MFS methods are typically classified into two main categories: problem transformation and algorithm adaptation. Problem transformation approaches convert multi-label tasks into multiple single-label problems, enabling the application of traditional single-label FS techniques such as entropy-based label assignment (ELA), binary relevance (BR), and label powerset (LP) [23]. However, BR neglects the dependencies among labels, whereas LP often suffers from class imbalance and increased computational complexity.

Algorithm adaptation techniques overcome these limitations by directly extending single-label FS methods to handle multi-label data. Representative strategies include mutual information-based approaches for evaluating feature relevance and redundancy, as well as causal discovery frameworks for identifying causally informative features [24]. Moreover, MAs such as GA [11], ACO [12] and PSO [13] have been successfully employed to explore high-dimensional feature spaces.

Sparse learning has become a key focus in recent MFS research [25], with L1-norm and L2,1-norm regularizations as mainstream techniques. Huang et al. [26] proposed LLSF, using L1-norm regularization to learn low-dimensional representations while preserving label dependencies. Jian et al. [27] combined L2,1-norm regularization with latent space mapping to improve the performance of FS. Manifold learning methods, such as the PMFS-LRS based on low-rank sparse factorization proposed by Sun et al. [28], decompose the candidate label matrix into low-rank and sparse components, enabling the distinction between ground-truth and noisy labels, thus addressing performance degradation in traditional methods. Additionally, Zhang et al. [29] introduced manifold regularization to model label correlations and enhance feature relevance, while Zhang et al. [30] proposed LRDG, an MFS method that optimizes feature selection through deep learning-based latent representation and pseudo-label learning.

Federated FS has recently advanced in both single-label and multi-label domains [31]. Inspired by the FL paradigm, existing methods are generally categorized into vertical and horizontal federated FS. Vertical FS applies when clients share the same instance IDs but possess different feature spaces [32], whereas horizontal FS is used when clients hold different data instances while sharing a common feature set [33].

Within horizontal federated MFS, Mahanipour and Khamfroush [18] introduced FMLFS, which employs information-theoretic measures to evaluate feature-label associations and mitigate redundancy. They further proposed a fuzzy logic-based approach that integrates reinforcement learning with ACO [19]. Similarly, Song et al. [20] developed FedCMFS, a causal federated MFS method incorporating three novel components to enhance the performance of FS. However, most existing methods rely solely on the inherent data-locality of FL for privacy protection, without incorporating more rigorous mechanisms such as DP or SMPC—leaving them susceptible to potential information leakage.

This subsection introduces the DHBCPSO-MSR algorithm, which is executed by the client in the proposed Fed-MFSHBCPSO framework, including its inner modeling layer and outer optimization layer. The detailed flowchart of DHBCPSO-MSR is shown in Fig. 1.

Centralized MFS methods face significant challenges in distributed environments: centralized approaches risk privacy breaches, while federated methods rely on FL’s inherent privacy guarantees, which are often insufficient. Moreover, limited data sharing hinders the capture of inter-feature correlations, causing convergence to the local optima and limiting the global performance of FS. To address these issues, we propose Fed-MFSDHBCPSO—a FL framework that integrates DHBCPSO-MSR, DP, and SMPC, enhanced with manifold regularization and sparsity constraints (see Fig. 2).

1) Client-side MFS process

Each client performs local FS using the following the following steps:

Step 1: Local data preprocessing. Clients load local datasets, initialize parameters, and perform data cleaning and normalization to ensure high-quality inputs.

Step 2: Local FS via DHBCPSO-MSR. Each client executes DHBCPSO-MSR, integrating an inner modeling layer with manifold construction and sparsity constraints, alongside an outer optimization layer driven by HBCPSO. This dual-layer algorithm ensures optimal feature subset selection that aligns with the client’s local data distribution.

Step 3: Privacy-preserving transmission. To ensure privacy, the selected feature weights and their corresponding indices are perturbed using a differential privacy (DP) mechanism before being transmitted to the central server, thereby achieving ε-DP as defined in Eq. (8). Specifically, Gaussian noise is added to each feature weight to obscure the influence of individual data samples and defend against potential inference attacks. The perturbation process is given by:(8)W~i=Wi+𝒩(0,σ2),where W~i denotes the perturbed feature weight matrix for the i-th feature, and 𝒩(0,σ2) represents Gaussian noise with zero mean and variance σ2. The noise scale σ is calibrated based on the desired privacy level using the standard (ε,δ)-DP framework. In this paper, we follow common practices in the literature and set the privacy budget to ε=1.0, which achieves a good balance between privacy preservation and model utility [21]. Smaller values of ε (e.g., <1) provide stronger privacy but may degrade performance, whereas larger values (e.g., >5) weaken privacy guarantees. By setting ε=1.0, we align with the commonly accepted range [0.5,5] in FL scenarios, ensuring both practical utility and privacy protection.

Step 4: Local multi-label classification. Using the refined features, each client applies the multi-label k-nearest neighbors (ML-KNN) [19] for local multi-label classification. This decentralized approach minimizes communication overhead while ensuring data privacy.

2) Server-side dynamic collaborative optimization

The server implements a dynamic collaborative optimization strategy comprising the following steps:

Step 1: Key management. A public key infrastructure (PKI) is employed to securely distribute encryption keys, enabling end-to-end secure communication across the federated network.

Step 2: Feature aggregation and distribution.

(i) Secure aggregation via SMPC: Encrypted feature weights from clients are aggregated using SMPC, which ensures data privacy by allowing the server to compute aggregated feature weights without decryption. In this study, the SMPC protocol is simulated through a lightweight, custom implementation on the MATLAB platform. While standard secure computation frameworks such as CrypTen or PySyft are not utilized, our implementation adheres to core SMPC principles, enabling secure aggregation without decryption. This ensures that the server remains unable to access any client’s plaintext feature weights or index information during the aggregation process. The prototype is designed to evaluate the feasibility and computational efficiency of secure aggregation in resource-constrained edge computing environments.

(ii) Global feature weight computation: The global feature weight vector Wglobal is computed as in Eq. (9).(9)Wglobal=∑i=1NγcW(c),where Wglobal represents the aggregated feature importance vector across all clients, and W(c) is the sparse, encrypted vector from each client. The weighting factor γc is calculated based on the dataset size: γc=|Dc|∑i=1N|Di|.

Step 3: Global iterative optimization. The server iteratively aggregates encrypted feature weights using SMPC to update Wglobal, ensuring data confidentiality without accessing plaintext data, and sends the updated model back to clients for further iterations.

In this framework, clients apply DP to perturb their feature weights for privacy, while the server aggregates encrypted feature weights securely using SMPC. This process ensures that no sensitive data is exposed during aggregation.

To thoroughly evaluate the practical applicability of the proposed method, we analyze the privacy preservation capability and computational complexity of Fed-MFSDHBCPSO.

We conducte experiments with five clients and three datasets of varying sizes (Flags, Education, and Mediamill), selecting the final number of features according to the method in [39]. A sensitivity analysis of the hyperparameters α, β, and λ is performed to evaluate their impact on the method’s performance. Different parameter settings are tested by varying one hyperparameter at a time, and the model’s performance is assessed using AP and HL. The results, shown in Fig. 3, demonstrate that regularization weights significantly influence feature sparsity, label structure preservation, and model convergence. The optimal hyperparameter combination of [0.5, 0.5, 0.1] is identified, providing a strong foundation for further optimization and application.

To validate the effectiveness of the proposed method, Figs. 4–11 compare it against the initial baseline, five recent centralized methods, and three federated MFS methods across eight datasets. The experiments are conducted with five clients, assessing performance across varying feature subsets. The results show that Fed-MFSDHBCPSO outperforms other methods on most datasets with only 10 features, including Mediamill, Image, Scene, Flag, and Education. On the Enron and Emotions datasets, Fed-MFSDHBCPSO, using 80 features, achieves comparable or superior Macro-F1, Micro-F1, and Hamming loss scores, while demonstrating more consistent performance across other metrics.

These results indicate that the proposed method has minimal impact on communication overhead and model performance, despite the size of the feature set transmitted between clients and the edge server. It simultaneously enhances the effectiveness of the model, achieving an optimal balance between communication efficiency and predictive accuracy.

To evaluate the efficiency of the proposed method, we conducted a single federated iteration with five clients and compared the runtime of Fed-MFSDHBCPSO against several baseline methods, as presented in Table 2, where the bold values represent the best results. The results demonstrate that Fed-MFSDHBCPSO consistently achieves the shortest runtimes, particularly on large-scale datasets such as Mediamill, Enron, and Education. This superior efficiency stems from its dual-layer optimization, manifold regularization, sparsity constraints, and FL framework. In contrast, the Org method, which lacks FS, leads to significantly longer runtimes. Furthermore, methods such as Fed-LRDG, Fed-MOEA/D, Fed-NSGA-III, and PDMFS exhibit higher computational overhead on large datasets. Overall, Fed-MFSDHBCPSO delivers the best runtime efficiency among all evaluated algorithms.

To evaluate the contribution of each component, we conducted ablation experiments on five clients, determining the final number of selected features using the method in [39]. Four model variants were constructed by individually removing PSO (Proposed/PSO), HBO (Proposed/HBO), manifold regularization (i.e., removing Laplacian regularization, called Proposed/MR), and the sparsity constraint (Proposed/SC). In addition, we removed the inner optimization to create Fed-HBCPSO and compared it with Fed-NSGA-III and Fed-MOEA/D, using AP as the primary metric. As shown in Table 3, where the bold values indicate the best results. Excluding PSO or HBO led to significant performance degradation, while removing manifold regularization or the sparsity constraint also reduced accuracy and stability. Moreover, Fed-HBCPSO consistently outperformed Fed-NSGA-III and Fed-MOEA/D, benefiting from its three-population co-evolutionary mechanism, where sub-populations of varying quality periodically exchange best-solution information. This design effectively balances exploration and exploitation, avoids the local optima, and accelerates convergence. In contrast, the single-population strategies of NSGA-III and MOEA/D in federated settings struggle to maintain both diversity and precision, resulting in inferior performance. These findings demonstrate that all components are complementary and indispensable to the overall effectiveness of the proposed model.

To assess the performance differences between Fed-MFSDHBCPSO and other comparison methods, we apply the Friedman test followed by the Nemenyi post-hoc test. As shown in Table 4, the Friedman statistics (FF) for all evaluation metrics exceed the critical value of 2.0320 at the 0.05 significance level, and the corresponding p-values are all below 0.05. These results strongly reject the null hypothesis of no significant performance difference, indicating that Fed-MFSDHBCPSO demonstrates statistically significant improvements compared to the other methods.

Following this, the Nemenyi post-hoc test is applied to identify which pairs of methods differ significantly. This test compares the mean ranks of the methods, where a lower rank indicates better performance. A significant difference between two methods is confirmed if the gap in their mean ranks exceeds the critical distance (CD), illustrated by the red line in the figure. The CD is computed as shown in Eq. (11).(11)CD=qαk(k+1)6N,where k is the number of methods being compared, and N is the number of datasets, and qα=3.098 corresponds to a significance level of α=0.05, resulting in CD=3.7943. This threshold is used to determine whether the performance differences between methods are statistically significant.

Fig. 12 presents the results of the Nemenyi test, with the left side highlighting methods with superior performance rankings and the horizontal axis indicating the average ranks of these approaches. The differences in rankings between the proposed Fed-MFSDHBCPSO and FMLFS, PDMFS, and GLFS exceed the CD, demonstrating that Fed-MFSDHBCPSO significantly outperforms these methods. Conversely, the rankings of Fed-CFMS and Fuzzy FMFS lie within the CD threshold, indicating no statistically significant difference from Fed-MFSDHBCPSO. Nevertheless, Fed-MFSDHBCPSO consistently attains the highest rank, while Fed-CFMS and Fuzzy FMFS exhibit comparative.