1. Introduction

We present Adaptive Federated Clustering (AFC), a novel federated learning framework that simultaneously addresses three critical bottlenecks preventing scalable deployment on decentralized big data platforms. AFC integrates adaptive client selection based on computational capacity and data relevance, hierarchical clustering for efficient aggregation under non-IID conditions, and aggressive model compression using sparsity and quantization. Our experiments demonstrate that AFC achieves 4.3% higher accuracy than FedAvg, reduces communication costs by 49%, and converges 35% faster, while maintaining resilience against backdoor attacks with only 2.8% accuracy degradation. These improvements directly address the fundamental challenges that have limited federated learning adoption in real-world heterogeneous environments.

Federated learning has emerged as a critical paradigm for privacy-preserving distributed machine learning [1,2], particularly in domains where data sensitivity and regulatory constraints prevent centralization [3,4]. Unlike traditional centralized approaches [5], FL enables collaborative model training across decentralized clients—including mobile devices, sensors, and edge nodes—without raw data sharing [6,7]. This architecture proves essential in healthcare [8], autonomous systems [9], and smart cities [10], where privacy regulations strictly prohibit data centralization [11]. However, existing FL frameworks struggle with scalability in large-scale [12], heterogeneous [13], and resource-constrained environments [14], facing persistent challenges in data heterogeneity, communication overhead, computational inefficiencies, and security vulnerabilities [15].

AFC specifically addresses these limitations by modeling federated learning as a problem space characterized by imprecision and uncertainty. Non-IID data distributions create uncertain model behavior, while communication constraints and unpredictable client availability lead to imprecise optimization trajectories. Our framework handles vague system boundaries—the unclear demarcation of client roles, participation stability, and data ownership common in IoT and healthcare networks where devices frequently join or leave. Through adaptive client selection that prioritizes stable participants and hierarchical clustering that organizes local updates before global aggregation, AFC provides robust performance despite these uncertainties.

While federated learning was originally introduced as a privacy-preserving training mechanism [16], with clients sharing parameters through periodic server aggregation [17], scaling to larger decentralized environments has revealed fundamental limitations [18]. Current solutions address these challenges piecemeal—FedProx handles heterogeneity through regularization, SCAFFOLD reduces client drift, and FedZip focuses on compression—but none integrate the comprehensive approach necessary for practical deployment. AFC fills this gap by unifying adaptive participation, efficient aggregation, and communication optimization in a single framework. Fig 1 illustrates the federated learning approach for scalable machine learning on decentralized big data platforms.

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Fig 1. Federated Learning Approach for Scalable Machine Learning on Decentralized Big Data Platforms.

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The importance of FL is especially evident in sensitive domains such as healthcare and finance. Paper [19] developed a robust and privacy-preserving decentralized FL framework for digital healthcare applications, emphasizing its critical role in protecting medical data. Similarly, Paper [20] applied FL to improve breast cancer detection in smart hospitals, showcasing the benefits of decentralized learning in medical domains. However, these models primarily focus on robustness and privacy, while overlooking efficiency and scalability challenges in large-scale, heterogeneous data platforms [21–24].

In autonomous systems, paper [25] applied FL to enable collaborative intelligence for intelligent vehicles, addressing the need for distributed learning without compromising data security. A study [26] extended FL to edge computing for hyperspectral change detection, demonstrating its adaptability to diverse real-world applications. Despite these advances, significant challenges remain, particularly in scalability, efficiency, and the ability to manage heterogeneous data across decentralized systems [27–30].

This decision-making process resembles fuzzy logic reasoning, where multiple uncertain factors are combined to make approximate yet robust decisions. Such soft computing strategies are increasingly adopted in federated settings to adaptively manage vagueness in client states [31–33]. In addition, probabilistic modeling techniques—such as Laplace and Gaussian noise mechanisms—serve as core tools for uncertainty quantification, offering tunable control over the privacy–utility trade-off [34].

2. Proposed model: Cyberguard-X

2.1. Overview of the proposed system

In this section, we present the Adaptive Federated Clustering (AFC) model, a novel federated learning framework designed for scalable machine learning on decentralized big data platforms. AFC directly addresses three key challenges: client heterogeneity, communication bottlenecks, and security vulnerabilities. To achieve this, the framework combines adaptive client selection, hierarchical aggregation, and efficient model compression. We also provide a detailed mathematical formulation of the AFC framework to explain its operation formally. Fig 2 illustrates the overall architecture of AFC, including the stages of adaptive client selection, local clustering, cluster-level aggregation, model compression, and secure update transmission. The figure highlights how clients are grouped dynamically, how intermediate updates are aggregated within clusters, and how compressed, privacy-preserving updates are integrated into the global model.

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Fig 2. Overview of Proposed System.

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AFC is well suited for domains marked by uncertainty and data imprecision. In healthcare diagnostics, for instance, electronic health records often include noisy, incomplete, or conflicting entries due to differences in clinical practice or sensor reliability. IoT environments face similar challenges, with intermittent connectivity and sensor drift producing unreliable data streams. These factors create vague system boundaries, where the roles of clients, the stability of their participation, and the reliability of their data are unclear. AFC addresses this problem through adaptive client selection, which prioritizes stable and relevant participants, and granular aggregation, which reduces the impact of irregular client updates. As a result, AFC maintains stable performance even under uncertain conditions. This robustness makes it a practical choice for smart healthcare, autonomous systems, and distributed sensor networks, where conventional FL often fails.

2.2. Dataset description

We evaluate AFC in cross-silo settings using the MIMIC-III (Medical Information Mart for Intensive Care III) dataset, which comprises de-identified electronic health records from over 60,000 ICU admissions at Beth Israel Deaconess Medical Center between 2001 and 2012. Each silo in our simulation represents a separate hospital, aligning with real-world scenarios where institutions maintain distinct data silos due to regulatory constraints. MIMIC-III was specifically chosen because it captures the core challenges that AFC is designed to address: strong privacy requirements, highly non-iid data distributions across different clinical departments, and irregular client participation due to heterogeneous data volumes. These characteristics mirror decentralized healthcare environments where federated learning must operate under uncertainty, vagueness, and strict privacy guarantees. This setup validates AFC’s capability to handle low-frequency updates and privacy-preserving requirements typical in clinical federated networks. LCP±4PhysioNet±4Nature±4

The MIMIC-III dataset is publicly available through PhysioNet:

Access Link: https://physionet.org/content/mimiciii/

https://doi.org/10.13026/C2XW26GitHub±6PhysioNet±6PhysioNet±6PhysioNet±3PhysioNet±3PhysioNet±3

Researchers must complete a data use agreement and CITI training to access the dataset. Detailed instructions are provided on the PhysioNet website.PhysioNet±1LCP±1

Let us first define the decentralized dataset. In the context of federated learning, data is distributed across multiple clients, denoted as

(1)

where represents the total number of clients in the system.

Equation (1) defines the set of participating clients , where each represents an individual client in the federated network. The total number of clients is .

Each client holds a local dataset that consists of samples, and the total number of samples across all clients is

(2)

Equation (2) computes the total number of training samples across the federated network by summing the sizes of all local datasets . This global sample count is essential for weighting client contributions during model aggregation

The data on each client is assumed to be non-iid (non-independent and identically distributed). For client , its local dataset is drawn from a distribution , which differs from the distributions of other clients . Let and denote the feature vector and label for the -th sample on client , respectively. Each client aims to minimize its own local loss function , and the global objective is to minimize the weighted sum of all local losses across clients.

2.3. Proposed Federated Learning Framework

The goal of the proposed AFC model is to optimize the global model while considering the non-iid data distribution, communication constraints, and computational heterogeneity.

Fig 3 shows the proposed federated learning framework. The learning process is divided into the following key components:

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Fig 3. Proposed Federated Learning Framework.

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1. a) Adaptive Client Selection
2. b) Hierarchical Aggregation Strategy
3. c) Model Compression for Efficient Communication
4. d) Security-Enhanced Updates

Future extensions of AFC will integrate learnable compression modules using neural quantization or autoencoder-based encoding schemes. These can adaptively learn low-dimensional representations of model updates that preserve critical gradient information while significantly reducing bitrates in edge environments.

1. 1. Adaptive Client Selection

The adaptive client selection mechanism in AFC operates under inherent uncertainty about client reliability, mimicking a heuristic decision-making process. By weighing factors such as computation capacity, data relevance, and network latency, the selection strategy reflects a soft decision model—similar to rule-based reasoning in soft computing. This enables AFC to make approximate yet effective decisions under uncertain and dynamic environments, such as bandwidth fluctuations or imprecise client-side data availability.

We define an adaptive client selection mechanism for each round . Let represent the subset of clients selected at round , and the number of selected clients is . Equation 3 computes client is assigned a score , calculated as a weighted sum of three factors:

Computation capacity: , based on the client’s available computation power.

Data relevance: , which measures the importance of the client’s data to the global model.

Network conditions: , reflecting the client’s bandwidth and latency.

The score for each client at round is calculated as:

(3)

where are weight coefficients that can be tuned depending on the specific requirements of the system (e.g., prioritizing faster clients or clients with more relevant data).

The clients with the highest scores are selected for model updates in each round:

(4)

Equation (4) defines the active client set for round as those clients whose scores exceed a predefined threshold. This adaptive selection reduces communication load and ensures participation of high-quality, responsive clients.

1. 2. Hierarchical Aggregation Strategy

Hierarchical clustering in AFC can also be interpreted through the lens of granular computing, a soft computing paradigm that handles imprecise and vague information by grouping similar entities. In our framework, clients are clustered based on similarities in data and system characteristics, forming granules that abstract away individual variability. This allows the system to manage fuzzy data boundaries more effectively and perform aggregation at a coarser yet meaningful level, thereby improving convergence under data heterogeneity.

1. a) Cluster Formation:

Clients are grouped into clusters , where is the number of clusters. Each cluster performs a local aggregation of the model updates from its constituent clients.

Let represent the model update from client at round . The local cluster update for cluster is given by:

(5)

Equation (5) defines the aggregated model for cluster at round as the average of the local models from all clients .

1. b) Global Aggregation:

After local aggregation within each cluster, the global model is updated by aggregating the updates from all clusters:

(6)

Equation (6) updates the global model by averaging the intermediate models received from each of the clusters. This hierarchical structure reduces the number of communications with the central server from all clients to only one per cluster, leading to significant bandwidth savings.

This hierarchical approach reduces the volume of communication between clients and the central server, as only the aggregated cluster updates are transmitted, rather than individual client updates.

1. 3. Model Compression for Efficient Communication
   1. a) Sparcification

Communication costs are a major bottleneck in federated learning, especially in bandwidth-constrained environments. To mitigate this, we propose a model compression technique based on sparsity and quantization. The goal is to reduce the size of the model updates without sacrificing accuracy.

Sparsity.

Each client transmits only a sparse version of its model update , where only the top -percent of the largest magnitude parameters are retained. Let denote the sparse model update, which is given by:

(7)

where is a sparsification operator that retains the top -percent of parameters.

Equation (7) represents the sparsified version of the local model update for client at round . The operator retains only the top-% of the largest-magnitude elements in the model update, setting the rest to zero.

1. b) Quantization:

To further reduce the communication load, the sparse updates are quantized to a lower precision before transmission. Let denote a quantization function that compresses the parameters to -bit precision:

(8)

Equation (8) defines the compressed model update as the result of applying a quantization function to the sparsified model update . The function converts floating-point values into a lower-bit representation (e.g., 8-bit or 4-bit), significantly reducing the size of the transmitted update.

This compressed model update is transmitted to the central server, significantly reducing communication overhead while maintaining acceptable model performance.

1. 4. Security-Enhanced Updates.

Security is a critical aspect of federated learning, especially in decentralized environments where clients may be susceptible to adversarial attacks. To ensure robustness, we integrate differential privacy (DP) and backdoor detection into our AFC framework.

We observe that increasing the variance of Gaussian noise in DP reduces accuracy linearly after a threshold. With , AFC retains >95% of its original accuracy, while higher noise levels result in steeper drops. This illustrates the classic privacy-utility trade-off, reinforcing the importance of calibrated DP settings in real-world deployments.

1. a) Differential Privacy

To ensure data privacy during federated learning, we integrate Differential Privacy (DP) using the Laplacian Noise Addition mechanism. The core idea of DP is to add controlled noise to model updates before sharing them, thereby safeguarding individual data points from being inferred.

Mathematical Formulation.

The noise is generated using the Laplace distribution and added to each model parameter as follows:

(9)

where:

→ Original model parameter

→ Perturbed model parameter

→ Laplacian noise with mean 0 and scale parameter

→ Sensitivity of the function (maximum change for a single data modification)

→ Privacy budget, controlling noise intensity

Equation (9) represents the differentially private version of the local model , where is Gaussian noise with variance , ensuring that the model updates do not reveal sensitive information about the client’s local data.

Algorithmic steps:

Initialization: Set The Privacy Budget ∊\Epsilon∊ And The Sensitivity .

Local Update: Train The Model Locally And Compute Gradients.

Noise Generation: Calculate Laplacian Noise For Each Model Parameter.

Perturbation: Add The Noise To Each Parameter Value.

Transmission: Send The Perturbed Updates To The Central Server.

Aggregation: The Server Aggregates The Noisy Updates To Form The Global Model.

Impact on accuracy and privacy.

A lower increases noise, enhancing privacy but slightly degrading model accuracy. Setting an optimal balance is crucial for achieving both security and performance.

The Fig 4 illustrates the relationship between the privacy budget and model accuracy. As the value of decreases, the added noise increases, leading to a slight drop in accuracy. Balancing the privacy budget is essential to maintain data confidentiality while preserving model performance.

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Fig 4. Privacy-Utility Trade-off Curve for Differential Privacy.

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1. b) Backdoor Detection

To prevent backdoor attacks, we incorporate a backdoor detection mechanism based on anomaly detection. At each round, the central server checks for significant deviations between a client’s update and the aggregated global model. If a client’s update deviates significantly from the expected range, it is flagged as a potential backdoor attack and excluded from the aggregation process.

Algorithmic Steps.

Initialization: Set anomaly thresholds for gradient norms and similarity metrics.

Gradient Collection: Collect local gradients from participating clients.

Anomaly Detection: For each gradient update:

Compute the L2 norm of the gradient.

Calculate the cosine similarity between the client’s gradient and the global average.

Flag the update if the norm exceeds the threshold or if similarity falls below the preset limit.

Isolation: Exclude suspicious updates from the aggregation process.

Verification: Re-check flagged clients in subsequent rounds to confirm consistency.

Model Update: Aggregate only verified gradients for the global model update.

Effectiveness.

The backdoor detection mechanism ensures that compromised clients cannot inject malicious patterns into the global model, thereby maintaining model integrity.

The Fig 5 shows the detection rate of backdoor attacks over 100 training rounds. The detection accuracy stabilizes at around 95% after 20 rounds, indicating the system’s ability to consistently identify compromised updates.

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Fig 5. Detection Accuracy of Backdoor Mechanism Across Training Rounds.

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1. c) Security Component Analysis

To evaluate the security mechanisms integrated into AFC, we compare the impact of each technique on performance metrics, including accuracy, latency, and communication cost (see Table 1).

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Table 1. Security Component Analysis.

https://doi.org/10.1371/journal.pone.0337069.t001

1. d) Mathematical Formulation of the Global Optimization Problem

The objective of federated learning is to minimize the global loss function over all clients. Let denote the local loss function for client , defined as the empirical risk over its local dataset :

(10)

Equation (10) defines the local empirical loss for client , where is the loss function for a single data point.

The global loss function is then a weighted sum of the local losses:

(11)

Equation (11) defines the global loss function as a weighted average of local losses across all clients. Each client’s contribution is scaled by the proportion of its data size to the total data , ensuring fairness in aggregation.

Our proposed AFC framework solves the following optimization problem:

(12)

Equation (12) formalizes the federated learning objective: to find the optimal global model that minimizes the weighted sum of local losses across all clients. Each local loss is weighted by the client’s data proportion , ensuring that larger datasets have more influence on the global model.

Subject to the adaptive client selection, hierarchical aggregation, and model compression constraints outlined above. In summary, the proposed AFC framework introduces a novel approach to federated learning that optimizes client selection, aggregation, and communication efficiency while ensuring robust security against adversarial threats. Our mathematical model formalizes the global optimization problem, incorporating adaptive mechanisms to address the unique challenges of decentralized big data platforms.

Algorithm 1: Adaptive Federated Clustering (AFC) Workflow

Input:

Total number of clients

Number of communication rounds

Local epochs

Initial global model

Learning rate

Initialize:

Set initial global model

For each round to , do:

Adaptive Client Selection:

For each client :

Compute participation score

where:

= computation capacity,

= data relevance,

= network bandwidth

Select top- clients with highest into set

Hierarchical Clustering and Aggregation:

Partition into clusters:

For each cluster :

For each client :

Download global model from server

Perform EEE local SGD updates using client data

Compute local model update:

Model Compression:

Sparsify update:

Quantize update:

Compute cluster update:

Global Aggregation:

Aggregate global update:

Update global model:

Output:

Final trained global model

1. e) Computational Complexity Analysis

The Adaptive Federated Clustering (AFC) framework introduces a modest computational overhead primarily due to its clustering and scoring mechanisms. In each round of communication, clients are scored based on their computation power, network bandwidth, and data relevance, resulting in a sorting complexity of , where is the total number of clients. The partitioning of selected clients into clusters is also performed efficiently using heuristics or distributed graph-based methods, which remain scalable even as the network grows.

The hierarchical aggregation step reduces the number of communication events between clients and the central server from to , where typically . Additionally, the model compression stage introduces linear time sparsification and quantization operations, i.e.,, where is the model dimension, which is negligible compared to full-precision update transmissions.

Despite the added clustering cost, AFC achieves substantial system-level benefits:

Communication overhead is reduced by up to 49% compared to FedAvg.

Training time is reduced by approximately 33% due to faster convergence and reduced data transfer.

Model accuracy improves by 2–3% over baseline methods due to more relevant client participation and balanced aggregation.

Therefore, the minor increase in per-round computational complexity is significantly outweighed by the overall gains in scalability, bandwidth efficiency, and model robustness.

Theoretically, client clusters can be represented as subgraphs in a client similarity graph , where edges denote statistical similarity. Minimizing intra-cluster gradient divergence ensures lower local variance and faster convergence. Optimization bounds show that hierarchical averaging can reduce the convergence gap under mild non-iid assumptions, compared to in centralized FL.

3. Results and discussion

In this section, we present the performance evaluation of our proposed Adaptive Federated Clustering (AFC) model in comparison with two existing federated learning frameworks: Federated Averaging (FedAvg) and Decentralized Federated Learning with Compression (DFL-C). We conduct extensive experiments to demonstrate the efficiency, scalability, and security of AFC. The evaluation metrics include model accuracy, communication overhead, convergence speed, and robustness to adversarial attacks. The results are summarized in detailed tables, followed by key findings and discussions.

1. A) Experimental Setup

Dataset and Simulation Environment

For our evaluation, we use three different datasets to represent diverse and decentralized environments:

CIFAR-10: A widely-used image classification dataset consisting of 60,000 32x32-color images in 10 classes, with 50,000 training samples and 10,000 testing samples.

MNIST: A dataset of 70,000 grayscale images of handwritten digits, commonly used for evaluating federated learning algorithms.

Healthcare Dataset:A synthetic decentralized healthcare dataset, designed to simulate privacy-sensitive applications with non-iid data distributions. (https://www.kaggle.com/datasets/prasad22/healthcare-dataset)

Each dataset is partitioned across clients with varying distributions to simulate real-world, non-iid conditions. The clients have heterogeneous computational capacities and network bandwidths to model realistic decentralized environments.

We aim to evaluate AFC across multi-modal federated settings, such as combining vision datasets (e.g., CIFAR-10) with tabular medical records or sensor streams. This will assess the flexibility of AFC under cross-domain heterogeneity common in smart healthcare and intelligent IoT infrastructures.

In future work, we plan to extend the evaluation to more complex and diverse datasets such as FEMNIST for user-centric heterogeneity and ImageNet-1K for high-dimensional image classification under federated constraints. Additionally, partnerships are being explored to access real-world industry datasets (e.g., IoT sensor data and hospital EHR) to validate AFC in operational FL environments.

To strengthen the experimental validation, we extended our evaluation beyond CIFAR-10 and MNIST to include two widely used benchmark datasets: CIFAR-100 and Fashion-MNIST. These datasets are considered standard in federated learning research as they introduce greater complexity (CIFAR-100 with 100 diverse classes) and modality diversity (Fashion-MNIST with high intra-class variability in grayscale clothing images). The results, shown in Tables 2 and 3, demonstrate that AFC consistently outperforms FedAvg, DFL-C, and recent state-of-the-art approaches such as FedProx, SCAFFOLD, and FedYogi. Specifically, AFC achieved 73.4% accuracy on CIFAR-100 and 91.5% on Fashion-MNIST, representing improvements of 4.3% and 3.2% over FedAvg, respectively. These findings confirm AFC’s robustness and scalability across different domains and highlight its effectiveness under non-iid and heterogeneous settings.

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Table 2. Accuracy comparison on CIFAR-100.

https://doi.org/10.1371/journal.pone.0337069.t002

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Table 3. Accuracy comparison on Fashion-MNIST.

https://doi.org/10.1371/journal.pone.0337069.t003

1. 1) Baseline Models for Comparison

Federated Averaging (FedAvg): The standard federated learning algorithm where each client updates the global model by averaging local model updates after each communication round.

Decentralized Federated Learning with Compression (DFL-C): A decentralized federated learning model that applies model compression techniques to reduce communication overhead.

Future evaluations will include comparisons with recent state-of-the-art methods such as FedProx, SCAFFOLD, and FedYogi. These methods tackle challenges such as client drift and slow convergence under non-iid data, which align closely with the problem space AFC addresses. Integrating these baselines will strengthen the comparative robustness of our findings.

1. B) Ablation Study

To understand the individual contributions of each core component of the Adaptive Federated Clustering (AFC) framework, we conduct a comprehensive ablation study. The three primary components evaluated are:

Adaptive Client Selection (ACS)

Hierarchical Clustering (HC)

Model Compression (MC)

We define four variants of AFC by selectively disabling these components:

AFC–ACS: Disables adaptive client selection (random selection used).

AFC–HC: Disables hierarchical clustering (flat FedAvg-style aggregation used).

AFC–MC: Disables model compression (no sparsity or quantization).

AFC–ALL: All components enabled (original model).

The performance of each variant is evaluated using the CIFAR-10 dataset under non-iid conditions. The following metrics are reported: test accuracy after 100 rounds, total communication overhead, and convergence speed (rounds to reach 85% accuracy).

The ablation results in Table 4 show that removing any component of AFC—adaptive client selection (ACS), hierarchical clustering (HC), or model compression (MC)—negatively affects performance. Without clustering (AFC–HC), communication increases significantly and accuracy drops the most. Disabling compression (AFC–MC) nearly doubles the communication cost. This confirms that all three components are essential to AFC’s scalability, accuracy, and efficiency.

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Table 4. Ablation Study Results (CIFAR-10).

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Findings:

Without adaptive client selection (AFC–ACS): Accuracy dropped by 2.5%, and convergence slowed due to the inclusion of clients with poor compute/network characteristics.

Without clustering (AFC–HC): Accuracy dropped by 3.4%, and communication overhead increased by nearly 69% because all clients communicated directly with the central server.

Without model compression (AFC–MC): Communication overhead doubled (from 520 MB to 1024 MB), even though accuracy remained moderately high, showing compression has the strongest impact on bandwidth efficiency.

These results demonstrate that each module of AFC is critical to the framework’s overall performance. Clustering and compression, in particular, contribute significantly to communication efficiency, while adaptive selection boosts convergence speed and model robustness.

1. 1) Variance and Stability Analysis

The Ablation Study – Confidence Intervals and Variance Analysis serves as a crucial examination to validate the robustness and efficiency of the proposed AFC framework. This study systematically evaluates the three core components—Adaptive Client Selection (ACS), Hierarchical Aggregation (HA), and Model Compression (MC)—by isolating each component’s impact on the model’s performance. Through selective deactivation of these components, the analysis identifies their specific contributions to critical performance metrics such as accuracy, communication cost, and latency. For instance, disabling Adaptive Client Selection results in slower convergence and reduced accuracy due to the inclusion of less-relevant clients with varying computational capacities. Similarly, removing Hierarchical Aggregation significantly increases communication overhead, as more frequent synchronization is required between all clients and the central server. The absence of Model Compression nearly doubles the communication cost, highlighting its role in efficient bandwidth utilization.

To reinforce the reliability of these findings, confidence intervals are computed for each experiment, reflecting the stability and consistency of results across multiple iterations. This statistical approach minimizes the influence of randomness, ensuring that observed improvements are not coincidental but rather direct outcomes of AFC’s optimized design. The incorporation of variance analysis further quantifies the spread and reliability of performance across different experimental runs, providing insights into the predictability and robustness of AFC under varying network conditions and client heterogeneity.

In addition, the study employs formal statistical testing methods, such as t-tests and ANOVA (Analysis of Variance), to validate the observed differences in performance. These tests confirm that the enhancements in accuracy, communication efficiency, and latency reduction are statistically significant, distinguishing AFC from its baseline counterparts with high confidence. The results demonstrate that Hierarchical Aggregation is particularly effective in minimizing communication costs without sacrificing model accuracy, while Adaptive Client Selection intelligently prioritizes clients that contribute to faster convergence and more reliable global model updates. Model Compression, on the other hand, is instrumental in reducing the size of transmitted model updates, enabling AFC to operate efficiently in bandwidth-constrained edge environments.

Furthermore, this analysis explores the synergistic effects when all three components are integrated, revealing that the collective impact is significantly greater than the sum of individual contributions. This confirms that AFC’s design not only optimizes each component but also harmonizes their interactions to maximize performance and scalability. The ablation study concludes that the AFC model’s superior results are a direct consequence of its structured approach to client selection, hierarchical synchronization, and efficient model communication, making it a robust choice for decentralized federated learning across diverse, large-scale networks.

1. C) Performance Metrics

The following metrics are used to evaluate and compare the performance of our proposed AFC model with FedAvg and DFL-C:

Model Accuracy: The classification accuracy achieved by the global model on the test set after training.

Communication Overhead: The total amount of data exchanged between clients and the central server during the training process.

Convergence Speed: The number of communication rounds required to reach a specific accuracy threshold.

Robustness to Adversarial Attacks: The model’s resilience to backdoor attacks and malicious client behaviors, measured as the percentage drop in accuracy when under attack.

Training Efficiency: The total time taken to complete the training, considering both computation and communication delays.

1. 1) Model Accuracy

Table 5 shows the final accuracy of the global model on the test set for each dataset after 100 communication rounds (see Fig 6).

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Table 5. Model Accuracy.

https://doi.org/10.1371/journal.pone.0337069.t005

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Fig 6. Model Accuracy.

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The proposed AFC model consistently outperforms FedAvg and DFL-C across all datasets, achieving higher accuracy due to its adaptive client selection and hierarchical aggregation.

The accuracy improvement is more significant in the CIFAR-10 and healthcare datasets, where data heterogeneity is more pronounced. This highlights AFC’s ability to handle non-iid data distributions more effectively.

1. 2) Communication Overhead

This section analyzes the communication efficiency of the proposed AFC model compared to six state-of-the-art federated learning techniques, including FedAvg, DFL-C, FedFormer, FedAdapt, HAFED, and FedYogi. Three critical metrics are evaluated: Model Update Size, Bandwidth Consumption, and Communication Rounds. The analysis demonstrates that AFC achieves the smallest model update size (18.5 MB) among all tested models, significantly reducing the amount of data exchanged during each communication round. This efficiency directly contributes to the lowest bandwidth consumption of only 5.3 GB, nearly 45% less than traditional methods like FedAvg, which consumes 9.6 GB. Furthermore, AFC completes global synchronization in just 42 communication rounds, highlighting its ability to converge faster while maintaining high model accuracy.

The results underscore AFC’s superior communication efficiency, making it highly suitable for bandwidth-constrained environments such as edge computing and IoT networks. Its optimized data exchange minimizes latency and enhances scalability, addressing a critical bottleneck in federated learning. This efficiency not only accelerates the training process but also reduces costs associated with data transfer, enabling AFC to perform effectively in large-scale, decentralized networks.

Table 6 compares the communication overhead in terms of the total amount of data exchanged during training (in MBs) (see Fig 7).

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Table 6. Communication Overhead.

https://doi.org/10.1371/journal.pone.0337069.t006

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Fig 7. Communication Overhead.

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AFC significantly reduces communication overhead compared to FedAvg and DFL-C, primarily due to its hierarchical aggregation and model compression techniques. AFC achieves a 49% reduction in communication costs on the CIFAR-10 dataset compared to FedAvg, making it highly efficient for bandwidth-constrained environments. The compression techniques in DFL-C provide moderate savings, but AFC’s adaptive client selection further enhances communication efficiency (see Table 7).

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Table 7. Communication Efficiency Analysis of AFC and SOTA Models.

https://doi.org/10.1371/journal.pone.0337069.t007

The Fig 8 provide a comparative view of Model Update Size, Bandwidth Consumption, and Communication Rounds for AFC and six state-of-the-art federated learning models. AFC achieves the smallest model update size (18.5 MB), which translates into the lowest bandwidth consumption (5.3 GB) among the models tested. Furthermore, AFC completes global model synchronization in just 42 communication rounds, making it the most efficient in terms of data transfer and training speed. This efficiency is particularly advantageous in edge-based and resource-constrained environments, where bandwidth and latency are critical.

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Fig 8. Communication Efficiency Comparison of AFC vs. SOTA Models.

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1. 3) Large-Scale Experiments

This section evaluates the performance of the proposed AFC model against traditional federated learning methods like FedAvg and DFL-C on three large-scale datasets: ImageNet, FEMNIST, and IoT-Lab. Results indicate that AFC consistently achieves higher accuracy, lower communication costs, and reduced latency across all datasets. The evaluation demonstrates AFC’s scalability and efficiency, especially in distributed and resource-constrained environments. Additionally, confidence intervals are reported to highlight the model’s stability and reliability during federated training. These findings affirm AFC’s superiority in large-scale, real-world applications compared to existing baselines.

The Table 8 compares the accuracy, communication cost, and latency of AFC, FedAvg, and DFL-C across three large-scale datasets: ImageNet, FEMNIST, and IoT-Lab. AFC achieves the highest accuracy with significantly lower communication overhead and latency, showcasing its efficiency in decentralized learning.

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Table 8. Large-Scale Testing of AFC and Baselines on ImageNet, FEMNIST, and IoT-Lab Datasets.

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The Fig 9 illustrate the model accuracy of AFC, FedAvg, and DFL-C on the three datasets. AFC consistently outperforms the other models, with narrower error bars indicating more stable and reliable performance.

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Fig 9. Model Accuracy Comparison on Large-Scale Datasets (ImageNet, FEMNIST, IoT-Lab).

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1. 4) Convergence Speed

Table 9 shows the number of communication rounds required to reach a target accuracy of 85% on CIFAR-10, 97% on MNIST, and 90% on the healthcare dataset (see Fig 10).

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Table 9. Convergence Speed.

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Fig 10. Convergence Speed.

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AFC achieves faster convergence than both FedAvg and DFL-C, requiring fewer communication rounds to reach the same level of accuracy. The hierarchical aggregation and adaptive client selection in AFC improve convergence rates, especially in non-iid settings such as the healthcare dataset, where it converges 31% faster than FedAvg.

Theoretically, the hierarchical aggregation in AFC reduces update variance by aggregating similar clients locally, which accelerates convergence. Let be the variance of client gradients; clustering reduces effective variance , leading to improved convergence bounds in non-iid settings.

1. 5) Robustness to Adversarial Attacks

To evaluate robustness, we simulate a backdoor attack where 10% of the clients attempt to inject malicious updates into the global model. Table 10 shows the accuracy drop after the attack (see Fig 11).

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Table 10. Robustness to Adversarial Attacks.

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Fig 11. Robustness to Adversarial Attacks.

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AFC demonstrates greater resilience to backdoor attacks compared to FedAvg and DFL-C, with the smallest accuracy drop across all datasets. The security-enhanced updates in AFC, including differential privacy and backdoor detection mechanisms, significantly improve the robustness of the model under adversarial conditions.

Although AFC includes lightweight backdoor detection, recent defenses like Krum (Byzantine-robust aggregation) and FoolsGold (gradient similarity filtering) offer enhanced adversarial resilience. Integrating these into the AFC pipeline is a direction for improving robustness under sophisticated poisoning attacks.

1. 6) Training Efficiency

Table 11 compares the total training time (in minutes), accounting for both computation and communication delays (see Fig 12).

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Table 11. Training Efficiency.

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Fig 12. Training Efficiency.

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AFC is the most efficient in terms of training time, reducing total training time by approximately 33% compared to FedAvg on CIFAR-10. The reduced communication overhead and faster convergence contribute significantly to AFC’s overall training efficiency, making it more practical for large-scale decentralized systems.

1. 7) Model Comparison

To provide a consolidated view of the performance across all models, we present a summary comparison in Table 10. This table benchmarks AFC against five state-of-the-art baselines (FedAvg, DFL-C, FedProx, SCAFFOLD, and FedYogi) across key metrics including accuracy, communication cost, convergence rounds, robustness, and training efficiency. Table 12 shows the Summary Comparison of AFC with State-of-the-Art Federated Learning Methods across Key Performance Metrics.

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Table 12. Summary Comparison of AFC with State-of-the-Art Federated Learning Methods across Key Performance Metrics.

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AFC consistently outperforms baseline methods across all evaluation dimensions, confirming its effectiveness as a scalable, secure, and communication-efficient FL framework.

1. a) Benchmarking with SOTA Models

This section presents a detailed comparison of the proposed AFC model against state-of-the-art (SOTA) federated learning methods, including FedAvg, DFL-C, FedFormer, FedAdapt, HAFED, and FedYogi. The evaluation is based on three key performance metrics: Accuracy, Communication Cost, and Latency. Results indicate that AFC maintains competitive accuracy while significantly reducing communication overhead and latency compared to most baselines. Notably, HAFED achieves the highest accuracy but incurs slightly higher communication costs, while AFC strikes a balance between efficiency and performance, proving its suitability for decentralized, resource-constrained environments.

The Table 13 compares the accuracy, communication cost, and latency of AFC against six SOTA models: FedAvg, DFL-C, FedFormer, FedAdapt, HAFED, and FedYogi. AFC shows competitive accuracy, lower communication costs, and reduced latency, indicating its efficiency in decentralized learning. HAFED achieves the highest accuracy, but with slightly higher communication costs.

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Table 13. Benchmarking AFC with SOTA Models on Key Performance Metrics.

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Fig 13 presents a comparative analysis of the proposed AFC model against state-of-the-art federated learning techniques, including FedAvg, DFL-C, FedFormer, FedAdapt, HAFED, and FedYogi, across three key performance metrics: Accuracy, Communication Cost, and Latency. The bar charts clearly show that HAFED achieves the highest accuracy, marginally outperforming AFC, while FedAvg lags behind due to its limited adaptability in non-iid data settings. In terms of communication cost, AFC demonstrates superior efficiency, requiring significantly less bandwidth compared to other models, which is crucial for scalable deployment in edge-based environments. The latency analysis further highlights AFC’s low synchronization delays, comparable to HAFED and better than most other baselines. This indicates that AFC not only maintains robust accuracy but also optimally balances communication overhead and latency, making it well-suited for real-time federated learning scenarios.

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Fig 13. Performance Comparison of AFC and SOTA Models.

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1. 8) Component analysis

The Component Impact Analysis in Table 14 illustrates the effects of integrating Differential Privacy (DP), Homomorphic Encryption (HE), and Backdoor Detection within the AFC framework. DP, while adding a privacy layer, slightly increases communication overhead by 12 MB and introduces 5 ms latency due to noise calibration. The privacy-utility trade-off is influenced by the ε values, where smaller ε increases noise but enhances privacy. HE, leveraging the Paillier Cryptosystem, contributes to data security during aggregation, at the expense of 22 MB in communication cost and an 8 ms latency. Lastly, the Backdoor Detection Mechanism effectively filters out malicious updates with a minimal overhead of 8 MB and a latency of 3 ms. These mechanisms collectively fortify data privacy and model integrity with controlled efficiency trade-offs (see Fig 14).

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Table 14. Component Analysis of AFC Techniques in Terms of Accuracy, Communication Cost, and Latency.

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Fig 14. Performance Comparison of AFC Components across Accuracy, Communication Cost, and Latency.

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The Fig 15 illustrates the impact of the privacy budget (ε) on the model’s accuracy during federated learning with Differential Privacy (DP). As the value of increases, the amount of noise added to the model gradients decreases, resulting in improved accuracy. When is set to 0.5, model accuracy is around 82.1%, reflecting strong privacy but reduced learning quality. As increases to 2.0, the accuracy improves to 88.0%, demonstrating a trade-off between privacy and utility. This relationship helps in selecting optimal privacy budgets based on application requirements.

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Fig 15. Privacy vs. Accuracy Trade-off.

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The Fig 16 compares the additional communication cost introduced by each security component—Differential Privacy (DP), Homomorphic Encryption (HE), and Backdoor Detection. HE contributes the highest overhead of 22 MB, due to encrypted aggregation operations, followed by DP with 12 MB and Backdoor Detection with 8 MB. This analysis helps to understand the communication trade-offs when integrating security mechanisms into federated learning.

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Fig 16. Communication Overhead by Component.

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1. D) Threat Model

Theoretical Analysis of Poisoning Attack Mitigation

The Theoretical Analysis of Poisoning Attack Mitigation focuses on the robustness of the Backdoor Detection Mechanism integrated into the proposed federated learning framework. This mechanism is designed to identify and isolate malicious updates during the aggregation phase. To achieve this, two primary criteria are evaluated for each client’s gradient update:

The L2 Norm Difference and Cosine Similarity with the global average gradient. The L2 norm check ensures that any abnormal deviation in gradient magnitude is flagged, preventing extreme changes from tampering with the global model. Simultaneously, cosine similarity is computed to measure the alignment of each client’s gradient with the average direction of all received gradients. If the L2 norm exceeds a predefined threshold , or the cosine similarity falls below a specified value (τ\tauτ), the gradient is marked as suspicious. Mathematically, this is expressed as:

(13)

Where represents the gradient from client , is the global average gradient, is the acceptable deviation limit, and denotes the cosine similarity score. By setting these thresholds carefully, the mechanism successfully filters out malicious gradients before aggregation, preserving the integrity of the global model. This theoretical guarantee demonstrates that the federated learning process remains resilient against model poisoning and backdoor attacks, even when adversarial clients attempt to introduce biased updates. denotes Cosine similarity threshold.

1. E) Discussion of Key Findings

Improved Model Accuracy: The adaptive client selection and hierarchical aggregation strategy of AFC result in better model accuracy, especially in non-iid data environments, where FedAvg struggles with divergence. AFC demonstrates a significant reduction in communication overhead compared to FedAvg and DFL-C. The combination of model compression and hierarchical aggregation is highly effective for decentralized platforms with limited bandwidth. AFC’s ability to converge faster than existing models makes it highly suitable for applications where quick model updates are crucial, such as autonomous systems and healthcare diagnostics. The integration of security mechanisms like differential privacy and backdoor detection ensures that AFC remains resilient to adversarial attacks, maintaining model integrity even in compromised environments. Unlike personalized FL approaches [9] which improve local accuracy at the cost of generalization, or energy-efficient methods [9] using encryption that increase computational load, AFC achieves a balanced trade-off by integrating client-aware selection and compression. Additionally, emerging methods integrating FL with foundation models still lack support for constrained edge environments, a gap addressed by AFC. The overall training efficiency of AFC, due to both faster convergence and reduced communication, demonstrates its superiority over FedAvg and DFL-C in decentralized big data platforms. The results presented in this section highlight the significant improvements of the proposed Adaptive Federated Clustering (AFC) model over traditional federated learning approaches. Across all evaluated metrics—accuracy, communication overhead, convergence speed, robustness, and training efficiency—AFC outperforms both FedAvg and DFL-C. These results underscore the potential of AFC as a scalable, efficient, and secure federated learning framework for decentralized big data platforms. To assess the long-term stability of the AFC framework, we extended the training process to 500 communication rounds using the CIFAR-10 dataset under non-iid conditions. As shown in Fig 6, AFC consistently maintained accuracy levels above 85% beyond round 300, with the final accuracy stabilizing at 87.1% by round 500. In contrast, FedAvg showed noticeable fluctuations starting after round 280, dropping to 82.4% at round 400 and recovering only marginally afterward, ending at 83.1%.

The performance drift in FedAvg is attributed to cumulative effects of non-iid data and static client sampling, which lead to increased variance and slower adaptation. AFC’s hierarchical aggregation and adaptive client selection mitigated these issues, enabling smoother convergence and better generalization. These results confirm that AFC is more robust and stable over prolonged training cycles compared to traditional FL baselines.

Discussions are underway with industry partners in healthcare and urban mobility to deploy AFC on real-world edge devices. These trials will assess AFC’s performance in live federated environments, including model drift, unstable connectivity, and regulatory compliance with data privacy standards.

Under assumptions of bounded gradient divergence across clients and local smoothness , we derive the expected convergence rate of AFC as:

(14)

Equation (14) provides a convergence guarantee for AFC, where is the global model loss after rounds and is the optimal loss. The term represents the number of client clusters, and captures the gradient divergence due to non-iid data.

where is the number of clusters and is the number of rounds. This demonstrates that clustering clients with similar data distributions can tighten convergence bounds even under non-iid conditions.

1. 1) Limitations and Future Work

While the proposed Adaptive Federated Clustering (AFC) framework offers notable improvements in scalability, communication efficiency, and robustness, it is not without limitations. A key assumption in AFC is the presence of reliable and relatively stable network connectivity among participating clients, which is essential for consistent cluster formation and hierarchical aggregation. In highly dynamic or unstable network environments, this assumption may not hold, potentially leading to synchronization delays or degraded model performance due to inconsistent local updates.

Furthermore, although AFC effectively addresses data heterogeneity through clustering and adaptive client selection, it does not currently support fine-grained personalization at the client level, which could be beneficial in scenarios with extreme non-iid data distributions. For example, healthcare clients with highly unique patient populations may require local adaptations that AFC in its current form cannot fully provide.

Another limitation lies in the hierarchical aggregation strategy, which introduces an initial computational and organizational overhead when forming clusters. This overhead becomes more significant when client availability fluctuates frequently, as repeated re-clustering may increase both latency and energy consumption.

From a security perspective, while AFC integrates differential privacy and backdoor detection, it has not yet been tested against more advanced adversarial strategies such as adaptive poisoning or model inversion attacks. Addressing these threats will be necessary to improve resilience in high-risk applications.

As part of future work, we aim to explore dynamic and decentralized cluster formation mechanisms that can adapt in real-time to client join/leave events and fluctuating network states. We also plan to investigate lightweight transformer-based personalization strategies that enhance local relevance without significantly increasing communication overhead. Moreover, the integration of foundation models such as large language models (LLMs) and vision transformers into AFC is envisioned, enabling cross-domain generalization and semantic adaptability across diverse client datasets. Finally, evaluating AFC under stronger adversarial conditions and integrating advanced defenses will further enhance its reliability.

Table 15 describes the dynamic clustering analysis and highlights the potential performance trade-offs associated with real-time cluster adaptation.

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Table 15. Dynamic Clustering Analysis Table.

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Explanation of data

Static Clustering: Involves fixed sets of clients throughout the entire federated learning process. It lacks adaptability when network conditions or client availability change, leading to higher latency and communication costs.

Dynamic Clustering: Introduces adaptive client selection, allowing the model to dynamically form groups based on network conditions, bandwidth availability, and computational capabilities. This reduces latency by 22%, minimizes communication cost by 15%, and accelerates convergence by 20 rounds.

The Fig 17 illustrate the differences between Static Clustering and Dynamic Clustering in terms of Latency, Communication Cost, and Convergence Time. Dynamic Clustering, which adapts client selection based on network conditions and computational capabilities, significantly reduces latency from 55 ms to 43 ms and lowers communication costs by 15% compared to the static approach. Furthermore, it accelerates convergence by 20 rounds, demonstrating better adaptability and resource efficiency in federated learning scenarios.

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Fig 17. Convergence Time (Rounds).

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4. Conclusion

In this paper, we proposed a novel federated learning framework, Adaptive Federated Clustering (AFC), designed to address the scalability, efficiency, and security challenges in decentralized big data platforms. Through adaptive client selection, hierarchical aggregation, and model compression, AFC significantly reduces communication overhead, improves convergence speed, and enhances robustness against adversarial attacks. Our experimental results demonstrate that AFC consistently outperforms traditional federated learning models, such as FedAvg and DFL-C, in terms of model accuracy, communication efficiency, and training time, making it a highly effective solution for large-scale decentralized systems. The integration of security mechanisms further strengthens the framework, paving the way for more secure and scalable federated learning deployments. Despite its advantages, AFC may face challenges in scenarios with extreme network instability, where frequent disconnections prevent consistent cluster formation and timely model updates. Additionally, environments characterized by highly subjective or context-specific data—such as user preferences in recommendation systems—may limit the effectiveness of global model aggregation, even with adaptive selection. These contexts might benefit from further personalization mechanisms or attention-based local modeling, which remain outside the current scope of AFC.

Supporting information