Federated Community Detection in Bipartite Networks

Wanjie Wang

stat.MLOct 19, 2026

Federated Community Detection in Bipartite Networks

Authors: Wanjie Wang

Organizations: Department of Statistics and Data Science, National University of Singapore

Abstract

We study federated spectral estimation when a large matrix is horizontally partitioned across servers that cannot share raw data. We propose FLICKER, a target-specific gradient-based power iteration that recovers a singular direction associated with a prescribed spectral target using only matrix-vector products on local blocks. Different target directions can be recovered independently and in parallel. We establish non-asymptotic convergence guarantees and provide a recursive grid-search procedure for spectral target selection. Building on FLICKER, we develop BiFLICKER for federated community detection in bipartite networks, together with a sequential projected variant for nearby or repeated singular directions. Under a sparse bipartite stochastic block model, we show that properly rescaled leading singular values from a reference server provide valid global targets, and that Sequential BiFLICKER achieves a vanishing misclustering rate and exact recovery under stronger sparsity conditions. Simulations show that BiFLICKER remains close to centralized spectral clustering and is more robust than existing federated spectral baselines when local sample sizes are small. On a LastFM user-artist network naturally partitioned by country, Sequential BiFLICKER attains an overall ARI of 0.94 against centralized clustering while revealing cross-country communities with distinct listening profiles.

Figures & tables

Panel of Figure 1 — Figure 1: Illustration of recovering $BB^{\top}v^{t}$ from $v^{t}$ in the federated setting.

Figure 2: Left: estimation errors of the left singular subspace

\mathrm{Err}(\hat{U};U)

in ( 6 ). Right: misclustering errors on

\mathcal{L}

\mathrm{Err}(\hat{z}_{1};z_{1})

in ( 7 ).

Figure 3: Left: estimation errors of the right singular subspace

\mathrm{Err}(\hat{V};V)

. Right: misclustering errors on

\mathcal{R}

\mathrm{Err}(\hat{z}_{2};z_{2})

Figure 4: Top: estimation errors of the left singular subspace

\mathrm{Err}(\hat{U};U)

versus

T

. Bottom: misclustering errors on

\mathcal{L}

versus

T

. Curves show mean error

\pm

one standard deviation for

K=5

servers (solid),

K=10

servers (dashed), and

K=20

servers (dotted).

	US	UK	Poland	Germany	Finland	Norway	Canada
Users $n_{k}$	216	121	46	36	31	31	30
Mean user degree	575	636	487	560	405	493	569
Density	6.7%	7.4%	5.6%	6.5%	4.7%	5.7%	6.6%

Table 1: Summary of the 7 country servers in the cleaned LastFM user–artist network.

Figure 5: Agreement of user-community assignments within each country. The three bars compare the centralized, local, and Sequential BiFLICKER assignments using the adjusted Rand index. Country sample sizes are shown with the country labels.

Figure 6: Listening behavior by Sequential BiFLICKER user community, summarizing listening breadth (left panel), activity (middle panel), and within-community similarity (right panel) with

95\%

leave-one-user-out jackknife confidence intervals.

Community	Users	Main countries	Representative artists
C1	224	US 43.8%; UK 21.4%	Architecture in Helsinki; Rilo Kiley; Aerosmith
C2	73	US 43.8%; UK 30.1%	The Rakes; The Futureheads; Art Brut
C3	68	US 29.4%; Finland 25.0%	Pantera; Disturbed; Rammstein
C4	62	US 67.7%; Norway 8.1%	T.I.; Ludacris; Usher
C5	35	UK 51.4%; US 28.6%	Dexys Midnight Runners; Dusty Springfield; Rod Stewart
C6	33	UK 36.4%; Poland 30.3%	The Cinematic Orchestra; Nightmares on Wax; Bonobo

Table 2: Country composition and representative artists of the Sequential BiFLICKER user communities. Country percentages are relative to community size.

Figure S1 : Degree distributions in the retained LastFM user–artist network.

Figure S2 : Leading singular values of the retained LastFM user–artist network.

Component	Target $\widetilde{\sigma}_{i}$	Centralized	Sequential BiFLICKER	Relative difference
1	269.875	250.991	250.991	$0.00\%$
2	102.865	96.448	96.311	$-0.14\%$
3	92.053	82.502	81.894	$-0.74\%$
4	77.837	76.594	74.262	$-3.05\%$
5	75.150	70.858	72.939	$2.94\%$
6	71.256	62.878	63.706	$1.32\%$

Table S1: Comparison of the target, centralized, and Sequential BiFLICKER singular values for the first seven components. Relative differences are computed relative to the centralized singular values.

Community	Users	Representative artists	Coverage
C1	224	Architecture In Helsinki; Rilo Kiley; Aerosmith; Incubus; Mgmt	71.9%
C2	73	The Rakes; The Futureheads; Art Brut; The Go! Team; Maxïmo Park	97.3%
C3	68	Pantera; Disturbed; Type O Negative; Rammstein; Megadeth	98.5%
C4	62	T.I.; Ludacris; Usher; Jay-Z; Gym Class Heroes	98.4%
C5	35	Dexys Midnight Runners; Dusty Springfield; Rod Stewart; The Pretenders; Squeeze	100.0%
C6	33	The Cinematic Orchestra; Nightmares On Wax; Tosca; Bonobo; Kosheen	100.0%

Table S2: Representative artists for the seven Sequential BiFLICKER user communities. Coverage is the percentage of users in a community who listened to at least one of the five listed artists. For Community 1, the listed artists are selected by the prevalence-based fallback described in the text.

Dataset	1	2	3	4	5
$n_{k}$	75	101	494	1275	249
$m$	3129	3129	3129	3129	3129
Average # of Movies Rated	774	364	204	95	37

Table S3 : Number of users and movies in each dataset, and the average number of movies rated per user.

User Community	1	2	3	4	5	6	Total
Dataset 1	25 (33.3%)	6 (8.0%)	10 (13.3%)	6 (8.0%)	17 (22.7%)	10 (13.3%)	75
Dataset 2	35 (34.7%)	14 (13.9%)	18 (17.8%)	8 (7.9%)	14 (13.9%)	11 (10.9%)	101
Dataset 3	179 (36.2%)	77 (15.6%)	85 (17.2%)	62 (12.6%)	52 (10.5%)	38 (7.7%)	494
Dataset 4	681 (53.4%)	182 (14.3%)	116 (9.1%)	114 (8.9%)	100 (7.8%)	81 (6.4%)	1275
Dataset 5	217 (87.1%)	11 (4.4%)	4 (1.6%)	5 (2.0%)	2 (0.8%)	9 (3.6%)	249
Community Size	1142 (52.1%)	290 (13.2%)	233 (10.6%)	195 (8.9%)	185 (8.4%)	149 (6.8%)	2194

Table S4 : Number of users in each estimated community. Row-wise proportions are shown in brackets.

Figure S3 : Edge densities between user communities and movie communities.

Figure S4 : Analysis of movie communities using exogenous movie covariates: year of production, region, type, and genre. These covariates are not used in the clustering algorithm and are employed only for post-hoc interpretation.

Graph Clustering

Graph clustering groups network nodes by connectivity, attributes, or shared roles to reveal communities and other mesoscale structure.

See all 78 papers

RIPPLE in Still Water: Zero-Shot Clustering in Federated Learning with Wavelet Scattering Transform
Oct 2, 2026Alessandro LicciardiWavelet Scattering Transforms Clustered Federated Learning
Department of Mathematical Sciences Politecnico di Torino, Turin, Italy
Federated Clustering with Unknown Local and Global Cluster Cardinalities
Sep 29, 2026Mitushi Goyal, Tarun S., Riddhanya Senapathi +1Cluster Number Estimation Clustering
BITS Pilani K. K. Birla Goa Campus, Goa, India.
Federated Independent Component Analysis via Spectral Alignment and Robust Aggregation
May 26, 2025Xin Bing, Dian Jin, Yuqian ZhangFederated Learning Aggregation Independent Component Analysis
University of Toronto · National University of Singapore · Rutgers University

Oct 2, 2026J/K move · Enter open · S save

RIPPLE in Still Water: Zero-Shot Clustering in Federated Learning with Wavelet Scattering Transform

Alessandro Licciardi

Department of Mathematical Sciences Politecnico di Torino, Turin, Italy

Wavelet Scattering Transforms Clustered Federated Learning Non-IID Federated Learning Clustering

Open paper AskPDF arXiv

Clustered Federated Learning (FL) partitions a client population into groups of similar local distributions and trains one specialized model per cluster, mitigating client drift that degrades single-model methods under non-IID data. Prior methods discover cluster structure inside the training loop through gradient similarity, loss evaluation, or EM-style updates, thus increasing communication overhead, exposing gradients to inversion attacks, and providing no mechanism to assign clients absent from training. We propose RIPPLE, a clustered FL framework in which cluster assignment is computed entirely offline from a spectral characterization of each client's local data: a variance-weighted principal-component prototype embedded via the Wavelet Scattering Transform and decoded by a Gaussian Mixture VAE trained server-side on synthetic client populations before federation begins. Per-round communication cost matches FedAvg exactly, and a client absent from training obtains a personalized model from a single forward pass, without gradient computation, model evaluation, or extra communication round. We prove that the gap between RIPPLE's surrogate clustered objective and the oracle is bounded by a computable quantity decaying with client sample size and independent of federation duration; per-cluster convergence matches the minimax-optimal rate for non-convex smooth objectives. Across five benchmarks spanning controlled and realistic heterogeneity, RIPPLE consistently outperforms all baselines, with margins growing on the most realistic partitions.

Abstract

Graph Clustering

Explore similar work

RIPPLE in Still Water: Zero-Shot Clustering in Federated Learning with Wavelet Scattering Transform

Federated Clustering with Unknown Local and Global Cluster Cardinalities

Federated Independent Component Analysis via Spectral Alignment and Robust Aggregation