Efficient Federated Incomplete Multi-View Clustering
Authors: Suyuan Liu
Hao Yu
Hao Tan
KE LIANG
Siwei Wang
Shengju Yu
En Zhu
Xinwang Liu
Venue: ICML 2025 poster (2025)
Keywords: Multi-view Clustering
Incomplete Multi-view Clustering
Federated Learning
Primary area: general_machine_learning->clustering

Abstract: Multi-view clustering (MVC) leverages complementary information from diverse data sources to enhance clustering performance. However, its practical deployment in distributed and privacy-sensitive scenarios remains challenging. Federated multi-view clustering (FMVC) has emerged as a potential solution, but existing approaches suffer from substantial limitations, including excessive communication overhead, insufficient privacy protection, and inadequate handling of missing views. To address these issues, we propose Efficient Federated Incomplete Multi-View Clustering (EFIMVC), a novel framework that introduces a localized optimization strategy to significantly reduce communication costs while ensuring theoretical convergence. EFIMVC employs both view-specific and shared anchor graphs as communication variables, thereby enhancing privacy by avoiding the transmission of sensitive embeddings. Moreover, EFIMVC seamlessly extends to scenarios with missing views, making it a practical and scalable solution for real-world applications. Extensive experiments on benchmark datasets demonstrate the superiority of EFIMVC in clustering accuracy, communication efficiency, and privacy preservation. Our code is publicly available at https://github.com/Tracesource/EFIMVC.

Efficient Federated Incomplete Multi-View Clustering
Suyuan Liu
Hao Yu?
Hao Tan
Ke Liang'
Siwei Wang? 2 Shengju Yu
En Zhu Xinwang Liu'
Abstract
which typically operate single data representation, MVC integrates complementary and consensus informa- tion from multiple views, thereby significantly enhancing clustering robustness and accuracy (Yang et al., 2022; Wang et al., 2013; Pan & Kang, 2021; Wan et al., 2024a). Over the past decade, numerous MVC approaches have been de- veloped, refining performance from different perspectives (Sun et al., 2024; Cui al., 2024b; Wan al., 2024b).
Multi-view clustering (MVC) leverages comple- mentary information from diverse data sources to enhance clustering performance. However, its practical deployment in distributed and privacy- sensitive scenarios remains challenging. Feder- ated multi-view clustering (FMVC) has emerged as potential solution, but existing approaches suffer from substantial limitations, including ex- cessive communication overhead, insufficient privacy protection, and inadequate handling of missing views. To address these issues, we propose Efficient Federated Incomplete Multi- View Clustering (EFIMVC), a novel framework that introduces localized optimization strat- egy to significantly reduce communication costs while ensuring theoretical convergence. EFIMVC employs both view-specific and shared anchor graphs as communication variables, thereby en- hancing privacy by avoiding the transmission of sensitive embeddings. Moreover, EFIMVC seamlessly extends to scenarios with missing views, making practical and scalable solu- tion for real-world applications. Extensive ex- periments on benchmark datasets demonstrate the superiority of EFIMVC in clustering ac- curacy, communication efficiency, and privacy preservation. Our code is publicly available at
Despite these advancements, most existing MVC methods assume centralized data storage paradigm. In practical applications. however, multi-view data are often distributed across multiple clients due to privacy concerns, regulatory constraints, or logistical limitations (Che et al., 2022; Huang et al., 2022). Direct data sharing among clients typically infeasible, making traditional MVC approaches unsuitable for such scenarios. To bridge this gap, Federated Multi- View Clustering (FMVC) has been introduced, combining (FL) with MVC to enable tering (Feng et al., 2024b; Chen et al., 2024). For instance, Feng et al. (Feng et al., 2024a) integrated matrix factor- ization and K-Means clustering within a federated learning framework, while Jiang al. (Jiang al., 2024) proposed contrastive learning- based local-globe model alignment to handle data heterogeneity in FMVC.
distributed clus-
However, existing FMVC methods still face several criti- cal challenges: 1) High Communication Overhead. All existing FMVC frameworks rely on itcrative exchanges of client- and server-side variables within tightly coupled op- timization processes. Each update step necessitates com- munication round, making the communication cost propor- tional to the number of optimization iterations. Furthermore, some methods transmit large X similarity matrices, ex- acerbating bandwidth consumption. 2) Limited Privacy Protection. Most FMVC approaches employ either embed- ded representations or sample-level similarity matrices as communication variables. While embeddings encapsulate feature information, similarity matrices reveal the intrinsic relationships between samples. Both contain substantial view-specific private information, posing privacy risks. 3) Ineffective Handling of Missing Views. Real-world multi- view data often suffer from missing modalities due to sensor failures, transmission errors, or incomplete data collection. Many existing FMVC methods assume complete multi-view data, rendering them ineffective in handling missing views.
1. Introduction
Multi-view clustering (MVC) has garnered significant at- tention in the field of unsupervised learning, primarily due to the increasing availability of diverse data from various sources or perspectives (Cui et al., 2024a; Liang et al., 2023; Liu et al., 2021). Unlike traditional clustering methods,
'College of Computer Science and Technology, National Uni- versity of Defence Technology, Changsha, China 2 'Academy of Military Sciences, Beijing, China. Correspondence to: Xinwang Liu <xinwangliue nudt.cdu>.
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Efficient Federated Incomplete Multi- Viel Clustering
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Figure Overview the proposed EFIMVC framework. EFIMVC follows an alternating local optimization strategy between clients the server. Clients perform single-view view anchor learning and anchor graph construction, guided by the global anchor graph from the server. The optimized anchor graph and anchor relationship matrix are then sent to the server, which aligns and fuses received anchor graphs through local optimization. The updated glohal anchor graph and alignment matrices transmitted back clients, and this process continues until global convergence.
To tackle these challenges, we propose Efficient Feder- ated Incomplete Multi- View Clustering (EFIMVC), a novel FMVC framework designed to enhance communication effi ciency, privacy protection, and robustness to missing views. As illustrated in Figure EFIMVC introduces federated optimization strategy that confines variable updates to local environments, thereby reducing communication overhead while ensuring theoretical convergence. By leveraging view- specific and shared anchor graphs as communication vari- ables, EFIMVC mitigates bandwidth demands and avoids the direct transmission of sensitive embeddings, enhancing privacy protection. Furthermore, we introduce dual-anchor alignment mechanism based on structural and feature consis- tency to mitigate anchor misalignment during graph fusion. Finally, EFIMVC seamlessly extends to incomplete multi- view scenarios, offering a practical solution for real-world federated clustering tasks.
address anchor misalignment during graph fusion, im- proving the robustness and reliability of clustering re- sults.
EFIMVC effectively handles missing views, ensuring robust clustering performance even in the presence of incomplete multi-view data.
2. Related Work
2.1. Federated Multi-view Clustering
Federated Multi-View Clustering has emerged promis- ing approach for exploring the cluster structure of multi- view data distributed across multiple clients while preserv- ing data privacy (Yan et al., 2024; Chen et al., 2023). Exist- ing FMVC methods can be categorized based on the type of communication variables exchanged between clients and the server.
The key contributions of EFIMVC are summarized fol- lows:
One common approach is to transmit embedded representa- tions, where each client sends view-specific embeddings of size n. x d (with y as the sample size and d as the feature dimension). Chen et al. (Chen et al., 2024) proposed a framework integrating local collaborative contrastive learn- ing and global weighted aggregation address challenges posed by heterogeneous hybrid-vien scenarios. Similarly, Yan et al. (Yan et al., 2024) introduced heterogeneous graph neural network and global pseudo-labeling strategy to mitigate view incompleteness and feature heterogeneity, demonstrating the effectiveness of embedding- based com- munication. However, this approach risks privacy leakage since embeddings may retain sensitive feature information.
We propose novel federated optimization framework that minimizes communication overhead by confining variable updates to local environments, significantly improving communication efficiency without sacrific- ing clustering performance.
To enhance privacy, EFIMVC employs anchor graphs as communication variables, avoiding the transmission of sensitive embeddings or sample-level similarity ma- trices, thereby reducing privacy risks.
We introduce dual-anchor alignment mechanism to
2

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Efficient Federated Incomplete Multi- Clustering
Another strategy involves transmitting similarity matrices of size n, encoding the structural relationships between samples. For instance, Wang al. (Wang et al., 2020) pro- posed a federated multi-view spectral clustering method that leverages similarity matrices to enable distributed spectral clustering. While this approach helps retain local struc- ture information, the transmission of full similarity matrices can lead excessive communication costs, especially for large-scale datasets.
and enhance privacy protection.
3. Methodology
3.1. Motivation
Federated Multi-View Clustering aims to alleviate the com- putational burden on individual clients by distributing the learning process across multiple nodes while preserving data privacy. Unlike traditional multi-view clustering ap- proaches, FMVC introduces significant communication overhead, which becomes critical bottleneck affecting its efficiency. The communication overhead is determined by two key factors: communication frequency, i.e., the num- ber of communication rounds, and communication band- width, i.e., the amount of data transmitted per round. Ex- isting FMVC methods generally transmit local variables immediately after each update, leading a communication frequency proportional to the number of optimization iter- ations. Regarding communication bandwidth, most meth- ods fall into three categories: transmission of embedded representations, similarity matrices, or clustering partition matrices. While embedded representations are more space- efficient than similarity matrices, they can directly expose local client data, posing risk of privacy leakage. Fur- thermore, existing FMVC methods are primarily designed for complete multi-view data and struggle to handle see- narios with missing views. To address these limitations, we propose an Efficient Federated Incomplete Multi- View Clustering (EFIMVC) framework that effectively balances communication efficiency, privacy preservation, and robust- ness to missing views
A third category of FMVC methods exchanges partition matrices, where each client transmits a clustering partition matrix of size n x k (with k as the number of clusters). Feng et al. (Feng et al., 2024a) integrated matrix factorization and miet k-manns to address the separation between feature extraction and clustering. Feng et al. (Feng et al., 2024b) further proposed tensor ietooiization-bssed FMVC framework to enhance multi-view data integration and im- prove clustering stability. Partition matrix-based methods often strike balance between privacy and communication efficiency, but they may still struggle with view inconsisten- cies and incomplete data.
Despite these advancements, existing FMVC methods suffer from high communication overhead, privacy risks due to the transmission of sensitive information, and poor handling of missing views. Addressing these challenges remains a key focus of federated multi-view clustering research.
2.2. Anchor-based Multi-view Clustering
To mitigate the computational complexity associated with large-scale multi-view clustering, anchor-based MVC meth- ods have been proposed (Wang et al., 2023; Yan et al., 2022; Zhang et al., 2023b). These methods construct a compact set of representative anchors to approximate the data structure, significantly reducing the cost of similarity computations (Liu et al., 2022; Zhang et al., 2023a).
3.2. Local Learning in Clients
To mitigate the high communication frequency in existing FMVC methods, we introduce novel framework that de- couples local optimization from global optimization. In our approach, both clients and the server maintain their respec- tive optimization objectives. Instead of transmitting updates at every iteration, communication occurs only after local optimization converges to a stable state, reducing unneces- sary transmissions. Additionally, to lower communication bandwidth, we design the transmitted variables as anchor graphs, where the view-specific encoding of these graphs safeguards client data privacy.
Traditional unchor-based MVC methods rely on sampling- based anchor selection strategies (Qiang et al., 2021; Shi et al., 2021; Yang et al., 2020). More recent approaches fo- cus on learning anchor representations to improve clustering quality (Liu et al., 2024; Ma et al., 2024; Wu et al., 2023; Qin et al., 2024). By replacing pairwise sample similari- ties with anchor-sample relationships, these methods reduce both storage and computational overhead, making them particularly well-suited for scalable clustering applications.
Specifically, given the data (()) E Rd. xn for the v-th view, the local objective function on the corresponding client is formulated as follows.
Unlike traditional MVC approaches that establish relation- ships among all samples, unchor-based methods optimize clustering by focusing only on anchor relationships. This facilitates efficient multi-view fusion and clustering while maintaining high accuracy and robustness. In the context of federated learning, integrating anchor-based clustering with FMVC can further reduce communication overhead
min A (
X (v) ZZ))
(1)
s.t. (Z))) (.)( 2 0,
where A (v) E Rd xm represents the anchor matrix, and
3

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Efficient Federated Incomplete Multi-View Clustering
Z(0) R is the incomplete anchor graph that encodes the relationships between anchors and the available sam- ple points. The column-sum constraint ensures that each sample can be expressed as a linear combination of all an- chors. Additionally, an index matrix G E (0, 1 nxx,, introduced to indicate the positions of available samples in missing views (Wang et al., 2022). Importantly Eq. (1) leverages only local single-view information.
By ensuring both row and column alignment, the accuracy of the fused information is guaranteed.
Additionally, inspired by manifold learning principles, we enforce structural consistency by incorporating anchor sim- ilarity constraints. Specifically, the similarity between an- chors in each view should be preserved when aligning them with the global anchor graph. This ensures that similar an- chors maintain consistent clustering structures across views. The local objective function in server is as follows,
To further guide the learning process with global informa- tion, we incorporate federated alignment term that en- forces consistency between local and global anchor graphs as follows,
V
min Σ 2.P
p( - Z 2Z))
p
(P(')) (5)
(5)
min A
X X (()))) A (1)Z(()))
s.t. Z 1 = 1, 2 0, (P()) T())) (.
+
P 2
i.
P(") =I.
+ pC) (o) ( G
(2)
Z T 1, z 2
From the perspective of anchor alignment, the first term ensures row-level alignment by matching the structural sim- ilarity between the unified and view-specific anchor graphs, while the second term enforces structure-level aligmment using anchor similarity.
where Z E R denotes the global anchor graph, and p(o) E Rm is an alignment matrix ensuring structural consistency across views. By enforcing dual alignment at both the anchor and sample levels with the global anchor graph Z, the learning of the local anchor graph (z)) is effectively guided.
3.4. Optimization
Unlike previous approaches that alternately optimize all vari- ables on both the client and server within the same frame- work, our method ensures that variables at one end are trans- mitted only after being optimized to their local optimum.
Once the local learning process is completed, each client computes an anchor similarity matrix ((v) E Rmx* based on the pairwise distances between anchor features. The element of (") at the i-th row and j-th column is calculated as follows:
To achieve this, we propose two alternating optimization algorithms to solve Eq. (2) and Eq. (5). In each iteration, we optimize one variable while keeping the others fixed at their values from the previous iteration.
(-
|||
[A(7-A A 20
$ = cxp
(3)
1.4.1. OPTIMIZATION IN THE U-TH CLIENTS
Finally, the learned anchor graph (0) and similarity matrix ((#) are transmitted to the server for global fusion.
Update A (o); Fixing (0)) Eq. (2) is transferred to the optimization problem related to A (v);
max (A (o) C()) (A (T) 2(A (v)) (D))) A
3.3. Global Fusion in Server
(6)
Upon receiving the anchor graphs from all clients, the server aggregates them construct a unified global anchor graph. However, due to independent learning processes across dif- ferent views, anchor misalignment naturally arises, neces- sitating an additional alignment mechanism. Too address this issue, we introduce an alignment matrix p(v) to ensure structural consistency between the global anchor graph and view-specific anchor graphs:
where ((v)
Z (Z (w))T D(v)
X ( (() (Z()), (()) GO (G()T
By taking
the derivative of Eq. (6) with respect to A (v) and setting it
to zero, we get the closed-form solution for (v) as follows:
A (v) D(e)
Update Z (e); Fixing A (0), We get the optimization problem
related (*) as follows:
V
min Σ 7.
P 1 ZG!)) Z (0) G(O F
(4)
min Tr ((Z()) (A (c) (AA))))(AA))
A (v) B()) (z)
T (Z) (())
S.L. 1= > 0, (P()) Tp()) 11 1,
Z(0)
-(((X()) T A (0) XXP(()) +X
where (v) extracts the columns corresponding to existing points in each view to participate in the anchor graph fusion.
s.t. T 1,2 20.
(8)

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Efficient Federated Incomplete Multi- Clustering
Algorithm 1 The proposed EFIMVC
Table 1. Datasets description.
Input:
Incomplete multi-view datasets (X(")) J==1 and the corresponding index matrix {G Jv=1 V local
Dataset
n
V
k
de 1, I...., V)
clients, the number of anchors m, the parameter X, 3, and the number of clusters k.
ProteinFold
694
12
27
271...
WebKB
1051
2
2
334/2949
Output: Clustering results.
100L
1600
100
64/64/64
CCV
6773
20
20/20/20
// Initialis zation Initialize A A ((), p(+) and Z;
YTFI0
38654
10
512/576/640/944
CIFAR1O
50000
10
512/1024/2048
while not converged do // Clients Optimization
MNIST
60000
3
10
64/342/1024
for v 1 do
while not converged do
To solve the optimization problem in Eq. (11), we reformu-
Update A (v) with Eq. (7);
late it into the following equivalent form:
Update (0) with Eq. (10);
Calculate (t)) according Eq. (3);
max Tr (B(P(c))T (Ymaa L(U) 'Z
Send (v) and S(e) server; Server Opt imi zation while not converged do for = V do
p(a)
+(P(v))T B() s.t. (P())) TP()) =I,
(12)
where Ymaz is the largest eigenvalue of (o), In the ap- pendix, we will provide details on how to solve Eq. (12) based on the approach outlined in (Zhang et al., 2020).
Update ( with Eq. (12); Update with Eq. (14);
for V 1 + V do
Update Z: Fixing P("), we have the following optimization problem:
L Send ((v) and Z to the v-th client.
// Final Results Generation
Perform k-means on the left singular vector of Z.
min 2
Σ
Tr ZZ T ZB (n) + 2,3 (P(")) (P()))L(())
P=1
s.t. T 1 = 1, 0. 2 TP())
To facilitate the identification of missing samples, we define an indicator vector ((v) as follows,
(13)
olo) = { 0,
1, j-th sample exists in the v-th view, else.
Next, we derive the optimization problem for the j-th col- umn of Z as follows:
(9)
min Z
HZ - Zr;
Note that in Eq. (8), each column of ()) is independent, and only the columns corresponding to existing samples need to be optimized. For all (()) = 1, we optimize Z! as follows:
Z
(14)
s.t. Z = 1, 2 20,
where H Σv= V
0 4 +33 ( (p)o)) rj
Σ ((Z TP())) ) Similarly, solve Eq. (14)
(p) (+)
(0) ..
min
with the quadratic programming package.
(10)
s.t.
(1) 11
Z (0) 2 0,
The optimization process of EFIMVC is presented in Al- gorithm 1. In the appendix, we will sequentially prove the convergence of the objective function on both the client and server. Additionally, we will demonstrate that, despite independent optimization each end, the overall objective function is still convergent.
(1) ( + AI, - where W (A
(x (X A
A(P(*)) J-j Eq. (10) is a standard quadratic programming problem, which we solve using existing software packages.
3.4.2. OPTIMIZATION SERVER
Update p(v); Fixing Z, p(e) in each view is independent,
4. Experiment
optimize it as follows:
4.1. Experimental Setup
min Tr ()(P()) (o) p ZZ -(P(w)) (()) p(e)
Employed Datasets. We conduct experiments on seven multi-view datasets: ProteinFold, WebKB, 100Leaves, CCV, YTF10, CIFAR1O, and MNIST, with detailed descriptions
s.t. (P())) Tpt)_ = I.
(11)
5

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Efficient Federated Incomplete Multi-Viee Clustering
Table Clustering performance comparison of four incomplete MVC methods and four FIMVC methods datasets. The best marked in bold and underlined. the second best is marked in bold.
Datasets
FIMVC SCBGL
DVSAI
DAQINT
FMVC
HFMVC
FMCSC
FedMVFPC
Proposed
ACC (%)
ProdeinFold
28.15
28.33
32.36
29.62
16.73
23.02
23.85
19.39
31.71
WebKB
91.51
75.21
68.64
78.09
81.78
57.64
58.27
75.70
90.64
100Leaves
47.12
47.00
53.73
52.15
10.24
35.09
47.97
15.94
72.88
CCV
19.23
19.33
20.98
19.14
16.24
20.27
17.62
20.04
YTFI0
77.80
80.55
78.38
80.27
42.19
17.69
47.26
84.95
Cifar 10
96.56
96.50
95.83
95.22
57.65
18.73
69.80
96.62
MNIST
98.70
98.28
98.64
98.59
56.18
60.30
63.68
98.66
NMI (%)
ProteinFold
36.22
36.15
39.95
36.75
19.05
32.05
32.96
21.59
40.33
WebKB
48.89
16.60
16.44
26.03
15.16
3.36
2.73
9.15
50.62
100Leaves
70.37
70.36
74.24
73.93
30.14
63.77
70.42
41.33
84.76
CCV
14.93
14.89
15.95
15.14
12.74
15.72
12.40
15.66
YTFI0
80.22
81.58
83.79
82.70
39.76
6.09
47.02
83.86
Ci
91.38
91.23
89.98
88.75
55.47
7.60
65.82
91.52
MNIST
96.17
95.26
95.95
95.79
53.21
58.90
60.89
96.04
Purity (%)
ProteinFold
33.67
33.85
37.01
34.87
19.07
27.63
33.14
22.44
37.95
WebKB
91.51
78.12
79.03
81.92
81.78
57.04
61.28
78.12
90.64
100Leaves
49.41
49.39
55.97
54.49
11.90
43.72
54.41
16.08
74.79
CCV
22.48
22.77
23.73
22.08
18.93
22.16
19.57
23.45
YTFI0
81.19
83.72
82.83
85.01
47.63
19.84
50.97
87.14
Cifar10
96.56
96.46
95.83
95.22
58.44
19.91
69.89
96.62
MNIST
98.70
98.28
98.64
98.59
60.09
68.81
64.22
98.66
Fscore (%)
ProteinFold
15.53
15.34
18.98
16.21
9.19
12.16
13.52
10.48
18.71
WebKB
88.66
69.02
64.38
74.34
79.99
58.62
59.11
71.44
86.80
100Leaves
31.77
31.68
38.48
37.60
2.56
19.21
33.74
6.68
61.84
CCV
11.27
11.21
12.08
11.01
10.26
11.45
11.46
11.79
YTF10
74.23
77.02
77.27
77.54
32.41
13.09
36.34
79.57
Cifar10
93.35
93.18
91.99
90.85
46.00
13.33
59.03
93.46
MNIST
97.44
96.63
97.30
97.19
45.88
50.73
48.67
97.36
provided in Table 1. Following the definition in (Wang et al., 2022), we generate nine versions of each dataset with missing rates increasing in 10% increments, ensuring that no sample entirely missing from views.
parameter settings from their corresponding literature and evaluate them on datasets with different missing rates, re- porting the final averaged results. Specifically, for federated multi-view clustering algorithms that cannot handle missing views, fill the missing entries with zeros before inputting the data. Additionally, for methods that obtain final results through k-means, we repeat the clustering process 20 times and report the average performance to mitigate the impact of initialization randomness.
Compared methods. Since no existing federated multi- view clustering methods specifically address the incomplete multi-view scenario, we compare EFIMVC with two cate- gories of baseline methods. The first includes incomplete multi-view clustering algorithms: FIMVC (Liu et al., 2022), SCBGL (Zhao et al., 2023), DSVAI (Yu et al., 2024a), and DAQINT (Yu al., 2024b). The second comprises feder- ated multi-view clustering methods: FMVC (Feng et al., 2024a), HFMVC (Jiang et al., 2024). FMCSC (Chen al., 2024), and FedMVFPC (Hu et al., 2023).
4.2. Performance Evaluation
We evaluate EFIMVC against eight state-of-the algo- rithms across seven datasets, as summarized in Table 2. The first four baselines are designed for incomplete multi-view clustering, while the latter four are tailored for federated learning. EFIMVC achieves competitive or superior results
Implementation details.
For all baselines, we follow the
6

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Efficient Federated Incomplete Multi- Multi-View Clustering
ProteinFold
WebKB
100Leaves
FIMVC
ACO
20
25
30
ACC
60
80
70
ACC
40
SCBGL
DVSAI
15
0.1
0.2
0.8
0.4
0.5
0.5
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.5
0.7
0.8
0.1
02
0.8
0.4
0.5
0.7
0.8
DAQINT
missing ratio
missing ratio
missing ratio
HFMVC
CCV
YTF10
MNIST
FMCSC
100
000
FedMVFPC
ACC
200
ACC
ACC
80
FMVC
Proposed
10
20
0.1
0.2
0.5
0.4
missing ratio
missing ratio
missing ratio
Figure The clustering performance curves of different methods six datasets under varying missing rates (ACC).
Objective Value
100
Objactive Value
Clert
Cieer
80
429
1000
A000%
428
10
15
20
25
30
0
10
15
20
25
30
Iteration Number
Iteration Number
Objecivv Value
Objective Value
801
110
130
Server
Server
100
125
(a) ProteinFold
(b) WebKB
30
Figure 4. Sensitivity analysis of À and 3 on ProteinFold and We- bKB, Others are displayed appendix.
lteration Number
Iteration Number
Objective Value
200
Objective Value
All
100
methods, which struggle to handle missing multi- view data (requiring zero-padding for missing val- ues during experiments), EFIMVC demonstrates su- perior clustering accuracy. On the ProteinFold and WebKB datasets, EFIMVC outperforms the second- best method by 32.9% and 19.7% in terms of ACC, respectively.
725
10
15
25
30
15
20
30
Iteration Number
Iteration Number
(a) ProteinFold
(b) WebKB
Figure 3. The objective function value curves of the client, server, overall optimization process with respect to the number of iterations.
In Figure 2, we compare the ACC curves of EFIMVC with other methods under varying missing view rates.
compared both sets of methods, especially in handling incomplete multi-view data.
EFIMVC consistently achieves superior results across all missing rates, maintaining stable accuracy even as the missing view rate increases. This highlights the robustness of EFIMVC in both incomplete data and federated learning scenarios.
Compared to state-of-the sate-offthheart incomplete MVC meth- ods designed for centralized storage of multi-view data, EFIMVC achieves comparable or even superior clus- tering performance. Specifically, on the 100Leaves and YTF10 datasets, EFIMVC outperforms the best incomplete MVC method by 35.6% and 5.5% in terms of ACC, respectively.
4.3. Ablation Study
To assess the effectiveness of key components in EFIMVC, we conduct an ablation study by removing (1) the regular- ization term by setting = 0, (2) the feature alignment term by setting O. and (3) anchor alignment by setting P(e)
Compared four federated multi-view clustering

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Efficient Federated Incomplete Multi-View Clustering
Table 3. Ablation study on different modules.
Datasets
ProdeinFold
WebKB
100Leaves
CCV
YTFI0
Cifar10
MNIST
ACC (%)
lambda=0
30.80
78.68
64.09
17.96
79.44
96.01
98.51
beta=0
30.85
90.36
68.12
14.85
78.42
96.54
98.64
P=
20.18
73.61
54.46
14.82
77.04
82.70
91.25
Proposed
31.71
90.64
72.88
20.04
84.95
96.62
98.66
NMI (%)
lambda=0
39.87
29.43
79.91
12.90
81.70
90.30
95.73
beta=0
40.17
49.78
82.10
10.77
79.71
91.39
95.99
P=I
26.96
22.66
74.86
10.96
77.88
73.91
88.10
Proposed
40.33
50.62
84.76
13.66
83.86
91.52
96.04
Purity (%)
lambda=0
37.79
82.34
66.66
21.48
84.50
96.01
98.51
beta=0
37.83
90.36
70.44
18.54
81.47
96.54
98.64
P=I
25.21
81.60
56.83
18.70
80.21
83.19
91.92
Proposed
37.95
90.64
74.79
23.45
87.14
96.62
98.66
Fscore (%)
lambda=0
17.81
73.21
50.67
10.34
74.94
92.28
97.07
beta=0
17.79
86.42
55.60
9.06
73.51
93.32
97.32
P=1
9.01
69.83
39.62
9.05
72.42
73.50
87.56
Proposed 18.71
86.80
61.84
11.79
79.57
93.46
97.36
as the identity matrix. As shown in Table 3, removing any module degrades clustering performance. Specifically, moving the regularization term results in suboptimal anchor graph learning, highlighting the importance of guidance by global anchor graph. Completely removing the anchor alignment mechanism results significant performance drop due to misaligned anchor graph fusion on the server. In contrast, omitting the feature alignment term leads more gradual decline in performance.
WebKB dataset, À 0.1 provides the optimal results, When À is fixed, the algorithm's performance is not significantly affected by changes in B.
5. Conclusion
In conclusion, we propose EFIMVC, a novel federated multi-view clustering method that effectively addresses com- munication overhead, privacy preservation, and incomplete multi-view data in federated learning. By leveraging feder- ated optimization framework and anchor graphs for privacy, EFIMVC achieves strong clustering performance while min- imizing communication costs. It also demonstrates robust performance in handling incomplete data, making it suitable for real-world applications. Experimental results validate the superiority EFIMVC over existing methods, offering practical solution for federated multi-view clustering.
4.4. Convergence Analysis
In Figure 3, we present the curves showing the objective function values on the client, on the server, and the overall objective function values iterations. All three objective function values monotonically decrease and converge to stable values within 30 iterations. Notably, we observe that the overall objective function con- verges more quickly than the ones on the client and server, indicating reduced communication overhead.
function of the number of
A Acknowledgement
This work is supported by the National Science Fund for Distinguished Young Scholars of China (No. 62325604), and the National Natural Science Foundation of China (No. 62476281 and 62276271).
4.5. Sensitivity Analysis
EFIMVC has two hyperparameters, and with search ranges of [0.001, 0.1, 1, 100). The performance of EFIMVC under different combinations of these hyperparameters are shown in Figure 4. Specifically, ProteinFold, setting À 0.001 yields the best clustering performance, while on the
8

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Efficient Federated Incomplete Multi- Vulti-View Clustering
Impact Statement
Jiang. X., Ma, Z., Fu, Y., Liao, Y., and Zhou, P. Heterogeneity- federated deep multi-view cluster- ing towards diverse feature representations, In Proceed- ings of the 32nd ACM International Conference on Multi- media, pp- 1184-9193, 2024.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which feel must be specifically highlighted here.
Langley, P. Crafting papers on machine learning. In Langley, P. (ed.), Proceedings of the 17th International Conference on Machine Learning (ICML 2000). pp. 1207-1216, Stan- ford, CA, 2000. Morgan Kaufmann.
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Efficient Federated Incomplete Multi-View Clustering
A. Appendix
A.I. Algorithm for Solving Eq. (12)
Define C Ymaa -(0, D= zz and H Z B(o) ZT, Eq. (12) can be rewrite as follows,
Tr ((P()) CP(2) (P()))H))
max plo)
(15)
s.t. (P(")) TP()) =I
Theorem A.1. Given Rmxx, ZZ is a positive semidefinite matrix.
Proof. For any vector IRm,, we have
x_ ZZZ
x =x
T
Z Z
Z Z 20
(16)
Since squares of real numbers are always non-negative, we have
T (ZZ x x=
x 2Z,) 20
(17)
Since x: (ZZ x 2 0 for all i, the matrix zz is positive semi-definite.
According (Nie al., 2014), given positive semidefinite matrices C and D the function s(P())
Tr (eppiiTTTp(Pp)) + (P(e))TIT H) is convex. The optimal solution of
f(p(t)) is equal to solve the fol- Ple))
lowing problem,
max Tr ((P()))TQ) pt),Q s.t. (P(v)) T II
(18)
where Q - f = 2CP(") + H. Eq. (18) is easy to solved by iteratively optimizing P(") and Q until converge.
A.2. Theoretical Analysis for Convergence
In this section, first analyse the convergence of the optimization process the client side, followed by the convergence analysis on the server side, and finally, we provide the overall convergence analysis of the algorithm.
First, the objective function of the e-th client is defined as follows:
To (A (0) (0)) x (() (z)) G + ) Z())
(19)
When solving Eq. (19), we iteratively optimize each variable while keep others fixed. The optimal variables in the t. iteration are defined A. (v) z!!). In the to iteration, we optimize A (v)) with fixed Z ( We have
(r) Te (1) 2 2 To (A 2
(20)
Then we optimize (v) with fixed (v) We have
To (A 2 To (A 2,01
(21)
Along with Eq. (20), we have
To (A))) 2.-0) 2 Jo
(1) (1)
A (
( (
(22)

---

Efficient Federated Incomplete Multi- Clustering
which indicates that the objective function of the u-th client is monotonically decreasing as the number of iterations increases. Moreover, since the objective function is lower-bounded by the optimization process the v-th client is guaranteed to converge.
Defining the objective function of the server as follows:
J. (z, p(u)) = Σ | - [)
1 (P())))) 1
(23)
Similar to the previous analysis, let Z₁, and ((.) be the optimal variables at the t. iteration. Then, we can derive that
J. Zz, P( 2 To 4...1.P(%1 ((.)
(24)
The objective function value also decreases monotonically with the number of iterations. Moreover, since Eq. (23) lower-bounded by 0, the optimization process on the server guaranteed converge.
Finally, we defined the overall function of EFIMVC by combining Eq. (19) and Eq. (23) follows,
To z)) (())
Σ p ZG z (b)) x X
AWZ
(25)
-9 (P()))) (P Z)
After the to-th iteration optimization, the optimal variables are defined as A Z 1, in the to + 1-th round, Z, and P( are transmitted from the server to the clients for the optimization of A (v) and Z(o)
Ze and P! According to Algorithm
(n) After the alternating optimization process on each client, to+1 and (0) are obtained. Based on Eq. (22), we have
t1+11
To
AA
2 Ze, ((v) - To
A (())
1o+1 tot1 Zi, P(.)) (v) (e)
(26)
= Jo
A
(v)
to Z - ttJ
[Alot (,+1 20.
Therefore,
To (A - Zt, (!
2 To
(A)
t1+ Ze,- P!())
(v)
(0)
(27)
Then the optimal A (w)
lot1 and Z (v)
iot1 are input to the server for optimizing Z and P(.) Based Eq. (24), we have
To AA()) (v)
1: 2 Zi,, p(()) To
Z (v)
(A
(v) Z((0
Z,o+1, P(.+ (tt11
1o+1
(28)
Js Ze,, to In [1,,1, (Z,,t,,((u)
2
fo+1
which means
To (A (0)
(0) 11 Ze, (1) 2o (A 2.t Z, Zr. p(o) p(o))
(29)
By combining Eq. (27) and Eq. (29), we derive that,
To A (v) Z100 Ze,, p(.)) 2 To (A 2(0) te (1,(())))) p(.))))
(30)
A.3. Supplementary Experiments
1. MORE IMPLEMENTATION DETAILS
The parameter settings in EFIMVC are grid search. For both À and 3, we search them in [0.001, 0.1, 1, 100). To evaluate all methods, we employ four widely used metrics, including Accuracy (ACC), Normalized Mutual Information (NMI), Purity, and Fscore. All experiments are conducted on a computer with Intel Core 19- 19-00XX0X CPU and 64G RAM.
12

---

Efficient Federated Incomplete Multi-View Clustering
A.3.2. DETAILS OF EMPLOYED DATASETS
ProteinFold : A biological dataset containing structural representations of protein folding processes.
WebKB 2: A text dataset collected from webpages four universities, where views correspond to content and citations.
100Leaves ?;
A leaf species classification dataset containing multi-view representations corresponding shape descriptor, fine scale margin and texture histogram.
CCV 4; A video dataset consisting different types of features extracted from frames, including SIFT, GIST, and deep features.
YTFI0 9: A subset of the YouTubeFaces dataset, containing facial videos with multiple feature extraction methods applied.
CIFARIO 6: well-known image dataset with different views extracted by ResNet18, ResNet50, and 1enseNet
MNIST 7: A handwritten digit dataset where views generated by different feature extractor.
A.3.3. DETAILS OF COMPARED METHODS
To evaluate the performance of EFIMVC, we compared it against eight state-of-the-an methods, categorized into two groups: incomplete multi-view clustering methods and federated multi-view clustering methods.
Incomplete multi-view clustering methods:
FIMVC (Liu et al., 2022): This method introduces view-independen anchors to enhance clustering efficiency while preserving multi-view consistency. By constructing an anchor graph rather than full pairwise graph, reduces computational complexity and scales well to large datasets.
SCBGL (Zhao et al., 2023): It uses bipartite graph learning to construct consensus anchor matrices, enabling effective feature alignment across views. A self-completion mechanism ensures robustness to missing views while maintaining low computational overhead.
DSVAI (Yu al., 2024a): It proposes diverse view-shared anchors with multiple dimensions and sizes to better represent multi-view data. A linear integration strategy ensures computational efficiency while improving clustering accuracy in large-scale scenarios.
DAQINT (Yu al., 2024b): This method introduces an adaptive weighting mechanism assign varying numbers of anchors per view, eliminating manual tuning. It improves the flexibility of anchor-based clustering while balancing computational complexity and clustering performance.
Federated multi-view clustering methods:
FMVC (Feng et al., 2024a): integrates matrix factorization and K-Means clustering within federated learning framework, enabling collaborative clustering without sharing data. The method preserves data privacy while maintaining strong clustering performance.
HFMVC (Jiang et al., 2024): This method addresses heterogeneity in federated multi-view clustering by employing contrastive learning and local-global model alignment. effectively adapts to both IID and non-IID data distributions, ensuring more stable clustering results.
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13

---

Efficient Federated Incomplete Multi-Vies Clustering
FMCSC (Chen al., 2024): It focuses on hybrid-view heterogeneity by leveraging contrastive learning align single-view and multi-view clients. A global-specific weighting aggregation strategy enhances consistency across distributed clients, improving clustering quality.
FedMVFPC (Hu al., 2023): This method extends fuzzy clustering into federated setting by introducing consensus prototype learning. It ensures stability in clustering performance across federated clients while maintaining privacy- preserving optimization.
A.3.4. CLUSTERING RESULTS ON MORE METRICS
Beyond the ACC results reported in the main paper, we present additional evaluation metrics including NMI, purity, and Fscore. As shown in Figures 5, 6, and 7, EFIMVC consistently achieves superior results across all datasets and missing rates. The improvements are particularly significant high-missing-rate scenarios, demonstrating the robustness of our approach in handling incomplete multi-view data.
ProteinFold
WebKB
100Leaves
80
FIMVC
NMI
NMI
NMI
80
SCBGL
20
40
DVSAI
10
0.1
0.2
0.3
0.4
0.5
06
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20
022
0.3
0.4
0.5
0.7
0.8
DAQINT
missing ratio
missing ratio
missing ratio
HFMVO
CCV
YTF10
MNIST
FMCSC
25
20
FedMVFPC
NMI
150
NMI
NMI
80
FMVC
10
Proposed
0.1
0.2
0.5
0.5
0.4
missing ratio
missing ratio
missing ratio
Figure The clustering performance eurves of different methods across datasets under varying missing rates (NMI).
ProteinFold
WebKB
100Leaves
100
FIMVC
Purity
Purity
80
Purity
30
604
SCBGL
20
DVSAI
DAQINT
missing ratio CCV
missing ratio
missing ratio
HFMVC
YTF10
MNIST
FMOSC
80
FedMVFPC
Purity
Purity
Purity
80
20
FMVC
Proposed
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
missing ratio
missing ratio
missing ratio
Figure 6. The clustering performance curves of different methods across six datasets under varying missing rates (Purity).
A.3.5. PARAMETER ANALYSIS ON MORE DATASETS
To further investigate the impact of hyperparameters, we analyse the performance of EFIMVC under varying values and 3 on more datasets. Figure illustrates how different parameter settings affect clustering performance across additional
14

---

Efficient Federated Incomplete Multi- Viel Clustering
ProteinFold
WebKB
100Leaves
FIMVC
Fscore
Fscore
Fscore
80
SCBGL
8
60
0.4
05
0.6
DAQINT
missing ratio CCV
missing ratio YTF10
missing ratio
HFMVC
MNIST
100
FMOSC
16:
80
Fscore
145
Fscore
60
Fscore
80
FedMVFPC
80
FMVC
Proposed
0.3
044
0.5
0.7
0.8
0.1
0.2
0.3
0.5
0.6
0.7
0.1
0.4
0.5
0.6
0.8
missing ratio
missing ratio
missing ratio
Figure 7. The clustering performance curves of different methods across six datasets under varying missing rates (Fscore).
(a) 100Leaves
(b) CCV
(c) YTFI0
(d) Cifar10
(c) MNIST
Figure Sensitivity analysis of and /3 on other datasets.
datasets, including 100Leaves, CCV, YTFIO, CIFARIO, and MNIST. The results indicate that while EFIMVC relatively stable to changes in 3, setting À too high too low negatively impact clustering accuracy. Dataset-speciffc tuning thus recommended for optimal results.
15


Reviews:
[{"review_id": "Yw5XBdfSf0", "reviewer": "Reviewer_JeXy", "summary": "This paper proposes an Efficient Federated Incomplete Multi-View Clustering (EFIMVC) method to reduce communication overhead, enhance privacy protection, and handle missing views effectively. It employs a localized optimization strategy to lower communication costs, utilizes view-specific and shared anchor graphs to improve privacy, and introduces a dual-anchor alignment mechanism to enhance graph fusion stability. Experimental results demonstrate that EFIMVC outperforms existing methods in clustering accuracy, communication efficiency, and privacy preservation, highlighting its advantages in federated incomplete multi-view clustering tasks.\n\n## update after rebuttal\nThanks for your careful response, and I consider the previous score reasonable and will keep the previous 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 thank Reviewer JeXy for the thorough and constructive review. We provide point-by-point responses to the questions raised as follows:**\n\n---\n\n**Q1:** It is recommended that all illustrations use vector graphics.\n\n**A1:** We sincerely appreciate your constructive suggestion. In the final version, we will convert all figures to vector graphics (e.g., PDF formats) to ensure optimal resolution and scalability.\n\n---\n\n**Q2:** Some of the data sets listed are not the highest results. Can you add relevant explanations?\n\n**A2:** We sincerely thank you for raising this critical point. We clarify that the first four methods in Table 2 (FIMVC, SCBGL, DVSAI, DAQINT) are state-of-the-art centralized incomplete multi-view clustering methods. While they achieve marginally higher performance on specific datasets, they fundamentally address centralized scenarios and **cannot handle distributed multi-view data with privacy constraints**. In contrast, our federated framework achieves comparable or superior performance to these centralized SOTA methods while operating under strict distributed data storage protocols. This demonstrates our method’s unique capability to balance clustering accuracy with federated learning requirements. We will emphasize this distinction in the final version.\n\n---\n\n**Q3:** Although the dual anchor point alignment mechanism improves the quality of graph fusion, its computational complexity is not analyzed in detail. If there are more anchor points, the computational overhead may increase. It is recommended to provide theoretical analysis or experimental results.\n\n**A3:** We sincerely appreciate the important technical concern. The computational complexity of the dual anchor alignment mechanism comes from optimizating the permutation matrix $\\mathbf{P}^{(v)}$ on the server, which is $\\mathcal{O}(m^3 + m^2n)$. Specifically, constructing matrix $\\mathbf{Q}$  requires $\\mathcal{O}(m^3 + m^2n)$ to process matrix multiplications. Solving $\\mathbf{P}^{(v)}$ by performing SVD decomposition on $\\mathbf{Q}$ requires $\\mathcal{O}(m^3)$. While increasing anchor points $m$ raises time costs, our method fundamentally avoids the prohibitive space complexity ($\\mathcal{O}(n^2)$) and time complexity ($\\mathcal{O}(n^3)$) of full-graph approaches. We acknowledge the reviewer's concern and will explore hierarchical anchor optimization to further enhance efficiency while maintaining performance.   \n\n---\n\n**Q4:** The data distribution from different perspectives may be quite different, and the selection of anchor points may directly affect the final clustering effect. The paper does not discuss how to ensure the robustness of anchor point selection.\n\n**A4:** We sincerely thank you for the insightful comment. To evaluate anchor robustness, we conducted ablation studies using three strategies:  \n1. $k$-means (default)  \n2. Random selection  \n3. Density-based sampling \n\nThe comparison results of different strategies are shown in below:\n \n|  **Datasets** | **ProteinFold** | **WebKB** | **100Leaves** |  **CCV**  | **Cifar10** |\n|:-------------:|:---------------:|:---------:|:-------------:|:---------:|:-----------:|\n|               |                 |    ACC    |               |           |             |\n|    $k$-means    |    **31.71**    | **90.64** |   **72.88**   | **20.04** |  **96.62**  |\n|     Random    |      30.83      |   76.48   |     69.27     |   15.53   |    96.18    |\n| Density-based |      30.99      |   79.63   |     69.63     |   15.53   |    96.13    |\n|               |                 |    NMI    |               |           |             |\n|    $k$-means    |    **40.33**    | **50.62** |   **84.76**   | **15.66** |  **91.52**  |\n|     Random    |       39.4      |   22.65   |     82.93     |   11.49   |    90.59    |\n| Density-based |       39.8      |   21.08   |     83.08     |   11.49   |    90.54    |\n|               |                 |   Purity  |               |           |             |\n|    $k$-means    |    **37.95**    | **90.64** |   **74.79**   | **23.45** |  **96.62**  |\n|     Random    |      36.87      |   81.81   |      71.3     |   19.22   |    96.18    |\n| Density-based |       37.1      |    80.5   |     71.61     |   19.36   |    96.13    |\n|               |                 |   Fscore  |               |           |             |\n|    $k$-means    |    **18.71**    |  **86.8** |   **61.84**   | **11.79** |  **93.46**  |\n|     Random    |        18       |   71.71   |     56.72     |    9.31   |    92.62    |\n| Density-based |      18.15      |   73.73   |     57.09     |    9.35   |    92.55    |\n| ||\n\nWhile $k$-means achieves the most stable performance, we acknowledge that advanced anchor initialization could further improve robustness. We will discuss this limitation and cite relevant techniques [1] in the final version.\n\n[1] Liu et al. Learn from View Correlation: An Anchor Enhancement Strategy for Multi-view Clustering. CVPR 2024.", "claims_and_evidence": "The main points of the paper are supported by convincing evidence. Extensive experiments on seven datasets demonstrate the superiority of the proposed method.", "methods_and_evaluation_criteria": "The proposed methods make sense for the problem. EFIMVC innovatively employs an anchor graph optimization strategy to reduce communication overhead and leverages local optimization to minimize data transmission, enhancing privacy protection. Additionally, the dual-anchor alignment mechanism ensures consistency between global and local anchors, thereby improving graph fusion quality. The experimental evaluation utilizes widely recognized multi-view clustering (MVC) benchmark datasets and state-of-the-art baseline methods to validate the effectiveness of the approach.", "theoretical_claims": "I checked the correctness of the proofs for theoretical claims, including the effectiveness of the method of decoupling local optimization from global optimization in theoretical analysis, including the optimization problem solving process of quadratic programming.", "experimental_designs_or_analyses": "I checked the validity of the experimental designs and analyses. Extensive experiments are conducted on multiple widely-used multi-view clustering (MVC) benchmark datasets, with results averaged over multiple runs to ensure statistical reliability. The experiments cover different missing-view scenarios, ablation studies, and parameter sensitivity analysis to comprehensively evaluate the proposed method. The issues are listed behind in the Weaknesses.", "relation_to_broader_scientific_literature": "The EFIMVC method first introduced anchor graph optimization and dual anchor alignment mechanism in the federated incomplete multi-view clustering problem. Based on the existing research on federated multi-view clustering, this method improves communication efficiency, privacy protection and missing view adaptability, filling the shortcomings of previous methods in these aspects.", "essential_references_not_discussed": "There are no related works that are not currently discussed in the paper.", "other_strengths_and_weaknesses": "This paper proposes an efficient federated incomplete multi-view clustering method (EFIMVC), which combines anchor graph optimization with a dual anchor alignment mechanism for the first time to reduce communication overhead, enhance privacy protection, and improve clustering performance in missing view scenarios. This method effectively reduces data transmission in federated learning while maintaining high clustering accuracy.\nThere are also some weaknesses：\n1. It is recommended that all illustrations use vector graphics.\n2. Some of the data sets listed are not the highest results. Can you add relevant explanations?\n3. Although the dual anchor point alignment mechanism improves the quality of graph fusion, its computational complexity is not analyzed in detail. If there are more anchor points, the computational overhead may increase. It is recommended to provide theoretical analysis or experimental results.\n4. The data distribution from different perspectives may be quite different, and the selection of anchor points may directly affect the final clustering effect. The paper does not discuss how to ensure the robustness of anchor point selection.", "other_comments_or_suggestions": "I would like to learn about the authors' response to the weaknesses listed above, which may give me a clearer perspective on the paper's contribution.", "questions_for_authors": "I would like to learn about the authors' response to the weaknesses listed above, which may give me a clearer perspective on the paper's contribution.", "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": "yWKUM68zjP", "reviewer": "Reviewer_9Soy", "summary": "Tha authors propose a novel federated incomplete multi-view clustering method named EFIMVC. By introducing localized optimization with anchor graphs and dual-alignment mechanisms, the propposed method reduce communication costs while preserving privacy. Experiments on seven datasets demonstrate the superiorty of EFIMVC.", "questions": "", "limitations": "", "rating": 5, "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 Reviewer 9Soy for the thorough and constructive review. We provide point-by-point responses to the questions raised as follows:**\n\n---\n\n**Q1:** The paper uses excessive mathematical symbols without proper definitions. For instance, $\\mathbf{L}$ in Eq. (13) is never explained.\n\n**A1:** We sincerely appreciate your feedback. The symbol $\\mathbf{L}^{(v)}$ in Eq. (13) denotes the Laplacian matrix derived from the anchor similarity matrix $\\mathbf{S}^{(v)}$ of the $v$-th view, where $\\mathbf{L}^{(v)} = \\mathbf{D}^{(v)} - \\mathbf{S}^{(v)}$ and $\\mathbf{D}^{(v)}$ is the degree matrix. We acknowledge the oversight in explicitly defining this notation and will comprehensively explain all mathematical symbols in Appendix to ensure full clarity in the final version.\n\n---\n\n**Q2:** The \"dual-anchor alignment\" concept remains vague. How does it differ from single-level alignment in [1]?\n\n[1] Align then Fusion: Generalized Large-scale Multi-view Clustering with Anchor Matching Correspondences. NeurIPS 2022.\n\n**A2:** We sincerely thank you for this insightful comparison. While [1] achieves alignment through sequential feature alignment and structural alignment, our dual-anchor alignment **unifies these two objectives** into a single optimization framework in Eq. (5). Specifically:  \n- Feature alignment (anchor embedding matching): \n$$\\left\\|\\left\\|\\mathbf{P}^{(v)}\\mathbf{Z}\\mathbf{G}^{(v)} - \\mathbf{Z}^{(v)}\\mathbf{G}^{(v)} \\right\\|\\right\\|_{\\mathbf{F}}^2$$  \n- Structural alignment (anchor graph topology preservation): \n$$\\operatorname{Tr}\\left((\\mathbf{P}^{(v)})^\\top\\mathbf{L}^{(v)}\\mathbf{P}^{(v)}(\\mathbf{Z}\\mathbf{Z}^\\top)\\right)$$ \n\nBesides, our method introduces **missing-view robustness** through the indicator matrix $\\mathbf{G}^{(v)}$, enabling alignment even when partial data observations are absent across views. This differs fundamentally from [1], which assumes complete data availability.\n\n---\n\n**Q3:** The missing view definition is ambiguous. Is it sample-level missing (some samples lack views) or feature-level missing (entire view channels unavailable)?\n\n**A3:** We sincerely thank you for highlighting the problem. Our work addresses **sample-level missing views**, where individual samples may lack specific view channels (e.g., a patient missing MRI data but having CT scans). Formally, given the indicator vector $r^{(i)} \n\\in \\mathbb{R}^{n_v}$ containing the index for $n_v$ existing samples for $v$-th view in sort, the indicator matrix $ \\mathbf{G}^{(v)} \\in \\lbrace 0,1 \\rbrace^{n \\times n_v} $ satisfies:  \n$$\n\\mathbf{G}^{(v)}{i,j} = \\begin{cases}\n1, & \\text{if the entry }  r^{(i)}{j}=i, \\\\\\\\\n0, & \\text{otherwise.}\n\\end{cases}\n$$\n\nwhere $\\mathbf{X}^{(v)}\\mathbf{G}^{(v)}$ denotes the sorted complete data matrix in the $v$-th view.\n\n---\n\n**Q4:** Table 2 shows empty results for FMVC on four datasets. Is this due to implementation errors or intentional omission?\n\n**A4:** We sincerely thank you for the question. The empty entries of FMVC in Table 2 stem from its prohibitive memory demands when handling large datasets. Specifically, FMVC constructs Laplacian matrices with size of  $n \\times n$, which resulted in an out-of-memory error when running large-scale datasets. We will give further explanation in the final version.", "claims_and_evidence": "Yes. The claims made in the submission are supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "Yes. The proposed methods make sense for the federal multi-view scenario.", "theoretical_claims": "Yes.The proofs are correct.", "experimental_designs_or_analyses": "Yes.", "relation_to_broader_scientific_literature": "EFIMVC is related to the federal multi-view methods.", "essential_references_not_discussed": "Related work are referenced in this paper.", "other_strengths_and_weaknesses": "The practical focus on incomplete view scenarios is valuable. The anchor graph communication strategy effectively balances efficiency and information preservation. The paper is well-written. While there are some issues need to be addressed:\nI. The paper uses excessive mathematical symbols without proper definitions. For instance, L in Eq.13 is never explained.\nII. The \"dual-anchor alignment\" concept remains vague. How does it differ from single-level alignment in [1]?\nIII. The missing view definition is ambiguous. Is it sample-level missing (some samples lack views) or feature-level missing (entire view channels unavailable)?\nIIII. Table 2 shows empty results for FMVC on four datasets. Is this due to implementation errors or intentional omission?\n[1] Align then Fusion: Generalized Large-scale Multi-view Clustering with Anchor Matching Correspondences. NeurIPS 2022.", "other_comments_or_suggestions": "See weakness.", "questions_for_authors": "See weakness.", "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": "VXajNAbDIe", "reviewer": "Reviewer_3S7F", "summary": "This paper proposes a novel framework called EFIMVC, addressing key challenges in federated multi-view clustering such as high communication overhead, limited privacy protection, and poor handling of missing views. EFIMVC introduces a localized optimization strategy that significantly reduces communication costs while ensuring theoretical convergence. It employs both view-specific and shared anchor graphs as communication variables to enhance privacy by avoiding the transmission of sensitive embeddings. The framework also features a dual-anchor alignment mechanism to mitigate anchor graph misalignment during graph fusion, improving clustering robustness.", "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 thank Reviewer 3S7F for the thorough and constructive review. We provide point-by-point responses to the questions raised as follows:**\n\n---\n\n**Q1:** The authors claim their method solves three key challenges (communication overhead, privacy preservation, incomplete views) but fail to explicitly demonstrate how each component of the framework addresses these issues in the method part.\n\n**A1:** We sincerely appreciate your question. Our framework explicitly addresses the three challenges through dedicated components:  \n1. Communication Overhead: By decoupling optimization variables into server-side and client-side, we significantly reduce the variable transmission costs inherent in conventional frameworks, where optimization is performed alternately between the server and clients.\n2. Privacy Preservation: The proposed framework employs anchor graphs as communication variables, avoiding the transmission of sensitive embeddings or sample-level similarity matrices, thereby reducing privacy risks.\n3. Missing-View Handling: We learn partial anchor graphs with available data on each client via Eq. (2), and integrates them into a consistent full anchor graph on server-side via Eq. (5).\n\n---\n\n**Q2:** The clustering performance does not demonstrate superiority. As shown in Table 2, EFIMVC underperforms state-of-the-art methods on ProteinFold, WebKB, CCV and MNIST datasets.\n\n**A2:** We sincerely thank you for the critical perspective. While centralized SOTA methods (FIMVC, SCBGL, DVSAI, DAQINT) achieve marginally higher accuracy on some datasets, they fundamentally violate federated constraints. In contrast, our federated framework achieves comparable or superior performance to these centralized SOTA methods while operating under strict distributed data storage protocols. This demonstrates our method’s unique capability to balance clustering accuracy with federated learning requirements. We will emphasize this distinction in the final version.\n\n---\n\n**Q3:** In experiments, the federated baselines perform poorly compared to centralized methods. Were these baselines adapted fairly to handle missing view?\n\n**A3:** We sincerely appreciate the comment. First, federated multi-view clustering methods inherently underperform centralized approaches because they cannot simultaneously access all view data. Second, since existing federated MVC methods lack the capability to handle missing multi-view data, we filled all missing values with zeros in our experiments. This also leads to slightly inferior performance compared to specialized missing MVC algorithms with built-in imputation mechanisms. Notably, as the first federated incomplete MVC method proposed, our approach ensures a fair experimental comparison by benchmarking against both state-of-the-art centralized missing MVC methods and existing federated MVC methods.\n\n---\n\n**Q4:** The excessive mathematical notation severely impacts readability. A notation table should be added.\n\n**A4:** We sincerely appreciate the constructive suggestion. We will add a notation table in the final version. Specially, the main used notations through our paper is summarized as follows:\n\n| Notation       | Meaning |\n|--------------|---------|\n| $\\mathbf{A}^{(v)}$  | Anchor matrix|\n| $\\mathbf{Z}^{(v)}$ | Anchor graph |\n| $\\mathbf{Z}$  | Consistent anchor graph    |\n| $\\mathbf{G}^{(v)}$   | Incomplete indicator matrix  |\n| $\\mathbf{P}^{(v)}$| Alignment matrix  |\n| $\\mathbf{S}^{(v)}$ | Anchor similarity matrix    |\n| $\\mathbf{L}^{(v)}$  | Laplacian matrix  |\n| ||\n\n\n---\n\n**Q5:** What motivated the specific construction strategy for anchor similarity matrix in Eq. (3)? Would alternative similarity measures like cosine distance yield different results?\n\n**A5:** We sincerely thank you for the insightful question. The anchor similarity matrix quantifies pairwise distances between all anchors, serving as the foundation for subsequent server-side anchor structure alignment. In Eq. (3), we compute the distance between each anchor pair using the ℓ2-norm (Euclidean distance), though this metric can be substituted with alternative methods (e.g., cosine similarity). To evaluate the impact of distance metrics, we replace the L2-norm with cosine similarity and compare the results with existing approaches, as shown in the table below.\n\n| **Datasets** | **ProteinFold** | **WebKB** | **100Leaves** |  **CCV**  | **Cifar10** |\n|:------------:|:---------------:|:---------:|:-------------:|:---------:|:-----------:|\n|              |                 |    ACC    |               |           |             |\n|    ℓ2-norm   |    **31.71**    | **90.64** |   **72.88**   | **20.04** |  **96.62**  |\n|    Cosine    |      31.45      |   90.44   |     70.23     |   15.17   |    96.39    |\n| ||\n\nFrom the experimental results, ℓ2-norm performs slightly better than cosine similarity. We will include this ablation experiment in the final version.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "The method is relatively applicable.", "theoretical_claims": "There is relevant theoretical verification.", "experimental_designs_or_analyses": "The experimental design and analysis in the paper are generally sound and well-justified. The authors have taken appropriate steps to validate the performance of EFIMVC across diverse datasets and conditions. However, further exploration of computational efficiency could provide additional insights into the efficiency of the method.", "relation_to_broader_scientific_literature": "The authors point out that existing FMVC methods still face challenges such as high communication overhead, limited privacy protection, and ineffective handling of missing views. These issues indeed exist in federated multi-view scenarios. To address the problem of limited privacy protection, the authors use anchor graphs as communication variables, employing both view-specific and shared anchor graphs to avoid the direct transmission of sensitive embeddings, thereby enhancing privacy protection. However, the authors do not provide detailed explanations on how the model handles missing data. Although large datasets were used and improvements in clustering performance were observed, the experimental section lacks analysis of time and space complexity and does not include experiments on time efficiency to validate its effectiveness.", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "Strengths: \nNovelty: The paper proposes a novel federated multi-view clustering framework, the introduction of a dual-anchor alignment mechanism to mitigate anchor graph misalignment during graph fusion is a unique contribution. \nSignificance: The authors' proposed local optimization mechanism enhances communication efficiency, enabling the model to handle large-scale datasets. Moreover, the use of anchor graphs for communication improves user privacy.\nClarity: The paper presents the methodology in a clear and structured manner, with detailed descriptions of the optimization process, algorithm design, and theoretical analysis.  This clarity makes it easier for readers to understand.\n\n\nWeaknesses: \n1.\tThe authors claim their method solves three key challenges (communication overhead, privacy preservation, incomplete views) but fail to explicitly demonstrate how each component of the framework addresses these issues in the method part.\n2.\tThe clustering performance does not demonstrate superiority. As shown in Table 2, EFIMVC underperforms state-of-the-art methods on ProteinFold, WebKB, CCV and MNIST datasets.\n3.\tIn experiments, the federated baselines perform poorly compared to centralized methods. Were these baselines adapted fairly to handle missing view?", "other_comments_or_suggestions": "The excessive mathematical notation severely impacts readability. A notation table should be added.", "questions_for_authors": "What motivated the specific construction strategy for anchor similarity matrix in Eq. (3)? Would alternative similarity measures like cosine distance yield different results?", "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": "uUKF051St6", "reviewer": "Reviewer_NJFx", "summary": "The work presents EFIMVC, an anchor-based federated MVC method employing view-specific/shared anchor graphs and alignment matrices. While the technical approach shows some novelty, fundamental design choices lack justification, and experimental comparisons appear skewed.", "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 Reviewer NJFx for the thorough and constructive review. We provide point-by-point responses to the questions raised as follows:**\n\n---\n\n**Q1:** Most anchor-based MVC methods enforce orthogonality constraints on anchor matrices to ensure diversity. The authors remove this constraint without justification. What performance changes would occur if orthogonality constraints were reinstated?\n\n**A1:** We sincerely appreciate your question. While many anchor-based methods enforce orthogonality to promote anchor diversity, we intentionally relax this constraint for two key reasons:\n\nWe aim to learn anchors that are representative of each category. However, in practice, the number of anchors typically exceeds the number of categories. Under such circumstances, it is unnecessary to enforce distinctness among all anchors - anchors from the same category may exhibit similarity. Imposing strict orthogonality constraints would be overly restrictive for this purpose.\n\nBesides, our ablation studies as follows show that removing orthogonality constraints actually improves clustering accuracy across all datasets, likely because it allows for more flexible anchor representations that better capture relationships in partial observation scenarios.\n\n| **Datasets** | **ProteinFold** | **WebKB** | **100Leaves** |  **CCV**  | **Cifar10** |\n|:------------:|:---------------:|:---------:|:-------------:|:---------:|:-----------:|\n|              |                 |    ACC    |               |           |             |\n|     Ours     |    **31.71**    | **90.64** |   **72.88**   | **20.04** |  **96.62**  |\n|  Orthogonal  |      29.39      |   71.74   |     61.85     |   15.47   |    95.09    |\n|||\n\n---\n\n**Q2:** Previous methods typically apply k-means directly on learned embeddings. The choice to cluster left singular vectors of $\\mathbf{Z}$ in Algorithm 1 lacks theoretical justification. Why not use standard spectral clustering?\n\n**A2:** We sincerely thank you for the problem. Standard spectral clustering can only operate on a complete $n\\times n$ similarity matrix and cannot directly process the anchor graph $\\mathbf{Z}$. According to [1], $\\mathbf{Z}^\\top \\mathbf{Z}$ can be interpreted as reconstructing the full similarity matrix from the anchor graph $\\mathbf{Z}$. Notably, performing $k$-means on the right singular vectors of $\\mathbf{Z}$ is theoretically equivalent to applying standard spectral clustering to $\\mathbf{Z}^\\top \\mathbf{Z}$.\n\n[1] Kang et al. Large-scale multi-view subspace clustering in linear time. AAAI 2020.\n\n---\n\n**Q3:** The huge performance gaps between the first four methods and the remaining methods in Table 2 suggest unfair experimental settings. Were all methods given equal hyperparameter tuning efforts?\n\n**A3:** We sincerely thank you for the question. The first four methods evaluated in Table 2 are centralized incomplete multi-view clustering algorithms. Compared to the subsequent four federated MVC methods, these centralized approaches hold inherent advantages in terms of full data accessibility and built-in mechanisms for handling missing values, thereby achieving superior clustering performance on incomplete multi-view datasets.\n\nIn contrast, our proposed method not only processes distributed multi-view data but also incorporates a dedicated incomplete data handling mechanism. As a result, it achieves comparable performance to state-of-the-art centralized incomplete MVC algorithms while significantly outperforming existing federated MVC methods.\n\nBesides, for all baseline methods, we strictly followed the parameter configurations reported in their original papers. Notably, for federated MVC methods, all missing values were imputed with zeros to ensure a fair comparison. We will add these implementation details to the final version.\n\n---\n\n**Q4:** Existing MVC methods optimize client/server variables under a unified objective to ensure convergence. How does EFIMVC guarantee convergence with separate client/server objectives?\n\n**A4:** We sincerely appreciate the comment. In contrast to conventional approaches that optimize server and client variables under a unified objective function, we propose a decoupled optimization framework that separates these two components. This innovation effectively reduces the communication overhead caused by frequent interactions. We further provide both theoretical and experimental convergence analyses for the decoupled objectives relative to the global objective function.\n\nSpecifically, Figure 3 illustrates the monotonic decrease of objective values (for server-side, client-side, and global objectives) with increasing iterations, demonstrating their eventual convergence to stable values. Additionally, in Appendix A.2, we present a rigorous theoretical analysis of convergence properties for each component.", "claims_and_evidence": "The clustering performance does not demonstrate superiority.", "methods_and_evaluation_criteria": "The application of anchor graphs in federated settings is novel. The computational efficiency through anchor sampling is practical.", "theoretical_claims": "Yes.", "experimental_designs_or_analyses": "I have doubts about the fairness of setting different comparison methods.", "relation_to_broader_scientific_literature": "Based on incomplete multi-view clustering and federal learning, this paper presents a new approach to handle federal incomplete multi-view data.", "essential_references_not_discussed": "None.", "other_strengths_and_weaknesses": "Strengths\nThe application of anchor graphs in federated settings is novel. The computational efficiency through anchor sampling is practical.\n\nWeaknesses\n1. Most anchor-based MVC methods enforce orthogonality constraints on anchor matrices to ensure diversity. The authors remove this constraint without justification. What performance changes would occur if orthogonality constraints were reinstated?\n2. Previous methods typically apply k-means directly on learned embeddings. The choice to cluster left singular vectors of Z in Algorithm 1 lacks theoretical justification. Why not use standard spectral clustering?\n3. The huge performance gaps between the first four methods and the remaining methods in Table 2 suggest unfair experimental settings. Were all methods given equal hyperparameter tuning efforts?", "other_comments_or_suggestions": "None.", "questions_for_authors": "Existing MVC methods optimize client/server variables under a unified objective to ensure convergence. How does EFIMVC guarantee convergence with separate client/server objectives?", "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, all reviewers agreed to accept this paper. To overcome the problems of excessive communication overhead, insufficient privacy protection, and inadequate handling of missing views, this paper proposes Efficient Federated Incomplete Multi-View Clustering (EFIMVC) that introduces a localized optimization strategy to significantly reduce communication costs while ensuring theoretical convergence. The paper is well-written. The incomplete view scenarios are valuable.
Decision: Accept (poster)