An Effective and Secure Federated Multi-View Clustering Method with Information-Theoretic Perspective
Authors: Xinyue Chen
Jinfeng Peng
YuHao Li
Xiaorong Pu
Yang Yang
Yazhou Ren
Venue: ICML 2025 poster (2025)
Keywords: Multi-View Clustering
Federated Learning
Primary area: general_machine_learning->clustering
TL;DR: In this paper, we propose an effective and secure federated multi-view clustering method, which is designed to alleviate the trade-off between privacy preservation and performance improvement in the field of federated multi-view clustering.

Abstract: Recently, federated multi-view clustering (FedMVC) has gained attention for its ability to mine complementary clustering structures from multiple clients without exposing private data. Existing methods mainly focus on addressing the feature heterogeneity problem brought by views on different clients and mitigating it using shared client information. Although these methods have achieved performance improvements, the information they choose to share, such as model parameters or intermediate outputs, inevitably raises privacy concerns. In this paper, we propose an Effective and Secure Federated Multi-view Clustering method, ESFMC, to alleviate the dilemma between privacy protection and performance improvement. This method leverages the information-theoretic perspective to split the features extracted locally by clients, retaining sensitive information locally and only sharing features that are highly relevant to the task. This can be viewed as a form of privacy-preserving information sharing, reducing privacy risks for clients while ensuring that the server can mine high-quality global clustering structures. Theoretical analysis and extensive experiments demonstrate that the proposed method more effectively mitigates the trade-off between privacy protection and performance improvement compared to state-of-the-art methods.

An Effective and Secure Federated Multi- Clustering Method with Enformation-Theorete Perspective
Xinyue Chen Jinfeng Peng? Yuhao Li
Xiaorong Pu 12 Yang Yang' Yazhou Ren 1.2
Abstract
multi-view data, which usually comes from multiple sources or perspectives (Fang et al., 2023; Huang et al., 2024; Xu et al., 2024; Pu et al., 2024). Multi-view clustering aims to explore and integrate multi-view data in an unsupervised manner and is applied in practical fields such as recommen- dation systems (Yu al., 2018), social network analysis (Cruickshank, 2020), and bioinformatics (Lin et al., 2024). Most existing multi-view clustering methods usually assume that multi-view data are stored centrally in single entity, However, due to the presence of data silos and the security issues associated with data exposure, unifying data from different sources incurs significant costs and privacy risks. Consequently, federated multi-view clustering (FedMVC) is gaining attention for its ability mine complementary clustering structures from multiple clients without exposing private data (Lin et al., 2023; Qiao et al., 2023).
Recently, federated multi-view clustering (Fed- MVC) has gained attention for its ability to mine complementary clustering structures from multi- ple clients without exposing private data. Existing methods mainly focus on addressing the feature heterogeneity problem brought by views on differ- ent clients and mitigating it using shared client in- formation. Although these methods have achieved performance improvements, the information they choose to share, such as model parameters in- termediate outputs, inevitably raises privacy con- cerns. In this paper, we propose an Effective and Secure Federated Multi-view Clustering method, ESFMC, to alleviate the dilemma between privacy protection and performance improvement. This method leverages the information- -hoomation-thhoreticc per- spective split the features extracted locally by clients, retaining sensitive information locally and only sharing features that are highly relevant to the task. This can be viewed as a form of privacy- preserving information sharing, reducing privacy risks for clients while ensuring that the server can mine high-quality global clustering structures. Thcoretical analysis and extensive experiments demonstrate that the proposed method more ef- fectively mitigates the trade-off between privacy protection and performance improvement com- pared to state-of-the-ard methods.
Existing FedMVC methods primarily address the issue of feature heterogeneity brought by views on different clients. For instance, federated deep multi-view clustering (Chen et al., 2023) mitigates the heterogeneity of local data by constructing global self-supervised information. Building resolving heterogeneity issues, some works further ex- plore incomplete data (Ren et al., 2024), communication variability (Huang et al., 2022), and Non-IID settings (Jiang et al., 2024). In these explorations, sharing client informa- tion is widely used as an effective means to alleviate data heterogeneity and improve method performance.
A Although extensive works indicate that sharing certain in- formation during client training significantly enhance the clustering performance of FedMVC methods, it unfortu- nately raises privacy concerns. For example, researchers can reconstruct raw data from model parameters or shared gradi- ents (Geiping et al., 2020), while model intermediate outputs may be vulnerable to model inversion attacks (Mahendran & Vedaldi, 2015). Techniques such differential privacy offer provable security for privacy protection (Abadi et al., 2016), but the addition of random noise can negatively im- pact performance. Therefore, maintaining the performance of proposed methods while further protecting data privacy remains critical challenge in the field of FedMVC.
1. Introduction
The advancement of technology and comprehensive atten- tion to various matters have facilitated the emergence of
'School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China "Shenzhen Institute for Advanced Study, University of Electronic Science Technology China, Shenzhen, China. Correspon- dence to: Yazhou Ren <yazhou. edu.....
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
We revisit the purpose of sharing information and propose Effective and Secure Federated Multi-view Clustering

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An Effective and Secure Federated Multi- Clustering Method with Information-Theorrticc Perspective
method, ESFMC, to alleviate the dilemma between pri- vacy protection and performance improvement. Specifi- cally, ESFMC splits the features extracted locally by clients based on the information theory perspective, only shar- ing clustering-related features to the server while keeping sample-related features locally. This can be viewed as a form of privacy-preserving information sharing, where sen- sitive information in the features is retained locally, and only task-relevant features are shared. ESFMC minimizes the risk of privacy breaches by preventing malicious attack- ers from reconstructing the original data using the shared information. Additionally, ESFMC collaboratively aligns the non-overlapping samples across clients from the global perspective, effectively extending its applicability to incom- plete scenarios. This approach reduces privacy risks for clients while ensuring that the server can mine comple- mentary and high-quality global clustering structures. Our contributions are summarized as follows.
graph neural networks, addressing the issues of data privacy and feature heterogeneity. (Ren et al., 2024) introduced VV method, which addresses the issues of unaligned and incomplete data by sharing embedded features and de- signing adaptive alignment and imputation strategies.
The above methods achieve good performance by sharing model information or intermediate outputs. However, while these methods are successful, the information they share still leads to potential data leakage risks. For instance, attackers can reconstruct raw data from model parameters (Geiping et al., 2020) or features (Mahendran & Vedaldi, 2015). Thus, we propose an effective and secure federated multi-view clustering method to alleviate the dilemma between privacy protection and performance improvement.
3. Methodology
3.1. Motivation
We propose an effective and secure federated multi- view clustering method that aims to mine complemen- tary global clustering structures while reducing privacy risks through limited information sharing.
Existing FedMVC methods aim to mine complementary clustering structures by sharing information such as model parameters (Che et al., 2022) and embedded features (Chen et al., 2023) from clients to the server. While this shared information significantly alleviates the heterogeneity issue caused by views on different clients, it often contains com- plete descriptions of clients' local data, retaining substantial critical information about the raw data. Attackers can easily reconstruct raw data using methods such as gradient- attacks (Geiping et al., 2020) and model inversion attacks (N (Nguyen et al., 2023), leading to privacy risks.
We design a collaborative alignment strategy that en- sures the consistency of locally shared information across clients from the global perspective, thus extend- ing the proposed method to incomplete scenarios.
Theoretical analysis and extensive experiments demon- strate that the proposed method more effectively mit- igates the trade-off between privacy protection and performance improvement compared to SOTAs.
Based on the intuitive idea that sharing partial information is more privacy-preservigg than sharing complete information, we aim to split the information to maximize the utility of shared information. The information bottleneck principle (Tishby et al., 2000) suggests that ideal features should com- press data while retaining as much task-relevant information as possible. This is achieved by minimizing the mutual information between X and Z while maximizing the mutual information between Y and Z:
2. Related Work
Federated multi-view clustering (FedMVC) is designed to handle multi-view data distributed across clients, ensuring data privacy while addressing the heterogeneity introduced by views on different clients through information sharing. Based on the type of information shared, FedMVC can be classified into two types. (1) Clients share information about local models, such as model parameters or shared gradients (Flanagan et al., 2021; Huang et al., 2022). (Che et al., 2022) aimed to improve local disease prediction per- formance by sharing training models among clients. (Jiang et al., 2024) introduced a heterogeneity-awar module that adapts FedMVC to IID and Non-IID scenarios by shar- ing model parameters and feature exchange. (Chen et al., 2024) addressed client and view gaps associated with het- erogeneous hybrid views by sharing model parameters. (2) Clients share model intermediate outputs, such as embedded features or clustering assignments (Chen et al., 2023; Hu et al., 2023). By sharing features and global lseudo-labels, (Yan et al., 2024) designed a FedMVC strategy based on
LIB = I= - Y)
(1)
Inspired by Eq. (1) and previous works (Lee & Pavlovic, 2021; Yang et al., 2023), ESFMC splits the commonly used shared information in FedMVC, embedded features extracted from local clients, into clustering-related features and sample-related features. Clustering- features focus on the similarities and differences among samples, facilitating the clustering process. Sample-related features focus on the properties and details of each individual sam- plc. We consider that sample-related features contain too much private information and are irrelevant to the clustering task. Thus, clients retain sample-related features locally to prevent privacy leakage while sharing clustering-related
2

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An Effective and Secure Federated Multi-Viss View Clustering Method with Information Theorette Perspective
Client I-View
( In Generul Scenarios
Feature Splitting
Server
CCIustering-rehate features
(.,()
.T(22)
Jogp's 1))
12
I[ Z
logp(a
Aoggree (x))
elustering
results Y
X
X!
22
(a.
x
Clustering
Clustering-related fentures 2,1
Cliiet M-View M (In Incomplete Scenarios
A dog is running on the grass.
Z
(t,(.)
Z
z
Global clustering results
ZM
AM
Local clustering assignments Q
Calculate
()
+
?
Z
Bx,())
(Q)
2
Global clustering assignments Q
XM
Feature Splitting
Figure The framework ESFMC. contains M clients and server. (1) In general scenarios: we propose feature splitting within clients from the information-theone thcoretic perspective, where clustering-related features shared to assist the server in mining the global clustering structures and enhancing performance, while sample-related features are retained locally to prevent privacy leakage. (2) In incomplete scenarios: design collaborative alignment strategy that leverages the server integrate information and provide a global perspective, ensuring alignment among non con-overlapping samples across clients.
features with the server, promoting the extraction of high- quality complementary clustering structures.
constructs a network structure fg (-) that can handle spe- cific views based on its local data, where 0" are learnable parameters. These networks aim to project the raw data into low-dimensional space and capture informative latent features. For the client with data of the m-th view type X" the latent features can be obtained by Z fmm. (X""). Based on the latent features, clustering-relan related features and sample-related features, de- fined as Z E NR. xdm and Z E IR Nm. x xdm respectively.
Additionally, inspired by (Hellström al., 2023; Alquier al., 2024), we introduce model-data mutual information (w; X) constraint mitigate the model's dependency on data during local training. It quantifies the correlation between the model and input data, while also serving as measure of model complexity for generalization analysis.
aim to split them into
3.2. Problem Statement
We hope that the Mustering-related features are primarily used to identify the similarities and differences among sam- ples, and highly correlated with the final clustering re- sults Y. In contrast, the sample-related features are mainly used to describe the properties and details of each individ- ual sample. Based on this idea, we construct the following optimization objective during local training on each client:
Given multi-view data with M views, denoted by X {x3, x²....,X8 XMM distributed among M clients, consist- ing of N samples, with the expectation of partitioning them into K clusters. For client m, its data are represented as Xm &R x,,,,..,,, where D,, is the dimensionality of sam- ples in the m-th view and Nm is the number of samples in the m-th client. We assume that all participating parties are semi-honest and do not collude. The attacker follows the training protocol but may attempt privacy attacks.
Cx (w = (Z" X ( - I Y) + I T
Combining the three mutual information terms achieves lo- cal training with feature splitting. The term - -I(Z X"") represents maximizing the mutual information between the sample-related features Z and the raw data X which helps 2 capture as much information about X as possi- ble, thereby better deseribing the attributes and details of each sample. Similarly, the term -I(Z Y) represents
3.3. Local Training with Feature Splitting and Model-Data Constraint
Since multi-view data are stored across distributed clients, we analyze the case of client m as an example. Each client
3

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An Effective and Secure Federated Multi- Clustering Method with Information-Theoreti Perspective
maximizing the mutual information between the clustering- related features n and the global clustering results Y, which helps Z better reflect the similarities and differences among samples. thereby mining local clustering structures. It is noted that the global clustering results Y are obtained by the server integrating the shared information from all clients and are optimized after each communication round. Additionally, the term [ - represents minimizing the mutual information between the clustering-relater fea- tures _e and the sample-related features ZT which aims to reduce the redundant information between Z and Z achieving high-quality feature splitting. Further, we obtain Zndh and z from latent features by designing two adaptive feature projection layers (.) and (.):
fundamental information and enhancing the generalization ability of the method. The original optimization problem in Eq. (4) is thus reformulated as:
min
L
E Eptum Xm)) (w")) + orl (w"; )"),,
p(wm (m))
(5)
where a > 0 is a parameter that balances fitting and gener- alization. Furthermore, inspired by previous works (Wang et al., 2021; Zhang et al., 2024a), adopt Bayesian infer- ence to transform the single-poin estimation of the local model wth into a distributional estimation p( p(w" th x'"), facilitating subsequent optimization. The following lemma is provided to find an optimal posterior.
Lemma 3.1. (Wang et al., 2021) Given an observed dataset Xm, the optimal posterior p(w"m X for client m update
Z.nh = - [
D = 0- (Z
(3)
in Eq. (5) should satisfy the following form that
To make the above feature splitting easy to handle, by con- structing the reconstruction network Iwz (.) and the cluster- ing layer I (.) separately, with wt" and w as learnable parameters, we derive an objective equal to the original ob-
p p( mm X X = B exp {
1
- 1-20
(6)
where B is normalizing factor that makes the integral of the distribution equal to 1, and U Uw"") is the energy function defined as U Lx (wm) ao loggp("" ))
jective in Eq. (2) for client m (see Appendix C.2 for more details) as follows:
Nm
Please see Appendix C.3 for the proof. The resulting optimal posterior follows a typical Gibbs distribution (Kittel, 2004) with energy function U U'("") and temperature a (the same a appears in Eq. (5)). Therefore, we use stochastic gradient Langevin dynamics (SGLD) (Welling & Teh, 2011) to opti- mize and obtain this Gibbs posterior, which has been shown to be effective and scalable for large-scale posterior infer- ence problems. Specifically, SGLD can be implemented through straightforward adaptation of stochastic gradient descent, as follows
Lx (1
Σ
|x Sw, (2/7.a)
1|2
Nm
i=1
Nm
K Yikk log (owo (2ii))
(4)
N m 1=1 k=1
log p (Z z
The underlying insight of the objective function in Eq. (4) is intuitive. Specifically, feature splitting decomposes the la- tent features Tm into two functionally distinct and mutually exclusive types of features. For clarity in the subsequent analysis, we define the three loss components that constitute Lx (w"") as CT CT, and LT The first loss component CT, aims for the sample-related features ZT to accurately reconstruct the raw data X The second loss component CT seeks to ensure that the clustering-related features z correctly identify clustering structures. The third loss com- ponent CT, imposes a constraint to minimize the correlation between Z and Z.". Notably, computing p (z.",, x!ie)) di- rectly is complicated. So we instead estimate it using his- tograms, discretizing the continuous variables z and z into bins and approximating the joint distribution based frequency counts (Scott, 2015).
t.A = w Te VU VU (wER-I) + V2n (7)
where wii represents client m's model at communication round and step k. nt. is the local step size, VU (wTh (w/--1)
is an unbiased estimate of energy function gradient, and Če,k ~ ~ ~N I) is a standard Gaussian noise vector.
After clients complete the current round of local training, they retain the sample-related features locally prevent privacy leakage while sharing the cesttering-reltte features with the server to mine complementary clustering structures.
3.4. Global Training with Shared Information
In our setting, the server does not require any additional information, such as public datasets or pre-trained models. It only uses the limited information shared by clients, i.c.. cestering-relateen features, to mine high-quality global clus- tering structures. Additionally, for semi- momeshoeett participants, namely, participants faithfully execute the training protocol
Building on the above loss terms, we introduce model-data mutual information constraint I T( x as a regulariza- tion term. This constraint limits the complexity of the model's s search space, encouraging local models to capture
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An Effective and Secure Federated Multi- Clustering Method with Inforoition-Theorrtic Perspective
but may launch privacy attacks infer other parties' private data, having only clustering-related features also prevents them from reconstructing the raw data by existing attack methods, as shown in Figure 3 (c).
corresponding the view type data. Similarly, we express the optimization objective in more intuitive form:
L = I(ZZ; Fw. (Q)
= H (Z Iw: (Q)) - H (Z
After receiving the clustering-related features uploaded by each client, the server concatenates them to generate the global features:
Retar Iw. (4)) [lgg P (z Dw, (q)))
(11)
+ Rp(ar)) [lg (2""))
Z - - 72. ..... 2n] E RRN
(8)
T Iw: (q:))l?
For the clustering task, the server applies K-means (Mac- Queen, 1967) on the global features Z obtained from Eq. (6) to mine complementary global clustering structures. Letting { j=1 denote the K cluster centroids, we have:
Since p ( is difficult to estimate, we directly optimize the upper bound of C. Thus, in the incomplete scenario, the total loss for client m is represented as:
Lime
L. + C
(12)
min C1.02
z
cc,l.
(9)
CK
After clients complete the current round of local training, they upload the clustering-related features z optimized from the global perspective by Eq. (13) and local clustering assignments Q" to the server.
1=1
Furthermore, the global clustering results are calculated by
yi = arg min Iz. c, E YY,
(10)
2 - Iw. (Q9) E RNxxm
(13)
where Y represents the global clustering results, which are distributed to all clients to aid in performing high-quality feature splitting and sharing clustering-relater features.
where we define Q = {q qu E QAq. & QQT).
The server receives clustering features TThh and local clustering assignments QT uploaded by each client. Then, it can calculate clustering results Y by Eqs. (8)-(10) and acquire global cluster assignments Q by following formula:
3.5. Extending to Incomplete Scenarios
Due to the inherent flexibility of ESFMC, it can be easily extended to handle incomplete scenarios, where the samples in all clients only partially overlap, meaning the number of client samples Nm is not equal the global sample number N. To maintain clustering performance in more complex scenarios, inevitably, more shared information exposure is required. Therefore, to protect privacy while dealing with incomplete scenarios, we introduce shared information clus- tering assignments QT These are extracted locally by each client and then uploaded to the server, which aggregates them obtain global clustering assignments Q and dis- tributes them all clients for collaborative training.
M I 9 Q
2m=1
9:
(14)
>m=1
where I E {0, 13 is the indicator matrix, Iim = 1 if the i-th sample exists in the m-th client; otherwise, I O. In incomplete scenarios, we extend the general ESFMC method to further explore how to maintain a balance be- tween privacy protection and performance improvement.
In incomplete scenarios, we can opt not to share additional information, such as clustering assignments, and instead rely on the model's generalization performance. Specif- ically, each client uploads clustering-relatee features for overlapping samples to the server, while non-overlapping samples are clustered locally. This strategy particularly effective when samples across clients exhibit high overlap, as shown in Figure 3 (b).
For client m, the clustering-related features Z are pro- cessed through the clustering layer (-) to produce cluster- ing assignments Qm E I M where Q" 9w. (Z ). These clustering assignments are then uploaded to the server. During local training, we introduce an additional loss to ex- plore overlaaplpi samples among clients, thus better addressing incomplete scenarios. Consequently, we design collaborative alignment strategy to maximize mutual in- formation T( 9w. (Q)), ensuring that the information shared among different clients remains consistent from the global perspective, thereby reducing errors due to incom- plete scenarios. Here, (-) R + dd aims to map the global clustering assignments to the latent feature space
4. Discussion and Analysis
4.1. Generalization Analysis
We denote the population risk as (ww) and recall the global empirical risk Lx (w) in Eq. (5), then the expected generalization error can be denoted as E [w)) - Ix(w))
5

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An Effective and Secure Federated Multi- Clustering Method with Information-Theorrii Perspective
Theorem 4.1. Suppose that fm (w", x ) for all m M is bounded by C and independent, then the expected gener- alization error satisfies
fully execute the training protocol but may attempt privacy attacks. Currently, our feature splitting strategy is suffi- cient to defend against common model inversion attacks in such settings, as shown in Figure 3 (c). For further privacy enhancement, we could integrate commonly used preeeeiiig techniques in federated learning, such as homomorphic encryption (Cheng et al., 2021) or secure multi-party computation (Gu et al., 2021), to offer additional privacy protection.
C M M
Iwm; X
E
S
Σ
(15)
2Nm
where M is the number of participating clients and Nm is the number of samples in the m-th participating client.
Please see Appendix C.4 for the detailed proof. The above theorem shows that increasing the number of participating clients or the sample size per client improves generaliza- tion performance. Furthermore, the mutual information constraint [w X introduced during local training is strongly correlated with generalization error, theoretically validating the effectiveness of our method.
4.3. Complexity Analysis
Suppose K, M, and N represent the number of clusters, clients, and total samples, respectively. Let H denote the maximum number of hidden neurons in the clients' net- works. And Z denotes the maximum dimensionality of latent features. Generally N > V,K, M holds. For client m, the complexity is O(NH + *NK + NZ*). For the server, the complexity is O(N M M KK). In conclusion, due to M clients rumning in parallel, the total complexity of our algorithm is O(NK + 2 + +NMZK) in each iteration, which is linear to the data size N.
We can rely on the model's generalization ability to extend to incomplete and cross-device scenarios. Specifically, for incomplete scenarios, each client uploads clustering-related features for overlapping samples to the server, while non- overlapping samples clustered locally. For drvsse scenarios, each client uploads clustering-relane rellted features ex- tracted from local data, with the server aligning overlapping samples. Our method leverages generalization to perform well, as shown in Figure (b) and Figure 4.
5. Experiment
5.1. Experimental Settings
Datasets. We conduct the experiments on six public multi- view datasets. Specifically, Caltech (Fei-Fei et al., 2004) contains 1400 RGB images in 7 categories, and includes five views. HW consists of 10 categories, each correspond- ing to the digits from 0 through 9, and includes total of 2,000 samples, with each sample represented by six views. MNIST-USPS (Peng et al., 2019) comprises 5000 sam- ples collected from two handwritten digital image datasets, which are considered as two views. Synthetic3d (Kumar et al., 2011) comprises 3 categories, containing a total of 600 samples, each with three views. BDGP (Cai al., 2012) encompasses 2,500 samples representing 5 different types of Drosophila embryos. Scene (Fei-Fei & Perona, 2005) contains 4,485 scene images, each captured from three views, across 15 categories. Our code is available at http://giitbb.ccmm//MMattianasss
4.2. Privacy Analysis
We divide the privacy analysis into two parts: differential privacy for each client and the overall privacy analysis for ESFMC. For each client, our approach ensures client-level (e, didfffeertt privacy through posterior inference based on SGLD sampling and feature splitting, as detailed in Ap- pendix C.5. Notably, our analysis proves that sharing the clustering-related features Z provides stronger privacy pro- tection than directly sharing the latent features Z Then, by combining the privacy analysis for each client with the composition theorem (Kairouz et al., 2015), we obtain the overall privacy guarantee.
Theorem 4.2. For M clients with (c, diifferennti privacy,
ESFMC satisfies (Eg.1 (ég.1-(1 (1 - -08)((1 - 8)) -differential
privacy, where
Note that in our federated setting, the multiple views of these datasets are distributed across different clients and are isolated from each other. Additionally, to evaluate the effectiveness of our method in incomplete scenarios, we ran- domly remove some samples from arbitrary views. Further- more, we introduce the sample overlapping rate Φ = m/n following (Chen et al., 2023), where n represents the total size of the dataset and m denotes the number of samples that have fully overlapping views across all clients.
(ef (f=-1)a -1)EM
VM
Eg = min
=mmin { Mee,
2M e+
6 +1
8
(e - -1)
}
e e11 +e
2M log
and = = (V2log(( 1.25/0)/o + Pa log(1/8)o..)
Our method is primarily designed for environments where all participating parties are semi-honest, meaning they faith-
hhupss/arcchie..i ics uci. www.mm/aaaaaaasst..ppp
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An Effective and Secure Federated Multi- Clustering Method with Information-Theoreti Perspective
Table Experiments on four datasets in general scenarios, The best result is shown in bold and the second-best is underlined.
Caltech
HW
MNIST-USPS
Synthetic3d
Methods
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
GIMC-FLSD
48.60
35.12
28.25
42.15
47.36
29.80
79.71
76.74
68.97
53.39
14.81
9.79
HCP-IMSC
78.37
69.68
64.93
82.55
79.33
74.34
95.82
90.79
91.04
80.00
45.11
49.07
IMVC-CBG
37.61
31.43
18.96
60.38
61.79
47.95
53.35
48.77
35.66
45.83
12.32
10.73
DSIMVC
78.86
67.50
60.53
81.70
79.23
73.50
98.08
94.81
95.05
94.83
81.10
85.31
AGDIMC
90.14
82.91
80.27
97.35
93.53
93.73
91.60
85.72
84.21
59.67
56.89
45.98
FedDMVC
89.07
81.11
78.52
96.48
92.52
92.35
84.56
89.73
82.29
58.24
56.28
43.58
FedMVFCM
59.37
55.40
53.47
64.14
64.57
56.22
58.12 18.12
53.05
47.60
93.07
75.78
87.03
FedMVFPC
43.38
31.30
22.78
52.67
40.85
33.10
48.48
41.90
29.05
91.74
75.55
77.59
FCUIF
89.14
80.79
78.24
97.85
95.16
95.30
82.92
83.06
74.13
63.67
58.57
48.27
ESFMC (ours)
91.50
84.54
83.45
98.02
95.34
95.57
97.24
93.19
94.02
97.32
87.67
91.23
GIMC-FLSD
HCP-IMSC
FedDMVC
1.0
1.0
0.9
0.8
0.8
ACC
NMI
0.6
0.5
0.5
0.1 0.4 0.7
1.0
0.2
0.5
0.8
0.1
0.4
0.6 0.7 0.9 1.0
Overlapping rate
Overlapping rate
Overlapping rate
Figure Performance analysis on BDGP different overlapping rates.
AGDIMC (Pu et al., 2024), and four federated multi-view clustering methods, i.e., FedDMVC (Chen et al., 2023), Fed- MVFCM (Hu al., 2023). FedMVFPC (Hu et al., 2023) and FCUIF (Ren et al., 2024). Notably, FedMVFCM and FedMVFPC not applicable incomplete scenarios, so they are excluded from comparison in this scenario.
Table Clustering results in incomplete scenarios. The best result shown in bold and the second-best is underlined.
BDGP
Scene
Methods
ACC
NMI
ARI
ACC
NMI
ARI
GIMC-FLSD
80.5
57.0
58.6
30.0
26.4
13.5
HCP-IMSC
90.1
76.9
75.9
32.5
27.3
14.3
5.2. Clustering Results
IMVC-CBG
36.3
17.6
5.6
26.8
27.0
14.4
DSIMVC
94.1
82.9
85.9
27.8
30.4
14.5
Tables and present the quantitative comparisons of ESFMC with baselines under both general scenarios and incomplete scenarios. Each experiment is independently re- peated five times, and the average values are reported. In Ta- ble 1, can be observed that the proposed method achieves the best performance across the Caltech, MNIST-USPS, and Synthetic3d datasets. with particularly significant im- provements the Synthetic3d dataset compared to the second-best method. These results demonstrate that ESFMC effectively maintains strong clustering performance while ensuring privacy, thereby alleviating the trade-off between privacy protection and performance enhancement. The suc- cess of ESFMC encourages us focus on methodological
AGDIMC
92.7
82.4
83.5
38.6
32.7
20.3
FedDMVC
91.5
77.4
80.3
39.3
34.3
22.5
FCUIF
93.3
86.2
85.9
41.0
37.6
22.9
Ours
94.9
84.9
87.8
40.8
42.4
26.2
Comparing Methods. To demonstrate the performance of our proposed ESFMC, we select several relevant algo- rithms as comparison methods. These include five cen- tralized multi-view clustering methods, i.e., GIMC-FLSD (Wen et al., 2020), HCP-IMSC (Li et al., 2022), IMVC- CBG (Wang et al., 2022), DSIMVC (Tang Liu, 2022) and

---

An Effective and Secure Federated Multi- View Clustering Method with Information- Theoretic Perspective
/
2
3
95
5
6
7
8
9
90-
Raw data X"
80-
Overiapping
Non-ovarlasping samples
70-
Total samples
1.00
Epech
150
300
(logu)
Attack on Z
(a) Loss Epoch.
(b) ACC us. a.
(c) Attack results ESFMC.
Figure 3. (a) Convergence analysis on BDGP. (b) Parameter analysis on BDGP. (c) Privacy verification on MNIST-USPS.
improvements directly related to the task. It enhances per- formance and further reduces information redundancy.
Table 3. Ablation study datasets with different settings. The
best in cach column is shown in bold. Settings
Table 2 reports the results of ESFMC and the comparison methods under incomplete scenarios with the overlapping rate of o = 0.5. The findings indicate that the extended ESFMC performs well in handling incomplete scenarios with limited information exposure, achieving strong cluster- ing results on both the BDGP and Scene datasets. Addition- ally, conduct experiments the BDGP dataset, explor- ing varying overlapping rates from 0.1 to with an interval of 0.1, as shown in Figure 2. The figure for IMVC-CBG omitted due to poor performance, to highlight clearer variations. The results show that ESFMC adapts to different levels of client sample overlap, with clustering performance improving as the overlapping rate increases.
Variants
ACC
NMI
ARI
w/o L
79.78
73.16
66.64
In general
w/o L
26.78
7.74
4.86
scenarios
w/o 2
87.28
78.74
76.22
(Caltech)
ESFMC
91.50
84.54
83.45
w/o CT
94.48
84.29
86.78
In incomplete
w/o L
25.04
2.55
2.15
scenarios (BDGP)
w/o L
94.44
85.16
87.3
w/o L
86.24
68.29
68.97
ESFMC
94.93
84.89
87.82
client. The results demonstrate that all loss components gradually converge and stabilize the number of epochs increases, indicating that ESFMC is stable and effective.
5.3. Model Analysis
Ablation Study. To further validate the contributions of the proposed method, we conduct ablation studies, as shown in Table 3. "w/o" indicates the absence of specific loss component in the method. The results show that LT and Ly have minimal impact on clustering performance. Their pri- mary role is to ensure that the shared features Z.", derived after feature splitting in the client, contain only clustering- related information, while salple-related information re- mains local to the client, thus preventing privacy leakage. In contrast, L significantly influences the global cluster- ing performance as it involves the extraction of the shared information z._ Additionally, in incomplete scenarios, LT also impacts global clustering performance, demonstrating the effectiveness of the proposed strategy.
Parameter Analysis. Reviewing Eq. (5), serves parameter to adjust [ww"; X"",, balancing fitting and gener- alization. Figure (b) illustrates the clustering performance for different samples on the BDGP dataset with an over- lapping rate of = 0.9 under varying a. Here we adopt the strategy of clustering non-overlapping samples depend- ing the model's generalization performance, implying positive correlation between generalization and cluster- ing performance. As increases, clustering performance for overlapping samples initially shows little change, but drops sharply when a = 10-2, indicating that excessive simplification of the model harms clustering performance. Additionally, a increases. the clustering performance for non-overlapping and total samples first increases, then decreases. This shows that when is small, the model overfits the training data, weakening its generalization and negatively impacting overall clustering performance. When a = 10-4, the model balances fitting and generalization. Additionally, when a is small, effectively removes the constraint term T(w x x,), which can be viewed as an
Convergence Analysis. We conduct the convergence anal- ysis of our method in incomplete scenarios on the BDGP dataset with the overlapping rate of & = 0.5. Figure 3 (a) depicts the changes in _m L.m the epochs, with the results reported for randomly selected
and the total loss Cm over
8

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An Effective and Secure Federated Multi- Clustering Method with Information- Perspective
ablation analysis of the constraint.
bounds. Foundations and Trends@) in Machine Learning. 17:174-303, 2024.
Privacy Verification. We provide empirical analysis to support ESFMC's privacy guarantee. Specifically, we assess whether all semi-honest participants can reconstruct the original data through certain attack methods based on shared information. To simulate potential attacks, apply the widely-used model inversion attack (He et al., 2019) to reconstruct data from the MNIST-USPS dataset using the shared clustering-relater features, as shown Figure (c). The results indicate that while achieving good performance, ESFMC also enhances privacy protection.
Cai, X., Wang, H., Huang, H., and Ding, C. Joint stage recognition and anatomical annotation drosophila gene expression patterns. Bioinformatics, 28(12)ii6-i24, 2012.
Chao, G., Wang, S., Yang, S., Li, C., and Chu, D. In- complete multi-view clustering with multiple imputation and ensemble clustering. Applied Intelligence, 52(13): 14811-14822 2022.
Chao, G., Jiang, Y., and Chu, D. Incomplete contrastive multi-view clustering with high-confidence guiding. In AAAI, volume 38, pp. 11221-11222 2024.
6. Conclusion
In this paper, we propose ESFMC, which is designed to alleviate the trade-off between privacy preservation and per- formance improvement in FedMVC. Specifically, we split the features extracted locally by clients to reduce privacy risks while ensuring the server can mine complementary extend the
Che, S., Kong, Z., Peng, H., Sun, L.,, Leow, A., Chen, Y., and He, L. Federated multi-view learning for private medical data integration and analysis. TIST, 13(4):1-23, 2022.
Chen, X., Xu, J., Ren, Y., Pu, X., Zhu, C., Zhu, X., Hao, Z., and He, L. Federated deep multi-view clustering with global self-supervision. In ACM MM, pp. 3498-3506, 2023.
global clustering structures. Additionally, proposed method incomplete scenarios by designing collaborative alignment strategy. We further analyze the generalization performance and privacy guarantees of our method, confirming its effectiveness and security. Experi- mental results on multiple real-world multi-view datasets demonstrate that our method outperforms state-of- tate-of-theeaat methods in effectiveness and security.
Chen, X., Ren, Y., Xu, J., Lin, F., Pu, X., and Yang, Y. Bridging gaps: Federated multi-view clustering in het- erogeneous hybrid views. NeurlPS, 37:37020-37049, 2024.
Cheng, K., Fan, T., Jin, Y., Liu, Y., Chen, T., Papadopoulos, D., and Yang, Q. Secureboost: A lossless federated learning framework. IEEE intelligent systems, 36(6):87- 98, 2021.
Acknowledgements
This work was supported in part by National Key Research and Development Program of China (Nos. 2024YFC2310800 and 2024YFC2310801) National Natu- ral Science Foundation China (No. 62476052). Sichuan Science and Technology Program (No. 2024NSFSC1473), and Central Guidance for Local Science and Technology Development Fund Projects (No. 2024ZYD0268).
Cruickshank, I. Multi-view Clustering of Social-based Data. PhD thesis, Carnegie Mellon University, USA, 2020.
Dai, H., Liu, Y., Su, P., Cai, H., Huang, S., and Lv, J. Multi-view clustering by inter-cluster connectivity guided reward. In ICML, pp. 1-10, 2024.
Impact Statement
Duan, L. L. Latent simplex position model: High dimen- sional multi-view clustering with uncertainty quantifica- tion. JMLR, 21(3)) 2020.
This paper presents work whose goal advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Dwork, C., Roth, A., et al. The algorithmic foundations of differential privacy. Foundations and Trends@ in Theo- retical Computer Science, 9:21 1-211-407, 2014.
References
Fang, U., Li, M., Li, J., Gao, L., Jia, T., and Zhang, Y. A comprehensive survey on multi-view clustering. TKDE, 15:12300-13361 2023.
Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., and Zhang, L. Deep learning with differential privacy. In ACM CCS, pp. 308-318, 2016.
Fei-Fei, L. and Perona, P. A bayesian hierarchical model for learning natural scene categories. In CVPR, pp. 524-531, 2005.
Alquier, et al. User-friendly introduction to pac-bayes

---

An Effective and Secure Federated Multi- Clustering Method with Information-Theoree Perspective
Fei-Fei, L.,, Fergus, R., and Perona, P. Learning generative visual models from few training examples: An incremen- tal bayesian approach tested on 101 object categories. In CVPR, pp. 59-70, 2004.
Kittel, C. Elementary statistical physics. Courier Corpora- tion, 2004.
Kumar, A., Rai, P., and Daume, H. Co-regularized multi- view spectral clustering. NeurIPS, 24, 2011.
Flanagan, A., Oyomno, W., Grigorievskiy, A., Tan, K. E., M. Federated multi- view matrix factorization for personalized recommenda- tions. In ECML-PKDD, pp. 224-347, 2021.
Khan, S. A., and
Lee, M. and Pavlovic, V. Private-shared disentangled multi- modal vae for learning of latent representations. In ICCV, pp. 1692-1700, 2021.
Geiping, J., Bauermeister, H., Dröge, H., and Moeller, M. Inverting gradients-how easy is it to break privacy in federated learning? In NewrlPS. pp. 16937-16947, 2020.
Li, 7.,, Tang, C., Zheng, X., Liu, X., Zhang, W., and Zhu, High-order correlation preserved incomplete multi-view subspace clustering. TIP, 31:2067-2088) 2022.
Glorot, X., Bordes, A., and Bengio, Y. Deep sparse rectifier neural networks. In AISTATS, pp. 315-323, 2011.
Lin, J., Zheng, Y., Chen, X., Ren, Y., Pu, X., and He, J. Cross-view contrastive unification guides generative pre- training for molecular property prediction. In ACM MM, pp. 1-9, 2024.
Gu, B., Xu, A., Huo, Z., Deng, C., and Huang, H. Privacy- preserving asynchronous vertical federated learning algo- rithms for multiparty collaborative learning. TNNLS, 33 (11):6103-6115, 2021.
Lin, Y.-M., Gao, Y., Gong, M.-G., Zhang, S.-J., Zhang, Y.- Q., and Li, Z.-Y. Federated learning multimodal data: A comprehensive survey. MIR, 20(4):539-55 2023.
He, Z., Zhang, T., and Lee, R. B. Model inversion attacks against collaborative inference. In ACSAC, pp. 148-162, 2019.
Liu, Z.., Huang, H., Letchmunan, S., and Deveci, M. Adap- tive weighted multi-view evidential clustering with fea- ture preference. KBS, 294:1-18, 2024.
Hellström, F., Durisi, G., Guedj, B., and Raginsky, M. Gen- cralization bounds: Perspectives from information theory and pac-bayes. arXiv preprint 2tti::22309044488.. 2023,
Lu, S., Xu, D., Zhang, C., and Zhu, Z. Fast dynamic multi- view clustering with semantic-consistency inheritance. KBS, pp. 1-10, 2024a.
Hu, S., Yan, X., and Ye, Y. Dynamic weighte multi- view co-clustering. Puttern Recognition, 99:1-12, 2020.
Lu, Y., Lin, Y., Yang, M., Peng, D., Hu, P., and Peng, X. Decoupled contrastive multi-view clustering with high- order random walks. In AAAI, volume 38, pp. 14193- 14201, 2024b.
Hu, X., Qin. J.. Shen, Y., Pedryez, W., Liu, X., and Liu, J. An efficient federated multi-view fuzzy c-means cluster- ing method. TFS, 2023.
Huang, H., Zhou, G., Zheng, Y., Qiu, Y., Wang, A., and Zhao, Q. Adversarially robust deep milti-view clustering: A novel attack and defense framework. In ICML., pp- 1-33, 2024.
MacQueen, J. Classification and analysis of multivariate observations. In BSMSP, pp. 281-297, 1967.
Mahendran, A. and Vedaldi, A. Understanding deep image representations by inverting them. In CVPR, pp. 5188- 5196, 2015.
Huang, S., Shi, W., Xu, Z., Tsang, I. W., and Lv, J. Efficient federated multi-view learning. Pattern Recognition, 131: 1-10, 2022.
Nguyen, N.-B., Chandrasegaran, K., Abdollahzadeh. M., and Cheung, N.-M. Re-thinking model inversion attacks against deep neural networks. In CVPR, pp. 16384- 16393, 2023.
Huang, Y., Guo, K., Yi, Li, Z., and Li, T. Incremental unsupervised feature selection for dynamic incomplete multi-view data. Information Fusion, 96:312-327, 2023.
Jiang, X., Ma. Z. Fu, Y., Liao, Y., and Zhou, Heterogeneity- aware federated deep multi-view cluster- ing towards diverse feature representations. In ACM MM, pp. 1-9, 2024.
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al. Pytorch: An imperative style, high-peeformance deep learning library. In NewrIPS, 2019.
Kairouz, P., Oh, S., and Viswanath, The composition theorem for differential privacy. In ICML, pp. 1376-1385, 2015.
Peng. X., Huang, Z., Lv, J., Zhu, H., and Zhou, J. T. Comic: Multi-view clustering without parameter selection. In ICML., pp- 5092-5101, 2019.
10

---

An Effective and Secure Federated Multi- Clustering Method with Information-Theoreee Perspective
Pu, J., Cui, C., Chen, X., Ren, Y., Pu, X., Hao, Z., Philip, S. Y., and He, L. Adaptive feature imputation with latent graph for deep incomplete multi-view clustering. In AAAI, volume 38, pp. 14633-14641 2024.
Yan, X., Wang. Z., and Jin, Y. Federated incomplete multi- view clustering with heterogeneous, graph neural net- works, arXiv preprint arXiv:2406.08533 2024.
Yang, B., Zhang, X., Nie, F., Wang, F., Yu, W., and Wang, Fast multi-view clustering via nonnegative and orthog- onal factorization. TIP, 30:2575-2586, 2020.
Qiao, D., Ding, C., and Fan, J. Federated spectral clustering via secure similarity reconstruction. In NeurlPS, pp. 1-36, 2023.
Yang, Z., Zhang, Y., Zheng. Y., Tian, X., Peng, H., Liu, T., and Han, B. Fedfed: Feature distillation against data heterogeneity in federated learning. In NeurlPS, pp. 1-32, 2023.
Ren, Y., Chen, X., Xu, J., Pu, J., Huang, Y., Pu, X., Zhu, C., Zhu, X., Hao, Z., and He, L. A novel federated multi- view clustering method for unaligned and incomplete data fusion. Information Fusion, 100, 2024.
Yin, H., Hu, W., Zhang, Z., Lou, J., and Miao, M. Incre- mental multi-view spectral clustering with sparse and connected graph learning. Neural Networks, 144:260- 270, 2021.
Scott, D. W. Multivariate density estimation: theory, prac- tice, and visualization. John Wiley & Sons, 2015.
Sharma, K. K. and Seal, A. Outlierrobuust multi-view clus- tering for uncertain data. KBS, 211:1-14, 2021.
Yu, H., Zhang, T., Chen, J., Guo, C., and Lian, Y. Web items recommendation based on multi-view clustering. In COMPSAC, volume pp. 420-425, 2018.
Tang, H. and Liu, Y. Deep safe incomplete multi-view clustering: Theorem and algorithm. In ICML, pp. 21090- 21110, 2022.
Yuan, C., Zhu, Y., Zhong, Z., Zheng, W., and Zhu, X. Robust self-tuning multi-view clustering. WwW, 25(2):489-512, 2022.
Tishby, N., Pereira, F. C., and Bialek, W. The informa- tion bottleneck method. arXiv preprint physics/0004057, 2000.
Zhang, H., Li, C., Kan, N., Zheng, Z., Dai, W., Zou, J., and Xiong, H. Improving generalization in federated learn- ing with model-data mutual information regularization: A posterior inference approach. In NeurIPS, pp. 1-33, 2024a.
Wan, X., Xiao, B., Liu, X., Liu, J., Liang, W., and Zhu, E. Fast continual multi-view clustering with incomplete views. TIP, 2024.
Wang, H., Yao, M., Chen, Y., Xu, Y., Liu, H., Jia, W., Fu, X., and Wang, Y. Manifold-based incomplete multi-view clustering via bi-consistency guidance. TMM, 2024.
Zhang, K., Du S., Wang, Y., and Deng, T. Deep incom- plete multi-view clustering via attention-based direct con- trastive learning. Expert Systems with Applications, pp. 1-14, 2024b.
Wang, S., Liu, X., Liu, L., Tu, W. Zhu, X., Liu, J., Zhou, S., and Zhu, E. Highly-efficient incomplete aagge-scale multi-view clustering with consensus bipartite graph. In CVPR, pp. 177997777777 20,,,998,,,22 2022.
Zhou, I.., Du, G., Lü, K., Wang, L., and Du, J. A sur- vey and an empirical evaluation of multi-view clustering approaches. ACM Computing Surveys, 56(7):1-38, 2024.
Wang, Z., Huang, S.-L., Kuruoglu, E. E., Sun, J., Chen, X., and Zheng, Y. Pac-bayes information bottleneck. In ICLR, pp. 1-16, 2021.
Welling, M. and Teh, Y. W. Bayesian learning via stochastic gradient langevin dynamics. In ICML, pp. 681-688, 2011.
Wen, J., Zhang, Z., Zhang, Z., Fei, L., and Wang, M. Gen- cralized incomplete multiview clustering with flexible locality structure diffusion. TCYB, 11(11:001-114 2020.
Wen, J., Deng, S., Wong, W., Chao, G., Huang, C., Fei, I.., and Xu, Y. Diffuusio- based missing-view generation with the application on incomplete multi-view clustering. In ICML, pp. 1-17, 2024.
Xu, C., Si, J., Guan, Z., Zhao, W., Wu, Y., and Gao, X. Reli- able conflictive multi-view learning. In AAAI, volume 38, pp. 16129-161377 2024.

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An Effective and Secure Federated Multi- Clustering Method with Information-Theoreii Perspective
We provide more details and results about our work in the appendix. Here the contents:
Appendix A: Framework of the proposed algorithm.
Appendix B: More related work.
Appendix C: Proofs.
Appendix D: More details about experimental settings.
Appendix E: Additional experiment results.
A. Framework of the Proposed Algorithm
Algorithm 1 summarizes the pipeline of ESFMC in general scenarios and incomplete scenarios respectively. In general scenarios, local clients perform feature splitting, extracting cluster-related features to be uploaded to the server. The server then utilizes this limited shared information to mine global clustering structures and distributes them back to the clients to assist them in feature splitting. In incomplete scenarios, in addition to the steps performed in general scenarios, alignment loss introduced to ensure alignment among non-overlapping samples across clients. This requires sharing clustering assignments facilitate training.
Algorithm 1 The optimization of ESFMC
input Data with M views X (X', X², X²,..,, X. which are distributed on M clients, number of clusters K, communi- cation round R.
output Global clustering predictions Y.
1: (In General Scenarios)
2: while not reaching rounds do
3: for m 1 M in parallel do
4: Perform feature splitting by Eqs. (3,
5: Use SGLD to optimize the local model by Eq. (7).
6: Upload cluster-related features Z to the server
7: end for
8: Update global features Z by Eq. (8).
9: Calculate clustering predictions Y by Eqs. (9)-(10).
Distribute Y each client.
11: end while
12: (In Incomplete Scenarios)
13: while not reaching R rounds do
14: for m = 1 to M in parallel do
15:
Optimize the total loss by Eqs. (5, 7, 11, 12).
16:
Upload cluster-related features Z and local clustering assignments Q Th to the server. end for
18:
Calculate clustering predictions Y by Eqs. (8)-(10).
19:
Obtain global clustering assignments Q by Eq. (14). Distribute Y and Q to each client.
20:
21:
end while
B. More Related Work
The diversity and large scale of multi-view data present greater challenges to traditional clustering techniques. Unlike single-view clustering, Multi-view clustering (MVC) can integrate information from different perspectives to reveal hidden structures within the data. Based on the types of multi-view data, existing multi-view clustering methods can be classified into four main categories. (1) Complete multi-view clustering (Yang et al., 2020; Dai et al., 2024; Zhou et al., 2024; Lu et al., 2024b), which performed when all view information is fully available. (Hu et al., 2020) proposed dynamic auto- weighte
12

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An Effective and Secure Federated Multi- Clustering Method with Information-Theoree Perspective
MVC method with mutual information, optimizing multi-view feature representation by learning view weights. (Yuan et al., 2022) designed a robust self-tuning MVC that addresses initialization sensitivity, cluster number determination, and outlier issues. (2) Incomplete multi-view clustering (Chao et al., 2022; Wen al., 2024; Wang et al., 2024; Chao et al., 2024), which addresses clustering analysis when some views have missing data. (Zhang et al., 2024b) proposed a framework for incomplete multi-view contrastive clustering that leverages a self-attention mechanism and cross-view prediction. (3) Uncertain multi-view clustering (Liu et al., 2024; Duan, 2020), which is used for clustering data that contains noise, ambiguity, or uncertainty. (Sharma Seal, 2021) proposed self-adaptive mixed similarity function, aiming to reduce the effects of outliers and noise. (4) Dynamic multi-view clustering (Yin al., 2021; Wan al., 2024; Lu et al., 2024a), which is designed for clustering multi-view data that evolves over time. (Huang et al., 2023) introduced incremental unsupervised feature selection method to achieve feature selection for incomplete multi-view streaming data.
Although the above methods effectively address issues like missing data, uncertainty, and dynamism in MVC, most assume centralized data storage, overlooking the existence of data silos and the need for privacy protection. To address these issues, FedMVC has been proposed and attracted attention, which can mine complementary clustering structures from multiple clients without exposing private data.
C. Proofs
C.1. Prerequisite Definitions and Lemmas
Definition C.1. (Kullback-Leebler Divergence). Let P and Q be probability measures on the same space X, the KL divergence from P Q is defined as DKI(PPlQ fxx P(x) log ((a)dr.
Q(z) dr.
Definition C.2. (Mutual Information). Let (X, Y) be a pair of random variables defined over the space X x V, with joint distribution Px,y and marginal distributions Px and Py. The mutual information between and Y is defined as: T(X;Y) = DEL (Px.y||PxPv).
Definition C.3. (Differential Privacy). let A be a random mechanism that takes dataset D as input and belongs S. Assuming D2 and D2 two neighboring datasets differing in only one point, A is (e,d))differential)) private if:
Pr (Di) E S] S exp(e) Pr (A22) E S]+ +
(16)
where is the privacy budget and 5 is the failure probability.
Lemma C.4. (Hoeffding's Inequality). Let Xτ, for E [n], be independent random variables with distribution Px, range [a, 6), and [[ = μ.. Let X = E Xi denote the average of the X,. Then, for any X E R,
log [e
(17)
8n
Lemma C.5. (Donsker- Varadhan Variational Formula). For any measurable, bounded function h b O - R we have:
log Ea-xx [ch100] sup PEP(O)
[B~)]h(()]] - [p
(18)
Lemma C.6. (Gaussian Mechanism (Dwork et al., 2014)). Let E E (0,1) be arbitrary. The Gaussian mechanism with A2f / logg(1.2))) log5/.2//8)// is -dd))effreenniillll private.
Lemma C.7. (Differentially Private SGD (Abadi et al., 2016)). There exist constants 01 and 0g so that given the sampling L and the number of steps T, for any e < TT .. The algorithm of DP-SGD is (s, (c,,)-differentiall) private
probability g N
for any > 0 if we choose o 202 (//1og(1/8)
C.2. Local Training with Feature Splitting
Recall Eq.(2), we have
Cxm (w" 1(Z,, (Z Y) (Z
= -H(ZM) - H(X*) HZ. ( H(ZT) H(Y) + H( Y) H(Z + H( H 2
=H(ZT X + (Z Y) - H.Z
(19)
13

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An Effective and Secure Federated Multi- Clustering Method with Information-Theorrticc Perspective
Then, by constructing the reconstruction network Swz (+) and the clustering layer Owr (+) separately, with wy and w as learnable parameters, the local loss function is transformed below into more concrete form:
/ p(z" xx)) p(z."
/ x) yydzz" dy
Lx (w"
x" dzz" dx"
+ / / p(zz" ==²) log pepp Ze )zz" dz
(20)
Bp(ay x [log (z. )x=)]] - Eplny y)) [logp (z. Iy)l + E Eplay an)
[log p (zz xx"
N..
N..
x Dum (2 1|2 N m
Mi,k log (9wo (KiTc) +
log p (2 2i,ec)
Nm
C.3. Proof of Lemma 3.1
Lemma C.8. (Wang et al., 2021) Given an observed dataset X the optimal posterior p(w! { for client m update in
Eq. (5) should satisfy the following form that
1 1-1u(um)
{
(w"")
x=)
exp
(21)
B
where normalizing factor that makes the integral of the distribution equal 1, and Uw"") the energy function defined as Uw" -x= log p( ))
Proof. Recalling the local optimization objective in Eq. (5) for client m. have
min Xm)
m =Ep(wrn Ep(wo (x
m (w + tal [=")
=Ep Ep(wmpxx (x)) [xxm (w + (xE)( [DKL Ip (w x'" [[p(w"))]]
= -f p (w
x Lxm (w dwn + a p (XXm) / pww" xT) [logp (w I - logg (w")) dww""""""" dxm
(22)
Differentiating n w.r.t. pl m Xm) results in
ptw" pm Lxm (w + a log (wo ( + a logp(u"))
(23)
Setting V p(( [x m Cm
and solving for pm xm) yields
logp (wm 1 -x (2 ) + log ) -1
(24)
Xm) =(w=") exp - -xx (xm eexp(-1).
(n
To integrate the distribution to I, we add a normalization factor B. Then, we define energy function U(w") Lx (mm)
log p) and obtain the optimal posterior solution as
B (( exp { {- Lxm (wm))
(w
B exp
(Cxm(w"") a log (ogp(w"))]
(25)
U(wm)
B exp
14

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An Effective and Secure Federated Multi- View Clustering Method with Information-Theoreii Perspective
C.4. Generalization Analysis
Theorem C.9. Suppose that mm (w"", for all I error satisfies
E M is bounded by C and independent, then the expected generalization
C M Σ
[w X
E [[Lp(w) -x(w))
(26)
2N
where M is the number of participating clients and Nm is the number of samples in the m-th participating client.
Proof. In our settings, we denote the population risk is
M
M E 0 ~ (Xm) (m (w x²)
[p(ww)=
1
Σ m==1
Σ
(27)
M
M
==
and define the empirical risk is
M
M
Nm Lm (w x.:²
1
Lx(w)=
Σ
Lx m (w
=
(28)
M m=1
M
Nm 1=1
m==
Then, the generalization error can be written as
M
E [Tp((t)= Ix(ww] M
Σ m=
E ppp Eptwm(X"))
( (10
Iix (w)))
(29)
where ) [up(x))(wm))) pating client m.
Lxm (w] can be regarded as the expected generalization error of any partici-
Lemma C.10. (Generalization Bound for client m). Suppose that lm (w",, generalization error for client m satisfies
) is bounded by C, then the expected
(x)) Ey(x"" Eptrr xx") [Lx(x=>("")) - Lxm (w")] s
(30)
2N
where pl (!")) denotes distribution over examples client m and Nm the number of samples for client m.
Proof. For client m, its generalization error can expressed
N fm (w" x m
[ Lxm (w"") = (x em (wTT. x²)
(31)
N
By recalling Hoeffding's inequality in Lemma C.4 and suppose that fm (wth , is bounded by C, we have
X²C2
Ep(xm) (" (wo")) (w)" Toxm (wo (wm) (ox
S exp 8NN
(32)
Then, we apply the Donsker- Varadhan variational formula in Lemma C.5, P(@) denotes the of all probability distributions, and p(w) is prior distribution over hypothesis. Then we obtain
Donsker-Varadhan
sup e A (wo ) Loxm -Dx (pllT) pEP(()
A2 &N
Ep(x')
<
(33)
3202 A Al[pcxm3(w"" Lxm -- -De 3Nm
Ep(x")
sup pEP(()
51
15

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An Effective and Secure Federated Multi- Clustering Method with Eeformation-Theorel Perspective
Further, by replacing p(u" ) with p have
- (Lxm(w²) + DKI(p("") x ) (x") (1(x)))(0)))) Bo
AC
S
(34)
A
8N
DKL. (p(w"
x
AC
Pp(Xm)) aptw ( (x))
(1=" (Ixm [w]" S Bp(Xmm Boom (
8.N m
AC2
8.
(35)
8N (m
When =
O2
we get
C² 12I Xm)
Exicm Epcw (xm) (em)
(pp(x=)(w")) Lx (w S
(36)
2Nm
Based on Eq. (29) and Eq. (30), we have
C Lx(w)] S
Iw" Xm)
E [Lp((w)
Σ
(37)
M
2N
C.5. Privacy Analysis
Our privacy analysis contains two steps, saying, differential privacy for each client and the overall analysis for ESFMC.
C.5.1. DIFFERENTIAL PRIVACY FOR EACH CLIENT
Our proposed approach provides client-level privacy protection through posterior inference based SGLD sampling and feature splitting, using client m an example for analysis. Firstly, under the Gaussian mechanism in Lemma C.6, SGLD in the local posterior inference has been demonstrated to provide strict differential privacy.
Lemma C.11. (Differentially Private SGLD). Assuming that lm (w xx") is L-smooth, when k 2 O algorithm in client m preserves (e, -)--))ereeetti privacy.
). the log(2/6)
Proof. Based on the Gaussian mechanism in Lemma C.6, attain O (V2 (oll.g(222///) for selecting After rearrang-
ing, we have E = log (1.25/0)/a for further analysis. Previous work has shown that under this Gaussian mechanism, in N standard SGLD, k > 32r log(2/J] ensures the privacy loss be smaller than where is the local epoch, Nm is the number of samples in client m and T represents the samples sampled in current epoch. Additionally, we have extra parameter vā in the noise variance. That is, need k 2 log(2/8) (e, ())-))diit difffcrretia privacy client m.
v /332k log(28)) with probability
evN.
78 2N
Vāe²N.. for preserving
We also use differential privacy to analyze the feature-splitting strategy for preserving privacy, demonstrating that sharing the clustering-related features Z provides stronger privacy protection than sharing the latent features T directly.
Lemma C.12. For sharing clustering-related features Z (e.8))differentic privacy in client m if o (pe Nevertheless, For sharing latent features zm, (e',8)-differee) -)dffferrett privacy in client m if e' = o OVk (Vllog(1/5) (pe/o. + p=/ox))-
16

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An Effective and Secure Federated Multi- View Clustering Method with Information-Theorrii Perspective
Proof. To facilitate the privacy analysis, we add the noise by the similar way DP-SGD (Abadi al., 2016), i.e., employ the idea of the fe-norm clipping relating the selection of the noise level a. Specifically, We apply the random mechanism with noise distribution N' (0, I to Z and / o to Z Recall Eq.(3), we obtain Z and D from latent features T by designing two udaptive feature projection layers. we define - = P. and - = P Z Building on Lemma C.7, we attain (pe / le log(1 ( /e) and (p2 v A log ( /e) for selecting o, and Øz. respectively, where k: corresponds to T' in the original equation, denoting times of using private data for differentially private training. By rearranging variables, we have e, - P-v Rl (16)) o. and E - Pr / R log a.. Since Z + - = Po + p2 P= zT can be viewed (og(1/8) (Do/a. + pa/am)) Since ZT
as a combination of z and z by combining ε, and E.. we attain - are kept local, adversaries cannot access them, effectively adding large noise (a= + oo). Our analysis shows that sharing Z instead of n offers stronger privacy guarantees, leading to smaller privacy budget
Combining Lemma C.11 and Lemma C.12, we have the following theorem.
Theorem C.13. Assuming that lm (w" ) is L-smooth, when & 2 O vac² 1og(2/8) our proposed ESFMC preserves
client-level (e, 8) diffferenti privacy, where E = (v22log(.2550) + P. (1/8)//))
C.5.2. PRIVACY ANALYSIS FOR ESFMC
In addition to privacy analysis for each client, we conduct the overall privacy analysis the proposed ESFMC by composition theorem.
Lemma C.14. (Composition Theorem (Kairouz et al., 2015)). For any > O, 8 E [0, 1]. and ő E [0, 1}, the class of
(e, -idiffrerettil private mechanisms satisfies E53 1 - (1 -5)- 5) 11-)) 5) -differential privacy under M M-fold adaptive
composition.for for E3 fiminn/
min Ms,
1 + + 2M log (e+ MM3 -eM + + 2M log ())
e++
The composition theorem indicates that when the interactive mechanisms are individually differentially private, their concurrent composition maintains privacy parameters (in terms of pure or approximate differential privacy). By combining Lemma C.13 and Lemma C.14, we derive Theorem 4.2.
D. Experimental Details
D.1. Datasets
We conduct the experiments on the following public datasets.
Caltech (Fei-Fei et al., 2004) is an RGB image dataset that provides multiple views including 40-dim wavelet moments (WM), 254-dim CENsus TRansform hISTogram (CENTRIST), 928-dim Local Binary Patterns (LBP), 512-dim GeneralIzed Search Trees (GIST), and 1984-dim Histogram of Oriented Gradients (HOG) features. We adopt 200 samples from each class and 1400 samples in total for evaluating the robustness of the multi-view clustering methods.
HW are represented by six kinds of features extracted from its binary image. Each class has 200 samples. Each instance has six visual views, including profile correlations, Fourier coefficients the character shapes, Karhunen-Love, morphological features, pixel averages x windows, and Zernike moments.
MNIST-USPS (Peng et al., 2019) is a widely-used dataset for handwritten digits (0-9) and consists of 5000 examples with two views of digital images. The MNIST feature size is 28 x 28, while the USPS is 16 x 16.
Synthetie3d (Kumar et al., 2011 I) comprises categories, containing a total 600 samples, each with three views, and each view having a dimensionality of 3.
BDGP (Cai et al., 2012) comprises 2500 examples related to drosophila embryos, each represented by 1750- dimensional visual feature and a 19-dimensional textual feature. GIST and LBP features
Scene (Fei-Fei & Perona, 2005) includes 4,485 images in 15 classes, each sample has three views: 20-dim Generallzed Search Trees (GIST), 59-dim Histogram of Oriented Gradients (HOG) and 40-dim Local Binary Patterns (LBP)..
17

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An Effective and Secure Federated Multi- Clustering Method with Information-Theoreti Perspective
D.2. Implementation Details
The models of all methods are implemented on the PyTorch (Paszke et al., 2019) platform using NVIDIA RTX-3090 GPUs. The activation function is ReLU (Glorot et al., 2011). For all the datasets used, the learning rate is fixed 0.001. Before conducting the first communication round, clients have not received global clustering results to assist in feature splitting, we use local clustering results to assist in splitting in this round. In subsequent communication rounds, local training is conducted for 300 epochs for all datasets on each client. The communication rounds between the server and clients are set to R 13 for Caltech, MNIST-USPS, and Synthetic3d datasets, and R = 5 for other datasets.
D.3. Comparison Methods
To demonstrate the performance of our proposed ESFMC, we select several relevant algorithms as comparison methods. These include five centralized multi-view clustering methods:
GIMC-FLSD (2020) (Wen et al., 2020) handles incomplete data through graph-regularized matrix factorization and semantic consistency constraints.
HCP-IMSC (2022) (Li et al., 2022) uses tensor decomposition regularization to preserve high-order view and sample correlations.
IMVC-CBG (2022) (Wang et al., 2022) utilizes anchor learning and a bipartite graph framework to achieve efficient incomplete multi-view clustering (IMVC).
DSIMVC (2022) (Tang & Liu, 2022) uses bi-level optimization framework to reduce the impact of semantic inconsistency IMVC performance.
AGDIMC (2024) (Pu al., 2024) is an IMVC method that combines view-specific deep encoders with partial latent graphs for adaptive feature imputation.
Four federated multi-view clustering methods are included:
FedDMVC (2023) (Chen et al., 2023) is a FedMVC that concurrently tackles feature heterogeneity and IMVC.
FedMVFCM (2023) (Hu et al., 2023) primarily focuses on achieving FedMVC through the sharing and aggregation of cluster centroids.
FedMVFPC (2023) (Hu et al., 2023) uses federated learning to address the challenges of multi-view fuzzy clustering on distributed devices.
FCUIF (2024) (Ren et al., 2024) introduces adaptive alignment and unsupervised imputation techniques to address the challenges of unaligned and incomplete multi-view data.
E. Additional Experiment Results
E.1. Communication Overhead
Table Runtime and communication overhead by ESFMC.
Dataset
Runtime
Communication overhead
Caltech
703.6s
2.5KB
HW
617.2s
1.4KB
MNIST-USPS
1199.5s
3.6KB
Synthetic3d
296.2s
0.7KB
BDGP
265.4s
0.6KB
Scene
450.5s
1.6KB
We report some results on the runtime and communication overhead by ESFMC to give the reader some information about the computational resources used by the method. Table shows that runtime and communication overhead by ESFMC small and easy to reproduce.
18

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An Effective and Secure Federated Multi- Clustering Method with Information-Theoreii Perspective
E.2. Ablation Study about Shared Features
We also explore the impact of sharing different feature types on clustering performance on Caltech dataset. The results indicate in Table 5, while sample-related and complete features reveal partial clustering structures, the clustering- features obtained through feature splitting exhibit superior accuracy and effectiveness in mining clustering structures, thereby validating the efficacy of our feature-splitting strategy.
Table 5. Ablation study about shared features on Caltech dataset.
Types of sharing features
ACC
NMI
ARI
Sample-related features
79.93
73.27
66.82
Clustering-related features (ESFMC)
91.50
84.54
83.45
Complete features
87.29
77.86
74.79
E.3. Extending to Cross-Devier Scenarios
Our proposed method operates under the assumption that M views are distributed across M clients, with each client holding data for unique view. Several existing FedMVC methods (Huang et al., 2022; Chen et al., 2023) also follow this assumption. So our approach is particularly suitable for cross-silo scenarios with limited number of clients, such as hospitals or large institutions. Luckily, can also be extended to cross-device scenarios involving numerous clients and has shown promising performance on certain datasets.
Clursiing pafieesane (50
Chanarngg peffermmnne (K6)
ACC
XMI
AB
Chetering pectommrreer 150
10
35
30
50
ACC
XVI
A31
mumber
number
number clicetts
(a) HW
(b) BDGP
(c) Caltech
Figure 4. Clustering performance with the varying number of clients.
Figure 4 illustrates the impact of the number of clients clustering performance without sharing any additional information. Notably, increasing the number of clients reduces the number of samples per client, which can hinder the feature-splittin process during local training, leading to suboptimal clustering-relater feature extraction. The results show that ESFMC maintains stable performance on the HW and BDGP datasets when the number of clients increases moderately. However, with a significant increase, the sample size per client becomes insufficient for effective training, resulting a sharp decline in clustering performance. To adapt ESFMC the Caltech dataset and scenarios with a large number of clients, sharing partial local model information may be necessary. While this strategy could help maintain clustering performance, it introduces new privacy concerns that require further investigation.
19


Reviews:
[{"review_id": "ZD4JrZEXTy", "reviewer": "Reviewer_qNsU", "summary": "The paper proposes a novel federated multi-view clustering (FedMVC) method, Effective and Secure Federated Multi-View Clustering (ESFMC), which aims to address the privacy-performance trade-off in federated learning settings. The key contribution of this work is an information-theoretic feature-splitting mechanism, where clients retain sample-sensitive features locally and share only clustering-related features with the central server. This design effectively mitigates privacy risks while ensuring high-quality clustering results. To extend its applicability, ESFMC introduces a collaborative alignment strategy that ensures consistency across non-overlapping samples in incomplete multi-view scenarios, where certain data samples are missing across different clients. The paper provides theoretical guarantees on privacy protection and generalization performance, as well as extensive empirical evaluations on six real-world multi-view datasets. Experimental results demonstrate that ESFMC outperforms state-of-the-art centralized and federated multi-view clustering methods in both clustering accuracy and privacy preservation.\n\n## update after rebuttal\n\nThe authors have addressed my concerns and I would like to keep my rating.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate your constructive comments and suggestions. \n\n**Q1: Have you considered evaluating ESFMC on real-world federated datasets,to better assess its applicability in practical scenarios?**\n\n**A1:** Thank you for your suggestion. We have considered evaluating ESFMC on real-world datasets and have obtained some preliminary results. The Organ{A,C,S}MNIST [1] dataset is derived from the liver tumor segmentation benchmark (LiTS), which consists of 3D computed tomography (CT) scans. We generate 2D images by extracting center slices from the 3D bounding box in the axial, coronal, and sagittal planes, corresponding to three visual views, resulting in a total of 13,000 samples. Below are our experimental results:\n\n| Method | IMVC-CBG  (2022) | DSIMVC(2022) | AGDIMC(2024) | FedDMVC(2023) | FCUIF (2024) | ESFMC(Ours) |\n| :----: | ---------------- | ------------ | ------------ | ------------- | ------------ | :---------: |\n|  ACC   | 37.35            | 46.33        | 47.92        | 44.80         | 49.28        |    53.62    |\n|  NMI   | 24.68            | 53.69        | 55.25        | 50.73         | 57.26        |    59.88    |\n|  ARI   | 34.32            | 30.44        | 43.28        | 18.31         | 46.53        |    48.96    |\n\n[1]Yang J, Shi R, Wei D, et al. MedMNIST v2-A large-scale lightweight benchmark for 2D and 3D biomedical image classification. Scientific Data, 2023, 10(1): 41.\n\n**Q2: More extensive empirical experiments—such as testing ESFMC against more sophisticated adversarial attacks (e.g., gradient inversion, membership inference attacks).**\n\n**A2:** Thank you for your valuable comment. Our primary focus is on privacy verification against model inversion attacks, which are among the most common threats targeting shared intermediate results. These attacks leverage model outputs to reconstruct the original input data and are a type of sophisticated adversarial attack. They are also one of the most prevalent and effective attacks in federated learning settings that share intermediate results (such as the features in our paper).\n\nRegarding the other attacks you mentioned, they may not be applicable to our federated learning scenarios. For instance, **gradient inversion attacks** reconstruct original data by exploiting gradient information, which is commonly observed in federated learning settings that share model parameters or gradients. However, in our method, all client model training parameters remain strictly local, making such an attack infeasible. Similarly, **membership inference attacks** aim to determine whether a specific sample was part of the training dataset, thereby probing data privacy. However, since our training data are entirely unlabeled and does not include explicit sample membership information, attackers would gain no meaningful insights merely by inferring whether a sample participated in the training.\n\nAdditionally, we wish you to refer to our response to Reviewer pjmK Q2, where we elaborate on how our proposed method addresses **potential threats from malicious clients**, further strengthening its ability to safeguard sensitive information across different scenarios. Lastly, it is important to highlight that our method specifically tackles the trade-off between privacy preservation and performance improvement. Unlike existing works, which typically focus on one aspect at the cost of the other, our approach strives to maintain strong performance while minimizing privacy leakage as much as possible.\n\n**Q3: Can you provide additional quantitative results on privacy guarantees, such as empirical differential privacy noise impact analysis?**\n\n**A3:** Yes, we have included additional quantitative results on privacy guarantees. Specifically, we incorporate differential privacy by adding noise to the clustering-related features uploaded from clients to the server. The table below presents the clustering performance of ESFMC under different privacy bounds $\\varepsilon$ on Caltech dataset. We observe that ESFMC achieves both high performance and privacy at $\\varepsilon=50$. However, as the level of noise increases at $\\varepsilon=25$, the performance of ESFMC unavoidably degrades. \n\n| Privacy Bound | No Privacy | $\\varepsilon=50$ | $\\varepsilon=25$ |\n| :-----------: | ---------- | ---------------- | ---------------- |\n|      ACC      | 91.50      | 90.78            | 86.29            |\n|      NMI      | 84.54      | 83.21            | 74.03            |\n|      ARI      | 83.45      | 81.98            | 73.13            |", "claims_and_evidence": "The main claims made in the paper include:\n\n**Claim 1**: ESFMC mitigates the privacy-performance trade-off by using feature splitting to retain privacy-sensitive information locally while sharing only clustering-relevant features. **Evidence**: The paper provides theoretical privacy guarantees, including differential privacy analysis and empirical validation against model inversion attacks. The results show that ESFMC successfully prevents sensitive information leakage while maintaining superior clustering performance compared to traditional FedMVC approaches.\n\n**Claim 2**: ESFMC is extendable to incomplete multi-view settings using collaborative alignment to ensure feature consistency across clients. **Evidence**: The collaborative alignment strategy is evaluated on incomplete datasets, where certain clients have missing views. The results demonstrate that ESFMC maintains high clustering performance even when data is incomplete. Additionally, ablation studies confirm that the collaborative alignment mechanism plays a crucial role in improving global clustering quality and robustness.", "methods_and_evaluation_criteria": "The proposed method is well-motivated, particularly for federated multi-view clustering in privacy-sensitive scenarios where direct data sharing is infeasible. The evaluation covers six real-world datasets with varying sample/view completeness, ensuring robustness across different conditions. Comparisons against five centralized and four federated clustering methods provide a strong performance benchmark. Standard metrics, including Accuracy, Normalized Mutual Information, and Adjusted Rand Index, ensure fairness in evaluation.", "theoretical_claims": "I reviewed the Methodology section, which included generalization analysis, privacy analysis, and complexity analysis. The theoretical derivations appear correct, demonstrating ESFMC’s ability to scale effectively across multiple clients through upper bounds on clustering error. The privacy analysis provides differential privacy guarantees, theoretically proving that feature splitting minimizes privacy risks by ensuring that only clustering-relevant information is shared. The complexity analysis confirms that ESFMC remains computationally efficient and scalable for large-scale federated deployments. There are no major issues.", "experimental_designs_or_analyses": "Yes, I checked the experimental settings, results, and analysis. ESFMC consistently outperforms existing methods in clustering performance while preserving privacy, as demonstrated by extensive evaluations across multiple datasets.", "relation_to_broader_scientific_literature": "This work contributes to federated multi-view clustering by tackling the fundamental challenge of balancing privacy protection and clustering performance. It builds on prior research in federated learning and privacy-preserving techniques by integrating differential privacy and information-theoretic principles.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "Strengths \n- The paper introduces a feature-splitting strategy that distinguishes clustering-related features from sample-related features, allowing privacy-sensitive data to remain local while sharing only task-relevant information. This significantly enhances privacy protection without compromising clustering performance. The proposed collaborative alignment strategy effectively addresses challenges arising from incomplete multi-view scenarios, where clients have non-overlapping samples.\n- The method is computationally efficient and scalable, making it highly suitable for large-scale federated learning applications. Unlike methods that require extensive client-server communication or computationally expensive privacy-preserving mechanisms, ESFMC optimizes information sharing without introducing significant computational overhead. The feature-splitting mechanism reduces the amount of information transferred between clients and the server, enhancing communication efficiency.\n- The paper provides strong experiments, demonstrating that ESFMC outperforms state-of-the-art methods in both clustering performance and privacy preservation.\n\nWeaknesses\n- The experimental validation primarily relies on synthetic and public benchmark datasets, which may not fully capture the complexities of real-world federated learning environments. In practice, data distributions in federated settings tend to be non-IID, with significant noise, missing information, and domain-specific constraints. While the inclusion of six multi-view datasets provides a strong foundation for evaluation, additional experiments on real-world federated datasets (e.g., healthcare, financial transactions) would strengthen the practical impact of ESFMC and demonstrate its applicability beyond academic benchmarks.\n\n- While the paper provides theoretical guarantees for privacy preservation using differential privacy analysis, the empirical validation of privacy guarantees is somewhat limited. The experiments focus primarily on clustering performance, with only basic privacy attack simulations. More extensive empirical experiments—such as testing ESFMC against more sophisticated adversarial attacks (e.g., gradient inversion, membership inference attacks) would provide stronger evidence that the method effectively protects sensitive information in real-world deployment scenarios.", "other_comments_or_suggestions": "NA", "questions_for_authors": "- Have you considered evaluating ESFMC on real-world federated datasets, such as medical imaging data, financial records, or IoT sensor networks, to better assess its applicability in practical scenarios?\n- Can you provide additional quantitative results on privacy guarantees, such as empirical differential privacy noise impact analysis?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Uh490gNn7z", "reviewer": "Reviewer_1SCH", "summary": "This paper introduces an effective and secure federated multi-view clustering method from an information-theoretic perspective. The proposed approach preserves privacy while effectively mining complementary global clustering structures. Additionally, the paper provides theoretical analyses of its generalization bounds and privacy guarantees.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for these valuable comments.\n\n**Q1: The paper lacks results on large-scale datasets.**\n\n**A1:** We conduct further experiments on the large-scale YoutubeVideo dataset, which contains 101,499 samples across 31 classes, where each sample has three views of cuboids histogram, HOG, and vision misc. The clustering results of ESFMC and several comparison methods in incomplete scenarios are shown below:\n\n| Method | IMVC-CBG (2022) | DSIMVC (2022) | AGDIMC (2024) | FedDMVC (2023) | FCUIF (2024) | ESFMC(Ours) |\n| :----: | --------------- | ------------- | ------------- | -------------- | ------------ | :---------: |\n|  ACC   | 18.32           | 15.01         | 24.42         | 21.52          | 23.04        |    25.52    |\n|  NMI   | 11.83           | 8.11          | 20.25         | 16.96          | 18.46        |    23.40    |\n|  ARI   | 2.04            | 1.20          | 5.22          | 3.42           | 3.72         |    5.65     |\n\nWe select the YoutubeVideo dataset, which is 20 times larger than the Scene dataset with 4,485 samples. The results demonstrate that our method adapts well to large-scale datasets and outperforms other methods in terms of performance, ensuring the proposed method's robustness and broader applicability.\n\n**Q2: In the incomplete multi-view setting, more scenarios of data heterogeneity, such as quantity skew, should also be explored.**\n\n**A2:** Thank you for your suggestion. To explore the scenario of data heterogeneity, such as quantity skew, we introduce Dirichlet distribution when constructing incomplete datasets. A smaller Dirichlet parameter $\\alpha$ leads to more heterogeneous splits, resulting in highly imbalanced sample sizes among clients. The table below presents three levels of heterogeneity by setting  $\\alpha$ to $10^{-2}$ (high),  $10^{0}$(moderate), and $10^{2}$ (none) on BDGP dataset in incomplete scenarios. The results demonstrate that ESFMC maintains strong performance even under high heterogeneity, with only a slight performance drop.\n\n| Levels of Heterogeneity | None  | Moderate | High  |\n| :---------------------: | ----- | -------- | ----- |\n|           ACC           | 94.92 | 94.40    | 93.67 |\n|           NMI           | 84.93 | 84.11    | 82.86 |\n|           ARI           | 87.83 | 86.67    | 84.64 |\n\n**Q3: How do the authors evaluate the correctness of their feature-splitting strategy?**\n\n**A3:** This is indeed an issue worthy of attention. Our feature splitting strategy is guided by an intuitive training loss function. Specifically, $\\mathcal{L}^m_{1}$ ensures that sample-related features accurately reconstruct the original data, $\\mathcal{L}^m_{2}$ encourages clustering-related features to capture meaningful clustering structures, and $\\mathcal{L}^m_{3}$ minimizes redundancy between different feature types, promoting high-quality feature splitting. In the ablation studies **(Table 3)**, removing $\\mathcal{L}^m_{1}$ and $\\mathcal{L}^m_{3}$ in the variants results in performance degradation, demonstrating that the feature splitting strategy effectively splits different features, thereby ensuring the effectiveness of our method. Furthermore, **in Table 5**, we analyze the impact of sharing different types of features on clustering performance. The results indicate that the clustering-related features extracted through our feature splitting strategy are more effective and accurate in capturing clustering structures, further validating the strategy’s accuracy and effectiveness. Overall, these ablation studies confirm that our feature splitting strategy successfully separates sample-related and clustering-related features, significantly enhancing clustering performance.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes, I checked the theoretical proof of the work.", "experimental_designs_or_analyses": "Yes, I reviewed the experimental analyses for this paper. The multi-view datasets chosen for this paper are common but simple, and I would like the authors to add experimental results of the method on large-scale dataset.", "relation_to_broader_scientific_literature": "This paper can inspire researchers to use multi-view methods for privacy-constrained scenarios, which is meaningful for the development of the federated multi-view learning field.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "Strengths:\n1.The paper is well-written and clearly presents the proposed method.\n2.The method is supported by both theoretical analysis and experiments, demonstrating its effectiveness in balancing privacy protection and clustering performance.\n3.The method is extendable to incomplete scenarios and cross-device scenarios.\n\nWeaknesses:\n1.The multi-view datasets used in the experiments, while common, are relatively simple, and the paper lacks results on large-scale datasets.\n2.In the incomplete multi-view setting, only different sample overlapping rates among clients are considered. More scenarios of data heterogeneity, such as quantity skew, should also be explored.", "other_comments_or_suggestions": "Refer to the weakness", "questions_for_authors": "The effectiveness of the proposed method depends on the accuracy of feature splitting. How do the authors evaluate the correctness of their feature-splitting strategy?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PXzVK2bRFW", "reviewer": "Reviewer_HHRD", "summary": "The paper proposes ESFMC which aims to address the privacy concerns and performance trade-offs in federated learning for multi-view clustering. The main idea is to allow all clients to do collaborative clustering without leaking sensitive data, and they follow a privacy-preserving strategy based on information theory by only sharing the clustering-related features, instead of the raw or sample-related features to minimize the risk of privacy leakage. Additionally, ESFMC is extended to handle incomplete multi-view clustering by introducing a collaborative alignment strategy. The paper also conducts extensive experiments to show that ESFMC outperforms existing state-of-the-art methods in terms of clustering accuracy and privacy preservation", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for valuable comments and suggestions that have greatly improved our paper.\n\n**Q1: While the paper focuses on information-theoretic privacy preservation, it does not provide a detailed comparison with other commonly used privacy-preserving techniques in federated learning.**\n\n**A1:** Thank you for your valuable feedback. Our method can be integrated with commonly used privacy-preserving techniques in federated learning to further enhance privacy protection. Specifically, for clustering-related features shared across clients, our feature splitting strategy already prevents common attacks, such as model inversion attacks, preventing attackers from reconstructing the original data. However, for stronger privacy guarantees, additional privacy-preserving techniques can be added. For instance, as referenced in our response to Reviewer qNsU Q3, we report the impact of **differential privacy** on our method’s performance under different privacy budgets. Additionally, our method aims to balance privacy protection and clustering performance. Excessive privacy constraints inevitably lead to performance degradation, as confirmed by our experimental results. Similarly, **homomorphic encryption** could be integrated with our method to further enhance privacy protection, though at the cost of increased computational overhead in both training and inference.\n\n**Q2: The authors do not provide a clear definition or description of the privacy under the federated multi-view clustering scenario.**\n\n**A2:** Thank you for your feedback. We describe the privacy protection scenario of ESFMC in Lines 416–418: we assess whether all semi-honest participants can reconstruct the original data through certain attack methods based on shared information. However, this may not be explicitly stated. To clarify, we will restate ESFMC’s privacy protection scenario in the problem statement: we assume that all participating parties are semi-honest and do not collude. An attacker follows the training protocol but may attempt privacy attacks to infer private data from other parties.\n\n**Q3: What is the advantage of the collaborative alignment strategy over the cross-view alignment strategy based on adaptively calculate alignment matrices in FCUIF (Ren et al., 2024)?**\n\n**A3:** First, in terms of performance, our proposed method demonstrates superior effectiveness in handling incomplete scenarios compared to FCUIF on the same datasets (BDGP and Scene), achieving better results. Second, from a methodological perspective, FCUIF leverages sample commonality and view versatility, enabling the server to adaptively compute alignment matrices for cross-view alignment. In contrast, our collaborative alignment strategy with an information-theoretic perspective, aligns features by maximizing mutual information. Compared to FCUIF, our method serves as a generalizable interface module that can be integrated into other methods. It offers greater adaptability and scalability while also achieving improved performance.\n\n**Q4: To optimize $\\omega^m_{t,k}$, why traditional SGD is not suitable?**\n\n**A4:** Traditional SGD seeks a single optimal point estimate of the parameters by minimizing the loss function. In contrast, our method focuses on the posterior distribution of the parameters rather than a single estimate. To achieve this, we employ SGLD, which integrates SGD with Langevin dynamics by introducing noise into the gradient updates. This added noise facilitates sampling from the posterior distribution rather than converging to a single mode.\n\n**Q5: For privacy preservation, if the work aims to minimize the information to be shared, a straightforward way is to minimize $I(X^m;Z_c^m)$, but it seems that the method uses $I(Z_x^m, Z_c^m)$ instead.**\n\n**A5:** This is an interesting perspective. Minimizing $I(X^m;Z_c^m)$  is indeed a more direct approach to reducing the amount of sensitive information from $X^m$ in the shared information $Z_c^m$. However, we choose to minimize $I(Z_x^m, Z_c^m)$ to emphasize the feature splitting strategy better. We aim to ensure that the extracted features,  $Z_x^m$ and $Z_c^m$, serve distinct purposes with minimal redundancy, thereby achieving high-quality feature splitting. We believe that both optimization strategies serve a similar goal, differing primarily in their formulation and optimization approach.", "claims_and_evidence": "Yes, the paper provides several experiment results and theoretical analysis to support its claim.", "methods_and_evaluation_criteria": "The methods and evaluation criteria(ACC,NMI, and ARI) are well-suited to the problem of federated multi-view clustering.", "theoretical_claims": "Yes, I have checked the proofs in the appendix, including the proof of Lemma 3.1, the generalization analysis, and the privacy analysis.", "experimental_designs_or_analyses": "Yes, the authors conducted several experiments on the popularly used datasets, and the results demonstrate the effectiveness.", "relation_to_broader_scientific_literature": "The work provided a privacy solution for federated multi-view clustering based on information theory, and extended the work to incomplete scenarios.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "1.\tThe paper's main contribution is further solving the privacy-preservation in federated multi-view clustering. While there are existing methods for federated learning and multi-view clustering, the information-theoretic feature splitting used in ESFMC is a novel contribution. By only sharing the clustering-related features, the paper successfully balances the privacy and performance in federated learning.\n2.\tThe collaborative alignment strategy to deal with incomplete data in a federated setting is another significant innovation. This strategy extends its application.\n3.\tThe paper is well-organized. The ablation studies and theoretical analysis are detailed, helping to validate the contributions effectively. The extensive experiments conducted on various datasets and the ablation study provide support for the method's effectiveness. \nWeaknesses:\n1.\tWhile the paper focuses on information-theoretic privacy preservation, it does not provide a detailed comparison with other commonly used privacy-preserving techniques in federated learning.\n2.\tThe authors do not provide a clear definition or description of the privacy under the federated multi-view clustering scenario", "other_comments_or_suggestions": "Refer to the above comments.", "questions_for_authors": "1.\tWhat is the advantage of the collaborative alignment strategy over the cross-view alignment strategy  based on adaptively calculate alignment matrices in FCUIF (Ren et al., 2024)?\n2.\tTo optimize \\omega^m_{t,k}, why traditional SGD is not suitable?\n3.\tFor privacy preservation, if the work aims to minimize the information to be shared, a straightforward way is to minimize I(X^m;Z_c^m), but it seems that the method uses I(Z_x^m, Z_c^m) instead.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {"ethical_review_concerns": "None"}}, {"review_id": "1Sq4FZs1Ma", "reviewer": "Reviewer_pjmK", "summary": "Focusing on federated multi-view learning, this paper presents a novel method to alleviate the dilemma between privacy protection and multi-view clustering performance improvement. The authors conduct both theoretical analysis and empirical evaluations, demonstrating superior performance over baseline methods while offering enhanced privacy protection.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable comments and suggestions. \n\n**Q1: In order to analyze their impact to the final performance, could the author provide the hyperparameter experiment about $\\mathcal{L}^m$ and $\\mathcal{L}_a^m$ of Equation 12? Even if the author do not tune hyperparameter in their experiments.**\n\n**A1:** Thank you for your suggestion. We redefine Equation 12 as $\\mathcal{L}^m_{inc}=\\mathcal{L}^m+\\beta\\mathcal{L}_{a}^m$ and analyze the hyperparameter $\\beta$. The table below shows the sensitivity of this parameter by varying $\\beta$ the range on $[10^{-2},10^{2}]$ the BDGP dataset in incomplete scenarios. The results show that the model achieves the best performance at $\\beta=1$, reflecting the fact that the two parts of Equation 12, $\\mathcal{L}^m$ and $\\mathcal{L}_a^m$, are similarly weighted and are both important for model optimization, so the hyperparameter is not tuned in our experiments.\n\n| $\\beta$ | $10^{-2}$ | $10^{-1}$ | $10^{-0}$ | $10^{1}$ | $10^{2}$ |\n| :-----: | --------- | --------- | --------- | -------- | -------- |\n|   ACC   | 87.48     | 91.88     | 94.92     | 93.76    | 89.28    |\n|   NMI   | 78.08     | 80.67     | 84.93     | 82.94    | 72.27    |\n|   ARI   | 75.33     | 81.20     | 87.83     | 85.05    | 75.45    |\n\n**Q2: How does the proposed method address potential threats from malicious clients, as it currently only demonstrates effectiveness against reconstruction attacks on the server side?**\n\n**A2:** Thank you for your careful reminder. Our proposed method primarily addresses model attack threats caused by semi-honest participants. Although we did not explicitly delve into defenses against data attacks initiated by dishonest participants such as malicious clients, our method remains effective in such cases. Specifically, if there exists malicious clients with false or manipulated data, their local clustering structures are likely to significantly deviate from that of other clients. By comparing the local cluster assignments or centroids uploaded by each client, the server can set a malicious threshold to flag outliers. If a client's data exceed this threshold, its shared information can be disregarded, and the client can be marked as malicious, effectively mitigating such attacks. \n\n**Q3: Could the authors integrate the discussion on extending the method to cross-device scenarios (currently in the appendix) into the main text and provide more in-depth analysis?**\n\n**A3:** Thank you for your suggestion. We will include experimental results and a discussion on extending to cross-device scenarios in Section 5.3. We believe that enhancing the scalability of the method to adapt to various scenarios is an essential area of exploration. In the new version, we will present additional experimental results on more multi-view datasets and provide further analysis of these results. Furthermore, we have envisioned a solution for the scenario where the sample size per client becomes insufficient for effective training as the number of clients increases. To maintain good performance, we will consider strategies such as continuing training based on existing models or sharing partial local model information to alleviate the issue of insufficient samples per client, enabling collaborative training across multiple clients.\n\n**Q4: Section 4, titled \"Discussion and Analysis,\" seems to lack discussion on key findings—could the authors elaborate further to strengthen this section?**\n\n**A4:** Thank you for your feedback. In the new version, we plan to add two parts discussing model generalization and privacy protection. **Regarding model generalization**, we will focus on the scalability of the proposed method, including extensions to incomplete and cross-device scenarios. These scenarios primarily aim to limit shared information, only relying on the model’s generalization ability. For example, for incomplete scenarios, each client uploads clustering-related features for overlapping samples to the server, while non-overlapping samples are clustered locally. For cross-device scenarios, each client uploads clustering-related features extracted from local data, with the server aligning overlapping samples. Our method leverages generalization to perform well with a few extensions. **Regarding privacy protection**, we will discuss the privacy-preserving scenarios addressed by our method and potential strategies for further enhancing privacy. Our method is primarily designed for environments where all participating parties are semi-honest, meaning they faithfully execute the training protocol but may attempt privacy attacks. Currently, our feature splitting strategy is sufficient to defend against common model inversion attacks in such settings. For further privacy enhancement, we could integrate commonly used privacy-preserving techniques in federated learning, such as differential privacy or homomorphic encryption, to offer additional privacy protection.", "claims_and_evidence": "Yes, the authors provide the detailed description of the method and multiple experiments to support the points.", "methods_and_evaluation_criteria": "Yes,  the proposed methods and evaluation criteria make sense for the problem.", "theoretical_claims": "Yes, I have verified the privacy analysis in this paper.", "experimental_designs_or_analyses": "All experiments and their analysis have been checked.", "relation_to_broader_scientific_literature": "This methodology and theoretical results of this paper are mainly about  federated learning and multi-view clustering.", "essential_references_not_discussed": "There are no Not Discussed Essential References have been found.", "other_strengths_and_weaknesses": "The paper is well-structured, with a clear motivation and thorough theoretical and experimental support. The proposed method makes a meaningful contribution to the advancement of the multi-view learning community. \n\nHowever, several aspects require further clarification and improvement:\n1) The proposed method only demonstrates its effectiveness against reconstruction attacks on the server side, without addressing potential threats from malicious clients.\n2) The authors extends the method to cross-device scenarios in appendix, which is valuable. It would be beneficial to integrate this discussion into the main text and provide further analysis.\n3) Section 4 is titled \"Discussion and Analysis,\" but lacks discussion on key findings.", "other_comments_or_suggestions": "See weakness", "questions_for_authors": "1)  In order to analyze their impact to the final performance, could the author provide the hyperparameter experiment about $L^m$ and $L^m_a$ of Equation 12? Even if the author do not tune hyperparameter in their experiments. \n2) How does the proposed method address potential threats from malicious clients, as it currently only demonstrates effectiveness against reconstruction attacks on the server side?\n3) Could the authors integrate the discussion on extending the method to cross-device scenarios (currently in the appendix) into the main text and provide more in-depth analysis?\n4) Section 4, titled \"Discussion and Analysis,\" seems to lack discussion on key findings—could the authors elaborate further to strengthen this section?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: After the rebuttal and discussion phases, the paper received scores of 4, 4, 4, and 3, which exceed the expected threshold for acceptance.  All reviewers are satisfied with the paper and the authors' response. After briefly reviewing the comments and the authors' responses, I believe the paper meets the acceptance criteria for ICML.
Decision: Accept (poster)