Low-pass Personalized Subgraph Federated Recommendation

Wooseok Sim; Hogun Park

cs.IRMar 20, 2026

Low-pass Personalized Subgraph Federated Recommendation

Authors: Wooseok Sim, Hogun Park

Organizations: Department of Artificial Intelligence, Sungkyunkwan University, Suwon, Republic of Korea

Abstract

Federated Recommender Systems (FRS) preserve privacy by training decentralized models on client-specific user-item subgraphs without sharing raw data. However, FRS faces a unique challenge: subgraph structural imbalance, where drastic variations in subgraph scale (user/item counts) and connectivity (item degree) misalign client representations, making it challenging to train a robust model that respects each client's unique structural characteristics. To address this, we propose a Low-pass Personalized Subgraph Federated recommender system (LPSFed). LPSFed leverages graph Fourier transforms and low-pass spectral filtering to extract low-frequency structural signals that remain stable across subgraphs of varying size and degree, allowing robust personalized parameter updates guided by similarity to a neutral structural anchor. Additionally, we leverage a localized popularity bias-aware margin that captures item-degree imbalance within each subgraph and incorporates it into a personalized bias correction term to mitigate recommendation bias. Supported by theoretical analysis and validated on five real-world datasets, LPSFed achieves superior recommendation accuracy and enhances model robustness.

Figures & tables

Figure 1: Empirical observations from the federated recommender systems on the Amazon-Book ( He et al., 2020 ) dataset. (a) Subgraph size-degree variation: each point is one of 15 client subgraphs, partitioned using spectral clustering, grouped into L arge- D ense ( LD ), M edium- B alanced ( MB ), S mall- S parse ( SS ) by node count and average degree. (b) Structural divergence: Laplacian eigenvalue histograms averaged over each group, highlighting distinct spectral signals. (c) Group-wise Performance Gap: NDCG@20 for FedAvg ( McMahan et al., 2017 ) , PFedRec ( Zhang et al., 2023a ) , FedPUB ( Baek et al., 2023 ) , and Ours across groups, showing that performance varies significantly depending on subgraph structure. Detailed experimental results in Table 2 .

Figure 2: Overview of LPSFed - On the Client: Stage 1 applies low-pass GCN and a localized popularity bias-aware loss to train client subgraphs. Stage 2 computes similarities between each client subgraph and a server-provided random graph using structural signals. On the Server: Stage 3 aggregates client parameters and distributes them based on personalized similarity scores. Colored arrows indicate stage-wise interactions.

Figure 3

Dataset	Amazon-Book		Gowalla		Movielens-1M		Yelp2018		Tmall-Buy
Model	Recall	NDCG	Recall	NDCG	Recall	NDCG	Recall	NDCG	Recall	NDCG
FedAvg	0.0642	0.0312	0.1425	0.0660	0.2454	0.1240	0.0721	0.0292	0.0317	0.0164
FedPUB	0.0633	0.0322	0.1433	0.0667	0.2558	0.1209	0.0684	0.0296	0.0333	0.0180
FedMF	0.0153	0.0072	0.0765	0.0409	0.1679	0.0906	0.0318	0.0150	0.0122	0.0063
F2MF	0.0451	0.0225	0.0961	0.0565	0.1788	0.1120	0.0510	0.0247	0.0207	0.0132
PFedRec	0.0713	0.0242	0.1371	0.0478	0.1508	0.0997	0.0750	0.0225	0.0323	0.0170

Table 1: The overall performance comparison Recall@20 and NDCG@20 on five datasets, with the best scores highlighted in bold and the second-best in underlined . The improvement row highlights the gains achieved by our model ( LPSFed ) compared to the second-best-performing model.

Group	Large-Dense		Medium-Balanced		Small-Sparse		Overall
Model	Recall	NDCG	Recall	NDCG	Recall	NDCG	Recall	NDCG
FedAvg	0.0620	0.0280	0.0411	0.0208	0.0275	0.0117	0.0334	0.0152
FedPUB	0.0605	0.0355	0.0528	0.0267	0.0300	0.0123	0.0381	0.0177
FedMF	0.0176	0.0094	0.0127	0.0056	0.0058	0.0027	0.0084	0.0039
F2MF	0.0402	0.0231	0.0341	0.0174	0.0225	0.0085	0.0268	0.0118
PFedRec	0.0619	0.0250	0.0525	0.0185	0.0310	0.0131	0.0388	0.0153

Table 2: Performance for measuring the impact of subgraph structural imbalance on the Amazon-Book dataset, evaluated using Recall@20 and NDCG@20 across a 15-client partition. Clients are grouped into three categories: L arge- D ense, M edium- B alanced, S mall- S parse, and Overall (averaged across all clients). The best scores are highlighted in bold and the second-best in underlined . The improvement row shows the gains achieved by our model ( LPSFed ) compared to the second-best-performing model.

Data Setting	Balanced Dataset [NDCG@20]				Imbalanced Dataset [NDCG@20]
Model	Tail	Mid	Head	Overall	Tail	Mid	Head	Overall
FedAvg	0.0017	0.0077	0.0570	0.0264	0.0040	0.0108	0.0924	0.0312
FedPUB	0.0024 $\uparrow$ 41	0.008 $\uparrow$ 16	0.0620 $\uparrow$ 9	0.0279 $\uparrow$ 6	0.0064 $\uparrow$ 60	0.0130 $\uparrow$ 20	0.0998 $\uparrow$ 8	0.0322 $\uparrow$ 3
FedMF	0.0002 $\downarrow$ 88	0.0009 $\downarrow$ 88	0.0130 $\downarrow$ 77	0.0074 $\downarrow$ 72	0.0003 $\downarrow$ 92	0.0013 $\downarrow$ 88	0.0140 $\downarrow$ 85	0.0072 $\downarrow$ 77
F2MF	0.0037 $\uparrow$ 118	0.0112 $\uparrow$ 45	0.0438 $\downarrow$ 23	0.0225 $\downarrow$ 15	0.0050 $\uparrow$ 25	0.0119 $\uparrow$ 10	0.0436 $\downarrow$ 53	0.0225 $\downarrow$ 28
PFedRec	0.0055 $\uparrow$ 224	0.0125 $\uparrow$ 62	0.0277 $\downarrow$ 51	0.0244 $\downarrow$ 8	0.0068 $\uparrow$ 70	0.0145 $\uparrow$ 34	0.0262 $\downarrow$ 72	0.0242 $\downarrow$ 22

Table 3: Comparison of the localized popularity bias mitigation on the Amazon-Book using NDCG@20. Best scores are in bold . Balanced data includes all data, while the imbalanced dataset excludes less active participants. Arrows show (%) change relative to FedAvg:

\uparrow

gain (%) ,

\downarrow

loss (%) .

Dataset	Amazon-Book		Gowalla		Movielens-1M		Yelp2018		Tmall-Buy
Model	Recall	NDCG	Recall	NDCG	Recall	NDCG	Recall	NDCG	Recall	NDCG
w/o LGCN	0.0388	0.0216	0.0965	0.0427	0.1622	0.0893	0.0471	0.0207	0.0256	0.0121
w/o bias-aware	0.0643	0.0322	0.1529	0.0711	0.2604	0.1281	0.0769	0.0301	0.0362	0.0186
w/o per	0.0652	0.0368	0.1576	0.0788	0.2625	0.1299	0.0775	0.0315	0.0370	0.0190
w/o per & bias-aware	0.0642	0.0312	0.1425	0.0660	0.2454	0.1240	0.0712	0.0292	0.0317	0.0164
w/o statistics for $G_{R}$	0.0714	0.0403	0.1581	0.0856	0.2625	0.1330	0.0764	0.0372	0.0393	0.0199

Table 4: Ablation study of LPSFed on five datasets, reporting Recall@20 and NDCG@20 for different model variants. Bold indicates best performance per column, and the last row shows relative improvements over the second-best.

Figure 3: Hyperparameter sensitivity on the Amazon-Book dataset: (a) Bias-aware margin strength $\gamma$ ; (b) Impact of $\gamma$ on Bias Amplification in Imbalanced set; (c) Low-pass cut-off frequency $\mathit{\Phi}$ ; (d) Loss Temperature $\tau$ .

General Notations
Symbol	Description
$C$	The total number of clients
$c$	An index for a specific client, $c\in\{1,...,C\}$
$u,i$	A user and an item, respectively
$U,I$	The sets of all users and items in a given graph
$M,N$	The number of users and items in a given graph

Table 5: Table of Notations.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Movielens-1M	Gowalla	Yelp2018	Amazon-Book	Tmall-Buy
Number of Users	6,040	29,858	31,668	52,643	885,759
Number of Items	3,900	40,981	38,048	91,599	1,144,124
Number of Interactions	1,000,290	1,027,370	1,561,406	2,984,108	7,592,214
Density	5.431%	0.084%	0.130%	0.062%	0.010%

Appendix

Table 6: The statistics of datasets.

Method $(Avg.\pm std)$	Ego-graph	Random-Const.	Interconnected-Const.	Spectral-Clust.
Avg. Subgraph Size	$141.1\pm 16.8$	$172.8\pm 9.8$	$2105.6\pm 135.7$	$196.2\pm 36.2$
Size variance	$22276.8\pm 6905.9$	$3198.5\pm 1039.8$	$85083.4\pm 45597.3$	$33370.3\pm 17210.8$
Avg. Degree	$1.97\pm 0.0$	$5.68\pm 0.24$	$7.29\pm 0.47$	$7.57\pm 1.07$
Degree Variance	$1.0\pm 0.0$	$6.34\pm 0.08$	$2.19\pm 1.08$	$30.22\pm 11.45$
Avg. Density	$0.032\pm 0.004$	$0.035\pm 0.001$	$0.003\pm 0.000$	$0.070\pm 0.022$
Spectral Entropy	$1.0\pm 0.0$	$6.34\pm 0.08$	$6.42\pm 0.15$	$5.69\pm 0.68$

Appendix

Table 7: Comparison of different client construction strategies on Movielens-1M .

Anchor Design	Amazon-Book	Gowalla	ML-1M	Yelp2018	Tmall-Buy
ER	0.0734	0.1599	0.2631	0.0767	0.0410
GNMK	0.0738	0.1621	0.2646	0.0783	0.0419
w/o statistics for $G_{R}$ (GNMK)	0.0714	0.1581	0.2625	0.0764	0.0393

Appendix

Table 8: Sensitivity analysis of the anchor graph design in LPSFed. Performance is reported using Recall@20 across five datasets. "w/o statistics for

G_{R}

(GNMK)" constructs the GNMK reference solely from global assumptions, without any client-derived statistics. Bold indicates best performance per column.

Model	Time/Epoch	#Epoch	Training Time	Memory Usage
FedAvg	20s	90	30m	6.2GB
FedPUB	25s	90	37m	10.2GB
FedMF	23m 48s	150	59h 30m	6.2GB
F2MF	39m 12s	100	65h 20m	6.4GB
PFedRec	38m 47s	135	87h 16m	1.4GB
FedRAP	73m 29s	160	195h 56m	1.6GB

Appendix

Table 9: Comparison of training efficiency across different models. Metrics include time per epoch, number of epochs to converge, total training time, and memory usage, with the best scores highlighted in bold .

Iteration	20	40	60	80	100
$\gamma$ = 0.0	0.0482	0.0497	0.0536	0.0568	0.0600
$\gamma$ = 0.3	0.0478	0.0490	0.0529	0.0554	0.0592
$\gamma$ = 0.5	0.0477	0.0489	0.0522	0.0544	0.0576
$\gamma$ = 0.7	0.0476	0.0486	0.0512	0.0541	0.0570
$\gamma$ = 1.0	0.0474	0.0478	0.0501	0.0522	0.0553

Appendix

Table 10: Average Jaccard index for paired users over iterations, with rows corresponding to margin strengths

\gamma

and columns to training iterations.

Cut-off Frequency $\mathit{\Phi}$	2	4	6	8
Recall@20	0.2556	0.2614	0.2615	0.2622
Eigengap $\delta$	$1.17\times 10^{-15}$	$4.36\times 10^{-3}$	$1.61\times 10^{-2}$	$1.46\times 10^{-1}$
Pearson Correlation (Recall $\leftrightarrow\delta$ )	0.5004

Appendix

Table 11: Correlation analysis between eigengap and model performance in Movielens-1M . Recall@20 and corresponding eigengap values are reported for different cut-off frequencies

\mathit{\Phi}

. Pearson correlation quantifies linear dependence between eigengap magnitude and model performance.

# of Clients	4		10		20
Model	Recall	NDCG	Recall	NDCG	Recall	NDCG
FedAvg	0.0642	0.0312	0.0395	0.0186	0.0220	0.0098
FedPUB	0.0633	0.0322	0.0417	0.0180	0.0232	0.0102
FedMF	0.0153	0.0072	0.0091	0.0058	0.0033	0.0035
F2MF	0.0451	0.0225	0.0325	0.0182	0.0158	0.0078
PFedRec	0 .0713	0.0242	0.0406	0.0169	0.0236	0.0100

Appendix

Table 12: Effect of client variability on performance using the Amazon-Book dataset. Metrics include Recall@20 and NDCG@20, bold indicates the best results and underlined the second-best results in each setting.

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