementary features from FedPOT (in this embodiment) show a significant improvement in the local neighborhood consistency of samples, increased clustering of similar samples, reduced inter-class overlap, and effective supplementation of the class discrimination information carried by the features. In summary, the visualization results of both datasets consistently demonstrate that the source domain style complementary features generated by FedPOT (in this embodiment) through transmission condition guidance can effectively supplement the missing class discrimination information in the target domain, enhance the intra-class cohesion and inter-class discriminative power of the features, provide higher-quality input features for downstream classifiers, and verify the actual role of the generation enhancement module.

[0056] Probabilistic calibration performance analysis. To evaluate the probabilistic reliability of the classification results output by FedPOT (in this embodiment), a reliability plot was used to verify the probabilistic calibration performance. The results are as follows: Figure 7 and Figure 8 As shown. Among them. Figure 7 The calibration results for the CWRU dataset, Figure 8 The calibration results are for the Office-Home-10 dataset. The horizontal axis of both graphs represents the predicted confidence level of the classifier output, and the vertical axis represents the actual classification accuracy of samples within the corresponding confidence level interval. The diagonal line in the graph represents the ideal calibration state, where the predicted confidence level and the true accuracy are completely consistent. The closer the curve is to the diagonal line, the better the probability calibration quality, and the higher the reference value of the output confidence level. Each graph contains three comparison curves: t-only represents the baseline classifier using only the original target domain features, FedPOT aug represents the enhanced classifier using the original features and generated complementary features, and FedPOT fused represents the final ensemble classifier of this invention after employing a three-classifier fusion strategy. Experimental results show that on both datasets, compared to the baseline classifier using only target domain features, the calibration curves of the FedPOT (in this embodiment) enhanced classifier and the final fusion classifier are closer to the ideal diagonal line, with smaller deviations between the confidence level and the actual accuracy, indicating better probability ranking quality. Especially in the high-confidence range, FedPOT (in this embodiment) shows a higher match between its actual accuracy and predicted confidence, effectively mitigating the overconfidence problem caused by pseudo-label noise. This feature makes the classification results output by FedPOT (in this embodiment) have more reliable probabilistic reference value, making it more suitable for risk-sensitive scenarios with high requirements for confidence accuracy, such as industrial fault diagnosis and risk decision-making.

[0057] Communication cost comparison. In the experiment, the cross-party communication overhead of FedPOT (in this embodiment) was compared with that of various baseline methods, such as... Figure 9 and Figure 10 As shown. Figure 9 The results are a comparison of total communication costs. Figure 10 This is a comprehensive comparison chart of the number of communication rounds and the amount of data transmitted per round. Figure 9 The logarithmic scale shows the total number of floating-point numbers transmitted across privacy boundaries for each method. It can be observed that FedPOT (in this embodiment) only requires a single round of communication from the source to the target, transmitting only K differential privacy class prototypes, with a total communication volume of only [missing information]. The total transmission volume is only 256 floating-point numbers in the CWRU dataset scenario and only 10240 floating-point numbers in the Office-Home-10 dataset scenario. Compared with the original data transmission and multi-round model aggregation methods, FedPOT (in this embodiment) reduces communication volume by tens to hundreds of times, and the communication reduction factor can reach the ratio of the total number of source domain samples to the number of categories. .Figure 10 This is a comprehensive comparison chart of the number of communication rounds and the amount of data transmitted per round on a logarithmic coordinate system. The horizontal axis represents the amount of data transmitted per round, and the vertical axis represents the number of communication rounds. The area of ​​the bubble in the chart is positively correlated with the total communication cost of the corresponding method. As can be seen from the chart, most federated transfer learning baseline methods require multiple rounds of iterative interaction, resulting in high total communication costs and complex system deployment interactions. FedPOT (in this embodiment), located in the lower left area of ​​the chart, has the dual advantages of small data volume per round and fewer communication rounds, completing all cross-domain knowledge transfer without multiple rounds of federated aggregation. The single-round prototype transmission architecture of FedPOT (in this embodiment) allows the entire process of clustering, alignment, generation, and classification at the target end to be completed locally without additional cross-party interaction, greatly reducing network bandwidth dependence and system deployment threshold. It is particularly suitable for scenarios such as industrial edge devices and bandwidth-constrained industrial IoT, demonstrating excellent engineering practicality and feasibility.

[0058] In summary, the above experiments fully verified the effectiveness and beneficial effects of the method described in this invention from multiple dimensions, including overall performance, component contribution, privacy robustness, visualization effect, calibration quality, and communication overhead.

[0059] This embodiment also provides a privacy-preserving federated transfer learning system based on partially optimal transmission, used to implement the above-mentioned privacy-preserving federated transfer learning method based on partially optimal transmission, including source nodes and target nodes; Source nodes include: The differential privacy perturbation module is used by the source to calculate class prototype vectors of various categories based on labeled source domain data, apply differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and send them to the target. The target nodes include: The clustering module is used by the target party to cluster unlabeled target domain data and obtain clustering assignment results containing target cluster centers and samples; The partial optimal transmission solution module is used by the target to construct the distance matrix in the source domain and the distance matrix in the target domain based on the noisy class prototype and the target cluster center, respectively, obtain their respective structural signatures, construct the relation cost matrix, and obtain the optimal transmission plan through partial optimal transmission solution; The transmission condition generation module is used to solve the bijective mapping from cluster to class according to the optimal transmission plan, generate pseudo-labels for target samples, and calculate the transmission conditions corresponding to each target sample. The original generated features and the dimension-wise generated variance generation module are used by the target side to train a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features in the style of the source domain, while retaining the original generated features and the dimension-wise generated variance. The target domain classification result generation module is used by the target party to calculate the reconstruction uncertainty and semantic uncertainty for each target sample based on the original generated features, the dimension-wise generated variance and the corresponding transmission conditions. It presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier and the alignment classifier through a fusion strategy to obtain the target domain classification result.

[0060] This embodiment also provides a privacy-preserving federated transfer learning device based on partially optimal transfer, including a processor and a memory, wherein the processor implements the above-described privacy-preserving federated transfer learning method based on partially optimal transfer when executing a computer program stored in the memory.

[0061] This embodiment also provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the above-described privacy-preserving federated transfer learning method based on partially optimal transmission.

[0062] This embodiment provides a privacy-preserving federated transfer learning method based on partially optimal transmission. First, by extracting differential privacy class prototypes at the source end and performing local clustering at the target end, cross-domain knowledge sharing can be achieved with only a single round of transmission of desensitized statistics, significantly reducing communication overhead while strictly protecting the privacy of the original source domain data. Then, a relation cost matrix is ​​constructed based on domain-specific structural signatures, and partially optimal transmission is solved. Robust cluster semantic mapping can be established without direct cross-domain feature comparison, effectively adapting to heterogeneous or even disjoint feature spaces, and exhibiting strong resistance to differential privacy noise. Next, the transmission conditions derived from optimal transmission guide a conditional variational autoencoder to generate complementary features of the source domain style. Simultaneously, a two-dimensional uncertainty assessment is used to assign differentiated training weights to samples, supplementing the target domain's discriminative information through generated features and mitigating the negative impact of low-quality generated samples through quality filtering, ensuring the reliability of the generated enhancements. Finally, a weighted fusion of baseline, enhancement, and alignment classifiers in the later stages balances the classification advantages of different feature perspectives, while simultaneously improving the classification accuracy, macro-F1, macro-AUC, and probability calibration quality of the target domain, enhancing the cross-domain transfer performance under privacy constraints.

[0063] This embodiment provides a privacy-preserving federated transfer learning method based on partially optimal transmission, which features strong privacy protection and low communication overhead. It only requires a single round of transmission of K differential privacy class prototypes, with a communication volume of only [missing information]. This is far lower than the original data transmission or multi-round model aggregation; it provides formal differential privacy guarantees through a calibrated Gaussian mechanism, protecting individual sample information in the source domain.

[0064] This embodiment provides a privacy-preserving federated transfer learning method based on partially optimal transmission. It constructs a relation cost matrix using intra-domain structural signatures, eliminating the need for direct cross-domain feature comparison. This method is suitable for vertical federated scenarios with different feature dimensions and non-overlapping subspaces. Partial optimal transmission allows for partial quality matching, prioritizing the retention of high-confidence correspondences, and exhibits strong robustness against differential privacy noise and target cluster imbalance.

[0065] This invention provides a privacy-preserving federated transfer learning method based on partially optimal transfer. The semantic conditions derived from the optimal transfer guide the generation of a conditional variational autoencoder. The generated distribution is anchored to the source prototype manifold by combining the Sinkhorn optimal transfer loss, thus avoiding the generated features from deviating from the transfer semantics. After generation, the smoothing effectively reduces the variance of random generation and improves the stability of features and the quality of probability calibration.

[0066] While exemplary embodiments of the invention have been described herein, many other variations or modifications conforming to the principles of the invention can be directly determined or derived from the disclosure of this invention without departing from its spirit and scope. Therefore, the scope of the invention should be understood and recognized to cover all such other variations or modifications.

Claims

1. A privacy-preserving federated transfer learning method based on partially optimal transfer, applied to federated transfer learning involving a source party and a target party, wherein the source party holds a labeled source domain dataset and the target party holds an unlabeled target domain dataset, characterized in that, This includes the following operations: S1. The source calculates class prototype vectors for each category based on the labeled source domain data, applies differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and sends them to the target. The target performs clustering on the unlabeled target domain data to obtain clustering assignment results containing target cluster centers and samples. S2. Based on the noisy class prototype and the target cluster center, the target side constructs the distance matrix in the source domain and the distance matrix in the target domain, respectively, obtains their respective structural signatures, constructs the relation cost matrix, and obtains the optimal transmission plan through partial optimal transmission solution; according to the optimal transmission plan, it solves the bijective mapping from cluster to class, generates pseudo-labels for target samples, and calculates the transmission conditions corresponding to each target sample. S3. The target side trains a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features of the source domain style and retain the original generated features and the generation variance of each dimension. S4. Based on the original generated features, the dimension-wise generated variance, and the corresponding transmission conditions, the target side calculates the reconstruction uncertainty and semantic uncertainty for each target sample, presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier, and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier, and the alignment classifier through a fusion strategy to obtain the target domain classification result.

2. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S1, the operation of the differential privacy Gaussian mechanism perturbation is as follows: the feature vector of each source domain sample is pruned using the ℓ2 norm, and the source side performs perturbation on each category... k The conditional mean vector of the classes is used as the original class prototype. The calculation formula is as follows: , For category k The class prototype mean, For category k The number of samples, For the first i Feature vectors of source domain samples To assign corresponding labels, Gaussian noise is applied to each original class prototype to obtain the category. k Desensitizer prototype Among them, noise scale , The vector is Gaussian noise. This is the maximum amount that can be cut. For source domain feature dimensions, It is the identity matrix. This is a relaxation term for differential privacy.

3. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S2, the distance matrix in the source domain is the Euclidean distance between each pair of noisy class prototypes; the distance matrix in the target domain is the Euclidean distance between each pair of cluster centers in the target domain.

4. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S2, the source domain marginal distribution is set in the partially optimal transport solution. Target domain marginal distribution , , Given two column vectors of length K and C, both consisting entirely of 1s, the partial optimal transport problem is solved using the following formula: , For the optimal transmission plan, For the candidate transmission plan matrix, For Frobenius inner product, feasible region , As a row constraint, the total mass actually transmitted by each target cluster does not exceed the marginal distribution of the target domain. , As a column constraint, the total quality actually received by each source category does not exceed the marginal distribution of the source domain. , As a total quality constraint, the sum of all transmission quality is equal to the preset percentage of total transmission quality, m.

5. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S3, a joint loss function including reconstruction loss, KL divergence loss and Sinkhorn optimal transmission loss is used during training; during inference, post-generation smoothing is performed on the generated complementary features to obtain complementary features.

6. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S4, the formula for calculating reconstruction uncertainty is: , For the first j Uncertainty in the reconstruction of a target sample For source domain feature dimensions, The first output of the decoder j The sample at the th l The prediction variance of dimension; the formula for calculating semantic uncertainty is: , For the first j The semantic uncertainty of a target sample For the original complementary features of the j-th target sample, For the first j Transmission conditions for each target sample.

7. The privacy-preserving federated transfer learning method based on partially optimal transmission according to claim 1, characterized in that, In S4, the baseline classifier is trained with the original target domain features as input and pseudo-labels as supervision; the augmentation classifier is trained with the augmented features obtained by concatenating the original target domain features and complementary features as input and the training weights of the target samples are used for weighted training. The alignment classifier is based on the cluster-to-class bijective mapping and the noisy class prototype of the S1 output. It solves the least squares linear mapping to map the target domain features to the source domain space, and uses the mapped alignment features as input for training.

8. A privacy-preserving federated transfer learning system based on partially optimal transmission, used to implement the privacy-preserving federated transfer learning method based on partially optimal transmission as described in claim 1, characterized in that, Including source nodes and target nodes; Source nodes include: The differential privacy perturbation module is used by the source to calculate class prototype vectors of various categories based on labeled source domain data, apply differential privacy Gaussian perturbation to each class prototype vector to obtain noisy class prototypes that satisfy differential privacy, and send them to the target. The target nodes include: The clustering module is used by the target party to cluster unlabeled target domain data and obtain clustering assignment results containing target cluster centers and samples; The partial optimal transmission solution module is used by the target to construct the distance matrix in the source domain and the distance matrix in the target domain based on the noisy class prototype and the target cluster center, respectively, obtain their respective structural signatures, construct the relation cost matrix, and obtain the optimal transmission plan through partial optimal transmission solution; The transmission condition generation module is used to solve the bijective mapping from cluster to class according to the optimal transmission plan, generate pseudo-labels for target samples, and calculate the transmission conditions corresponding to each target sample. The original generated features and the dimension-wise generated variance generation module are used by the target side to train a conditional variational autoencoder based on the transmission conditions and target domain data. The conditional variational autoencoder takes the target domain features as input and the transmission condition vector as the decoder condition input to generate complementary features in the style of the source domain, while retaining the original generated features and the dimension-wise generated variance. The target domain classification result generation module is used by the target party to calculate the reconstruction uncertainty and semantic uncertainty for each target sample based on the original generated features, the dimension-wise generated variance and the corresponding transmission conditions. It presets the thresholds for reconstruction uncertainty and semantic uncertainty, assigns weights to each target sample, generates training weights for each sample, trains the baseline classifier, the augmentation classifier and the alignment classifier respectively, and performs weighted fusion of the outputs of the baseline classifier, the augmentation classifier and the alignment classifier through a fusion strategy to obtain the target domain classification result.

9. A privacy-preserving federated transfer learning device based on partially optimal transmission, characterized in that, It includes a processor and a memory, wherein the processor, when executing a computer program stored in the memory, implements the privacy-preserving federated transfer learning method based on partially optimal transfer as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the privacy-preserving federated transfer learning method based on partially optimal transfer as described in any one of claims 1-7.

Images