Federated multi-label text feature selection via manifold-aware sparse modeling and cooperative grey wolf optimization.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 7;16:11680. doi: 10.1038/s41598-026-46223-4 Search in PMC Search in PubMed View in NLM Catalog Add to search Federated multi-label text feature selection via manifold-aware sparse modeling and cooperative grey wolf optimization Yufeng Zheng Yufeng Zheng 1 Hubei Provincial Key Laboratory of Green Intelligent Computing Power Network, Hubei University of Technology, Wuhan, 430000 Hubei China Find articles by Yufeng Zheng 1 , Zhiwei Ye Zhiwei Ye 1 Hubei Provincial Key Laboratory of Green Intelligent Computing Power Network, Hubei University of Technology, Wuhan, 430000 Hubei China 2 School of Computer Science and Artificial Intelligence, Hubei University of Technology, Wuhan, 430000 Hubei China Find articles by Zhiwei Ye 1, 2, ✉ , Songsong Zhang Songsong Zhang 2 School of Computer Science and Artificial Intelligence, Hubei University of Technology, Wuhan, 430000 Hubei China Find articles by Songsong Zhang 2, ✉ , Kaiqi Wang Kaiqi Wang 3 Faculty of Engineering, The University of Sydney, Sydney, 2006 New South Wales Australia Find articles by Kaiqi Wang 3 Author information Article notes Copyright and License information 1 Hubei Provincial Key Laboratory of Green Intelligent Computing Power Network, Hubei University of Technology, Wuhan, 430000 Hubei China 2 School of Computer Science and Artificial Intelligence, Hubei University of Technology, Wuhan, 430000 Hubei China 3 Faculty of Engineering, The University of Sydney, Sydney, 2006 New South Wales Australia ✉ Corresponding author. Received 2025 Dec 15; Accepted 2026 Mar 24; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13062154  PMID: 41946792 Abstract Feature selection (FS) for multi-label text classification faces issues such as high dimensionality, strong label correlations, and sparse features, which often lead to suboptimal feature subsets. Moreover, most existing methods are centralized and thus ill-suited to real-world distributed or federated settings, where text data are scattered across multiple nodes and effective FS mechanisms are lacking. To overcome these issues, this paper proposes Fed-MSMCGWO, a federated multi-label text feature selection method based on manifold-aware sparse modeling and cooperative grey wolf optimization. Under a federated learning framework, Fed-MSMCGWO integrates manifold-aware sparse modeling (MSM), and incorporates a cooperative grey wolf optimization algorithm (CGWO) to enable multi-label text FS in distributed environments. On each client, Fed-MSMCGWO employs a two-stage optimization. In Stage 1, MSM is learned by constructing sample and label graphs from text embeddings, encoding their manifolds with Laplacians, and imposing a -norm on the feature-weight matrix to induce row sparsity and compress high-dimensional features. In Stage 2, CGWO with a three-line cooperative evolution scheme further refines these weights and conducts global search for a near-optimal subset of text features. After the two-stage optimization, each client obtains a locally optimal feature subset and engages in a multi-party privacy-preserving feature aggregation strategy: clients upload only intermediate feature-weight parameters (no raw data) to the server, which aggregates them and sends the result back to guide further local updates, yielding a collaborative cross-client FS framework with preserved privacy. Experiments on several publicly available multi-label text datasets indicate that, with privacy preserved, Fed-MSMCGWO consistently surpasses standard centralized and federated FS methods on multiple evaluation metrics. Subject terms: Computational biology and bioinformatics, Engineering, Mathematics and computing Introduction In recent years, progress in communication and networking technologies has accelerated the spread of intelligent transportation, smart healthcare and Internet of Things (IoT) applications, resulting in large volumes of high-dimensional text data with complex semantic structure. Multi-label text classification is an important problem in natural language processing (NLP), assigns each document to multiple semantic categories, which is fundamentally different from conventional single-label classification 1 . As the feature space grows, however, as the feature space becomes higher dimensional, large amounts of redundant or noisy information aggravate the “curse of dimensionality”, slow down the training process, raise the likelihood of overfitting, and ultimately impair the ability of the model to generalize 2 . Consequently, developing reliable and efficient FS techniques for multi-label text data is essential for improving classification performance. Driven by the rapid deployment of IoT devices, conventional centralized data processing architectures are increasingly unable to meet requirements on latency and privacy. To cope with these demands, many IoT applications are migrating to distributed paradigms such as edge computing 3 and federated learning (FL) 4 . Nevertheless, federated environments introduce additional challenges for FS algorithms, including heterogeneous and non-IID data distributions, restricted communication resources, and stringent privacy constraints. These characteristics call for FS methods that not only protect user data and reduce computational cost, but also maintain reliable and accurate selection performance. In multi-label text scenarios, there are often strong semantic relationships and higher-order dependencies among labels 5 , 6 , which substantially complicate the FS problem. Previous work has designed a variety of FS schemes that either treat labels as independent, model pairwise label interactions, or explicitly encode more complex, higher-order dependency patterns 7 . To more accurately model the latent dependencies between features and labels, these schemes are frequently coupled with sophisticated representation schemes such as manifold learning 8 , 9 , graph neural networks (GNNs) 10 , 11 , long short-term memory (LSTM) architectures 12 , 13 , semi-supervised learning methods 14 , 15 , and incremental learning strategies 16 , 17 . Despite these efforts, current multi-label FS techniques still face problems such as the local optima, unstable selection quality, and limited generalization, especially when dealing with high-dimensional and non-IID text data. Meta-heuristic algorithms (MAs) have recently gained attention for their outstanding global search and optimization capabilities in FS tasks. Representative MAs include Particle Swarm Optimization algorithm (PSO) 18 , Differential Evolution algorithm (DE) 19 , Genetic Algorithms (GA) 20 , Chaotic Dwarf Mongoose optimization algorithm (CDMO) 21 , Grey Wolf Optimization algorithm (GWO), and Ant Colony Optimization algorithm (ACO) 22 , all of which enhance search diversity and algorithmic stability. The Hybrid Breeding Optimization algorithm (HBO) was proposed by Ye et al. 23 , drawing inspiration from the heterosis theory of Chinese hybrid rice. In HBO, the population is partitioned into three groups (maintainer, restorer and sterile), and a cooperative evolution strategy is adopted to mitigate premature convergence, thereby enhancing FS performance 24 . A distance-based multi-objective GWO was later designed by Wang et al. 25 , in which adaptive distance and position-update mechanisms are introduced to reinforce the search behaviour. Furthermore, a two-stage FS framework for multi-label text classification was developed by Pradip Dhal and Chandrashekhar Azad 26 : a filter module is first used to perform coarse feature pruning, and a multi-objective GWO is subsequently employed to jointly decrease the Hamming loss and the size of the selected feature set. Collectively, these works suggest that the co-evolutionary mechanism of HBO and the global exploration capability of GWO are highly complementary, and that integrating them offers a promising route to improving both efficiency and robustness in multi-label text FS. Moreover, with the expansion of large-scale distributed text data such as news articles across different media agencies 27 , electronic medical records from multiple hospitals 28 , and social media posts distributed over regional servers 29 , centralized learning frameworks struggle to balance privacy protection and communication efficiency. FL 4 has recently emerged as a privacy-preserving distributed paradigm and has been applied to multi-label FS 30 – 32 . However, current federated multi-label FS techniques are still largely built on criteria derived from mutual information, fuzzy information theory, or causal analysis, and thus struggle to characterize the rich semantic dependencies among textual features. Moreover, when privacy protection is achieved only through the standard aggregation procedure in FL, large-scale communications may still expose the system to security vulnerabilities. Existing methods also seldom explicitly model the data’s inherent geometric organization or the severe redundancy in high-dimensional text representations, which leads to performance degradation and instability, especially under non-IID distributions. In response to these limitations, we propose Fed-MSMCGWO, a federated multi-label text FS framework that combines manifold-aware sparse modeling (MSM) with a cooperative GWO (CGWO). Under the FL architecture, a dual-stage optimization mechanism is implemented on each client to obtain a more effective locally optimal subset of textual features. After completing the two-stage optimization, each client acquires its locally optimal features and adopts a multi-party privacy-preserving feature aggregation strategy to achieve collaborative FS across clients while protecting data privacy and avoiding direct data exchange. Experiments carried out on several real-world multi-label text datasets indicate that Fed-MSMCGWO yields consistently superior results to typical centralized and federated FS methods. The improvements are observed on average precision, macro/micro-F1, coverage, hamming loss and ranking loss. Moreover, the proposed framework exhibits more stable behaviour and stronger privacy protection, particularly under non-IID data distributions. In this paper, our main contributions are as follows: We propose a novel Fed-MSMCGWO. Within a FL setting, each client first executes a Stage 1 MSM that incorporates manifold regularization and label correlation modeling, and then applies a bio-inspired Stage 2 CGWO to achieve efficient optimization. Furthermore, a multi-party privacy-preserving feature aggregation strategy is employed, enabling collaborative multi-label text FS in distributed environments without revealing raw data. A dual-stage optimization mechanism is designed for local FS on each client. In the first stage, the MSM module preserves manifold structures and enforces feature sparsity via a -norm regularization. In the second stage, the CGWO module further refines and globally optimizes the feature weights to obtain a more robust text feature subset. A multi-party privacy-preserving feature aggregation strategy is introduced. Each client uploads only intermediate feature-weight parameters to the central server, which performs weighted aggregation and synchronizes global weights, achieving collaborative feature selection across clients without sharing any raw data. The structure of the paper is outlined as follows. Section 2 summarizes related work, and Section 3 presents the Fed-MSMCGWO framework. Section 4 describes the experimental setup and results on real-world multi-label text datasets. Section 5 presents the conclusions. Related work Current approaches to multi-label text feature selection are usually grouped into two categories: problem-transformation schemes and algorithm-adaptation schemes. The former recast a multi-label task as several single-label problems, allowing traditional single-label FS techniques to be used without modification. Centralized multi-label FS Research on multi-label FS has historically focused on centralized settings, where all data are collected on a single server. In contrast, work specifically targeting federated multi-label text FS remains sparse, and only a handful of studies have explored this direction. The remainder of this section highlights the most relevant contributions. Typical examples include entropy-based label assignment (ELA), label powerset (LP), and binary relevance (BR) 33 . However, BR ignores label dependencies, while LP is prone to severe class imbalance and quickly becomes computationally expensive as the number of labels grows. Unlike problem-transformation strategies, existing single-label FS techniques are modified in algorithm-adaptation approaches so that they can be applied directly to multi-label data. In this line of work, mutual-information criteria are typically used to quantify the relevance and redundancy of candidate features, and causal-discovery frameworks are adopted to identify causally informative attributes 34 . In parallel, meta-heuristic algorithms such as GA 20 , ACO 22 , and PSO 18 have been employed to explore large, high-dimensional feature spaces. Sparse-learning techniques have recently attracted considerable attention in multi-label text FS 35 , where - and -type regularization are commonly used. In this line of work, LLSF was proposed by Huang et al. 36 , in which an penalty is introduced to obtain compact feature representations while preserving relationships among labels. Building on this idea, -norm regularization was combined with a latent-space mapping scheme by Jian et al. 37 to further improve the quality of the selected features. From a manifold-learning perspective, MCLS was put forward by Huang et al. 36 , where Laplacian scores are employed to describe local geometric structure in the feature space, and manifold regularization was incorporated by Zhang et al. 38 to better capture label correlations and strengthen feature–label associations. More recently, LRDG was introduced by Zhang et al. 10 , which leverages deep latent representations together with pseudo-label learning to further advance multi-label text FS. In traditional text classification, a rich body of filter-based FS methods has also been developed and can be adapted to the multi-label setting. Under the Naïve Bayes framework, Chen et al. 39 designed a feature selector for text classification, and a discriminative FS scheme. Numerous statistical filters measure the discriminative power of terms with respect to classes, including statistics 40 , 41 , information gain 42 , Gini index 43 , document frequency and odds ratio 44 , 45 , while 46 combines information gain with sequential forward selection. To alleviate multicollinearity in high-dimensional data, ridge regression has also been introduced into feature modeling 47 , where a penalty term is added to the least-squares objective to stabilize the model and mitigate overfitting. When multiple, often conflicting, evaluation criteria must be considered simultaneously, multi-criteria decision-making (MCDM) provides a unified framework for comparing and ranking alternatives. Various MCDM techniques have been systematically reviewed in 48 , 49 , and COPRAS is one of the most widely used methods in practical applications; for example 50 , employs COPRAS to assess regional COVID-19 prevention strategies and shows that it performs competitively against other approaches. MCDM has recently been introduced into text and multi-label FS as well: Abd Al-Aziz et al. 51 conduct a benchmark study on small-sample text classification using seven performance indicators and compare different FS methods within an MCDM framework. Overall, however, MCDM-based methods for multi-label text feature selection remain relatively scarce. For instance 52 , uses MCDM to select features for binary text classification, while 53 , 54 further extend MCDM to design multi-label FS methods and multi-label classifiers, respectively. Federated multi-label FS Federated FS has been studied in the contexts of both single-label and multi-label learning 55 . Within the FL paradigm, most existing methods are typically grouped into two types, namely vertical and horizontal schemes. In vertical federated FS, participating clients possess different feature sets but refer to the same group of instances 56 ; in contrast, horizontal federated FS assumes that each client holds a distinct subset of samples while sharing an identical feature space 57 . In the horizontal multi-label text scenario, Mahanipour and Khamfroush proposed the FMLFS method 30 , which employs information-theoretic measures to quantify feature–label dependencies and suppress redundancy. This work was later extended in 31 through a fuzzy logic–based federated framework that integrates reinforcement learning with ACO. They further developed SSFMLFS 58 , a semi-supervised federated multi-label FS approach that addresses the challenge of distributed environments where clients have only unlabeled data and the server possesses limited labeled data, achieving superior performance under non-IID data distributions. In related research, Song et al. proposed FedCMFS 32 , a causal federated multi-label FS framework that enhances feature quality through three specialized modules, while Zhang et al. 59 introduced Fed-MFSDHBCPSO, which effectively mitigates label dependency and feature redundancy in distributed, privacy-sensitive contexts. Additionally, Sun et al. 60 developed Fed-MGACO, combining manifold sparse constraints with game-theoretic evolutionary ACO to improve solution quality, convergence speed, and privacy preservation. Nevertheless, most existing federated multi-label text FS methods rely mainly on FL to protect privacy without additional defense mechanisms, leaving potential risks of information leakage, and they seldom exploit the manifold structure or address the severe redundancy of high-dimensional text representations, leading to degraded and unstable performance under non-IID distributions. Despite these advances, research on federated multi-label text FS is still quite limited. Most existing studies consider relatively simple horizontal FL scenarios with a small number of clients and do not explicitly tackle more challenging cross-client conditions, such as highly heterogeneous label distributions, varying degrees of feature sparsity, and dynamic client participation. In particular, there is a lack of federated frameworks that jointly account for manifold structures, label dependencies, redundancy control, and privacy-preserving aggregation for multi-label text data. This gap motivates the Fed-MSMCGWO framework proposed in this paper. The proposed method This section first provides a detailed description of MSM-CGWO and its federated extension, Fed-MSMCGWO, which incorporates the FL paradigm. We then analyze Fed-MSMCGWO in terms of privacy protection, time complexity, and communication overhead. A manifold-aware sparse modeling and cooperative grey wolf optimization algorithm (MSM-CGWO) Stage 1: Manifold-aware sparse modeling In multi-label text FS, data often lies on a low-dimensional manifold in both the feature and label spaces. Therefore, it is essential to preserve this intrinsic geometric structure while enforcing sparsity to eliminate redundant features. In the first stage, MSM constructs feature and label manifolds and integrates them with an -norm sparse regularization, providing a manifold-aware sparse modeling foundation for the subsequent evolutionary refinement. 1) Constructing the feature manifold The feature manifold is modeled via the graph Laplacian matrix . First, the pairwise similarity between samples is computed based on the similarity matrix , obtained using Eq. ( 1 ). 1 where denotes a parameter, typically set to infinity to construct the graph. is the set of the top- nearest neighbors of , based on Euclidean distance. Then, the degree matrix is computed as: 2 The final graph Laplacian matrix is then given by: 3 This feature manifold regularization encourages neighboring text instances in the initial feature space to remain close in the learned embedding, thus preserving local geometric structure during feature selection. 2) Constructing the label manifold To further exploit label information, we introduce label manifold regularization. The pairwise similarity between labels is computed via the label similarity matrix , defined as: 4 where and represent the label vectors of samples and , respectively. The label degree matrix is then computed as: 5 Finally, the label graph Laplacian matrix is obtained by: 6 By combining feature manifold and label manifold into the objective in Eq. ( 9 ), MSM constrains the learned representation and feature weights to respect the intrinsic structures of both feature space and label space. 3) Manifold-aware sparse feature selection via - norm On top of the manifold structure, an -norm penalty is imposed on the feature-weight matrix to promote row sparsity and discard irrelevant text features. For client , the regularization term is defined as: 7 where and denote the feature dimension and the number of tasks (labels) on client , respectively, and is the weight of the -th feature for the -th task. This term encourages entire rows of to shrink toward zero, realizing sparse selection of features while preserving manifold consistency. 4) Global best synchronization and population integration To balance exploration and exploitation across clients and generations, a global best synchronization mechanism is employed. The global best solution is updated by federated aggregation as: 8 where is the previous global best, represents the local best solution of client , denotes the number of clients, and controls the influence of historical information. At the end of each iteration, individuals from all lines are integrated to form a new population, while the current is retained as a reference for subsequent search. Importantly, this global best synchronization creates a feedback loop between the two stages: the manifold constraints from Stage 1 are continuously enforced through the fitness function in Eq. ( 9 ), which penalizes solutions that deviate from the learned manifolds L and . Meanwhile, CGWO’s evolutionary search progressively refines the sparsity pattern encoded by the -norm, potentially discovering sparser and more discriminative feature subsets than the initial MSM solution. This mutual reinforcement—manifold guidance from MSM and global optimization from CGWO—is the key to the superior performance of the integrated framework. 5) Overall objective of MSM By integrating the manifold regularization terms and the –norm sparsity, the overall objective of MSM for multi-label text FS can be written as 9 where denotes the task loss for client c , is the low-dimensional embedding or prediction induced by , L and are the feature and label graph Laplacians defined in Eq. ( 3 ) and Eq. ( 6 ), and , , and are non-negative trade-off parameters. The first term enforces discriminative modeling for the multi-label task, the second and third terms preserve the intrinsic manifold structures in the feature and label spaces, and the final term induces row sparsity on to perform feature selection. Through this manifold-aware sparse modeling stage, MSM obtains an initial set of structured and sparse feature weights that already respect both the data manifold and label manifold. In the next stage, CGWO is performed to further refine and globally optimize these weights. It is worth noting that MSM and CGWO are not merely combined sequentially, but rather form a synergistic integration where each stage reinforces the other. Specifically, MSM provides CGWO with a manifold-consistent and sparse initialization, which significantly narrows the search space and guides CGWO toward regions that already respect the intrinsic geometric structure of both feature and label spaces. Conversely, CGWO refines the initial solution from MSM through cooperative evolution, effectively escaping local optima introduced by the convex relaxation in Eq. ( 9 ) and identifying feature subsets with superior discriminative power. This bidirectional enhancement—where MSM constrains the search landscape and CGWO performs global refinement—constitutes the core methodological novelty of the proposed framework. Stage 2: Co-evolutionary refinement with cooperative grey wolf optimization In Stage 2, CGWO performs a cooperative evolutionary refinement that synergistically builds upon the manifold-aware sparse model learned in Stage 1. Rather than treating the output of Stage 1 as a mere initialization, CGWO actively leverages the manifold structure embedded in the Stage 1 solution: the population of candidate feature-weight matrices is initialized from the neighborhood of the MSM solution, ensuring that all individuals already respect the geometric constraints encoded by L and . The population is then ranked by the same fitness function (Eq. 9 ) used in Stage 1, creating continuity between the two stages. Subsequently, individuals are partitioned into three lines: the maintainer , restorer , and sterile lines. Within each line, an embedded GWO process is executed for a fixed number of iterations to refine the local search while maintaining manifold awareness. Afterwards, the top-ranking individuals from the three groups are selected to construct a new population via information exchange (Eq. 12 ), and this procedure is iterated until convergence. In this way, Stage 1 provides a manifold- and sparsity-consistent initialization that constrains the CGWO search space, while Stage 2 compensates for the potential suboptimality of the convex Stage 1 solution by exploring globally optimal feature subsets through cooperative evolution. Step 1: Fitness evaluation and line partition. CGWO is formulated as a minimization problem that searches for the most compact and discriminative feature subset. Therefore, the objective in Eq. ( 9 ) is directly used as the fitness function, and the population is partitioned into three equally sized lines: forming three groups, namely the maintainer, restorer, and sterile groups. Step 2: Line-wise GWO refinement. In each line, a standard GWO update is applied independently for a fixed number of iterations . Denote by the three best individuals ( wolves) in line for client . For any other individual in that line, its position (i.e., the feature-weight matrix) is updated according to the standard GWO rule in Eq. ( 10 ). 10 and analogously for and with respect to and . Then the new position of is obtained by averaging: 11 where is the standard GWO control parameter decreasing linearly with iteration , are random matrices with the same shape as , and denotes element-wise multiplication. This line-wise GWO refinement is performed in parallel for the maintainer, restorer, and sterile lines. Step 3: Information exchange among lines. After iterations, the current best individuals from the three lines, are collected to construct a temporary elite set . A new population is then formed by injecting these elites into all three lines and replacing the worst-performing individuals: 12 where denotes the exchange operator that broadcasts elites across lines and maintains population diversity. The algorithm then returns to Step 1 for the next co-evolutionary cycle. By performing GWO-based refinement within each line and periodically exchanging the best individuals across lines, MSM-CGWO realizes a CGWO on top of the hybrid breeding framework. The maintainer line focuses on exploiting high-quality solutions, the restorer line accelerates convergence toward promising regions, and the sterile line preserves diversity, together forming an effective co-evolutionary optimizer for multi-label text FS. The implementation process of MSM-CGWO is shown in Fig. 1 . Fig. 1. Open in a new tab The flowchart of MSM-CGWO. ( a ) The population is ranked by fitness and then evenly partitioned into three lineages. ( b ) After a fixed number of iterations, the lineages periodically exchange information about their best solutions. Federated multi-label FS via MSM-CGWO Traditional multi-label text FS methods face significant challenges related to privacy protection, data-sharing constraints, and distributed computing efficiency. Centralized FS approaches risk data leakage, since they require collecting raw text data on a single server. To address these issues while keeping the original data local, we introduce a horizontal FL framework into MSM-CGWO and propose Fed-MSMCGWO (as shown in Fig. 2 ). In this framework, each client independently performs multi-label text FS and uploads only its selected feature weight matrix, which contains no raw text content. Fig. 2. Open in a new tab The overall architecture of the proposed Fed-MSMCGWO, which adopts a multi-party, privacy-aware feature-weight aggregation mechanism, operates as follows: ( a ) Each client accesses its own local dataset and carries out feature selection to obtain a weight matrix corresponding to its preferred feature subset. ( b ) Only these feature weights are uploaded to the central server, while the raw data remain on the clients to protect privacy. ( c ) The server combines and processes the weight information collected from all clients. ( d ) The resulting global feature weights are then sent back to the clients and used to further refine their local optimization. ( e ) Feature importance: comparison between global aggregation and client results (example). This design significantly reduces privacy risks compared to centralized approaches by avoiding the transmission of raw text data. However, we acknowledge that sharing feature weights alone does not provide formal privacy guarantees, as certain attacks (e.g., model inversion) may still pose risks in adversarial settings. To mitigate these concerns, Fed-MSMCGWO incorporates the following privacy-enhancing mechanisms: (i) only aggregated feature-weight matrices are shared, containing no instance-level information; (ii) the -norm sparsity constraint naturally limits the amount of information encoded in the weights; and (iii) the framework remains compatible with additional privacy-preserving techniques (e.g., differential privacy or secure aggregation) if stronger guarantees are required. In this work, we focus on the privacy benefits inherent to the federated architecture itself, leaving the integration of cryptographic techniques as important future work. A multi-party privacy-preserving feature wight aggregation strategy To enable collaborative learning while protecting raw data, Fed-MSMCGWO adopts a multi-party privacy-preserving feature-weight aggregation strategy, whose implementation process is described as follows. 1) Client-side optimization process On each client, a layered procedure is used to perform local multi-label text FS, which can be outlined as follows. Step 1: Data preprocessing. Each client loads its local multi-label text dataset, initializes algorithm parameters, and performs text processing operations (such as tokenization, stop-word filtering, and normalization or TF-IDF transformation) to construct a high-quality feature representation for the subsequent FS process. Step 2: FS via MSM-CGWO. Each client then executes the MSM-CGWO framework, which integrates fitness evaluation, population manifold space construction, co-evolutionary optimization, sparse FS, and iterative refinement. Through this procedure, the client derives a locally optimal subset of features together with a feature-weight matrix that fits its own data distribution and label set. Step 3: Uploading feature weights. After local optimization, each client uploads only the selected feature weight matrix and the associated feature indices to the server. No raw text, label sets, or intermediate sensitive representations are transmitted, ensuring that the original multi-label text data remain strictly on the client side. Step 4: Multi-label text prediction on the client. Using the selected features, the client then trains and applies a local multi-label text classifier (e.g., Multi-Label k-Nearest Neighbor (ML-KNN) 31 ) for prediction. This decentralized classification strategy further reduces communication overhead and preserves data privacy, since inference is performed locally. 2) Optimization on the server side. On the server, a dynamic collaborative optimization procedure is carried out based on the uploaded feature weights, which proceeds as follows. Step 1: Feature aggregation. The server combines the feature-weight matrices uploaded by all clients to obtain a global feature-weight vector . Specifically, 13 where denotes the global feature weight vector aligned with the full text feature space, and each dimension represents the aggregated importance of a textual feature. The aggregation involves clients in the federated system, where each client contributes a sparse local feature weight vector containing non-zero values only at positions (the selected feature indices of client ), with other positions set to zero. The aggregation coefficient is computed by dataset size proportion: , where represents the local dataset size at client . Step 2: Global iterative optimization. Based on , the server performs iterative optimization to refine the global feature importance, and subsequently sends the updated global weights to all clients. Clients can incorporate these global weights as guidance for subsequent rounds of local FS, enabling collaborative improvement across all participants while keeping their original multi-label text data private. Further analyses To more comprehensively evaluate the practicality of our method, we further examine its privacy guarantees, computational complexity, and communication cost in the setting of multi-label text FS. Privacy protection analysis Fig. 2 shows that communication occurs exclusively between the server and each client, and clients are not allowed to exchange information directly with one another. During training, the exchanged information is restricted to feature-weight results obtained from local multi-label text feature selection, while the original documents and label sets remain on the clients. Similar to classical FL frameworks such as FATE 61 , only model-related parameters are transmitted. Thus, Fed-MSMCGWO prevents participants from inferring one another’s data distributions and enhances privacy protection. When the exposed information is restricted to feature identifiers (e.g., terms, n -grams) and their combinations are not inherently sensitive, Fed-MSMCGWO can already offer a satisfactory level of privacy, since it does not upload raw text or document-level representations. For example, several institutions may share a common vocabulary space but keep the actual document contents and label assignments local. In our design, clients only upload selected feature indices and the associated weight matrices. This setting provides privacy protection without requiring additional cryptographic operations. Computational complexity analysis The time complexity of Fed-MSMCGWO for multi-label text feature selection is analyzed by considering Stage 1 (MSM-CGWO manifold construction and mapping), Stage 2 (CGWO-based triad co-evolution), and the federated aggregation across clients. In Stage 1, constructing the manifold space involves computing feature–label interactions and building the manifold structure over all documents and labels. Let , , and denote the numbers of text samples, features (e.g., vocabulary size), and labels, respectively. The main cost of this step can be bounded by , as each sample–feature–label combination is processed at most once in the construction of the manifold-regularized representation. Updating the manifold mapping for the population (i.e., projecting the candidate feature subsets into the manifold space) again incurs , since it requires matrix–vector operations over all documents and labels. Evaluating the objective function on this space also requires , because each label is assessed over all samples and the currently selected features. In Stage 2, we perform CGWO-based triad co-evolution on the manifold-mapped population. Initializing the triad population for the CGWO stage requires , where is the population size, as each wolf maintains a feature-weight vector of length for each label (or a joint feature–label representation). During triad co-evolution, the position update of each wolf is an element-wise operation on its feature-weight vector, which costs per wolf. For a population size , one CGWO iteration therefore incurs for position updates and auxiliary operations. The fitness evaluation of all wolves, which computes the manifold-regularized objective over the training data, can be bounded by , since each candidate solution is evaluated on all samples, features and labels. Sorting the population by fitness adds an additional cost per iteration. Hence, the overall complexity of Stage 2 per iteration is For the federated coordination, global synchronization of the best solution costs , as it updates the global feature weights across all features and labels. Aggregating feature weights from clients on the server side requires . The convergence check is , since it only monitors changes in the objective value or feature weights across iterations. Combining Stage 1, Stage 2, and the federated aggregation, the total time complexity of Fed-MSMCGWO over iterations optimization rounds is 14 where is the number of text samples, the number of features, the number of labels, the population size, the number of clients, and iterations the number of optimization rounds. Discarding lower-order terms and constant factors, the simplified time complexity becomes 15 where all symbols retain the same meanings as above. This expression explicitly accounts for Stage 1 manifold construction and mapping, Stage 2 CGWO-based triad co-evolution, and federated aggregation across clients, and does not involve any cubic dependence on the feature dimension . Communication cost analysis Within the FL setting for multi-label text feature selection, Fed-MSMCGWO preserves privacy by limiting communication to server–client exchanges in each iteration. A single communication round includes three stages: 1) Each client uploads the indices of its selected features and the corresponding best feature-subset weight matrix to the server, without sending any raw text or label vectors. 2) The server fuses the uploaded weight information and then disseminates the resulting global feature weights to all participating clients. 3) Each client applies these global weights to its own multi-label text data, performs local evaluation, and sends the feedback to the server. At each communication round, only a D -dimensional index vector and a small set of weight parameters are exchanged, so the amount of transmitted data is relatively negligible relative to the computations performed locally on the clients. In addition, Fed-MSMCGWO typically reaches convergence within only a few rounds (e.g., 2–4 iterations), which further limits the overall communication overhead. Experiments In this section, the experimental environment and datasets are first described. Fed-MSMCGWO is then benchmarked against representative centralized and federated baselines, the effects of key hyperparameters are investigated, ablation studies are carried out, and a statistical significance analysis of the results is finally presented. Experimental settings Dataset description The proposed federated multi-label text FS method is assessed on eight benchmark multi-label text datasets drawn from a public repository 50 . Summary statistics for these datasets— including the number of documents, the number of labels, label cardinality, and label density—are provided in Table 1 . Label cardinality is interpreted as the average number of labels assigned to a document, whereas label density is obtained by dividing this average by the total number of distinct labels 62 . These two measures are computed as follows: Table 1. Statistics of the experimental datasets. Dataset #instance #labels #features Label Cardinality Label Density Education 5000 33 550 0.0443 1.4606 Reference 5000 33 793 0.0350 1.1690 Health 5000 32 612 0.0519 1.6622 Arts 5000 26 462 0.0629 1.6360 Entertainment 5000 21 640 0.0676 1.4204 Social 5000 39 1047 0.0329 1.2834 Recreation 5000 22 606 0.0647 1.4232 Science 5000 40 743 0.0360 1.4500 Open in a new tab A multi-label dataset with N text instances and label space is considered. For the i -th document, the associated label set is denoted by , and its cardinality is written as . Following standard practice, label cardinality and label density are computed as: 16 17 where is the total number of distinct labels. In the federated setting, we adopt a horizontal partitioning strategy tailored to multi-label data. Each dataset is split into several client subsets with unequal sizes, and the label sets on different clients are deliberately skewed to create a Non-IID scenario. Consequently, both the number of text samples and the multi-label distributions vary across clients, leading to heterogeneity in data quantity and label composition. This configuration is designed to mimic practical federated multi-label text applications, in which data heterogeneity often challenges model convergence and generalization. Evaluation metrics To assess the effectiveness of the proposed federated multi-label text FS framework, six commonly used multi-label evaluation measures are employed: Average Precision (AP), Macro-F1 (MA), Micro-F1 (MI), Coverage (CV), Hamming Loss (HL), and Ranking Loss (RL). Taken together, these metrics characterize ranking performance, label-wise prediction accuracy, and overall classification behaviour after FS. Let the multi-label text dataset be denoted by , where represents the feature vector of the -th document and denotes its associated label set. The function is used to indicate the predicted rank of label for sample . The six evaluation metrics are formally defined as follows. AP assesses how well the predicted ranking aligns with the ground-truth label set. A higher AP indicates that relevant labels are ranked earlier: 18 MA computes the unweighted mean F1-score over all labels, reflecting label-level performance under the selected features. Let and denote the numbers of true positives, false positives, and false negatives associated with label , respectively: 19 MI aggregates contingency counts over all labels and documents before computing a global F1-score: 20 CV indicates the position in the predicted ranking that must be reached in order to include all relevant labels of a document. Smaller values are preferred: 21 HL quantifies the fraction of label–document pairs that are predicted incorrectly. Let be the number of labels and the predicted label set for document : 22 where denotes the symmetric difference. Lower HL means better multi-label prediction after feature selection. RL quantifies the fraction of label pairs where an irrelevant label is ranked above a relevant one. A lower RL implies better ranking quality: 23 where and denotes the indicator function. MA and MI both characterize the trade-off between precision and recall of the multi-label text classifier built on the selected features. All six metrics are in the range (for AP, MA, MI) or non-negative with “smaller is better” (for CV, HL, RL); better feature subsets lead to higher AP/MA/MI and lower CV/HL/RL. Comparison algorithms and parameter configuration To validate the effectiveness of the proposed Fed-MSMCGWO, we compare it with several representative multi-label FS methods under two settings: (i) centralized (pooled-data) and (ii) federated learning. On the federated side, we include two recent federated multi-label FS algorithms, namely FMLFS 30 and Fuzzy FMFS 31 . As centralized (pooled-data) baselines, we consider: (i) the latest multi-label text feature selection method, ML-COPRAS 50 ; (ii) the deep neural network based multi-label FS model LRDG 10 ; (iii) two multi-objective evolutionary optimizers, MOEA/D 63 and NSGA-III 64 ; and (iv) two classical filter/wrapper methods, GLFS 65 and PDMFS 66 . In the centralized setting, all client data are consolidated on a single server, and each comparison method is trained once on the entire combined dataset. This setup corresponds to the standard definition of centralized training in FL and serves as an upper bound on performance when privacy and data-sharing constraints are disregarded. In the federated setting, the original data remain on the clients throughout the learning process. Each client performs local FS and model optimization based on its own data, while the server only operates on the feature-weight information provided by the clients to construct and refine a global feature-weight representation. The proposed Fed-MSMCGWO is evaluated in this setting and compared against the above federated multi-label FS methods. All federated methods follow the same client–server protocol and are trained under identical partitioning, optimization rounds, and stopping criteria. Unless otherwise specified, the hyperparameters of all baseline methods are set according to the guidelines provided in their original papers. For the proposed Fed-MSMCGWO, we largely follow the configuration in 22 . The swarm size is fixed at 30, the outer loop is allowed to run for at most 100 iterations, and each experiment is conducted 30 independent times. In Stage 1, the key hyperparameters are the trade-off coefficients , , and in Eq. ( 9 ), which balance task loss, manifold preservation, and -based sparsity; their values are determined through the parameter sensitivity analysis in Section. In Stage 2, the GWO control parameter a decreases linearly from 2 to 0 over iterations, and the random matrices and have the same dimensions as the feature-weight matrix . Experimental environment All runs were performed on a desktop machine running Windows 11. The hardware platform consists of a 13th-generation Intel ® Core™ i7-13700KF processor (with a base clock of 3.40 GHz) and 32 GB of RAM, which provides sufficient computational power for the repeated experiments and parameter studies. All algorithms and scripts were implemented and executed in MATLAB R2022a. Comparative analysis of Fed-MSMCGWO and other methods To verify the effectiveness and robustness of the Fed-MSMCGWO, Figs. 3 , 4 , 5 , 6 , 7 , 8 present a systematic comparison on eight datasets against six centralized and two recent federated multi-label FS methods. The experiments are conducted with five clients, and the performance is evaluated under different counts of selected features. In each figure, the subplots report the results on different datasets under the same evaluation metric. Fig. 3. Open in a new tab Average precision of the compared methods across the eight datasets. Fig. 4. Open in a new tab Macro-F1 of the compared methods across the eight datasets. Fig. 5. Open in a new tab Macro-F1 of the compared methods across the eight datasets. Fig. 6. Open in a new tab Coverage of the compared methods across the eight datasets. Fig. 7. Open in a new tab Hamming loss of the compared methods across the eight datasets. Fig. 8. Open in a new tab Ranking loss of the compared methods across the eight datasets. From the perspective of AP, on the Arts, Entertainment, Social, and Science datasets, Fed-MSMCGWO achieves performance with only 10 selected features that is comparable to its own performance with a larger count of features, and it clearly outperforms the competing methods even when they use 100 features. On the remaining datasets, Fed-MSMCGWO maintains similar performance between small and large feature subsets, while still achieving overall better results than the baselines. For the Macro-F1 metric, on the Education, Reference, Health, Arts, Entertainment, and Science datasets, Fed-MSMCGWO likewise attains performance with fewer features that is comparable to or better than that obtained with more features, and it consistently surpasses the other methods. Similar advantages can be observed for the remaining evaluation metrics on most datasets. These results suggest that model performance can be maintained or even enhanced by Fed-MSMCGWO, while a favorable balance between communication efficiency and predictive accuracy is achieved. Parameter sensitivity analysis To study the sensitivity of the key hyperparameters, we conduct experiments on three representative datasets, namely Arts, Reference, and Social. As shown in Table 1 , these datasets cover different feature scales (from 462 to 1047 features) and label characteristics (e.g., label cardinality and label density), and thus are representative of the overall range of our benchmark corpus. We perform a one-factor-at-a-time sensitivity analysis for , , and , and evaluate the impact on AP and HL. The results (Table 2 , with bold values indicating the best performance) reveal that Fed-MSMCGWO exhibits only mild performance variations across a wide range of parameter settings, suggesting that the framework is relatively insensitive to moderate changes in these hyperparameters. Based on these observations, we adopt as a robust configuration and use it across all eight datasets in the main experiments. Table 2. Effects of different values of , , and on the performance of Fed-MSMCGWO. Bold values indicate the best settings. AP HL AP HL AP HL 0.1 0.570 0.0392 0.1 0.575 0.0387 0.01 0.594 0.0371 0.2 0.585 0.0384 0.2 0.578 0.0378 0.05 0.612 0.0362 0.3 0.590 0.0373 0.3 0.584 0.0376 0.10 0.628 0.0358 0.4 0.614 0.0386 0.4 0.620 0.0363 0.15 0.621 0.0363 0.5 0.627 0.0362 0.5 0.629 0.0362 0.20 0.617 0.0375 0.6 0.610 0.0371 0.6 0.6150 0.0376 0.25 0.608 0.0372 0.7 0.600 0.0383 0.7 0.6065 0.0379 0.30 0.592 0.0385 0.8 0.597 0.0392 0.8 0.5902 0.0384 0.35 0.587 0.0391 0.9 0.590 0.0374 0.9 0.5832 0.0389 0.40 0.578 0.0398 1.0 0.560 0.0398 1.0 0.564 0.0401 0.45 0.561 0.0399 Open in a new tab Ablation study To quantify the role of each module in Fed-MSMCGWO (Proposed), five ablated variants are constructed: (i) without GWO (Proposed/GWO); (ii) without HBO (Proposed/HBO); (iii) with Stage-2 CGWO disabled so that only the Stage-1 MSM optimization remains (Proposed/CGWO); (iv) with the sparse constraint in Stage-1 removed by dropping Eq. ( 1 ) (Proposed/MC); and (v) with the -norm in Eq. ( 1 ) replaced by the -norm (Proposed/ ). These variants are further compared with the filter-based federated baselines MOEA/D and NSGA-III, using AP as the main evaluation index. Ablation experiments were carried out on five clients, and the resulting size of the selected feature set is determined following the procedure in 67 . Table 3 shows that omitting GWO or HBO noticeably degrades performance, while removing the sparsity term also reduces both accuracy and stability. Replacing the -norm with the -norm likewise leads to a consistent performance drop across all datasets. This is because the -norm enforces row-level group sparsity on the feature-weight matrix, thereby selecting or discarding entire features uniformly across all labels. In contrast, the -norm only induces element-wise sparsity and cannot guarantee structured feature elimination, which is particularly important in multi-label scenarios where a consistent feature subset shared across labels is desirable. Benefiting from its three-subpopulation cooperative evolution scheme, where subpopulations of different quality periodically share their best solutions, Fed-MSMCGWO achieves higher AP than MOEA/D and NSGA-III in all cases. This mechanism helps maintain an appropriate trade-off between global exploration and local exploitation, mitigates premature convergence, and speeds up convergence. However, in the federated setting, the single-population structures of MOEA/D and NSGA-III struggle to simultaneously maintain diversity and accuracy, which leads to inferior empirical performance. Overall, the ablation results suggest that the main components of Fed-MSMCGWO are mutually reinforcing and together are crucial for its performance. Table 3. Results for Fed-MSMCGWO versus its five ablation settings and two comparison methods. Datasets Proposed Proposed/GWO Proposed/HBO Proposed/CGWO Proposed/ Proposed/SC MOEA/D NSGA-III Education 61.83% 56.83% 57.83% 55.83% 55.24% 57.33% 58.83% 56.33% Reference 63.84% 60.34% 59.84% 61.34% 60.39% 58.34% 59.34% 60.84% Health 71.65% 67.65% 66.65% 68.15% 67.14% 65.65% 68.65% 67.15% Arts 52.43% 49.43% 47.93% 48.93% 48.29% 49.93% 47.43% 48.43% Entertainment 61.43% 56.93% 57.93% 58.43% 56.57% 55.93% 57.43% 58.93% Social 71.12% 65.62% 67.12% 66.12% 65.32% 65.12% 67.62% 68.12% Recreation 55.01% 52.01% 49.01% 50.51% 51.76% 51.51% 49.51% 51.01% Science 49.94% 46.44% 45.44% 47.44% 46.64% 46.94% 44.94% 47.94% Open in a new tab Statistical analysis of significance This subsection further examines whether the performance gaps among the federated multi-label FS methods are statistically meaningful, with a focus on validating the advantage of the proposed approach. To this end, two nonparametric tests that are widely adopted in multi-label FS are used, namely the Friedman test and the Nemenyi post-hoc test. First, the Friedman test is applied to the multi-label FS results of all competing algorithms. Under the null hypothesis, no performance difference is assumed among the compared methods. At a significance level of , the null hypothesis is rejected when the Friedman statistic exceeds the critical value of 2.1175. As reported in Table 4 , the obtained statistics for all six evaluation metrics are greater than this threshold, and the associated p -values are all below 0.05. Consequently, the hypothesis of equal performance is rejected, and the proposed Fed-MSMCGWO can be regarded as achieving statistically significant gains over the compared approaches. Table 4. Friedman test statistics and critical values for six evaluation metrics. Metrics Critical value AP 54.7898 0.0098 MA 63.8974 0.0104 MI 55.1412 2.1175 0.0050 CV 44.9430 0.0182 HL 54.4317 0.0107 RL 61.2012 0.0211 Open in a new tab To identify which methods differ from each other, the Nemenyi post-hoc test is then applied. This test compares algorithms based on their average ranks, where a smaller mean rank shows better overall performance. A difference between two approaches is regarded as statistically significant when the absolute gap between their mean ranks exceeds the critical distance (CD). The CD is computed by 24 where corresponds to and yields . This value is used as the decision threshold for determining whether differences in average ranks are statistically meaningful. The results of the Nemenyi test are depicted in Fig. 9 , where methods on the left-hand side have better rankings and the horizontal axis shows the mean rank of each algorithm. It can be seen that the rank gaps between Fed-MSMCGWO and NSGA-III, MOEA/D, FMLFS, GLFS and PDMFS all exceed the CD, indicating that Fed-MSMCGWO is significantly superior to these baselines. In contrast, the mean ranks of ML-COPRAS and Fuzzy FMFS lie within the CD interval, implying that the differences between our method and these two algorithms are not statistically significant. Nevertheless, Fed-MSMCGWO consistently attains the lowest average rank among all competitors. These findings jointly confirm that the proposed federated framework, manifold embedding, sparsity regularization, and CGWO-based optimization are effective in enhancing the performance of multi-label feature selection. Fig. 9. Open in a new tab The Nemenyi post-hoc test is further employed to compare Fed-MSMCGWO with the competing methods in terms of six evaluation criteria: ( a ) average precision, ( b ) macro-F1, ( c ) micro-F1, ( d ) coverage, ( e ) hamming loss, and ( f ) ranking loss. Conclusion In this paper, we propose Fed-MSMCGWO, a novel federated multi-label text FS framework that effectively combines MSM, CGWO, and a multi-party privacy-preserving feature aggregation strategy. Targeting key challenges in distributed environments—such as high-dimensional features, strong label correlations, feature sparsity, and strict privacy constraints—Fed-MSMCGWO performs efficient FS locally on each client under the federated learning paradigm. On the client side, a dual-stage optimization mechanism is designed. In Stage 1, the MSM module constructs sample and label graphs from text embeddings, encodes their manifold structures via Laplacian matrices, and imposes an -norm regularization on the feature-weight matrix to induce row sparsity and compress the high-dimensional feature space. In Stage 2, the CGWO module with a three-line cooperative evolution mechanism further refines and globally searches over the feature weights, approaching an optimal subset of text features. After the two-stage optimization, each client obtains a locally optimal feature subset and participates in a multi-party privacy-preserving feature aggregation process: clients upload only intermediate feature-weight parameters, while the server performs weighted aggregation and broadcasts the global weights back to the clients. In this way, collaborative cross-client feature selection is achieved without exposing any raw data. Experiments carried out on a range of real-world multi-label text benchmarks indicate that Fed-MSMCGWO achieves consistently better results than typical centralized and federated FS competitors across AP, MA, MI, HL, CV and RL. Statistical significance analysis further confirms that MSM, CGWO, and the proposed aggregationstrategy jointly yield substantial and robust performance gains, particularly under non-IID data distributions. Future work will focus on two main directions. First, we plan to extend Fed-MSMCGWO to more complex tasks, such as multi-modal or sequence-based multi-label learning. Second, we aim to incorporate adaptive or lightweight encryption mechanisms to better balance security and efficiency in large-scale deployments. Author contributions Yufeng Zheng: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Visualization. Zhiwei Ye: Conceptualization, Supervision, Methodology, Resources, Writing - review & editing, Funding acquisition, Project administration. Songsong Zhang: Methodology, Supervision, Validation, Formal analysis, Investigation, Writing - review & editing. Kaiqi Wang: Methodology, Formal analysis, Investigation, Visualization Funding The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (62376089, 62302153, 62302154, U23A20318). Additional funding was provided by the Program for Scientific and Technological Innovation Teams of Young and Middle-Aged Researchers in Higher Education Institutions of Hubei Province (T2023007). Data availability The eight benchmark multi-label text datasets used in this study are publicly available from the repository in 50 . Further information or reasonable requests can be addressed to the corresponding author. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Contributor Information Zhiwei Ye, Email: [email protected]. Songsong Zhang, Email: [email protected]. References 1. Li, Y. et al. Fusion-enhanced multi-label feature selection with sparse supplementation. Inf. Fusion 117 , 102813 (2025). [ Google Scholar ] 2. Fan, Y. et al. Learning correlation information for multi-label feature selection. 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