Federated learning algorithm based on prototype clustering and Fisher information matrix weighted fusion

doi:10.11772/j.issn.1001-9081.2025081017

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (9): 2741-2751.DOI: 10.11772/j.issn.1001-9081.2025081017

• Artificial intelligence • Previous Articles

Federated learning algorithm based on prototype clustering and Fisher information matrix weighted fusion

Xingyao WANG¹^,²^,³, Xuebin CHEN¹^,²^,³()

^1.College of Science，North China University of Science and Technology，Tangshan Hebei 063210，China
^2.Hebei Provincial Key Laboratory of Data Science and Application （North China University of Science and Technology），Tangshan Hebei 063210，China
^3.Tangshan Key Laboratory of Data Science （North China University of Science and Technology），Tangshan Hebei 063210，China

Received:2025-09-04 Revised:2025-10-10 Accepted:2025-10-20 Online:2025-11-07 Published:2026-09-10
Contact: Xuebin CHEN
About author:WANG Xingyao， born in 1999， M. S. candidate. His research interests include data security， privacy protection.
CHEN Xuebin， born in 1970， Ph. D.， professor. His research interests include big data security， internet of things security， network security.
Supported by:
National Natural Science Foundation of China(U20A20179)

基于原型聚类和费舍尔信息矩阵加权融合的联邦学习算法

王星尧¹^,²^,³, 陈学斌¹^,²^,³()

^1.华北理工大学理学院，河北唐山 063210
^2.河北省数据科学与应用重点实验室（华北理工大学），河北唐山 063210
^3.唐山市数据科学重点实验室（华北理工大学），河北唐山 063210

通讯作者: 陈学斌
作者简介:王星尧（1999—），男，河北唐山人，硕士研究生，CCF会员，主要研究方向：数据安全、隐私保护
陈学斌（1970—），男，河北唐山人，教授，博士，CCF杰出会员，主要研究方向：大数据安全、物联网安全、网络安全。
基金资助:
国家自然科学基金资助项目(U20A20179)

Abstract

Abstract:

Federated learning， as an important research direction in the field of artificial intelligence， constructs global models through distributed collaborative training under the premise of ensuring data privacy， providing a new paradigm for joint modeling in privacy-sensitive scenarios. However， the existing methods are challenged by performance degradation， training oscillation， and slow convergence when faced with heterogeneous client data. Therefore， a federated learning algorithm based on prototype clustering and Fisher information matrix adaptive weighted fusion， named FedPFA， was proposed. First， the prototypes uploaded by clients were clustered by the server to mitigate data distribution discrepancies and enhance the consistency and generalization capability of the global model. Subsequently， differentiated weights were assigned to the prototypes by incorporating the trace estimated values of the Fisher information matrix from each client， thereby highlighting the contributions of high-quality clients and suppressing interference from noisy or inadequately trained clients during the fusion process. Experimental results on the MNIST， Fashion-MNIST， and CIFAR-10 datasets demonstrate that， under the setting of 20 clients and a participation rate of 0.3， FedPFA achieves accuracy improvements of 19.64， 26.14， and 16.15 percentage points， respectively， compared to the Federated Global prediction Header （FedGH） algorithm. It can be seen that FedPFA ensures performance enhancement， and improves the convergence speed and stability of the global model significantly， exhibiting strong robustness and practical application value on various datasets.

Key words: federated learning, prototype clustering, Fisher information matrix, weighted fusion, client selection

摘要：

联邦学习作为人工智能领域的重要研究方向，在保障数据隐私的前提下，通过分布式协同训练构建全局模型，为隐私敏感场景下的联合建模提供了新范式。然而，现有方法在面对客户端异构数据时，存在性能退化、训练振荡和收敛缓慢等问题。因此，提出一种基于原型聚类与费舍尔信息矩阵自适应加权融合的联邦学习算法——FedPFA。首先，服务器对客户端上传的原型表示进行聚类，以缓解数据分布差异并增强全局模型的一致性与泛化能力；其次，结合客户端的费舍尔信息矩阵迹估计值为原型分配差异化权重，从而在融合过程中突出高质量客户端的贡献，抑制噪声或训练不足客户端的干扰。在MNIST、Fashion-MNIST和CIFAR-10数据集上的实验结果表明，与联邦全局预测头（FedGH）算法相比，在客户端数为20、参与率为0.3的情况下，FedPFA的准确率分别提高了19.64、26.14和16.15个百分点。FedPFA在保证性能提升的同时，显著提高了全局模型的收敛速度与稳定性，并在多种数据集上展现出良好的鲁棒性与实际应用价值。

关键词: 联邦学习, 原型聚类, 费舍尔信息矩阵, 加权融合, 客户端选择

CLC Number:

TP309.2

Xingyao WANG, Xuebin CHEN. Federated learning algorithm based on prototype clustering and Fisher information matrix weighted fusion[J]. Journal of Computer Applications, 2026, 46(9): 2741-2751.

王星尧, 陈学斌. 基于原型聚类和费舍尔信息矩阵加权融合的联邦学习算法[J]. 《计算机应用》唯一官方网站, 2026, 46(9): 2741-2751.

Figures/Tables 12

Fig. 1 Framework of FedPFA

Fig. 2 Accuracy and loss curve comparison of different algorithms on three datasets （20 clients）

Tab. 1 Performance comparison results of different algorithms on three datasets （20 clients）

算法	MNIST				Fashion-MNIST				CIFAR-10
	$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6
	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
FedAvg	82.96	0.479	86.66	0.371	63.41	1.037	67.19	0.858	40.95	1.722	47.09	1.445
FedProx	82.26	0.502	85.10	0.412	60.53	1.147	68.10	0.844	37.44	1.829	41.48	1.617
FedProto	81.61	0.076	96.69	0.040	65.37	0.134	85.34	0.102	75.55	0.153	84.28	0.014
FedGH	78.48	1.668	88.91	0.996	64.68	2.814	81.34	0.895	72.18	2.283	78.32	2.085
FedCross	97.80	0.066	97.77	0.067	89.30	0.287	89.43	0.285	88.19	0.258	88.94	0.268
FedPFA	98.12	0.047	98.86	0.006	90.82	0.614	92.40	0.302	88.33	0.047	89.19	0.001

Tab. 1 Performance comparison results of different algorithms on three datasets （20 clients）

算法	MNIST				Fashion-MNIST				CIFAR-10
	$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6
	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
FedAvg	82.96	0.479	86.66	0.371	63.41	1.037	67.19	0.858	40.95	1.722	47.09	1.445
FedProx	82.26	0.502	85.10	0.412	60.53	1.147	68.10	0.844	37.44	1.829	41.48	1.617
FedProto	81.61	0.076	96.69	0.040	65.37	0.134	85.34	0.102	75.55	0.153	84.28	0.014
FedGH	78.48	1.668	88.91	0.996	64.68	2.814	81.34	0.895	72.18	2.283	78.32	2.085
FedCross	97.80	0.066	97.77	0.067	89.30	0.287	89.43	0.285	88.19	0.258	88.94	0.268
FedPFA	98.12	0.047	98.86	0.006	90.82	0.614	92.40	0.302	88.33	0.047	89.19	0.001

Fig. 3 Accuracy and loss curve comparison of different algorithms on three datasets （50 clients）

Tab. 2 Performance comparison results of different algorithms on three datasets （50 clients）

算法	MNIST				Fashion-MNIST				CIFAR-10
	$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6
	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
FedAvg	80.30	0.586	82.66	0.539	65.11	0.984	69.10	0.891	43.05	1.561	47.09	1.423
FedProx	79.35	0.611	82.11	0.553	65.17	0.986	70.07	0.864	40.87	1.599	44.11	1.502
FedProto	88.40	0.153	96.22	0.079	79.80	0.177	88.61	0.118	83.77	0.189	86.91	0.039
FedGH	79.68	1.353	92.70	0.391	79.68	1.167	84.02	0.611	72.64	1.039	86.00	0.200
FedCross	97.02	0.087	97.54	0.082	95.35	0.144	95.45	0.142	87.05	0.330	87.19	0.323
FedPFA	97.21	0.059	98.59	0.004	96.36	0.085	96.63	0.057	87.64	0.046	88.22	0.001

Tab. 2 Performance comparison results of different algorithms on three datasets （50 clients）

算法	MNIST				Fashion-MNIST				CIFAR-10
	$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6		$λ$ =0.3		$λ$ =0.6
	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
FedAvg	80.30	0.586	82.66	0.539	65.11	0.984	69.10	0.891	43.05	1.561	47.09	1.423
FedProx	79.35	0.611	82.11	0.553	65.17	0.986	70.07	0.864	40.87	1.599	44.11	1.502
FedProto	88.40	0.153	96.22	0.079	79.80	0.177	88.61	0.118	83.77	0.189	86.91	0.039
FedGH	79.68	1.353	92.70	0.391	79.68	1.167	84.02	0.611	72.64	1.039	86.00	0.200
FedCross	97.02	0.087	97.54	0.082	95.35	0.144	95.45	0.142	87.05	0.330	87.19	0.323
FedPFA	97.21	0.059	98.59	0.004	96.36	0.085	96.63	0.057	87.64	0.046	88.22	0.001

Fig. 4 Accuracy and loss curve comparison of different cluster numbers on three datasets （20 clients， 0.3 participation rate）

Tab. 3 Performance comparison results of different cluster numbers on three datasets （20 clients， 0.3 participation rate）

m	MNIST		Fashion-MNIST		CIFAR-10
m	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
6	95.62	0.257	86.55	0.926	78.42	1.323
5	90.04	1.156	82.28	1.498	87.59	0.039
4	95.38	0.188	82.66	1.239	83.89	0.986
3	96.93	0.119	79.70	1.804	80.26	0.680
2	90.85	0.894	80.01	1.369	80.50	1.282

Fig. 5 Accuracy and loss curve comparison of different cluster numbers on three datasets （50 clients， 0.3 participation rate）

Tab. 4 Performance comparison results of different cluster numbers on three datasets （50 clients， 0.3 participation rate）

m	MNIST		Fashion-MNIST		CIFAR-10
m	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
15	89.71	0.474	88.80	0.580	84.45	0.248
12	90.91	0.568	85.31	0.844	80.96	0.547
9	96.76	0.123	86.23	0.803	85.49	0.177
7	95.74	0.159	89.41	0.415	81.71	0.383
5	89.13	0.542	87.41	0.596	83.40	0.258

Fig. 6 Accuracy and loss curve comparison using adaptive weighted fusion algorithm alone

Tab. 5 Performance comparison results using adaptive weighted fusion algorithm alone

算法	MNIST		Fashion-MNIST		CIFAR-10
算法	Acc/%	Loss	Acc/%	Loss	Acc/%	Loss
FedAvg	82.96	0.479	63.41	1.037	40.95	1.722
FedProx	82.26	0.502	60.53	1.147	37.44	1.829
FedProto	81.61	0.076	65.37	0.134	75.55	0.153
FedGH	78.48	1.668	64.68	2.814	72.18	2.283
FedCross	97.80	0.066	89.30	0.287	88.19	0.258
FedPFA	95.13	0.230	86.90	0.491	87.59	0.071

Tab. 6 Running time comparison of different algorithms

算法	$R 80$	$T 100$ /s
FedAvg	34	2 317.07
FedProx	45	2 829.78
FedProto	31	3 092.16
FedGH	48	2 669.11
FedCross	10	2 539.87
FedPFA	12	2 939.82

Tab. 6 Running time comparison of different algorithms

算法	$R 80$	$T 100$ /s
FedAvg	34	2 317.07
FedProx	45	2 829.78
FedProto	31	3 092.16
FedGH	48	2 669.11
FedCross	10	2 539.87
FedPFA	12	2 939.82

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Federated learning algorithm based on prototype clustering and Fisher information matrix weighted fusion

基于原型聚类和费舍尔信息矩阵加权融合的联邦学习算法

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