Learning from Disjoint Views: A Contrastive Prototype Matching Network for Fully Incomplete Multi-View Clustering
Authors: Yiming Wang
Qun Li
Dongxia Chang
Jie Wen
Hua Dai
Fu Xiao
Yao Zhao
Venue: NeurIPS 2025 poster ()
Keywords: multi-view learning
deep clustering
fully incomplete information
Primary area: general_machine_learning

Abstract: Multi-view clustering aims to enhance clustering performance by leveraging information from diverse sources. However, its practical application is often hindered by a barrier: the lack of correspondences across views. This paper focuses on the understudied problem of fully incomplete multi-view clustering (FIMC), a scenario where existing methods fail due to their reliance on partial alignment. To address this problem, we introduce the Contrastive Prototype Matching Network (CPMN), a novel framework that establishes a new paradigm for cross-view alignment based on matching high-level categorical structures. Instead of aligning individual instances, CPMN performs a more robust cluster prototype alignment. CPMN first employs a correspondence-free graph contrastive learning approach, leveraging mutual $k$-nearest neighbors (MNN) to uncover intrinsic data structures and establish initial prototypes from entirely unpaired views. Building on the prototypes, we introduce a cross-view prototype graph matching stage to resolve category misalignment and forge a unified clustering structure. Finally, guided by this alignment, we devise a prototype-aware contrastive learning mechanism to promote semantic consistency, replacing the reliance on the initial MNN-based structural similarity. Extensive experiments on benchmark datasets demonstrate that our method significantly outperforms various baselines and ablation variants, validating its effectiveness.

Learning from Disjoint Views: A Contrastive Prototype Matching Network for Fully Incomplete Multi-View Clustering
Yiming Wang 1.2
Qun Li
Dongxia Chang
Jie Wen
Hua Dai Fu 22.0 Yao Zhao
School of Computer Science, Nanjing University of Posts and Telecommunications State Key Laboratory of Tibetan Intelligence, Nanjing University of Posts and Telecommunications $Institute of Information Science, Beijing Jiaotong University 'Beijing Key Laboratory of Advanced Information Science and Network Technology 'School of Computer Science and Technology, Harbin Institute of Technology ymvang@njupt. edu. en, liqun@njupt edw.eenunpp..uuu.......m en, cn,
dxchang@bjtu edu. en, preien. com, daihua@njup wpp..du.....m edu. cn, xiaof@njupt.... edu. cn, rzhao@bjtu.edu.com edu.cn
Abstract
Multi-view clustering aims to enhance clustering performance by leveraging infor- mation from diverse sources. However, its practical application is often hindered by a barrier: the lack of correspondences across views. This paper focuses on the understudied problem of fully incomplete multi-view clustering (FIMC), a scenario where existing methods fail due to their reliance on partial alignment. To address this problem, we introduce the Contrastive Prototype Matching Net- work (CPMN), novel framework that establishes a new paradigm for cross-view alignment based on matching high-level categorical structures. Instead of aligning individual instances, CPMN performs more robust cluster prototype alignment. CPMN first employs correspondence-free graph contrastive learning approach, leveraging mutual k-nearest neighbors (MNN) to uncover intrinsic data structures and establish initial prototypes from entirely unpaired views. Building on the prototypes, introduce cross view prototype graph matching stage resolve category misalignment and forge a unified clustering structure. Finally, guided by this alignment, devise prototype-aware contrastive learning mechanism promote semantic consistency, replacing the reliance on the initial MNN-based structural similarity. Extensive experiments benchmark datasets demonstrate that our method significantly outperforms various baselines and ablation variants, validating its effectiveness.
1 Introduction
Over the recent years, the rapid increase in multi-view data has made effective analysis urgent necessity (I] [5]. Multi-view clustering, which seeks to uncover underlying data relationships by partitioning instances into distinct categories without supervision, has emerged prominent solution. While these algorithms have advanced significantly and are widely applied in applications like recommendation systems and multimedia analysis 226 38
29 most existing algorithms heavily rely on the assumption of complete multi-view information
37
33 However, in practice, is
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Partially Missing
Partially inaliigeed
Fully Missing
Felly Unlligned
+
0.1
0.5
0.5
0.2 0.3
View
Protetype Grapli Matchingg
Iniial Chosering
Clustering
(a) Partially Incomplete Multi-view Data
(b) Fully Incomplete Multi-view Data
(c) Our Key Idea
Figure Various incomplete multi-view data and our key idea. Without loss of generality, data from two views are presented and different shapes indicate distinct categories. The gray lines denote the availability cross-view correspondences. The blank shapes and the dashed lines with question marks represent the missing instances and the missing correspondences between views, respectively. To achieve unified clustering model first learns the initial cluster prototypes of
example. In the figure, different colors represent different views,
for multi-vise viet data without correspondence, each view and perform graph matching on the prototypes. Subsequently, the instances are assigned to the aligned prototypes to obtain the final clustering results.
common for only partial data be collected or transmitted due to sensor failure, varying acquisition costs, or privacy concerns, making the assumption of data completeness difficult to satisfy.
To address the issue of incomplete data, many efforts have been made explore ways of understanding multi-view data from partially incomplete information (Figure Ta), which is referred to as partially incomplete multi-view clustering (PIMC). The mechanism of PIMC lies in leveraging available partial cross-view correspondences to establish informative priors for learning. Two principal approaches have arisen based on the differing conditions of data incompleteness. For multi-view data with partially missing views, existing methods attempt to exploit known cross-view correspondences learn shared structures and recover missing information in the latent space [I5]] Alternatively, for partially aligned multi-view data, existing approaches aim to learn optimal transformations or permutation matrices that align the different view-specific spaces, establishing links between
matching views (35 28).
While these methods successfully mitigate the impact of partially incomplete information, their effectiveness fundamentally relies on the availability of at least partial cross-view information or alignment, which often difficult to guarantce [4]. many challenging real-world scenarios, data from different views is collected, processed, and stored entirely separately. Due to data heterogeneity, privacy regulations,
the nature of data acquisition, establishing correspondences even for small subset of instances can be infeasible. This leads to the critical problem of fully incomplete multi-view data, where instances are characterized by data from only one view, and no cross-view correspondences are known a priori (Figure Ib). An example is in clinical diagnostics, where patients may undergo only one type of pathological examination, resulting single-view information with no link between patients across different test types. Tackling this scenario requires learning shared cluster structures without any correspondences between views.
The Fully Incomplete Multi-view Clustering (FIMC) presents significant algorithmic challenges compared to PIMC. Unlike PIMC, where known correspondences provide direct guidance for imputation or alignment, the fully incomplete scenario lacks cross-view anchors that could guide representation alignment. Consequently, imputation approaches based on cross-view correspondences are inapplicable, and alignment methods relying paired instances cannot be initialized or directly learned. Recently, a limited number of pioneering studies have started to tackle the FIMC challenge. Notably, SMILE 41 focuses on learning semantic invariant representations for FIMC. This approach effectively mitigates the absence of correspondences by ensuring that instances belonging to same underlying cluster have similar representations regardless of their view. However, this approach assumes that semantic distributions are strictly invariant across views, which may fail under noisy views or class imbalance, leading biased alignment. This motivates the exploration of methods

---

that explicitly handle the alignment of cluster prototypes and utilize category-level information for representation refmement once initial cluster structures emerge.
This paper proposes the novel Contrastive Prototype Matching Network (CPMN) to introduce new paradigm of structure-level alignment address FIMC. Instead of aligning instances enforcing rigid distributional invariance, CPMN operates at a higher level of abstraction by aligning robust categorical prototypes ( (Figure Icl. Our approach first employs correspondence- cross-view graph contrastive learning strategy, utilizing mutual k-nearest neighbors (MNN) to learn initial representations and generate view-specific prototypes via K-means. Crucially, we then explicitly bridge the view-specific cluster structures by introducing a samilarity-basedr prototype graph matching to find the optimal mapping between these initial prototypes. Finally, CPMN refines the representations and prototypes through prototype contrastive learning mechanism, which leverages the established prototype correspondences and category information to contrast instances against their matched prototypes. The key contributions of our work include:
We propose a novel framework, Contrastive Prototype Matching Network (CPMN), designed to address the challenging fully incomplete multi-view clustering problem where no cross- view correspondences exist.
We introduce a two-stage contrastive learning approach: an initial correspondence-free graph contrastive learning phase based on cross-view viee MNN for structural alignment, followed by a prototype contrastive learning phase that utilizes category-leved information derived from matched prototypes for semantic refinement.
We incorporate an explicit prototype graph matching strategy to construct a bipartite graph between view-specific prototypes and find the optimal mapping between prototypes based on their feature similarity.
2 Related Works
Before introducing the proposed CPMN, we briefly review the related partially missing multi-view clustering and partially aligned multi-view clustering.
Partially Missing Multi-view Clustering (PMMC) aims to learn unified cluster assignments from multi-source data where some views are partially missing for certain instances. Among the methods that broadly employ either conventional shallow models 227 [8] or deep neural networks (DNN) 30, D. our attention here is restricted to the DNN-based approaches. Owing to the capability of the autoencoder (AE) to handle missing data through feature reconstruction, prevailing methods generally adopt AE as their backbone. Some approaches combine AE with graph information to mitigate the shortcomings of structural information mining in AE, For example, SDIMC-net (31 combines graph embedding strategies to capture the high-level features and local structure of each view. Likewise, CASEN [34] performs adaptive graph convolution on the reconstructed multi-view data to effectively extract the data structure. Some approaches introduce contrastive learning g 2 to learn shared representation that is robust to view missingness. DCP [15] performs data recovery and consistency learning simultaneously through dual contrastive prediction. Introducing deep subspace learning, PVC-SSN 4 employs contrastive learning to obtain more discriminative and consistent subspace representations. DCMVSC [40] combines contrastive learning and Cauchy- Schwarz divergence to propose new multi-view deep subspace clustering approach. While existing approaches demonstrate improved robustness to incomplete data, their dependence on at least partial cross-view correspondences persists as a limitation, particularly scenarios without alignment.
Partially Aligned Multi-view Clustering (PAMC) addresses the critical challenges of view misalign- ment and unknown correspondences caused by asynchronous data acquisition in multi-view clustering, Existing methods can be broadly classified into two categories. The first category focuses on explicit alignment learning, while the second category focuses on robust representation learning without explicit alignment. As a pioneering study, PVC [10] addresses the partial alignment problem by proposing differentiable Hungarian network to find correspondences between two views. Distinctly, EGPVC 42) employs Dykstra's 's cyclic constraint projection algorithm for the same purpose. How- ever, explicit instance-level alignment such methods is sometimes difficult to achieve and is overly restrictive for clustering tasks. To learn robust representation without explicit alignment, MvCLN [36] devises a noise-robust contrastive loss to reduce the impact of false negative pairs on aligning data and representation learning. SiMVC (25) completely avoids explicit representation alignment
3

---

Correspondence-Fes Graph Contrastive Learning
Encoder
Clustering
Stractural Consistency
Pull
Cross view
Decoder
Purh
Crosy View
Prototypes
Mutual K-WW
Biportite Graph
Incomplete Information
Zo
Neighbors
Matching
Prototypes
Encodar
Intra-View Prototypes
DOA ABO
Semantic Consistency
Clustering
Pull
Pull
XLO
Mathing
Decoder
Push
Prototypes
oo
Backbone
Prototype Graph Matching
Prototype Contrastive Learning
Figure 2: The framework of the proposed CPMN.
and instead uses learned linear combinations for view prioritization. The above methods achieve expected performance, but their alignment processes, which are often applicable only to two views or necessitate partial alignment information, consequently limit their broader applicability.
Method
In this section, we elaborate on the proposed Contrastive Prototype Matching network (CPMN) for learning unified clustering partition from fully incomplete multi-view data. As illustrated Fig. CPMN consists of three novel modules, namely correspondence-free graph contrastive learning, prototype graph matching, and prototype contrastive learning, which will detailed in Sec. 3.1 3.3
In fully incomplete multi-view clustering, paired information across views is absent. That is, all instances have features from only one view, the correspondences between views are completely unknown. Formally, given fully incomplete multi-view dataset X' (X(")) /==1 with N instances
[e) in V views. (v) = {-1 ...., N E NNxx, denotes the feature matrix in the v-th view, where indicator matrix W E {0, 1J to indicate the completeness of views. where W = 1 if instance I; exists in the v-th view, and W., 0 otherwise. Thus, for any instance I; of fully incomplete dataset, ΣV W., = 1. For datasets without known correspondences, an indicator vector U E {0, 1] is used record the aligned instances, where U, means the i-th instance is aligned in all views, otherwise Ug = 0. Thus, for a fully incomplete dataset, U. = 0 for all E [1, N]. Our goal is to partition these N instances into C' clusters.
d, is the feature dimension. For instances with only view, we introduce
3.1 Correspondence--Fre Graph Contrastive Learning
To effectively address the challenges of FIMC, the initial crucial step in our CPMN is to learn latent representations for each view independently, while simultaneously encouraging cross-view consistency without relying on paired data. This stage, termed correspondence- free graph contrastive learning, is designed to uncover underlying structural similarities across views. It achieves this by first reconstructing individual view data to preserve view-specific information, and then employing a novel graph-based contrastive learning strategy promote coherence between the learned view-specific representations, thereby laying foundation for subsequent prototype generation and matching.
A key component for learning these initial view-specific representations is the foundational backbone network: view-specific autoencoders. For each view v, the architecture comprises an encoder E, Rdd + Rd: and corresponding decoder D. Rdd Rd. The encoder maps the input data x a low-dimensional latent representation 2! F,, (a: (e)) ). and the decoder attempts to reconstruct the original input ((()) D.(2,))) The model is trained by minimizing the weighted

---

reconstruction error for observed instances in each view, formulated as:
LREC = ΣΣ We - -
While view-specific autoencoders can capture latent features within individual views, they do not inherently model cross-view relationships, resulting in divergent latent spaces that impede view alignment. Prevailing cross-view contrastive learning in multi-view clustering typically addresses this using cross-view instance pairs [16 6 [22]. However, the absence of view correspondences in FIMC renders such pairwise instance selection infeasible. To overcome this limitation, we pro- pose a correspondence-fiee graph contrastive learning strategy based on mutual k-nearest neighbors (MNN), which establishes pseudo-alignment through feature affinity without relying on prior cor- respondences. To learn discriminative representations while simultaneously mitigating cross-view discrepancies, CPMN involves the separate construction of intra- view and cross-view MNN graphs, which subsequently guide the establishment of positive pairs.
For intra-view consistency, positive pairs are identified based on the MNN criterion applied the latent representations. Specifically, a pair of representations (z. : 22)))
(0)) from the same view v is
designated as positive if =/") is found among the k-nearest neighbors of 2 and conversely, 2;
also present among the k-nearest neighbors of (v) All other pairs within this view are treated as negative pairs. To quantify the affinity between these pairs, cosine similarity is utilized:
(2) TT (0))
5 sim
(0))
1
The objective is to pull together the representations of connected samples the graph while pushing apart unconnected ones. Thus, the loss function can be formulated
exp(S)/ /T)
L = - Σ
log
(3)
Exe exp /T)
jEP(
where p(()) is the set of indices of instances forming positive pairs with 2. within view v, and is the temperature parameter.
Complementing the intra-view learning, cross-view positive pairs are established between different views, enabling alignment without correspondences. Considering a two-view example, positive
(1a)) are similarly established if they are MNNs of each other across views U. and Ub. All other pairings between these views are treated negative pairs. Cosine similarity is
pairs (2) (Ma) .2j
again employed to measure the similarity, denoted as Sfya = sim(z; (va) ((va)). Cross-view graph contrastive learning aims uncover and align latent structures, thereby achieving partial
((m) ,2
representation consistency despite the absence of correspondence. The loss function takes a similar form the single-view contrastive loss:
exp(S ((Ua))))))) (T) log
(Ma CGL
L
E
(4)
p ps)
Σn exp((S(a.00) (T)
(va.))))))
where p( the set of indices of instances from view ip forming positive pairs with (va)
The overall objective for this initial stage of correspondence-free graph contrastive learning, denoted as LCFGe, integrates the aforementioned losses:
LEFGC = LREE + MLG., LGI.
Σ
L
+
Σ 2/a
Σ
L (V))
CGL
(5)
2b
where À is trade-off parameter between the two losses.
Following the representation learning guided by LCFGC, initial view-specific cluster structures are derived. Specifically, K-Means applied to the latent representations (()) to obtain preliminary clustering assignments and set of prototypes ((v) e CCx:, These prototypes are crucial for the subsequent graph matching.
5

---

3.2 Prototype Graph Matching
Following the correspondence-freee contrastive learning, we successfully obtain view-specific repre- sentations and initial cluster prototypes for each view. However, these prototypes are independently derived and thus lack explicit cross-view correspondences. To bridge this gap, we devise a prototype graph matching strategy establish correspondence to enable -vew learning and fusion.
To establish an alignment between the independently derived sets of prototypes from different views (e.g., view Va and view vb), we formulate this challenge a principled optimization problem, specifically the classic Linear Assignment Problem (LAP),, which can be modeled via bipartite graph matching. In our model, one set of nodes in the bipartite graph consists of the C' prototypes from (va)) view Va. denoted ((v.)) {[]"")) ...... CC }. and the other set comprises the C prototypes from view
(1s)) (6b) ..... CC J. An edge between prototype ("aa and prototype (vs) represents potential correspondence, and the core task is to find the most plausible one-to-one mapping between these two sets.
Us. C(en) {c(m))
To quantify the suitability of each potential match, we construct cost matrix (M RCCC, where M((a))) represents the cost of matching the i-th prototype from view Vas with the j-th
prototype from view tb. This cost is based on the dissimilarity between prototypes, which is formulated as:
(c"²)²
Si 59 cg = 1
(6)
exp(sim(c;
(06) (va) coj
where cf- denotes the i-th prototype from view Va.
The goal is to find an optimal permutation of indices, π C(va) - C(ma), that establishes a one-to-one mapping. This mapping assigns each prototype ((e)) in view vo to unique prototype (x() (vv) in view
Ub such that the cumulative cost of all matches is minimized. This objective can be expressed as:
min
Mi,(0)
This formulation guarantees that the problem solvable in polynomial time. We find the globally optimal solution using the efficient Hungarian algorithm [13] The output of the algorithm is the optimal matching, providing a mapping from the prototype indices of view Va to those of view es.
The established correspondence between prototypes creates a vital bridge for transferring clustering information across views. This enables us incorporate cross-view category information into contrastive learning, using the category information in one view to guide the clustering in another.
3.3 Prototype Contrastive Learning
Leveraging the globally optimal prototype alignment, this stage transitions the learning objective from structure discovery to semantic refinement. utilizes the matched prototypes as robust categorical anchors refine both representations and prototypes. By contrasting instances with these anchors. this module elevates the alignment objective from the initial MNN-based structural similarity to higher-order, globally consistent semantic alignment in the latent space. Additionally, for dynamic updates to cluster assignments and prototypes, a learnable clustering layer is used to replace the previous K-means methodology.
This prototype contrastive learning leverages the prototype mapping π C(va) - ((vs) established previously to guide representation refinement. For given representation 2 (vo). let be the index of the prototype cf(a)) to which it is assigned within view ua- The core idea is to encourage (va), to be
simultancously similar to its assigned prototype (va) and to the corresponding prototype in view tb.

---

(v6) "b))'
This objective is realized through two complementary loss components, defined as:
exp(Sctf (0) /T)
SPL
Σ log
(8)
Ee exp(Se /T)
exp(Sec) (
(Mastt)) /T)
L Le
Σ log
(9)
>
exp(Scto (Ve. /T)
Here, for instance 2 the index j in the numerators Self and Sc (va.")) refers to its assigned prototype index for the positive term. Thus, L promotes the proximity of each representation ((")
to its assigned prototype (e) within view Concurrently, I (2)..)) fosters alignment by encouraging "j
(Pa) from view Vo be closer the cross-view corresponding prototype Cx()
(1x) in view vg. The terms
Sej (e) = sim(z? (v) ( and Seij (c(2))))) = sim(=; (Ma) (vs)
((()) represent the cosine similarity between
representations and prototypes, within or across views respectively.
To further enhance cluster coherence and embedding discriminability. self- seff-supervision strategy
inspired by 77 integrated within the learnable clustering layers. For each instance 2((") 9sk denotes
(0)
(a) which is computed using the Student's 's t-distribution 20 as:
its soft assignment to prototypes Ck
(1 || 11 1
(v) Pik
(10)
Σj= || 1
(v) Subsequently, an auxiliary target distribution Pik is formulated by sharpening like as:
(v)
(1) (g 9zk
Pik
(11)
Σn 11)
(2/
The clustering refinement is then driven by minimizing the Kullback-Leibler (KL) divergence between the current soft assignment distribution ((1) and the target distribution p(v) for each view:
LCLU Ex. (P(
(12)
where p(d) and O) are the target distribution and current soft assignment vectors for instance 2; respectively, and DxL. denotes the KL divergence.
(v)
The overall optimization objective for the prototype contrastive learning stage is weighted sum of the clustering loss and the prototype contrastive losses:
LrCL LCL LLL,
LPL
SPL
Σ
CPL
(s))s))
(13)
where 7 trade-off parameter between the two losses. Joint optimization of these terms produces discriminative representations and refined prototypes, culminating in a robust clustering solution for fully incomplete multi-view data.
Experiments
In this section, conduct experiments five popular nult datasets to evaluate the effective- ness of the proposed CPMN.
4.1 Experimental Settings
Datasets
Five widely-used datasets are used to evaluate the proposed CPMN. (1) Caltech-101 is an
image dataset containing 8677 instances from 101 categories. Following 41, deep features extracted by DECAF [22 and VGG19 [21 are used two views. (2) Cub includes several categories of
7

---

Table Fully incomplete multi-view clustering performance comparison on five widely-used multi- view datasets. "." denotes that the baselines are not scalable to large datasets, The best and second best results are shown in bold and underlined, respectively.
Type
Method
Caltech-101
Cab
NoisyMNIST
MNIST-USPS
YouTuheFaces
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
MVC-UM
43.3
67.3
31.9
44.3
40.7
23.0
19.3
9.9
4.7
53.5
48.4
35.0
100% Unaligned
GWMAC
16.0
28.3
21.0
UPMGC-SM
51,0
73.4
33.7
74.9
69.8
59.7
52.6
48.8
36.8
59.8
58.5
45.5
100%)
SMILE
47.6
74.0
33.0
63.4
61.9
48.2
82.7
79.5
74.2
85.2
S0L8
76.1
52.5
73.6
42.6
CPMN
57.0
77.0
68.4
72.5
72.1
55.2
84.8
80.2
79.8
88.0
82.1
80.8
70.0
82.5
57.5
100% Missing
DM2C
28.2
59.3
18.3
35.6
36.4
6.4
23,2
15.4
8.0
35.1
34.2
18.3
16.2
32.1
5.8
SMILE
30.5
60.1
20.4
40.2
37.5
20.8
69.0
63.8
51.1
74.3
69.6
61.8
26.5
49.9
(9- 100%)
CPMN
38.7
68.2
40.7
47,0
49.8
29.6
71.1
68.2
58.8
75.5
69.2
66.0
27.4
51.3
16.2
Table 2: Partially incomplete multi-view clustering performance comparison on five widely-used multi-view datasets. "_" denotes that the baselines are not scalable to large datasets, The best and second best results are shown in bold and underlined, respectively.
Caltech-101
Cub
Moisy
MNIST-USPS
YouTubeFaaees
Data Type
Method
ACC
NMI
ART
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ART
ACC
NMI
ARE
PVC
18.6
48.9
14.6
50.2
56.3
38.6
81.8
82.3
82.0
86.5
78.1
74.6
MvCLN
35.6
61.0
40.9
58.2
55.2
40.8
91.1
84.2
83.6
90.0
81.4
80.4
54.0
69.2
44.2
50%
70.7
33.0
62.0
47.9
95.2
89.7
92.1
82.8
83.5
54.7
68.8
43.4
Unaligned
GWMAC
4.4
15.4
0.4
30.6
27.2
12.2
11.4
0.2
0.1
16.1
4.0
1.8
3.2
2.2
0.2
50%)
UPMGC-SM
76.3
36.6
71.3
61.9
55.4
44.5
64.8
46.3
SMILE
50.9
79.4
35.2
21.1
70.4
58.2
97.9
94.2
95.4
98.6
96.3
97.0
57.8
77.1
48.8
CPMN
59.2
76.9
69.3
68.5
71.1
58.4
95.8
90.2
91.5
96.6
92.0
93.1
67.2
80.9
53.5
DAIMC
56.2
78.0
41.8
62.7
58.5
47.7
33.8
26.4
16:0
55.2
49.6
38.6
EERIMVC
43.6
69.0
26.4
68.7
63.9
53.8
55.6
45.9
36.8
65.2
55.7
48.9
50% Missing
$5.88
37.4
85.9
92.3
85.0
84.3
45.2
46.9
29.6
DCP
44.3
71.0
45.3
53.7
65.5
47.3
80.0
75.2
70.7
94.0
89.7
88.3
26.3
47.2
14.4
(v - 50%))
DSIMVC
16.4
24.8
9.2
54.4
$2.4
35.2
55.8
55.1
43.0
97.0
92.4
93.5
29.4
48.5
19.0
SMILE
79.0
96.8
91.7
93.0
98.5
95.7
96.6
54.6
76.3
45.2
CPMN
52.9
79.7
51.7
67.8
60.4
54.5
96.0
93.3
91.2
97.5
95.8
97.0
58.1
75.0
50.3
birds. Following [11, visual features extracted by GoogLeNet [23] and text features extracted by doc2vec [14) are used as two views. (3) NoisyMNIST includes 70,000 instances, each providing two views: the raw MNIST image and a rotated, Gaussian
variant. Following [41] 30, 000 instances are randomly selected for evaluation. (4) MNIST-USPS contains 67,291 digit images from the MNIST and USPS datasets. As in prior study [41), randomly sample 5,000 items from each dataset, covering all 10 digits. (5) YouTubeFaces features 152,549 faces across 66 identities, with each identity having over 1,500 images. For comparisons, we follow prior work [11] describe each image using multi-view features, specifically a 512-dimensional GIST feature, 1984-dimensional HOG feature, and a 1024-dimensional HIST feature.
Baselines We compared CPMN with 12 multi-view clustering baselines. These baselines can be divided into the following categories based the type of data they handle. Four baselines designed to handle partially missing multi-view data, including DAIMC (9) EERIMVC [19] DCP and DSIMVC [24]. PVC [0] and MvCLN (36] are designed for partially unaligned data. SURE can address both of the aforementioned partial incompleteness problems. Distinctly, MVC-UM
15]
35
39
GWMAC (5), and UPMGC-SM [32) are designed to handle fully unaligned multi-view data.
DM2C II] is designed to handle fully missing nult data. SMILE [41] can address both of the aforemenntoned problems. For fairness, we only show the clustering results of various methods on the incomplete data they can process.
Implementation Details We implement the proposed CPMN via the PyTorch public toolboxes, and we conduct the experiment on server rumning Ubuntu Linux 20.04 that is equipped with an Intel(R) Xeon(TM) W5-3425 CPU @ 3.20 GHz, NVIDIA RTX 4090 Graphics Processing Units (GPUs), and 1 128 GB of memory. Following previous studies 35 41, we define the missing rate as v = m/N, where m is the number of instances with missing views. To generate incomplete data, we randomly select m instances and drop one view for each instance. Similarly, we define the unaligned rate as ( = c/N, where e the number of instances without correspondences. We randomly sample instances and remove the correspondence between their views.
8

---

Table ACC comparison with SMILE on Caltech- 101 across a spectrum missing view rates.
Missing Rates
20%
40%
60%
80%
100%
SMILE CPMN
60.1
55.0
47.2
39.9
30.5
59.4
54.8
48.4
42.3
38.7
Table 4: Ablation study on Caltech- Cal. Each configuration uses the loss terms identified by " "V".
100%
Missing
100%
Unaligned
LAEG
LGL
LPL
Lew
ACC
ARI
NMI
ACC
ARI
NMI
31.3
52.0
24.2
47.3
59.4
45.9
32.8
54.1
26.3
49.2
67.6
49.3
33.7
61.4
39.1
53.8
75.3
59.1
34.8
65.5
36.3
53.2
76.6
55.9
V
38.7
68.2
40.7
57.0
77.0
68.4
4.2 Comparison with Baselines
Table provides comprehensive quantitative comparison of CPMN against several multi-view clustering methods under two challenging fully incomplete scenarios: 100% unaligned instances and 100% missing views. The experimental results lead to several key observations. Firstly, our CPMN outperforms baselines across nearly all datasets, a success attributed to novel prototype matching-based view alignment strategy. Secondly, with the unaligned rate of 100%, both CPMN and SMILE generally exhibit superior performance over other unaligned multi-view clustering methods, benefiting from the latent feature extraction capabilities of DNN. Conventional methods like UPMGC- SM achieve competitive performance, suggesting potential limitations DNN-based approaches in capturing essential data distributions within smaller-scale datasets.
Furthermore, to comprehensively evaluate the robustness of CPMN, its clustering performance is also tested under partially incomplete scenarios. Table 2 presents the clustering results for CPMN alongside several baseline methods under scenarios of 50% unaligned instances and 50% missing views. The results indicate that even though CPMN utilizes no view correspondence information and employs view-specific autoencoders without weight sharing. still achieves top-two performance across most datasets. Notably, it attains the best overall results on Caltech- 101 and You' Youeeu leading in at least two metrics per dataset. These results further demonstrate the effectiveness of CPMN and its capability to generalize to partially incomplete settings.
To further evaluate the robustness of CPMN against the strongest baseline, SMILE, conducted detailed analysis on the Caltech-101 dataset with different missing view rates. Table 3 presents the clustering results under missing view rates from 20% to 100%. From the results, we can observe that: (1) At lower missing rates (20%-40%) where substantial paired information is still available, SMILE shows a slight advantage. Notably, our CPMN achieves highly competitive performance even in this scenario, for which it was not specialized, underscoring the general effectiveness of its correspondence-Fie free framework. (2) Crucially, as the missing rate reaches 60% and paired information becomes scarce, SMILE's performance begins to degrade sharply. In contrast, CPMN's performance remains remarkably stable, surpassing SMILE. This trend intensifies as the problem difficulty increases 50%%-10%% clearly demonstrating the superior robustness of CPMN's matching paradigm precisely in the challenging scenarios.
4.3 Ablation Studies and Parameter Analysis
To verify the significance of each component in CPMN, we perform ablation studies to isolate the effect of the reconstruction loss LREC- graph contrastive loss LGL, prototype contrastive loss LPL. and clustering loss LeLU- The clustering results on the Caltech-101 dataset with 100% unalignment and 100% missing views are shown in Table From the results, one could observe that: (1) With the addition of components, the clustering performance improves significantly, and the best clustering performance can be achieved when using all loss terms. (2) LREC plays an essential role in the AEs

---

60
ACC (34
ACC/90
40
99
40
8.1
3.1
603 Po 91
90001
80000
Mosing Unallgged
(a) ACC vs. and À with fully missing multi-view data
(b) ACC vs. and A with fully unaligned multi-view data
(c) ACC vs. da with fully incomplete multi-view data
Figure Sensitivity studies of CPMN on the hyper-paramenee X, 7, and d₂
and is therefore retained. Augmenting this with LGr led notable enhancement. (3) Building upon the LEEC + Lar baseline, the introduction of either Lpr, and LCLU can further improve performance. This underscores the complementary benefits of these terms in the overall model.
There are two tunable loss terms. To better illustrate the stability of CPMN, conducted experiments investigate the sensitivity of the proposed method to these two apper-prrametrss.. Figure 3a 3bhsww values versus the hyper-parameters À and y the Caltech- 101 dataset with T00% unalignment and 100% missing views. The results show that the CPMN maintains relatively stable performance across considerable range of these hyper-pane syper-parameter settings within both incomplete scenarios. When À and are selected from the ranges of [le-3, I] and [le-2, 1J, CPMN can achieve desirable performance.
namely, À and 7 which impact the weights various
shows the ACC
The dimensionality of the latent space d2 is critical hyper-parameter in deep clustering models, exerting a considerable influence on clustering performance. To examine the effect of d a sensitivity analysis is conducted the Caltech- 101 dataset with d2 E [8, 128]. Figure 3e shows the ACC values versus de with 100% unalignment and 100% missing views. can be observed that ACC increases significantly d, is raised from 8 to 16. Subsequently, clustering performance gradually declines with further increases in d.. This phenomenon occurs because higher dimensionalities may introduce noise that adversely affects clustering, whereas lower dimensionalities might fail to capture the underlying structure.
Conclusion
In this paper, we propose the Contrastive Prototype Matching Network (CPMN), novel framework that establishes new structure-level alignment paradigm for fully incomplete multi-view clustering (FIMC). CPMN pioneers learning consistent global clustering by explicitly aligning prototypes across views. Initially, a correspondence-fiee graph contrastive learning stage with MNN establishes view- specific prototypes from entirely unpaired views. Subsequently, crucial similarity- prototype graph matching step explicitly aligns these prototypes, resolving category discrepancies and forging unified clustering structure across views. Building on this alignment, CPMN employs a prototype- aware contrastive learning mechanism that leverages matched prototypes and emerging category information to refine representations for enhanced semantic consistency. Extensive experiments demonstrate that CPMN achieves superior performance compared various baselines.
Despite its success, we acknowledge avenues for future work. The performance of CPMN is theoretically linked to the quality of the initial prototypes, suggesting further research into the convergence properties of the joint optimization. Furthermore, our method assumes a predefined cluster count C. Extending this structural alignment paradigm to non- parametric setting, where C dynamically inferred from the data, remains significant and open research direction.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant 62402235, 62276143 and 62272035, and the Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telccommunications under Grant NY223165.
10

---

References
[1] Guoqing Chao, Yi Jiang, and Dianhui Chu. Incomplete contrastive multi-view clustering with high- confidence guiding. In Proc. AAAI Conf. Artif. Intell. (AAAI), pages 11221-11229. 2024.
[2] Ting Chen, Simon Korblith, Mohammad Norouzi, and Geoffrey E. Hinton. simple framework for contrastive learning of visual representations. In Proc. Int. Conf. Mach. Learn. (ICML), volume 119, pages 1597-1607 2020.
[3] Zhibin Dong, Siwei Wang. Jiaqi Jin, Xinwang Liu, and En Zhu, Cross-view topology based consistent and complementary information for deep multi-viww clustering, In Proc. Int. Conf. Comput. Vis. (ICCV), pages 19383-19394, 2023.
[4] Wei Feng. Guoshuai Sheng. Qianqian Wang. Quanxue Gao, Zhiqiang Tao, and Bo Dong. Partial multi-view clustering via supe-vupe network. Proc. AAAI Conf. Artif. Intell. (AAAI), pages 11988 11995, 2024.
[5] Fengjiao Gong, Yuzhou Nie, and Hongteng Xu. Grssov- multi-modal alignment and clustering. In Proc. ACM Int. Conf. on Inform. & Knowl, Management (CIKM), pages 603-613, 2022.
[6] Ruiming Guo, Mouxing Yang. Yijie Lin, Xi Peng, and Peng Hu. Robust contrastive multi-view clustering against dual noisy correspondence. Proc. Ady Neurol Inform. Process. Syst. ( 2024.
[7] Xifeng Guo, Long Gao, Xinwang Liu, and Jianping Yin. Improved deep embedded clustering with local structure preservation. In Proc. Int. Joint Conf. Artif. Intell. (IJCAI), volume 17, pages 1753-1759, 2017.
[8] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross B. Girshick. Momentum contrast for unsu- pervised visual representation learning. In Proc. IEEE Conf. Comput. Vis. Pattern Recog. (CVPR). pages 9726-978 9735,9975,222 2020.
[9] Menglei Hu and Songean Chen. Doubly aligned incomplete multi-view clustering. In Proc. Int. Joint Conf. Artif. Intell. (ICCAI) pages
2018.
[10] Zhenyu Huang, Peng Hu, Joey Tianyi Zhou, Jiancheng Lv, and Xi Peng. Partially view-aligned clustering. In Proc. Adv Neural Inform. Process. Syst. (NeurIPS), 2020.
[11] Yangbangyan Jiang, Qianqian Xu, Zhiyong Yang. Xiaochun Cao, and Qingming Huang. DM2C: deep mixed-modal clustering. Proc. Adv. Neural Inform. Process. Syst. (NeurlPS), pages 5880-5890, 2019.
[12] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Communications of the ACM, 60(6):84 90, 2017.
[13] Harold W Kuhn. The hungarian method for the assignment problem. Naval research logistics quarterly, 2(1-2) (1-2))83 97, 1955.
[14] Quoc Le and Tomas Mikolov. Distrihuted representations of sentences and documents. In Proc. Int. Conf. Mach. Learn. (ICMI.). pages 1188-1196, 2014.
[15] Yijie Lin, Yuanbiao Gou, Xiaotian Liu, Jinfeng Bai, Jiancheng Lv. and Xi Peng. Dual contrastive prediction for incomplete multi-view representation learning. IEEE Trans. Pattern Anal. Mach. Intell., 454444444-44461, 2023.
[16] Yijie Lin, Yuanbiao Gou, Zitao Liu, Boyun Li, Jiancheng Lv, and Xi Peng. COMPLETER: incomplete multi-view clustering via contrastive prediction. In Proc. IEEE Conf. Comput. Vis. Pultern Recog. (CVPR). pages 11174-11 1113, 2021.
[17] Haoran Liu, Ying Ma, Ming Yan, Yingke Chen, Dezhong Peng, and Xu Wang. Dida: Disambiguated domain alignment for cross-domain retrieval with partial labels. In Proc. AAAI Conf. Artif. Intell. (AAAT), volume 38, pages 3612-3620, 2024.
[18] Suyuan Liu, Siwei Wang, Ke Liang, Junpu Zhang, Zhibin Dong, Tianrui Liu, En Zhu, Xinwang Liu, and Kunlun He. Alleviate anchor-shift: Explore blind spots with cross-view reconstruction for incomplete multi-view clustering. In Proc. Adv. Neural Inform. Process. Syst. (NeurIPS), 2024.
[19] Xinwang Liu, Miaomiao Li, Chang Tang, Jingyuan Xia, Jian Xiong, Li Liu, Marius Kloft, and En Zhu. Efficient and effective regularized incomplete multi-view clustering. JEEE Trans. Patiern Anal. Mach. Intell,, (8):2643 2646, 2020.
11

---

[20] Laurens Van Der Maaten and Geoffrey Hinton. Visualizing data using t-sne. J. Mach. Learn. Res.. 9(2605);579-2605 2008.
[21] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recogni- tion. In Proc. Int. Conf. Learn. Represent. (ICLR), 2015.
[22] Chao Su, Huiming Zheng, Dezhong Peng, and Xu Wang. Dica: Disambiguated contrastive alignment for cross modal retrieval with partial labels. In Proc. AAAI Conf. Artif. Intell. (AAAI), volume 39, pages 20610-20618, 2025.
[23] Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proc. IEEE Conf. Comput. Vis, Pattern Recog. (CVPR), pages 1-9, 2015.
[24] Huayi Tang and Yong Liu. Deep safe incomplete multi-view clustering: Theorem and algorithm. In Proc. Int. Conf. Mach. Learn. (ICML), volume 162. pages 21090-21110, 2022.
[25] Daniel J. Trosten, Sigurd Løkse, Robert Jenssen, and Michael Kamptfinyer. Reconsidering representation aligmment for multi view clustering. Proc. IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), pages 1255- 1265, 2021.
[26] Devesh Walawalkar and Pablo Garrido. Vidcoclusterne:: Self-supervised and adaptive face clustering for videos. In Proc. Eur. Conf. Comput. Vis. (ECCV), volume 15088, pages 377-396, 2024.
[27] Siwei Wang, Xinwang Liu, Suyuan Liu, Jiaqi Jin, Wenxuan Tu, Xinzhong Zhu, and En 7hu. Align then fusion: Generalized large-scale view clustering with anchor matching correspondences. In Proc. Adv. Neural Inform. Procexs. Syst. (NeurIPS), 2022.
[28] Xibiao Wang, Hang Gao, Xindian Wei, Liang Peng, Rui Li, Cheng Liu, Wu, and Hau-San Wong. Contrastive graph distribution alignment for partially view-aligned clustering. In Proc. ACM Int. Conf. Multimedia (ACM MM), pages 5240 5249, 2024.
[29] Zitai Wang, Qianqian Xu, Zhiyong Yang. Yuan He, Xiaochun Cao, and Qingming Huang. Openauc: Towards auc-oriented open-set recognition. Proc. Adv. Neural Inform. Process. Syst. (NeurIPS), 2022.
[30] Wen, Shijie Deng, Waikcung Wong, Guoqing Chan, Chao Huang, Lunke Fei, and Yong Xu. Diffusion- based missing-view generation with the application on incomplete multi-view clustering. In Proc. Int. Conf. Mach. Learn. (ICML). 2024.
[31] Jie Wen, Zhihao Wu, Zheng Zhang, Lunke Fei, Bob Zhang, and Yong Xu. Structural deep incomplete multi-view clustering network. In Proc. ACM Int. Conf. on Inform. & Knowl. Management (CIKM), pages 3538 3542, 2021.
[32] Yi Wen, Siwei Wang, Qing Liao, Weixuan Liang, Ke Liang, Xinhang Wan, and Xinwang Liu, Unpaired multi-view graph clustering with cross-view structure matching. IEEE Trans. Neural Networks Learn. Syst., 2023.
[33] Zichen Wen, Yawen Ling, Yazhou Ren, Tianyi Wu, Jianpeng Chen, Xiaorong Pu, Zhifeng Hao, and Lifang He. remaphily--ellted:: Adaptive hybrid graph filter for multi-view graph clustering, In Proc. AAAI Conf. Artif. Intell. (AAAI), pages 15841-15849, 2024.
[34] Zhe Xue, Junping Du, Changwei Zheng, Jie Song, Wenqi Ren, and MeiYu Liang. Clustering-idduced induced adaptive structure enhancing network for incomplete multi-view data, In Proc. Int. Joint Conf. Artif. Intell. (ICCAI). pages 3235-3333333 3241. ojcai.org. 2021.
[35] Mouxing Yang, Yunfan Li. Peng Hu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Robust multi-view clustering with incomplete information. JEEE Trans. Pattern Anal. Mach. Intell., 45(1))1055-1166) 2023.
[36] Mouxing Yang, Yunfan Li, Zhenyu Huang, Zitao Liu, Peng Hu, and Xi Peng. Partially view-aligned representation learning with noise-robust contrastive loss. Proc. IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), pages 1134-1 143, 2021.
[37] Zhiyong Yang, Qianqian Xu, Shilong Bao, Peisong Wen, Yuan He, Xiaochun Cao, and Qingming Huang. Auc-oriented domain adaptation: From theory to algorithm. IEEE Trans. Pattern Anal. Mach. Intell., 45(12):4461114417, 2023.
[38] Ziniu Yin. Yanglin Feng Ming Yan, Xiaomin Song. Dezhong Peng, and Xu Wang. Roda: Robust domain alignment for cross- dross-domain retrieval against label noise. In Proc, AAAI Conf. Artif. Intell, (AAAI). volume 39, pages 9535-9543, 2025.
12

---

[39] Hong Yu, Jia Tang, Guoyin Wang. and Xinbo Cao. A novel multi-view clustering method for unknown mapping relationships between cross-view samples. In Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. (KDD), pages 2075-2083, 2021.
[40] Xuejiao Yu, Yi Jiang, Guoqing Chao, and Dianhui Chu. Deep contrastive multi-view subspace clustering with representation cluster interactive learning. IEEE Trans. Knowl. Discov, Eng.. 37(1):188-199 2025.
[41] Pengxin Zeng, Mouxing Yang, Yiding Lu, Changqing Zhang, Peng Hu, and Xi Peng. Semantic invari- ant multi view clustering with fully incomplete information. IEEE Trans. Pattern Anal. Mach. Intell, 46(4):2139 21500, 2024.
[42] Liang Zhao, Qiongjie Xie, Sontao Wu, and Shubin Ma. An end-to-end framework for partial view-aligned clustering with graph structure. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), pages 1-5, 2023.
13

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The scope and contributions of this paper are clearly stated in the abstract and introduction.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
The limitations are discussed in the Conclusion section.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
14

---

This paper is experimental instead of theoretical. It includes no theorems or proofs.
Justification:
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: This paper provides a detailed algorithm, instructions on datasets, hardware and software configurations for the reproducibility of the proposed method.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, it may be necessary either make it possible for others replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
15

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [Yes]
Justification: This study uses public datasets. The code is provided in the supplementary material.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://niis.cc.
aublic/guudees/Codeetbbmsss cosssiiinplyyy for more details.
While encourage the release of code and data, understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
/ wwtps/cccppplgguuuiieeeeee
Saleee//CoSSSSbisssS.S.. www.sssoiccgyyy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: This paper provides the details of data preprocessing steps, hyperparameters, and optimization in the Experiments section.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [No]
Justification: Almost all compared baselines do not include the statistical significance in experiments; thus, we not report
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by emor bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
16

---

The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not show in tables figures symmetric error bars that would yield results that are out range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification:
The computer resources are stated in the Experiments section.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make into the paper).
9. Code ethics
Question: Does the research conducted the paper conform, in every respect, with the NeurlPS Code of Ethics https: ptattps:/neeurtie hww.npsu...../. httppp/bllc..tcccccc..........aa
Answer: [Yes]
Justification:
This paper conforms with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- cration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: The proposed algorithm has no socictal impact. All datasets used in this paper are publicly available and the algorithm only performs clustering on the datasets.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
17

---

If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), faimess considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The proposed algorithm has no misuse risk. All datasets used in this paper are publicly available and the algorithm only performs clustering on the datasets.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging. and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: All relevant papers and datasets are properly cited.
Guidelines:
The answer NA means that the paper does
existing assets. The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset used and, possible, include a URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
18

---

If assets are released, the license, copyright information, and terms of use in the thcode has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
package should be provided. For popular datasets, paperswi
latasets.paperssi
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information not available online, the authors are encouraged to reach out to the asset's s creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: This paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moode as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
This work does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [NA]
Justification: This work does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
19

---

We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors adhere the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Question:
Answer: [NA]
Justification: The proposed method does not involve LLMs as any important, original, or non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our LLM policy hbtp::///orrpss.cco/ooorrrrree/p for what should or should not be described.
20


Reviews:
[{"review_id": "iQRZytUt3C", "reviewer": "Reviewer_83hp", "summary": "This work proposes a CPMN framework to address the challenging fully incomplete multi-view clustering problem where no cross-view correspondences exist. It integrates a two-stage contrastive learning approach and an explicit prototype graph matching strategy. Experimental results on five benchmark datasets demonstrate improvements over baselines.", "questions": "Most of the problems have already been mentioned in Weaknesses. More implementation details can be provided for the following problems: \n1）In section3.1, the introduction of using MNN to construct positive pairs in Correspondence-Free Graph Contrastive Learning is not clear enough. There may be a failure to find MNN, so how to deal with it?\n2）Why use K-Means to initialize the prototype in the first stage, while using a learnable clustering layer to optimize the prototype in the second stage?", "limitations": "Yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths：\nIt provides a multi-stages approach to solve the problem of completely missing multi-view clustering. The paper is clearly and effectively written. Extensive experiments and ablation studies are conducted in the paper.\n\nWeaknesses：\n1）The authors use MNN instead of the commonly used kNN in the first stage of Correspondence-Free Graph Contrastive Learning. When dealing with large scale data, MNN takes increased time compared to kNN.\n2） The efficiency of CPMN is unknown. The authors should report the training time and inference time of CPMN on different sized datasets.\n3） To visualize the training process, please give the curve of the prototype matching accuracy versus the training process.", "was_revised": true, "final_justification": "Thank you for the authors’ detailed and well-organized rebuttal. I appreciate the thorough responses provided to each of the concerns.\nI believe the key concerns have been sufficiently addressed. I will maintain my original score.", "rebuttal": "We sincerely thank the reviewer for their insightful, thorough, and constructive feedback. Your comments regarding our model's efficiency, the visualization of the training process, the rationale for using MNN, and the clarity of our methodological design have been invaluable in refining our work. We have carefully addressed each of your points in the detailed, point-by-point responses below.\n\n## Reply to Weaknesses (1):\nWe sincerely thank the reviewer for this insightful and important question. We fully agree with the observation that MNN is computationally more intensive than kNN. This design choice is a deliberate trade-off we made to ensure the robustness of our model, which we argue is both necessary and highly justified for the FIMC problem. Our reasoning is as follows:\n\n__Limitation of kNN__: kNN establishes a one-way relationship; if point A is a k-nearest neighbor of B, B is not guaranteed to be a k-nearest neighbor of A. In the challenging FIMC setting, where the data is noisy and has no correspondences, this unidirectional link can introduce a significant number of spurious edges, severely degrading the quality of the initial graph.\n\n__Superiority of MNN:__ Mutual k-Nearest Neighbor (MNN) enforces a more stringent, reciprocal relationship. This strategy acts as a critical noise filter, pruning less reliable connections. For the FIMC problem, the quality of this initial graph is paramount to the success of all subsequent stages. MNN provides a much cleaner and more reliable graph structure to build upon.\n\n## Reply to Weaknesses (2):\nWe sincerely thank the reviewer for raising this important point about our model's efficiency. We agree that this is a critical metric for evaluating the practical utility of our method. To provide a clear comparison of CPMN's efficiency, we have benchmarked the total runtime of both CPMN and SMILE on two representative datasets under the same hardware environment (a single NVIDIA RTX 4090 GPU).\n\n| Dataset | Total Samples | CPMN | SMILE |Speed-up\n| :--- | :--- | :--- | :--- | :--- \n| **Caltech101** | 8677 | __659.55 sec__ | 1335.22 sec| 2.0x Faster\n| **NoisyMNIST** | 30000 | __1136.64 sec__ | 1609.92 sec | 1.4x Faster\n\nThe results show that despite being a multi-stage framework, our CPMN is significantly more computationally efficient in terms of total training time than SMILE. We attribute this significant advantage to the convergence efficiency gained from our structured learning process: \n1. Our first stage provides a structurally sound initial representation space in a computationally efficient manner, which is far superior to a random state. This provides a high-quality starting point for the subsequent optimization. \n2. With this strong start, our final PCL optimization stage begins its search in a more favorable and stable region, allowing it to converge to a high-quality solution much faster. This greatly reduces the overall training time required. In contrast, an end-to-end model like SMILE need more iterations to navigate a larger and more complex optimization landscape to reach stability.\n\n## Reply to Weaknesses (3):\nWe sincerely thank the reviewer for this excellent suggestion, which helps to better illustrate the dynamic learning process of our model. As we cannot include plots in the rebuttal, we present a quantitative table to represent this curve, showing how the prototype matching accuracy evolves over training epochs on the MNIST-USPS dataset. At the end of each epoch, we run the Prototype Graph Matching (PGM) module and calculate the percentage of matched pairs where the two prototypes share the same ground-truth label.\n\n| PCL Training Epoch | Prototype Matching Samples Accuracy (%) |\n| :--- | :--- |\n| 1 | 83.5% |\n| 20 | 85.0% |\n| 40 | 86.2% |\n| 60 | 86.5% |\n| 80 | 86.0% |\n| 100 | 86.8% |\n\nAs training progresses, our Prototype Contrastive Learning (PCL) uses the initial matching results to guide the representation learning. This pulls semantically similar samples from different views closer in the latent space. The improved representations lead to better-defined prototypes, which in turn results in an increase in matching accuracy. In later stages, the model reaches a highly synergistic state where the accuracy stabilizes at a very high level.\n\n## Reply to Questions (1):\n\nWe sincerely thank the reviewer for this insightful and specific question.\n\n### 1. Clarification on the MNN Construction Process:\n\nOur goal is to find high-quality, high-confidence positive pairs for contrastive learning. MNN is a powerful tool for this. In the mini-batch training, for a sample $x$ in View A, we first find its k-nearest neighbors in View B. Then, for each of these neighbors, we check if their k-nearest neighbors (back in View A) include $x$. A positive pair is formed only when this reciprocal relationship holds. This stringent strategy effectively filters out spurious connections caused by noise or distribution gaps, providing a reliable foundation for learning.\n\n### 2. Handling the \"Failure to Find MNN\" Case:\nIn our model, if a node fails to find any MNN pairs, our graph construction strategy automatically degrades to using its kNN pairs as the positive pairs. We prioritize the most reliable, reciprocal MNN connections. When these high-confidence links exist, we use them to provide the strongest supervisory signal. When such an ideal MNN link cannot be found, we do not want to abandon the data. Therefore, we use its kNN connections as a fallback. While kNN links have lower confidence than MNN, they still provide valuable neighborhood information that is far better than random, ensuring that every data point participates in the contrastive learning process and guaranteeing training stability.\n\nTo visualize the number of samples where MNN is not found during the training process, we have investigated its convergence by reporting the loss value and the count of samples with undetected MNNs as training progresses in the supplementary material. Experiments are run on Caltech-101 with $k=5$ under both defined incompleteness scenarios. As depicted in the figures in the supplementary material, the loss value decreases sharply in the first 10 epochs before converging gradually. Regarding the number of samples with undetected MNNs, this count drops sharply within the first two epochs and subsequently remains at a low level throughout the training. Although samples with undetected MNNs persist, they constitute a very small proportion of the total dataset.\n\n## Reply to Questions (2):\n\nWe sincerely thank the reviewer for this insightful question, as it addresses a key design choice in our model. We employ these two different strategies because the two stages of our model have fundamentally different objectives.\n\n### 1. Objective of Stage 1: To Obtain a Stable and Reliable Initial Prototype Estimation.\n\nIn the first stage, our primary goal is to derive a stable and meaningful initial cluster structure from the instance embeddings, which have been pre-trained by GCL but are still relatively coarse.K-Means is a classic, robust, and effective algorithm for this task. It operates on a fixed feature space and provides us with a reliable, non-random initialization of prototypes. This high-quality initialization is the cornerstone for the success of the subsequent Prototype Graph Matching (PGM) stage. Using a learnable layer at this early stage would be problematic. The initial instance embeddings are not yet well-optimized, so a learnable layer would lack a stable and meaningful gradient signal, potentially leading to training instability.\n\n### 2. Objective of Stage 2: To Perform End-to-End Joint Optimization.\n\nIn the second stage, our goal shifts from simple initialization to jointly and synergistically optimizing both the instance representations and the cluster centers (prototypes). The learnable clustering layer is differentiable. As part of the network, it allows gradients from the clustering-related loss to be backpropagated to the feature encoders."}, {"review_id": "EcJUbs5jHY", "reviewer": "Reviewer_hkBW", "summary": "This paper presents the CPMN (Contrastive Prototype Matching Network for multi-view clustering), designed to operate without requiring any cross-view correspondences. CPMN utilizes a prototype matching mechanism that circumvents the need for strong semantic consistency or strict view alignment assumptions. Extensive experiments conducted on various datasets demonstrate the effectiveness of the proposed method.", "questions": "-\tWhat is the rationale for using Mutual Nearest Neighbors  instead of the more commonly adopted k-Nearest Neighbors in the Correspondence-Free Graph Contrastive Learning phase?\n-\tHow does its computational efficiency compare with existing methods such as SMILE?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n(1)\tThe paper proposes a framework capable of handling fully incomplete multi-view clustering scenarios, addressing an important limitation of existing methods and broadening potential application domains.\n\n(2)\tThe proposed multi-stage architecture is intuitively structured and relatively easy to follow.\n\nWeaknesses:\n\n(1)\tThe core component prototype graph matching lacks rigorous theoretical grounding and interpretability.\n\n(2)\tAs a multi-stage training framework, early-stage clustering outcomes may adversely influence later modules such as prototype graph matching.\n\n(3)\tThe experimental evaluation includes only 100% and 50% missing view rates. Incorporating intermediate levels of incompleteness (e.g., 20%, 60%) and plotting clustering performance against the incompleteness rate would provide a more comprehensive assessment of robustness.\n\n(4)\tThe paper does not present convergence curves for loss functions or clustering metrics.\n\n(5)\tSome recent contrastive learning based clustering methods are encouraged to be reviewed, such as “Decoupled Contrastive Multi-view Clustering with High-order Random Walks” and “Incomplete Multi-view Clustering via Diffusion Contrastive Generation”.\n\n(6)\tThe ablation study lacks clarity. Components of CPMN were not strictly isolated or replaced to verify individual contributions. A more detailed description of the ablation design is needed to support the conclusions drawn.", "was_revised": true, "final_justification": "Thank you for your thoughtful responses. Your clarifications have addressed my primary concerns.", "rebuttal": "We thank the reviewer for their insightful and constructive feedback. We have carefully addressed each of your points in the detailed, point-by-point responses below.\n\n## Reply to Weaknesses (1):\n\nWe sincerely thank the reviewer for this deep and critical question.\n\n1. PGM is grounded in well-established combinatorial optimization theory. We formally model the task of finding the best cross-view prototype correspondences as the maximum weight bipartite matching problem and employ the Hungarian algorithm to solve it. This algorithm is guaranteed to find a provably optimal solution. Matching at the prototype level is a deliberate design choice, as prototypes serve as robust abstractions that ensure stability in the noisy FIMC setting. Therefore, our PGM component is built upon a rigorous theoretical foundation with a clear mathematical formulation and an optimal algorithmic solution.\n\n2. We believe high interpretability is precisely PGM's most significant advantage over other implicit alignment methods. The output of PGM is a clear, one-to-one mapping (e.g., \"Cluster A from View 1 corresponds to Cluster C from View 2\"), which is intuitive and human-readable. Unlike implicit alignment methods, our PGM provides an explicit semantic bridge, greatly enhancing the model's trustworthiness and practical value.\n\n## Reply to Weaknesses (2):\nOur model ensures robustness and avoids catastrophic error propagation through several key designs:\n\n1. The objective of our first stage (GCL) is not to achieve a flawless clustering result. Its core purpose is to leverage the robustness of MNN graphs to learn a structurally sound and semantically meaningful initial representation space. Running K-Means on this high-quality space ensures our initial prototypes are far superior to a random guess, providing a reliable starting point and thus minimizing the initial error.\n2. The initial prototype matching result is a guiding signal for subsequent learning. The process forms a mutually reinforcing, self-correcting virtuous cycle:\n3. In Stage 3, we use the prototype matching map $\\pi$ as supervision. This signal guides the model to pull closer the sample clusters from different views that are deemed semantically matched.\n\nTherefore, our framework is not a simple pipeline with one-way error propagation. It is a dynamic system that can tolerate initial imperfections and achieve iterative refinement through a closed-loop mechanism where representation learning and clustering optimization boost each other.\n\n## Reply to Weaknesses (3):\n\nFollowing your advice, we have conducted additional experiments comparing our CPMN with the strong baseline SMILE on the Caltech-101 dataset across a spectrum of missing view rates. As we cannot include plots in the rebuttal, we present the quantitative results in the table below.\n\n| Missing Rates | 20% | 40% | 60% | 80% | 100%\n| :--- | :--- | :--- | :--- | :--- | :--- |\n| **SMILE** |0.601 |0.550 | 0.472 |0.399 |0.305\n| **CPMN** |0.594 | 0.548 | 0.484 | 0.423 |0.387\n\nThis new experiment provides deep insights into the robustness and design philosophy of our model: \n1. SMILE shows a slight advantage at lower missing rates (20-40%). The fact that our CPMN achieves highly competitive performance here, despite not being specialized for this scenario, already speaks to the effectiveness of its correspondence-free framework. \n2. At a 60% missing rate, as the crucial paired information becomes scarce, SMILE's performance begins to degrade sharply. In contrast, CPMN's performance remains remarkably stable, surpassing SMILE and demonstrating its superior robustness. This trend continues as the problem becomes more difficult.\n\n## Reply to Weaknesses (4):\n\nWe have investigated the convergence by reporting the loss value and the count of samples with undetected MNNs as training progresses in the supplementary material. Experiments are run on Caltech-101 with $k=5$ under both defined incompleteness scenarios. As depicted in the figures in the supplementary material, the loss value decreases sharply in the first 10 epochs before converging gradually. Regarding the number of samples with undetected MNNs, this count drops sharply within the first two epochs and subsequently remains at a low level throughout the training. Although samples with undetected MNNs persist, they constitute a very small proportion of the total dataset.\n\n## Reply to Weaknesses (5):\n\nWe sincerely thank the reviewer for pointing out these two highly relevant and recent papers. We agree that discussing them is important for positioning our work, and we will add a detailed discussion to the Related Work section in the final manuscript.\n\n## Reply to Weaknesses (6):\n\nWe sincerely thank the reviewer for this critical point. We acknowledge that our original description could have been more detailed, and we provide that more detailed design here to clarify how we strictly isolated and evaluated each core component.\n\nOur ablation study follows a principled, additive approach, starting from a basic autoencoder and progressively incorporating each key component to verify its individual contribution. Below, we detail the precise design of each experimental variant, all of which were evaluated on the Caltech-101 dataset under the specified conditions.\n\n### 1. Variant (a): Baseline Autoencoder (AE)\nThis is our most basic model, containing only the autoencoder networks. To establish the baseline performance of the feature extractor without any advanced contrastive or clustering mechanisms. This measures the raw quality of the initial latent space. In this variant, $L_{REC}$ is used in the model. \n### 2. Variant (b): AE + Graph Contrastive Learning (GCL)\nWe build upon the baseline by adding our first-stage graph contrastive learning module. To strictly isolate and verify the contribution of our initial graph-based representation learning. The performance improvement from (a) to (b) is solely attributable to the effect of $L_{GL}$.\nIn this variant, $L_{REC} $ and $L_{GL}$ are used in the model. \n### 3. Variant (c): AE + GCL + Prototype Contrastive Loss (PCL)\nBuilding on the AE + GCL model, we introduce our core prototype-aware contrastive loss, but without the auxiliary clustering loss. The performance jump from (b) to (c) strictly isolates the individual contribution of Clustering Loss. In this variant, $L_{REC} + L_{GL} + L_{PL}$. are used in the model. \n### 4. Variant (d): AE + GCL + Clustering Loss\nAs an alternative path from the AE + GCL model, we add only the self-supervised clustering loss. This allows us to isolate and measure the independent effect of the clustering-enhancement objective ($L_{CLU}$), separate from the prototype contrastive loss. In this variant, $L_{REC} + L_{GL} + L_{CLU}$ are used in the model. \n### 5. Variant (e): Full Model (CPMN)\nThis is our complete proposed model, which combines all components. By comparing the full model's performance to variants (c) and (d), we can observe the synergistic benefits of combining both the prototype contrastive loss and the clustering loss, leading to the best overall performance. In this variant, $L_{REC} + L_{GL} + L_{PL} + L_{CLU}$ are used in the model. \n\n## Reply to Questions (1):\n\nWe sincerely thank the reviewer for this insightful and important question. We fully agree with the observation that MNN is computationally more intensive than kNN. This design choice is a deliberate trade-off we made to ensure the robustness of our model, which we argue is both necessary and highly justified for the FIMC problem. Our reasoning is as follows:\n\n1.kNN establishes a one-way relationship; if point A is a k-nearest neighbor of B, B is not guaranteed to be a k-nearest neighbor of A. In the challenging FIMC setting, where the data is noisy and has no correspondences, this unidirectional link can introduce a significant number of spurious edges, severely degrading the quality of the initial graph.\n\n2.Mutual k-Nearest Neighbor (MNN) enforces a more stringent, reciprocal relationship. This strategy acts as a critical noise filter, pruning less reliable connections. For the FIMC problem, the quality of this initial graph is paramount to the success of all subsequent stages. MNN provides a much cleaner and more reliable graph structure to build upon.\n\n## Reply to Questions (2):\nWe sincerely thank the reviewer for raising this important point about our model's efficiency. We agree that this is a critical metric for evaluating the practical utility of our method. To provide a clear comparison of CPMN's efficiency, we have benchmarked the total runtime of both CPMN and SMILE on two representative datasets under the same hardware environment (a single NVIDIA RTX 4090 GPU).\n\n| Dataset | Total Samples | CPMN | SMILE |Speed-up\n| :--- | :--- | :--- | :--- |:---\n| **Caltech101** | 8677 | 659.55 sec | 1335.22 sec| 2.0x Faster\n| **NoisyMNIST** | 30000 | 1136.64 sec | 1609.92 sec | 1.4x Faster\n\nThe results show that despite being a multi-stage framework, our CPMN is significantly more computationally efficient in terms of total training time than SMILE. We attribute this significant advantage to the convergence efficiency gained from our structured learning process: \n1. Our first stage provides a structurally sound initial representation space in a computationally efficient manner, which is far superior to a random state. This provides a high-quality starting point for the subsequent optimization. \n2. With this strong start, our final PCL optimization stage begins its search in a more favorable and stable region, allowing it to converge to a high-quality solution much faster. This greatly reduces the overall training time required. In contrast, an end-to-end model like SMILE need more iterations to navigate a larger and more complex optimization landscape to reach stability."}, {"review_id": "n7TaFiOleZ", "reviewer": "Reviewer_iVCK", "summary": "This paper proposes a novel framework, CPMN, to address the understudied problem of fully incomplete multi-view clustering. CPMN designs an explicit prototype matching strategy to effectively align cross-view instances through category-level correspondence. Additionally, it employs a correspondence-free graph contrastive learning approach and a prototype-aware contrastive learning mechanism to learn semantic consistency across views. The experiments are implemented on five datasets with the comparison of many methods.", "questions": "1) Critical components of CPMN, such as prototype matching lack theoretical explanation or deeper intuitive understanding.\n2) The innovation is limited since contrastive learning is widely used in multi-view clustering.\n3) Authors should extend the parameter sensitivity analysis to more key hyperparameters, such as $k$ and $\\tau$, to demonstrate the robustness of the model.\n4) Visualization is missing. Please visualize the matched cross-view prototypes to demonstrate the learned correspondences.", "limitations": "Yes. The limitations have been discussed in the conclusion and other concerns can be found in weaknesses.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1） The paper is straightforward and easy to understand.\n2） Relatively extensive comparisons are conducted with existing fully/partially incomplete multi-view approaches. \n\nWeaknesses\n1) Critical components of CPMN, such as prototype matching lack theoretical explanation or deeper intuitive understanding.\n2) The innovation is limited since contrastive learning is widely used in multi-view clustering.\n3) Authors should extend the parameter sensitivity analysis to more key hyperparameters, such as $k$ and $\\tau$, to demonstrate the robustness of the model.\n4) Visualization is missing. Please visualize the matched cross-view prototypes to demonstrate the learned correspondences.", "was_revised": true, "final_justification": "Their responses have addressed my concerns. I intend to increase my score.", "rebuttal": "We sincerely thank the reviewer for the insightful and constructive feedback. We have carefully considered all the points raised and have provided a detailed, point-by-point response to each concern below. We hope that our responses and the corresponding clarifications will adequately address your concerns and demonstrate the merits of our work.\n\n## Reply to Weaknesses (1):\nWe sincerely thank the reviewer for this insightful question regarding the theoretical support for Prototype Graph Matching (PGM). \n\n__Regarding the \"Theoretical Explanation\":__ PGM is grounded in well-established combinatorial optimization theory. We formally model the task of finding the best cross-view prototype correspondences as the maximum weight bipartite matching problem and employ the Hungarian algorithm to solve it. This algorithm is guaranteed to find a provably optimal solution. Matching at the prototype level is a deliberate design choice, as prototypes serve as robust abstractions that ensure stability in the noisy FIMC setting. Therefore, our PGM component is built upon a rigorous theoretical foundation with a clear mathematical formulation and an optimal algorithmic solution.\n\n__Regarding the \"Deeper Intuitive Understanding\":__ In fact, high interpretability is precisely PGM's most significant advantage over other implicit alignment methods. The output of PGM is a clear, one-to-one mapping (e.g., \"Cluster A from View 1 corresponds to Cluster C from View 2\"), which is intuitive and human-readable. Unlike implicit alignment methods, our PGM provides an explicit semantic bridge, greatly enhancing the model's trustworthiness and practical value.\n\nIn summary, Prototype Graph Matching is a core component that is both theoretically sound and highly interpretable. \n\n## Reply to Weaknesses (2):\nWe thank the reviewer for this crucial point. We agree that contrastive learning (CL) is a foundational tool. Our novelty lies not in using CL itself, but in how we design novel contrastive tasks specifically for the challenging Fully Incomplete Multi-View Clustering (FIMC) problem, where standard CL methods are fundamentally inapplicable.\n\nOur novelty is demonstrated on two key levels.\n\n1.First, standard CL requires paired samples, which the FIMC setting completely lacks. Our initial Correspondence-Free Graph Contrastive Learning stage creatively overcomes this by constructing Mutual $k$-Nearest Neighbor (MNN) graphs to generate pseudo-positive pairs in a correspondence-free manner. \n\n2.More importantly, we propose a novel Prototype Contrastive Learning paradigm. Here, the supervisory signal for CL undergoes a qualitative shift. It is no longer derived from low-level augmentations or local graph structures, but from the high-level, cross-view semantic correspondences (i.e., the matched prototypes) obtained via our Prototype Graph Matching. An instance is pulled not only toward its intra-view cluster center but also toward its \"semantic equivalents\" in all other views. \n\nIn conclusion, we contribute a novel, progressive framework that elevates CL from low-level structural alignment to high-level semantic consistency, specifically tailored to solve the FIMC problem.\n\n## Reply to Weaknesses (3):\nWe sincerely thank the reviewer for this constructive suggestion. Following the reviewer's advice, we have conducted extensive experiments to analyze the impact of key hyperparameters, specifically the number of neighbors $k$ in MNN and the temperature $\\tau$ in the contrastive loss. For brevity, we report the ACC results on the Caltech-101 dataset.\n\n|$k$| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **Unaligned** | 0.534 | 0.540 | 0.573 | 0.567 | 0.564 | 0.570 | 0.569 | 0.580 | 0.560 | 0.563 |\n| **Missing** | 0.350 | 0.360 | 0.372 | 0.396 | 0.378 | 0.376 | 0.382 | 0.379 | 0.381 | 0.393 |\n\n__Sensitivity to $k$__: The results show that the choice of $k$ has a moderate impact on performance. When $k$ is very small (e.g., $k$ < 3), performance is suboptimal. This is expected, as an overly small $k$ provides insufficient neighborhood structure to build a reliable graph. However, as $k$ increases, the performance quickly rises and then remains consistently high and stable within a reasonably wide range of $k$ in [3, 10]. This demonstrates the robustness of our model, as it does not require meticulous tuning of $k$ to achieve strong results.\n|$\\tau$| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| **Unaligned** | 0.317 | 0.453 | 0.518 | 0.543 | 0.545 | 0.552 | 0.559 | 0.575 | 0.569 | 0.573 |\n| **Missing** | 0.254 | 0.313 | 0.327 | 0.337 | 0.344 | 0.356 | 0.362 | 0.382 | 0.389 | 0.387 |\n\n__Sensitivity to $\\tau$__: The model's performance is sensitive to the temperature $\\tau$, which is a common characteristic of contrastive learning methods. A very small $\\tau$ (e.g., $\\tau$ < 0.4) leads to poorer performance, as it forces the model to push away even very similar negative samples, making optimization difficult. As $\\tau$ increases, performance improves significantly because the model can better learn the global clustering structure. Crucially, the performance stabilizes and reaches a high-level plateau once $\\tau$ enters a suitable range (e.g., [0.6, 1.0]). This again demonstrates the model's robustness: while $\\tau$ should be set to a reasonable value, precise fine-tuning within that effective range is not necessary.\nThank you again for your valuable feedback, which has helped us to provide a more thorough analysis.\n## Reply to Weaknesses (4):\nWe sincerely thank the reviewer for this excellent and constructive suggestion. We agree that visualizing the matched prototypes is crucial for intuitively demonstrating the correspondences learned by our model. Since we cannot include images in the rebuttal, we present a quantitative analysis of our visualization results instead. We conducted this analysis on the MNIST-USPS dataset with 100% unaligned views due to its clear class semantics.\n\nFirst, we identify the cross-view prototype pairs that are matched by our model's PGM component. Then, for each matched pair, we analyze the ground-truth label composition of the samples within each prototype. A successful match should consist of two prototypes in which the ground-truth label of the samples within each prototype is identical. The table below shows the label purity analysis for some representative matched prototype pairs:\n\n| Matched Pair | View 1 (MNIST) | View 2 (USPS) | Conclusion |\n| :--- | :--- | :--- | :--- |\n| **Pair A** | Label: '0' (88% Purity) | Label: '0' (86% Purity) | Successful Match |\n| **Pair B** | Label: '1' (86% Purity) | Label: '1' (85% Purity) | Successful Match |\n| **Pair C** | Label: '2' (83% Purity) | Label: '2' (79% Purity) | Successful Match |\n\nAs the table demonstrates, our model accurately matches prototypes that are semantically consistent across views. For example, in Pair A, a prototype primarily containing the digit '0' from MNIST is correctly matched with a prototype primarily containing the digit '0' from USPS. The other pairs show similarly high semantic coherence. This quantitative analysis provides strong evidence that our model learns meaningful and correct cross-view semantic correspondences."}, {"review_id": "OsABs3oER1", "reviewer": "Reviewer_cAZ9", "summary": "This paper introduces Contrastive Prototype Matching Network (CPMN), a novel framework for fully incomplete multi-view clustering. CPMN aims to learn consistent global clustering by explicitly aligning prototypes across views. It integrates three innovative stages: a correspondence-free graph contrastive learning stage, a similarity-based prototype graph matching, and a prototype-aware contrastive learning stage to learn unified clustering across disjoint views. Experiments verify the effectiveness of the proposed CPMN.", "questions": "（1）CPMN seems to be done in phases, first acquiring initial prototypes, then prototype matching, and finally optimizing the prototypes. It is better to explore end-to-end training to create a more integrated pipeline.\n\n（2）The complete optimization process of the model is not clear, it is better to add an algorithm description.\n\n（3）Although the authors give both fully incomplete and partially incomplete multi-view clustering results, the performance of CPMN in partially incomplete multi-view clustering is poorer than the baselines. The authors should explain this result.\n\n（4）The authors should provide more qualitative results, such as t-SNE visualization, to provide deeper insights beyond quantitative metrics.", "limitations": "The paper discusses some limitations, including the influence of the initial prototype quality on the clustering results and the assumption of the number of clusters. There is no potential negative societal impact of their work.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n（1）The paper is well-organized.\n\n（2）The problem addressed is novel and the motivation is clear.\n\n（3）The experimental results demonstrate a substantial improvement in fully incomplete multi-view clustering.\n\nWeaknesses\n- Please find the specifics in Questions section.", "was_revised": true, "final_justification": "Thanks to the author for solving my concerns, and I decided to keep the original score.", "rebuttal": "We thank the reviewer for their insightful and constructive feedback. We have carefully addressed each of your points in the detailed, point-by-point responses below. \n\n## Reply to Questions (1):\nWe sincerely thank the reviewer for this insightful question. We completely agree that an end-to-end model is an elegant ideal. Our choice of a phased training paradigm is not a compromise, but rather a deliberate and principled design choice made specifically to tackle the unique and extreme challenges of the Fully Incomplete Multi-View Clustering (FIMC) problem. Our core reasoning is as follows:\n\n### 1. Avoiding the optimization dilemma\n\nA fully end-to-end model lacks any reliable supervisory signal. This makes it highly susceptible to collapsing into catastrophic local minima, such as trivial solutions (e.g., clustering all samples into one group) or convergence to a meaningless state due to initial noisy matches.\n\nOur multi-stage approach resolves this optimization dilemma. In Stage 1, our model focuses on a simpler initial representation to provide a reasonable starting point. Then, in Prototype Graph Matching, it performs a reliable, optimal match on this relatively stable representation space. Finally, our model uses this high-quality match as a strong supervisory signal for a final, joint optimization. This ensures each step builds upon a reliable foundation, guiding the model toward a meaningful, high-quality solution.\n\n### 2. Overcoming the Non-Differentiable Bottleneck\n\nOne of our core innovations, Prototype Graph Matching (PGM), uses the Hungarian algorithm to find an optimal one-to-one match. This is a discrete, non-differentiable combinatorial optimization process. Directly embedding such a non-differentiable step into a standard end-to-end gradient backpropagation pipeline is extremely difficult. While differentiable approximations exist, they introduce new complexities and may not provide the same clean, optimal assignment that our method relies on for stability. Our phased approach elegantly bypasses this bottleneck.\n\nTherefore, for the challenging FIMC problem, Therefore, our phased approach is not just a pipeline, but a robust framework carefully designed to ensure optimization stability and the quality of the final solution. Nevertheless, we agree that exploring deeper end-to-end integration is a valuable direction for future work.\n\n## Reply to Questions (2):\n\nWe sincerely thank the reviewer for this excellent suggestion. Due to the formatting limitations of the rebuttal system, we cannot insert a formal algorithm box. However, we present the complete optimization process of our model, in a structured pseudocode format below to illustrate how the different stages are connected and optimized.\n\nAlgorithm 1: The CPMN Algorithm\n\nInput:\n- Multi-view datasets $\\mathcal{X}=\\{X^{(v)}\\}_{v=1}^V$\n- Number of clusters $C$\n- Number of neighbors for MNN $k$\n- Temperature for contrastive loss $\\tau$\n- Maximum epochs $ME_1$ and $ME_1$\n- Trade-off parameters $\\lambda$ and $\\gamma$\n\nOutput:\n- Final cluster assignments for all samples\n\n--- Stage 1: Correspondence-Free Graph Contrastive Learning  ---\n1. Initialize encoder $E_v$ and decoder $D_v$ for all views.\n2. for epoch = 1 to $ME_1$ do\n3. Input $x^{(v)}_i$ to view-specific autoencoders to obtain the representation $z^{(v)}_i$ and the reconstructed samples $\\hat{x}^{(v)}_i$.\n4. Construct the intra-view and inter-view MNN graphs.\n5. Compute the GCL loss based on the MNN graphs: $L_{GL} = L_{SGL} + L_{CGL}$.\n6. Compute the reconstruction loss $L_{REC}$.\n7. Compute the total loss $\\mathcal{L}\\_{\\text{CFGC}} = L\\_{\\text{REC}} + \\lambda L\\_{\\text{GL}}$.\n8. Backpropagate $\\mathcal{L}_{\\text{CFGC}}$  and update view-specific autoencoders.\n9. end for\n10. Generate final initial instance representations using the trained encoders $E_v$.\n11. Run K-Means on representations of each view to get initial prototypes $\\mathcal{C}^{(v)} = \\{c_1^{(v)}, \\dots, c_C^{(v)}\\}$.\n\n--- Stage 2: Prototype Graph Matching (PGM) ---\n\n12.\tCompute pairwise cost matrix $M^{(v_a,v_b)}$ between prototypes from different views.\n13.\tApply the Hungarian algorithm to find the optimal prototype matching map $pi$.\n\n--- Stage 3: Prototype Contrastive Clustering (PCL) ---\n\n14. Initialize the learnable clustering layer.\n15. for epoch = 1 to $ME_2$ do\n16. Input $x^{(v)}_i$ to view-specific autoencoders to obtain the representation $z^{(v)}_i$ and the cluster $c^{(v)}_i$.\n17. Compute the prototype contrastive loss $L_{PL} = L_{SPL} + L_{CPL}$ based on the matching map $\\pi$.\n18. Compute the self-supervised clustering loss $L_{CLU}$.\n19. Compute the total loss $L_{PCL} = L_{CLU} + \\gamma L_{PL}$.\n20. Backpropagate $ L_{PCL}$ and update view-specific autoencoders and the learnable clustering layer.\n21. end for\n22. Output the final cluster assignments.\n\n## Reply to Questions (3):\n\nWe sincerely thank the reviewer for this keen observation. We agree that our results show CPMN does not outperform all baselines in the Partially Incomplete Multi-View Clustering (PIMC) setting. This outcome is not accidental but stems from a fundamental difference in design philosophy between CPMN and methods specifically tailored for PIMC.\n\nPIMC methods are explicitly designed to leverage the \"paired samples\" (i.e., samples existing in multiple views). They use these paired samples as high-quality anchors to directly and explicitly align the feature spaces of different views. \n\nIn contrast, CPMN is conceived to solve the more challenging Fully Incomplete problem, where no such correspondences exist. Its core mechanisms, such as MNN graph construction and Prototype Graph Matching (PGM), are fundamentally correspondence-free approaches. When applied to the PIMC setting, CPMN does not have a specialized component to exploit this valuable paired information.\n\n## Reply to Questions (4):\n\nWe sincerely thank the reviewer for this excellent and constructive suggestion. As we cannot include images in the rebuttal, we present a quantitative analysis of our visualization results to provide the deep insights you requested. We conducted this analysis on the MNIST-USPS dataset with 100% unaligned views due to its clear class semantics.\n\nFirst, we identify the cross-view prototype pairs that are matched by our model's PGM component. Then, for each matched pair, we analyze the ground-truth label composition of the samples within each prototype. A successful match should consist of two prototypes in which the dominant ground-truth label of the samples within each prototype is identical. The table below shows the label purity analysis for some representative matched prototype pairs:\n\n| Matched Pair | View 1 (MNIST) | View 2 (USPS) | Conclusion |\n| :--- | :--- | :--- | :--- |\n| **Pair A** | Label: '0' (88% Purity) | Label: '0' (86% Purity) | Successful Match |\n| **Pair B** | Label: '1' (86% Purity) | Label: '1' (85% Purity) | Successful Match |\n| **Pair C** | Label: '2' (83% Purity) | Label: '2' (79% Purity) | Successful Match |\n\nAs the table demonstrates, our model accurately matches prototypes that are semantically consistent across views. For example, in Pair A, a prototype primarily containing the digit '0' from MNIST is correctly matched with a prototype primarily containing the digit '0' from USPS. The other pairs show similarly high semantic coherence. This quantitative analysis provides strong evidence that our model learns meaningful and correct cross-view semantic correspondences. \nThank you again for your valuable feedback, which has prompted us to provide this deeper analysis."}]

Author rebuttal:

Meta-review: After the rebuttal and discussion phases, the paper received scores of 5, 5, 4, and 4, exceeding the expected threshold for acceptance. The main concerns were the efficiency of CPMN, the rationale for using Mutual Nearest Neighbors, and the lack of theoretical explanation for key components like prototype matching. After the rebuttal, all of the reviewers' concerns were addressed. 

Having reviewed the comments and the authors' responses, I believe the paper meets the acceptance criteria for NeurIPS.
Decision: Accept (poster)