Incomplete Multi-view Deep Clustering with Data Imputation and Alignment
Authors: Jiyuan Liu
Xinwang Liu
Xinhang Wan
KE LIANG
Weixuan Liang
Sihang Zhou
Huijun Wu
Kehua Guo
Venue: NeurIPS 2025 poster ()
Keywords: multi-view clustering
deep clustering
incomplete clustering
Primary area: general_machine_learning

Abstract: Incomplete multi-view deep clustering is an emerging research hot-pot to incorporate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to a fixed set of data samples in all views. Meanwhile, the pair-wise similarities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment. Assuming that each data sample corresponds to a same latent representation among all views, it projects the latent representations into feature spaces with neural networks. As a result, not only the available data observations are reconstructed, but also the missing ones can be imputed accordingly. Moreover, a linear alignment measurement of linear complexity is defined to compute the pair-wise similarities of all data observations, especially including those of the missing. By executing the above two procedures iteratively, the discriminative latent representations can be learned and used to group the data into categories with off-the-shelf clustering algorithms. In experiment, the proposed method is validated on a set of benchmark datasets and achieves state-of-the-art performances.

Incomplete Multi-view Deep Clustering with Data Imputation and Alignment
Jiyuan Liu', Xinwang Liu'*, Xinhang Wan', Ke Liang', Weixuan Liang' Sihang Zhou', Huijun Wu' and Kehua Guo
1 National University of Defense Technology, Changsha, Hunan, China. 410072. 2 Central South University, Changsha, Hunan, China, 410083. liuj y edui. cn
Abstract
Incomplete multi-view deep clustering is an emerging research hot-pot incor- porate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to fixed set of data samples in all views. Meanwhile, the pair-wise wise similar- ities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment. Assuming that each data sample corresponds to a same latent representation among all views, it projects the latent representations into feature spaces with neural networks. As result, not only the available data observations are reconstructed, but also the missing ones can be imputed accord- ingly. Moreover, linear alignment measurement of linear complexity is defined to compute the pair-wise similarities of all data observations, especially including those of the missing. By executing the above procedures iteratively, the dis- criminative latent representations can be learned and used to group the data into categories with off-the-shelff clustering algorithms. In experiment, the proposed method is validated on set of benchmark datasets and achieves state-of-the-art performances.
1 Introduction
With the development of electronical device and information technology. the data observations are widely accumulated from different sources and modalities, collectively referred to as multi-view data in academic communities. For instance, when making advertisement recommendation to Internet users, the content provider would collect their personal details from multiple aspects in advance, such living habit, shopping record, etc. [I] In the diagnosis and treatment of Alzheimer's discase, multiple types of data are collected and analyzed along with a set of medical examinations, including blood test, Cerebrospinal Fluid (CSF) examination, Magnetic Resonance Imaging (MRI), Computed Tomography (CT), Positron Emission Tomography (PET), etc. (2) Therefore, how to integrate the multi-view data effectively and efficiently critical problem. In this background, multi-view clustering can explore the consensus and complementary information among different data views and improve the performance over single-view clustering by large margins, catching large volume of attentions from researchers
*Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Since most of the existing multi-view clustering are derived from single-view algorithms, they can be grouped into five categories accordingly. i.e., multiple kemel clustering 4
6 5. multi-view subspace clustering 7 & 99, multi-view spectral clustering [10 11, multi-view matrix factorization
12 13 and multi-view deep clustering [14 15]. Insides, multi-view deep clustering is emerging in recent years along with the rapid development of neural network techniques. Among the advances, Cui et al. propose to extract high-level features from data observations of each view with multiple view-specific fully connected auto-encoders, then design the dual contrasting losses to maximize the distance between different clusters and enhance the compactness within clusters [6]. Yu et al. employ graph convolutional encoder on each data view [17]. Subsequently, the contrastive learning technique and block diagonalization constraint are adopted to guide representation matrix learning, while representation learning is utilized into clustering result generation. Similarly, Chen et al. learn view-invariant data representations with auto-encoders and compute results by contrasting the cluster assignments among different views 18] Usually, multi-view deep clustering approaches achieve better performance than the others due to the superior capability of neural networks to generate high-quality latent representations on data observations.
Due to sensor failure or restricted conditions, the collected multi-view data are often incomplete where one or more views are missing completely. In such setting, the researchers propose number of incomplete multi-view deep clustering approaches to make the most of available data observations rather than discarding the data samples with missing views [19 20). Mostly, they first encode the available data observations into multiple view-specific latent representations and subsequently integrate them by designing different losses on them. For instance, Chao et al. adopt the contrastive loss to maximize representation similarities of the same data sample in different views while minimize those of different data samples [2]] At the same time, Lin et al. modify the contrastive loss to maximize mutual information across all data views, promoting the learning of informative and consistent latent representations [22].
Although the existing methods achieves satisfactory performance, they ignore the fact that the latent representations of fixed set of data samples are unique and invariant to different views. Meanwhile, they only concentrate on the integration of available data observations but overlook the pair-wise similarity information among missing data observations, limiting the further improvement of clustering performance. To address these issues, we propose a novel Incomplete Multi- view Deep Clustering with Data Imputation and Alignment (IMDC-DIA). Specifically, it assumes that all views share a same latent representation with respect to a certain data sample. Contrary to the mainstream methods of encoding data observations into latent representations, the proposed approach projects the unique latent representations to feature space of each view with multiple independent neural networks. As consequence, not only the available data observations are reconstructed, but also the missing ones can be imputed accordingly. Moreover, a linear alignment measurement is defined and analyzed accordingly. Then, we adopt it to align the latent representations with the data observations of each view, so as to utilize the pair-wise similarities of all data observations, especially including those of the missing. By executing the above data imputation and alignment coherently and iteratively, the discriminative latent representations can be learned and used to group the data into categories with off-the-shell clustering algorithms. To validate effectiveness of the proposed IMDC-DIA method, we conduct extensive experiments on a set of benchmark datasets and compare it with the most recent advances in literature. Corresponding results show it achieves state-of -f-the--------tt clustering performance in almost all settings, well validating its effectiveness and superiority.
2 Related work
2.1 Multi-view deep clustering
As representative of multi-view clustering, multi-view deep clustering is one of the most effective technique to group data samples with integrating their multi-view information. Typically, it achieves better performances than the other multi-view clustering methods, since the adopted neural networks can extract higher-quality latent representations on the data observations of each view. Among them, the Multiple Layer Perceptron (MLP) network is the most widely used in literature, such as those in 16 23 Besides, the other types of neural networks are also employed to further improve the quanlity of latent representations. For example, Yu et al. generate the view-specific latent representations with Graph Convolutional Network (GCN) encoder on each view, successfully capturing the structural data information along with learning attribute features [7 Observing the poor scalability of MLP,

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Zhu et al. transform the feature vector into image and use Convolutional Neural Networks (CNN) subsequently. achieving satisfactory clustering performance 244. Yang et al. adopt the Transformer structure by utilizing self-attention mechanism, enabling the encoder to better retain complementary information across different views and remove the exclusive information 25
Apart from the neural network structure, plenty of constraints and loss functions are developed in existing researches. Insides, contrastive loss is the most popular one of them. Commonly, it regards the latent representations of data sample in different views as positive pairs while the rest as negative pairs, and maximizes the similarities of the former while minimizes those of the latter [25] 231 At the same time, Cui et al. integrate the pseudo-labed in training stage and consider the latent representations of data samples in a same temporary cluster as positive pair, improving the clustering performance effectively [16]. In addition, a large number of researches employ the self-representationn loss derivate from the self-representatioon constraint classical multi-view clustering [24 26) assumes each latent representation to be a linear sum of the others and minimizes their differences. Nevertheless, some of the other popular constraints and loss functions would be the adversarial similarity constraint 27 the discriminative constraint [15 and the self-supervised loss [17]
2.2 Incomplete multi-view deep clustering
To deal with incomplete data in real-world scenarios, incomplete multi-view deep clustering is emerging to be promising approach and explored in recent literature. Some of them only rely on the available data observations to compute the clustering results 288 29 They usually encode the available data observations into latent representations with multiple neural networks with each in one data view. On the basis, Wen et al. propose a graph embedding strategy to simultaneously capture the high-level features and local structure of each data view, while self-paced strategy is also utilized to select the most confident samples in model training, reducing the negative influence of outliers [29]. Differently, Xu et al. learn latent representations by incorporating the cexture-of-Gaussiand prior information to enhance their clustering- cestering-friendlyy structure and develop a Product-of- of-Experts approach to efficiently aggregate them 30]. Xu et al. utilize all view-specific latent representations into consensus one with an adaptive feature projection module, avoiding to impute the missing data [II. Then, the correlated common cluster information is explored by maximizing its mutual information, while the distribution alignment is achieved by minimizing its mean discrepancy coherently.
Different from the above approaches, the other incomplete multi-view deep clustering methods try to recover the missing data along with the latent representation learning and data clustering [21 32 33) For instance, Wang et al. learn the low-dimensional latent representations with view-specific encoder networks and explicitly generate the missing data with generative adversarial networks at the same time B3) Lin et al. unify the cros-vview consistency learning and data recovery techniques by maximizing the mutual information of different views and minimizing the conditional entropy through dual prediction, respectively 22 34. Liu et al. propose two-stage autoencoder network with recurrent graph reconstruction mechanism to extract high-level latent representations and recover the missing data synchronously (35]
Methodology
In this section, the proposed IMDC-DIA method is introduced, where its framework is visualized in Fig. Briefly, it aims learn the high-quality latent representations which are subsequently fed to off-the-shelf clustering algorithms so as to group the data accurately. To accomplish this, the latent representations are assumed be unique all views. On the basis, three main components are concerned, i.e., data reconstruction, imputation and alignment. On the left of Fig. the proposed IMDC-DIA method projects the unique latent representations to feature space of each view with multiple independent neural networks. Thereby, not only the available data observations are reconstructed (data reconstruction), but also the missing ones can be imputed and completed (data imputation) accordingly. In data alignment, a linear alignment measurement is defined and, as shown on the right of Fig. [ is adopted align the unique data representations with the completed data observations of each view.
3

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complete multi-view data with imputations
generate
Z
input
linear alignment
So
missing data
reconstruct
impute
generate
input
Neural Networks
Latent Representation
Incomplete Data
Reconstructed Data
Completed Data
Figure I:
Framework of the proposed IMDC-DIA method. For the case of expression, only two data views are presented, but arbitrary number of views are supported. Also, any types of neural networks, apart from the fully-connected, be employed, only if they project the latent representations into data feature space.
3.1 Formulation
Denoting N, V and Du as the number of data samples, the number of views and the feature dimension
of v-th view, multi-view data observations can be specified to {x, (v) N.V
Ji,== in which (() E RP:, Corresponding availability indicators are {ar where is discrete vector in {0, 13 Here, the data observation of v-th view (*) available if the v-th element a, while missing if 0. In such setting, incomplete multi-viww deep clustering methods aim to group the data into clusters with
the available observations where the cluster number known in advance.
3.1.1 Data reconstruction and imputation
Instead of encoding the available data observations into multiple view-specific latent representations, the proposed IMDC-DIA method assumes that the data latent structure is intrinsic and corresponding latent representations should be unique to all data views. Denoting the latent representations to be (z) where z; E TRP, it proposes to reconstruct the multi-view data observations by projecting the latent representations into feature spaces with V independent neural networks as
x
gege (z.),
where + represents parameters of the v-th neural network. It is worth to note that the latent representation z; is not fixed but a variable which can be optimized in model training. Correspondingly, can obtain the reconstruction loss by minimizing the differences between the generated data and the available data observations via
L
ai.or ||x
x;
(1)
in which Vi2 refers to the number of available views of i-th data sample. Nevertheless, it can be observed in aforementioned reconstruction process that not only the available data observations are reconstructed, but also the missing ones are imputed accordingly. Therefore, the multi-view data can be completed by filling the missing with those imputed Eq. (I). As result, the complete data can be formulated
X (v) if ai.0 0.
if ai 1,
(3)

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3.1.2 Data alignment
On the basis of the complete multi-view data of Eq. (3) the proposed IMDC-DIA method also incorporate the pair-wise similarities of data observations, especially those of the missing, to regularize the latent representations. Primarily, the Linear Alignment of two matrices is defined in Definition 1
Definition (Linear Alignment) Given two arbitrary matrices X2 and X2 of size x d1 and n x d2 respectively, the linear alignment is computed as
LA (x(X (x,
(4)
in which Lr(-) denotes the Frobenius norm of matrix. Corresponding computation complexity is linear to
Denoting vector x, to the i-th row of an arbitrary matrix X, the pair-wise linear similarity between its i-th and j-th rows is measured by their dot-products that
k = xxx w.r.t. i,j E (1,2, ...,,..,,., ,)
(5)
With considering two arbitrary matrices X and X₂ coherently, their pair-wise linear similarities should be
M = x and = =
(6)
On this basis, the similarity consistency of these two matrices can be measured by the sum of their dot-products as
c=
E E E.
where the denominator is scaler term to ensure the obtained consistency in range [-1,
Theorem
The linear alignment of two arbitrary matrices measures the consistency of the puir-wise linear similarities of their rows.
Proof The consistency of Eq. 77 can be transformed to
Σnj=1 ki
Eij=1 ki.
1ij=1 1 k V Exj= hi
Rij=1 R 1L V /E h2
Kl, K₂ >F
Tr((X, x (X2x,)]
(8)
V< K1, K1 >F K2, K2 VTr[(X,X, X (X
Tr XxX, ) (X2X,,)
[X X2) (X]Xx,)
X X 11?
X |F |X X2llr = LA,
VTI[XX XI) X1)I Tr[(X, X2) (X, X2)]
in which the second equation holds for
k2,5 = X2,XI11 = -2, = k2-j
while the third holds for
x1,1I
x1
X1,1
1
k
x1,2%111
x1,281,2
x IN
k2,2
h
K1
and
x1,,
x1.NxI1
x1,NxI [.N_
k
(10)
X2,1
X2.1
X2,1x,N
k2
x2,22,11
X2,282,
x2,2%,
K2
X2,NX12
X2,N
This completes the proof.
5

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According to Theorem 1 the linear alignment of two arbitrary matrices measures the consisteney of the pair-wise linear similarities their rows. To consider the pair-wise similarities all data observations, especially including those of the missing ones, we propose to maximize the linear alignment between the latent representations and the completed data observations of u-th view, i.e., max LA(Z, X Therefore, corresponding loss can be formulated
L X())
_ LL
(11)
LF (Z 2) LF (X()
in which Z and ( are the matrix form of ) and {x Ji-1
) respectively, Furthermore, to consider the data quality of each view, additional set of weight parameters {w,) ) introduced
to balance their effect on latent representations. As consequence, the overall data alignment loss can be written
V
La
Σ
w L.
8.L. Σ
=1
(12)
==1
is worth to note that )= are variables to be optimized in model learning rather than hyper- parameters specified in advance.
3.1.3 Loss function
As seen in the framework Fig. [ the proposed IMDC-DIA method composed of three main components, including the data reconstruction, imputation and alignment. By utilizing the recon- struction loss of Eq. ( missing data imputation of Eq. (3) and data alignment loss of Eq. (12), the overall loss function written
V s.t.
== + BLas
Σ
=1
(13)
in which is a trade-off parameter and should be specified before model training.
3.2 Optimization
According to the overall loss of Eq. 13 there are three variables to optimize in model training, including the neural network parameter (O J the unique latent representation {z, J.W. and weight parameter [w.)Y= Each of them can be optimized in the following.
Optimization of neural network parameter (Q Same most of deep learning methods, the neural network parameter can be optimized with gradient descent strategy. In experiment, we adopt the popular Adaptive Moment Estimation (Adam) optimizer.
Optimization of latent representation [ Different from the existing multi-view clustering methods, such [13), the proposed IMDC-DIA method is difficult to find the close-form solution of data latent representation. Thereeore, the gradient descent strategy with Adam optimizer is adopted in its optimization.
Optinization of weight parameter (we IV overall loss of Eq. (13) equals to
With fixing the others, L is given and minimizing the
V s.t. w
max (wre W
Σ
W. (-(()
Σ
1.
(14)
1=1
==l
According to o Cauchy Schwarz inequality
36
V
Σ w. w.()) S
Σ
Σ
(1)2
(1)2
L
(0)2
(15)
where the equality holds for when
W1
W2
WV
(16)
7 (1)
T (2)
- (V)

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Unifying the constraint E w = 1 in Eq. (14)
the solution can be computed to
/ = -
La
(v)2
(17)
Overall, the aforementioned three parameters are optimized alternately and the latent representations can be achieved until the convergence or maximal epoch. Next, k-means algorithm applied on the computed latent representations { to group multi-view data into categories. Furthermore, the pseudo-code of the optimization procedure summarized in Alg.
Algorithm 1 Incomplete Multi-view Deep Clustering with Data Imputation and Alignment
Input: incomplete multi-viee view data {x] Output: data labels
Ji,== with availability indicator (a/ J cluster number
N.V
1: initialize latent representation {2:] and network parameters {0,
2: O:;
3: while 1 < epochs do
4: # forwardd
5: compute L, with Eq. (2):
6:
complete multi-view data with Eg.
3):
compute {T.g Je=1 ( with Eq. 11:
7:
8:
update the view weights {wo) ==1 with Eq. 17);
9:
compute the overall loss with Eq. 13
# back propagation
11:
update latent representation {z, J and network parameters {Or)
1;+1;
13:
end while
compute the data labels with k-means on latent representations {z)mi
3.3 Computation complexity
Specifically, the data reconstruction and imputation of Eq. and 3 only require projecting the latent representations into feature spaces with parameterized neural networks, hence introducing ((N) complexity. Also, corresponding updates on latent representations and network parameters are of ((N) complexity. Besides, the complexity of data alignment loss L(( in Eq. (12) is mainly on the computation of (Z " ( (Z Z) and Lx(X ((1)) which are all of O(N) complexity. Nevertheless, the optimization of weight parameter {w,} am via Eq. (17) is of (VV) complexity. In
summary, the overall complexity the proposed IMDC-DIA method is linear to the number of data samples, i.e., O(N).
4 Experiment
4.1 Experiment setting
To validate the proposed IMDC-DIA method, conduct extensive experiments on four benchmark datasets, including HandWritter 2 (37] Caltech5V basis, generate incomplete datasets by following the common strategy 41
38 Flowerl 7
33 and MSRCV 40). On the
literature. Specifi-
cally, assuming the missing ratio to be m, percent of data samples are selected to remove at least one views randomly. In the following experiments, m five recent incomplete multi-view deep clustering approaches are considered in comparison, including
(0.1, 0.3, 0.5, 0.7.0.9). Meanwhile.
DITA-IMVC [4]. DSIMVC
DCP 34
DVIMVC 30 and CPSPAN
4% Note that, we
https://archive httpa//ewe..eteeeaeeeeeae//aaaaa

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Table 1: Performance comparison between the proposed IMDC-DIA and recent incomplete deep mueti-view clustering approaches. The avg. column refers to performance averages of all missing ratios. Note that, the best results marked in bold, while the second-best with underline.
Metric
ACC
NMI
Missing ratio
0.1
0.3
0.5
0.7
0.9
avg.
0.1
0.5
0.7
0.9
avg.
DITA-IMVC
75.48
78.92
81.37
81.02
55.00
74.36
75.81
78.05
77.62
75.54
52.16
71.84
HandWritten
DSIMVC
79.55
80.73
78.83
77.48
50.87
73.49
78.57
77.76
74.93
71.97
48.53
70.35
DCP
81.95
75.73
77.23
71.77
13.07
63.95
84.37
78.95
79.22
74.39
0.93
63.57
DVIMC
86.42
83.05
45.48
25.20
18.92
51.81
87.64
84.78
56.58
35.43
17.96
56.48
CPSPAN
90.42
91.25
91.08
90.27
86.73
89.95
83.84
84.37
84.01
83.55
82.62
83.68
IMDC-DIA
96.37
93.68
91.80
90.65
87.93
92.09
91.80
93.68
91.80
90.65
87.93
91.17
DITA-IMVC
79.10
75.76
68.02
58.90
40.29
64.41
67.56
64.78
58.84
52.40
29.29
54.57
CaltechSV
DSIMVC
76.64
73.14
66.36
57.38
44,95
63.69
68.02
63.11
56.71
49.23
33.99
54.21
DCP
44.50
46.95
46.45
44.67
16.98
39.91
45.22
52.31
50.69
45.07
0.54
38.77
DVIMC
88.64
81.36
84.93
80.86
68.81
80.92
80.52
73.38
76.27
73.56
62.40
73.23
CPSPAN
83.29
81.10
77.21
76.79
79.02
79.48
73.81
71.30
68.73
68.43
69.26
70.31
IMDC-DIA
86.05
85.05
83.33
85.02
81.29
84.15
86.05
85.05
83.33
85.02
81.29
84.15
DÍTA-IMVC
18.75
17.52
T3.77
13.16
12.84
15.21
18.15
16.60
10.23
8.65
8.66
12.46
Flower17 17
DSIMVC
18.63
16.86
13.50
13.36
13.36
15.14
17.51
14.78
9.29
9.27
9.22
12.01
DCP
26.15
25.49
22.21
15.05
10.78
19.94
26.18
25.94
23.47
15.37
3.69
18.93
DVIMC
36.69
31.23
26.84
23.41
21.69
27.97
35.43
29.82
24.30
20.93
20.08
26.11
CPSPAN
36.27
39.34
31.15
37.35
36.00
36.02
37.13
39.65
30.88
38.15
35.97
36.36
IMDC-DIA
52.03
46.47
44.22
41.54
39.14
44.68
52.03
46.47
44.22
41.54
39.14
44.68
DITA-IMVC
76.03
74.60
70.95
66.83
55.87
68.86
67.62
63.02
60.61
54.96
43.32
57.91
DSIMVC
78.57
76.98
70.48
71.59
64.76
72.48
68.37
65.81
62.26
59.19
51.78
61.48
MSRCVI
DCP
17.94
20.00
22.06
22.22
22.70
20.98
7.11
7.54
7.05
4.95
4.62
6.25
DVIMC
74.60
61.43
56.67
43.17
38.25
54.82
66.68
56.40
54.91
42.02
30.08
50.02
CPSPAN
85.08
86.51
85.40
84.29
77.62
83.78
75.86
77.25
75.51
74.09
69.06
74.35
IMDC-DIA
91.27
92.22
86.03
85.08
83.02
87.52
91.27
92.22
86.03
85.08
83.02
87.52
directly adopt the public codes available on the authors' websites without modification. To ensure the comparison fairness, we grid-search their parameters and report the best. So does the proposed IMDC-DIA method with setting its only parameter / in {0.01, 0.1, 1, 10, 1003. By following the literature, four most common metrics are adopted to measure the clustering performance, including accuracy (ACC), normalized mutual information (NMI), purity (PUR) and adjusted rand index (ARI). Nevertheless, all methods executed multiple times and their averages are reported to remove randomness effect.
4.2 Effectiveness
In order to validate effectiveness of the proposed IMDC-DIA method, we compare it with the recent advances on incomplete deep multi-view clustering in literature. Corresponding results can be found in Table [ It is obvious that the proposed IMDC-DIA outperforms the recent advances in almost all missing ratios all datasets. Concretely, it achieves the improvements of 5.95%. 2.43%, 0.72%, 0.38% 1.20% in accuracy and 4. 16%, 8. 8.90%, 7.79%, 7.10%, 5.31% NMI on HrntWritten; 15.34%, 7.13%. 13.07%, 4.19%, 3.14% in accuracy and 14.90% 6.82%, 13.34%, 3.39%, 3.17% in NMI on Flower17; 6. 6.19% 5.71% %. 0.63%, 0.79%. 5.40% in accuracy and 15.41%. %, 14.97%. 10.52%. 10.99%, 13.96% in NMI, respectively. Although slight decreases in 0.1 and 0.3 missing ratios Caltech5V are observed, i.e., 2.59% and 1. 1.60%, the proposed IMDC-DIA obtains hetter performances on the other missing ratios consistently. Nevertheless, with averaging the results in all missing ratios, see that it improves the accuracy by 2. 14%. 2.27% 3. 3.14%, 3.74% and the NMI by 7.49% 10.92%. 8.32%, 13.17% on the four benchmark datasets. To be summarized, the aforementioned observations
'The code is available attttps///gttbbb.com///t

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Table 2: Performance comparison between the proposed IMDC-DIA method and its variants of modifying and removing the data imputation and alignment components. The avg. column refers to performance averages of all missing ratios, while the avg. reports the performances in the setting of completing missing data with average values. Note that, the best results are marked in bold, while the second-best with underline.
Metric
ACC
NMI
Missing ratio
0.1
0.3
0.5
0.7
0.9
avg.
0.1
0.3
0.5
0.7
0.9
avg.
avg.
75.58
66.17
56.47
50.63
41.78
58.13
75.30
64.92
55.95
51.55
42.18
57.98
w/o imp.
HandWritten
zero
83.85
68.87
61.33
48.23
44.72
61.40
76.90
64.85
56.41
49.60
42.58
58.07
rand
79.98
69.73
58.37
55.05
44.33
61.49
78.33
68.31
57.06
52.81
42.45
59.79
none
96.13
82.55
87.82
78.70
55.83
80.21
91.37
82.39
82.03
74.80
49.31
75.98
w/o align.
93.62
86.65
90.57
81.27
82.78
86.98
87.78
81.89
81.82
76.88
73.44
80.36
IMDC-DIA
96.37
93.68
91.80
90.65
87.93
92.09
91.80
86.68
83.31
82.05
77.39
84.25
avg.
74.14
73.19
63.86
52.07
46.98
62.05
72.26
66.11
56.68
47.16
39.89
56.42
w/o tmp.
CaltechSV
80.74
73.60
67.38
61.81
52.12
67.13
74.06
63.71
57.33
52.74
43.37
58.24
rand
78.76
68.31
62.05
58.10
47.95
63.03
72.70
60.89
53.63
50.37
37.17
54.95
none
87.98
82.14
81.71
76.31
61.74
77.98
78.57
72.57
70.35
62.81
46.61
66.18
w/o align.
80.21
81.90
80.07
83.50
81.60
81.46
73.42
72.84
71.04
72.08
67.51
71.38
IMDC-DIA
86.05
85.05
83.33
85.02
81.29
84.15
76.39
75.28
72.22
72.28
68.14
72.86
avg.
47.23
39.80
32.70
29.78
25.02
34,91
46.18
38.56
33.21
27.93
24.29
34.03
w/o imp.
Flower17
zero
45.15
36.86
31.81
27.38
24.63
33.17
44.51
34.58
29.05
25.27
22.77
31.24
rand
45.64
35.20
30.15
25.98
23.75
32.14
45.17
33.54
27.65
23.60
20.75
30.14
none
42.01
35.93
25.64
13.11
17.23
26.78
42.74
34.80
22.81
7.58
11.43
23.87
w/o align.
38.28
36.18
35.54
30.81
28.50
33.86
35.90
35.13
31.87
27.53
24.44
30.97
IMDC-DIA
51.13
45.00
42.89
40.69
37.06
43.35
47.15
45.02
41.33
38.42
34.81
41.35
w/o imp.
avg.
72.70
57.46
51.27
42.86
36.67
52.19
64.86
51.51
43.94
38.28
30.14
45.75
MRSCVI
zoro
68.10
62.86
56.83
45.56
42.38
55.14
59.26
46.69
46.66
36.53
30.58
43.94
rand
66.35
55.08
48.89
44.60
43.17
51.62
59.30
44.20
40.67
32.61
31.49
41.65
none
78.89
62.06
58.25
31.90
39.84
54.19
75.10
58.82
50.66
17.53
23.40
45.10
w/o align.
85.56
85.24
73.65
67.30
60.95
74.54
78.09
76.37
60.14
52.43
48.95
63.20
IMDC-DIA
91.27
92.22
86.03
85.08
83.02
87.52
84.37
85.63
77.84
74.21
70.47
78.51
well illustrate the effectiveness of the proposed IMDC-DIA method and its superiority over the recent advances in literature.
4.3
Ablation study
To demonstrate the rationality of our motivations and effectiveness of the proposed techniques, we further conduct an thorough ablation study in the following. Two settings are designed by modifying and removing the data imputation and alignment components. Specifically,
1. The avg., zero and rand of w/o imp. substitute the data imputation into completing the miss- ing data with averages of available data observations, zeros and random values, respectively. Meanwhile, the none of w/o imp. refers to only using the available data observations in data alignment module rather than completing the missing.
2. w/o align. removes the data alignment module, which can be easily implemented by setting parameter 3 to O.
By comparing results of the proposed IMDC-DIA method and its w/o imp. settings, the former achieves better clustering performances in almost missing ratios on all benchmark datasets. Although slight decreases in missing ratio 1.1 on Caltech5V are observed, i.e.. 1.93% accuracy and 281 NMI, the proposed IMDC-DIA obtains better performances on the other missing ratios, i.e., 2.91 %, 1. 1.62%, 8.71 %. 19.55% accuracy and 2.71 % 1.87%, 9.47% 21 1.33% NMI. In average, it improve the accuracy by 11 188%, 6. 17%, 8.44%, 32.38% and the NMI by 8.27% 6.68%, 7.32%, 32.76%. These observations well validate effectiveness of the proposed data imputation module. In addition,

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HandWWritenn
CaltechSV
Flower17
MSRCV1
100
100
60
100
80
80
Accuracy (%)
80
Accurscy (%)
Accuracy (8)
40
60
Accuracy
60
60
Missing:
Missing:
20
Missing:
Nissing:
40
Massing:
0.1
40
Missing:
Missing:
Massing:
Missing:
Nizsing:
20
Missing:
Missing:
Nizsing: 0.3
in: 0.8
20
0.01
0.1
10
100
0.01
0.1
10
100
0.01
0.1
10
100
0.03
0.1
10
100
Figure 2: Accuracy variation with respect to parameter 3 in different missing ratios on the four benchmark datasets. The shaded area represents the accuracy variance correspondingly.
find the proposed IMDC-DIA exhibits larger and larger performance improvements when increasing the missing ratio. Also, the results in none setting are better than those in avg., zero and rand settings in most cases. The two observations indicate that complementing the missing data without data-irrelevant values would introduce extra bias hence decreasing the performance.
By comparing results of the proposed IMDC-DIA method and its w/o align. settings, similar observations can be obtained. Specifically, 0.31% accuracy decrease presented in missing ratio 0.9 on Caltech5V, while different degrees of improvements are observed in the other missing ratios, i... 5.84%, 3.15%. 3.26%, 1.52% accuracy and 2.97%. 2.44%, 1.18%, 0.20% NMI. Also, with averaging the results in all missing ratios, the proposed IMDC-DIA method achieves better accuracies by 5.1 1%, 2.69%, 9. 9.49% 12.98% and NMIs by 3.89% 1.48% 10.38%, 15.31 %6 respectively. These well demonstrate that the defined linear aligmment is conducive to the performance improvement.
Globally, the proposed IMDC-DIA method achieves better clustering performances than its none of w/o imp. setting, i.e., 11.88% 6. 1.7, 16.57% 33.33% accuracies and 8.27%, 6.68%, 17. 17.48%, 33.41% % NMIs. This proves that incorporating the data similarities among missing data observations can largely enhance the learning of latent representations, hence obtaining better clustering results.
4.4 Parameter analysis
In the proposed IMDC-DIA method, the only parameter is the trade-off 3 between the data re- construction loss and data alignment loss. To investigate its effect on performance, we collect the clustering accuracies when 3 set in range f0.01, 0.1, 1, 10. 100) and present their average curves and corresponding variances in Fig. 2 In general, the clustering accuracy decreases with a larger B in almost all missing ratios all benchmark datasets. Specifically. it can be seen that the best accuracies are obtained mostly when setting 3 to 0.01 and sometimes when setting 33 to 0.1. Therefore, we recommend to set it from 0.01 0.1 in first priority.
5 Conclusion
In literature, existing incomplete multi-view deep clustering approaches overlook the fact that the latent representations should be unique for a specific set of data samples. Also, they fail to utilize the pair-wise similarities of missing data observations sufficiently. Therefore, this paper proposes an incomplete multi-view deep clustering method with data imputation and alignment by assuming each data sample corresponds to a same latent representation among all views. Insides, a novel linear alignment measurement of linear complexity is defined and incorporated to integrate the pair-wise similarities of all data observations, including those of the missing ones. Neverthcless, an alternate optimization strategy is proposed to learn high-quality latent representations for the next clustering task. In experiment, the proposed method is compared with recent advances, while its motivations and method design are validated. Also, its parameter effect is explored empirically.
Although the proposed method achieves state-of -he results compared to recent advances, it may be partially limited by lacking sufficient constraints on the latent representations, preventing from further improvement of the clustering performance. In the future work, we will explore more feasible constraints. Meanwhile, the evaluation on missing data imputation is also a promising research direction on the basis of this work.
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Acknowledgments and Disclosure of Funding
This work supported by the National Natural Science Foundation of China (No. 62306324, 62376279, U24A20333, 62325604, 62276271, 62421002), the Science and Technology Innovation Program of Hunan Province (No. 2024RC3128, and the National University of Defense Technology Research Foundation (No. ZK24-30).
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A Convergence analysis
In the optimization, the proposed IMDC-DIA method aims to minimize the loss L of Eq. Insides, three variables are optimized alternately, including the neural network parameter { the unique latent representation {z. and weight parameter {wo)em With little abuse of notation, let the loss be represented by
13
= {((O,) (2i) (wr (1w))==))
(18)
Taking the loss at epoch be
] L ((10, M 12, ( IN (w) Ju= By fixing (2 and {w,) at {z, ر and {wo JbzI optimizing ( at L ++11 epoch
(19)
induces
((10 (2 ( I.
Ji=1 (w ) z ((O ( J tw (w JEmz).
(20)
So do the optimizations of {2i and (w,) ) resulting in (( (z. Jiz (u!")y= s ((1O)+")) J (z. Ji=i {w [[( (E=z)
(
(
(21)
< E((O Je=1, (z. ( which can be simplified to
M= (w! S E(10 J0=1 (z+ )
Jizl (w 11
)(=))
0 L (141)
(22)
Nevertheless,
I= L, + BL 2 0 (-1)=
(23)
To be summarized, Eq. (22) indicates that the loss monotonically decreases, while Eq. that the loss is lower bounded. Therefore, the optimization algorithm is convergent.
23 illustrates
B Dataset detail
The specifics of the used benchmark datasets are presented in Table Also, they are briefly introduced as follows:
1. HandWritter 37 It consists of 2,000 digital images of ten classes from 0 to 9 in which there are 200 images in each class. Here, six features used, i.e., 216-D profile correlations, 76-D Fourier coefficients of the character shapes, 64-D Karhunen-Loov coefficients, 6-1) morphological features, 240-D pixel averages in 2x3 windows and 47-D Zemiie moments.
2. Caltech5 / well-known conventional feature descriptors are adopted. including 48-D wavelet moments, 40-D CENTRIST, 254-D LBP, 512-D GIST and 928-D HOG, respectively.
38 It collects 1400 object images belonging to 7 classes. I experiment, five
3. Flowerl 39 It collects flower images of 17 categories with 80 images for each class. Corresponding features are 5376-D Color Histogram, 512-D GIST, 5376-D HOG (2x2), 5376-D HOG (3 x3), 1239-D LBP, 5376-D SIFT and 5376-D SSIM features.
4. MSRCV 1 40
It collects 210 images of seven categories with each category provides 30 images. For each image, six features are extracted, including 1302-D CENTRIST, 48-D Color Moment, 512-D GIST, 100-D HOG, 256-D LBP and 210 SIFT, respectively.
For HandWritten, Flower17 7 and MSRCV1, the creators share them publicly but do not issue licenses, while Caltech5V is issued the Creative Commons Attribution 4.0 International (CC BY 4.0) license.
C Incomplete multi-view data setting
The incomplete multi-view data are generated by following the common strategy in literature. Specifically, assuming the missing ratio to be m, percent of data samples are selected to remove at least one views randomly, In the following experiments, m is set {0.1, 0.1.00....5500...000 Meanwhile, the corresponding psuedo-code is outlined in Alg i
21

---

Table 3: Details of the used benchmark datasets, Note that, in brackets are the feature dimensions of each data view.
Number of
Dataset
Samples Clusters
Views (Dimensions)
HandWritten
2000
10
6(216776664466/440/447
CaltechVV
1400
(48440/254/51//928
Flower17
1360
17
711225576/57701129955766666
MSRCVI
210
7
6 (10332/88/112/1000/5661110
Algorithm 2 Generation of Incomplete Multi-view Data
Input:
incomplete multi-view data {x[ N,V
Ji,0=1 missing ratio m
Output: availability indicator {a: )=
I: obtain the numbers of data samples and views, i.e. N and V:
2: random sample incomplete data index S with missing ratio m;
3: initialize availability indicator
{1,2, ... ,V} w.r.t E ,1,
4: for
do
5: random sample missing index mp C 2,, ... VJ and mp 0:
6: set availability indicator a, {1, (1, 2, .. V] }- mp:
7:
end for
D More experiment settings
In the experiments, we adopt fully-connected neural networks on all datasets where different numbers of neurons are adopted according to different feature dimensions, shown in Table Meanwhile, the unique data latent representation and parameters of neural netowrks are both optimized with gradient descent strategy with Adam optimizer whose learning rate is set to 0.001. Additionally, the codes of the proposed method and recent advances in comparison are executed on a server with 40 Intel(R (R Xeon(R) Silver 4210R CPU @ 2.40GHz CPUs and NVIDIA GeForce RTX 3090 GPUs. The software environment includes Python 3. 30. and PyTorch 1.1 optimized with CUDA 11.4.
E
Additional result
Apart from the ACC and NMI results in Table [ and [ we also provide the experiment results in PUR and ARI metrics in Table and 6 respectively. It can be observed that the PUR and ARI results follow similar trends with those in ACC and NMI. Nevertheless, to analyze the training process more deeply, we also record the loss value and corresponding performances at each training epoch, which are visualized Fig. 3 obvious that the loss value continuously decreases and finally converges to the minimum, while the ACC and NMI increase to the top and fluctuate around their top values. These observations well illustrate the effectiveness of loss design in Eq. (33 and the proposed IMDC-DIA method.
Table 4: The neuron numbers of the proposed IMDC-DIA method specific to different datasets.
HandWritten
Caltech5V
Flower17
MSRCVI
1st-view
(60, 64, 216)
(21, 16, 40)
(34, 512, 5376)
(21, 256, 1302)
niew
(60, 64.76)
(21, 64, 254)
(34, 256, 512)
(21, 32, 48)
view
(60, 32, 64)
(21, 128, 928)
(34, 512, 5376)
(21, 64. 512)
4th-view
(60, 16, 6)
(21, 128, 512)
(34,512 5376)
32, 100)
5th-view
(60, 64, 240)
(21, 256, 1984)
(34, 256, 1239)
(21, 64, 256)
6th-view
(40, 32, 47)
(34. 512, 5376)
(21, 64. 210)
7th-view
(34, 512, 5376)
22

---

Table 5: Performance (PUR and ARI) comparison between the proposed IMDC-DIA and recent incomplete deep multi-view clustering approaches. The avg. column refers to performance averages of all missing ratios. Note that, the best results are marked bold, while the second-best with underline.
Metric
PUR
ARI
Missing ratio
0.1
0.3
0.5
0.7
0.9
avg.
0.1
0.3
0.5
0.7
0.9
avg.
DITA-IMVC
77.85
80.90
81.38
81.02
55.00
75.23
66.61
70.78
70.87
68.67
35.92
62.57
HandWritte
DSIMVC
81.13
80.73
79.88
77.50
51.18
74.08
71.69
70.19
67.27
63.91
32.36
61.08
DCP
83.97
78.08
79.40
73.40
13.42
65.65
75.32
61.27
62.61
53.62
0.02
50.57
DVIMC
86.53
83.12
45.53
25.27
19.45
51.98
82.38
77.91
35.65
14.20
5.74
43.18
CPSPAN
90.42
91.25
91.08
90.27
87.82
90.17
80.83
82.12
81.69
80.46
78.02
80.62
IMDC-DIA
96.37
93.68
91.80
90.65
87.93
92.09
92.09
93.68
91.80
90.65
87.93
91.23
DITA-IMVC
79.10
75.76
68.02
60.64
41.31
64.97
61.06
57.26
48.75
40.62
18.10
45.16
CaltechSV
DSIMVC
76.64
73.14
66.36
58.57
46.31
64.20
60.87
54.83
47.05
37.67
22.88
44.66
DCP
49.24
54.31
51.52
48.40
17.29
44.15
23.18
27.54
28.11
20.46
-0.06
19.85
DVIMC
88.64
81.36
84.93
81.38
68,83
81.03
77.33
67.12
71.87
68.58
52.92
67.56
CPSPAN
83.29
81.10
78.14
77.76
80.05
80.07
69.41
65.71
62.80
61.27
63.60
64.56
IMDC-DIA
86.05
85.05
83.33
85.02
81.29
84.15
86.05
85.05
83.33
85.02
81.29
84.15
DITA-IMVC
20.61
19.53
15.10
13.80
13.41
16.49
5.63
4.81
2.20
2.10
1.96
3.34
DSIMVC
20.07
18.58
14.34
14.00
13.82
16.16
5.38
4.30
1.98
2.06
2.48
3.24
Flower17
DCP
27.11
27.18
23.87
15.76
11.10
21.00
10.07
8.02
3.86
1.76
0.03
4.75
DVIMC
37.84
32.57
27.87
24.53
22.97
29.16
18.88
14.32
10.93
8.47
7.71
12.06
CPSPAN
38.11
40.86
32.55
39.68
37.23
37.69
17.47
19.36
13.19
19.06
16.89
17.19
IMDC-DIA
52.03
46.47
44.22
41.54
39.14
44.68
52.03
46.47
44.22
41.54
39.14
44.68
DITA-IMVC
76.83
74.60
70.95
66.83
56.67
69.18
58.42
54.43
49.80
43.22
29.20
47.01
DSINVC
78.57
76.98
70.79
71.59
65.40
72.67
59.93
57.68
51.54
50.56
41.58
52.26
MSRCVI
DCP
18.10
20.63
22.54
22.54
23.17
21.40
-0.01
0.07
0.24
-0.16
-0.21
-0.01
DVIMC
74.60
61.43
56.83
43.81
38.25
54.98
57.67
45.83
41.15
27.52
19.05
38.24
CPSPAN
85.08
86.51
85.40
84.29
78.10
83.88
70.63
72.54
70.95
69.02
61.63
68.95
IMDC-DIA
91.27
92.22
86.03
85.08
83.02
87.52
91.27
92.22
86.03
85.08
83.02
87.52
HandWritten
Caltech5V
Flower17
MSRCV1
80
80
Loos value
Lass vali
Lass value
Loss value
80
0.4
40
0.4
0.2
-0.5
-0.5
1500
500
1500
1000
2000
1000
2000
Epoch
Epoch
Epoch
Epech
Figure 3: Loss and performance variation at each epoch on the four benchmark datasets. The blue curve represents loss value, while the yellow and green curves are accuracy and NMI, respectively.
23

---

Table 6: Performance (PUR and ARI) comparison between the proposed IMDC-DIA method and its variants of modifying and removing the data imputation and alignment components. The avg. column refers to performance averages of all missing ratios, while the avg. row reports the performances in the setting of completing missing data with average values. Note that, the best results marked in bold, while the second-best with underline.
Metric
PUR
ART
Missing ratio
0.1
0.3
0.5
0.7
0.9
avg.
0.1
0.3
0.5
0.7
0.9
avg.
w/o imp.
avg
78.12
68.
18.13
59.27
53.78
44.48
60.76
62.70
44.29
24.49
18.1 14
11.49
32.22
HandWritten
zero
83.98
70.98
62.73
51.35
46.63
63.14
71.39
47.75
32.75
21.58
15.48
37.79
rand
80.18
71.13
59.95
55.62
46.58
62.69
70.79
55.61
32.89
25.63
15.86
40.16
none
96.13
84.73
89.28
79.67
56.68
81.30
91.59
77.60
80.11
69.16
37.18
71.13
w/o align.
93.62
88.18
90.57
83.77
84.12
88.05
86.73
78.23
80.55
71.71
69.92
77.43
IMDC-DIA
96.37
93.68
91.80
90.65
87.93
92.09
92.09
86.37
82.60
80.53
75.42
83.40
avg
78.50
74.48
64.81
54.62
48.86
64,25
60.29
46.02
30.32
17.49
12.95
33.41
Caltech5V w/o imp.
82.17
73.60
67.88
61.81
53.00
67.69
65.43
50.59
38.09
27.57
16.36
39.61
rand
79.24
68.67
62.43
58.93
48.24
63.50
67.77
51.12
37.88
28.01
17.16
40.39
none
87.98
82.45
81.71
76.31
61.93
78.08
76.63
68.91
68.49
58.79
38.25
62.22
w/o align.
80.81
82.19
80.93
83.50
81.60
81.80
68.21
68.29
67.07
68.89
65.25
67.54
IMDC-DIA
86.05
85.05
83.33
85.02
81.29
84.15
73.54
72.05
69.00
71.06
65.78
70.29
avg
48.70
41.72
34.07
30.59
26.20
36.25
25.93
14.78
11.40
8.11
5.40
13.12
w/o imp.
Flower17
zero
45.81
37.55
32.70
27.97
25.42
33.89
27.61
19.97
13.97
9.85
7.61
15.80
rand
46.37
35.71
30.96
26.79
24.46
32.86
28.77
18.25
9.27
6.30
15.05
42.92
36.84
26.62
13.85
18.14
27.67
22.89
18.09
9.91
0.68
2.98
10.91
w/o align.
39.46
37.60
36.57
32.28
29.71
35.12
18.55
18.39
16.34
13.59
11.55
15.68
IMDC-DIA
52.03
46.47
44.22
41.54
39.14
44.68
27.04
25.11
21.99
20.89
17.73
22.55
w/o imp.
avg
72.86
59.52
52.22
44.60
38.10
53.46
52.89
27.30
20.49
10.75
7.80
23.85
MSRCVI
zero
69.05
63.33
57.30
46.51
43.81
56.00
43.29
33.62
25.93
14.12
11.75
25.74
rand
67.46
56.83
51.59
46.03
44.92
53.37
48.75
31.53
26.17
15.75
12.57
26.96
none
79.68
62.38
62.22
33.97
41.43
55.94
66.16
46.72
39.52
8.04
14.72
35.03
align.
85,56
85.24
73.65
67.62
62.86
74.98
72.51
70.51
$2.78
43.35
39.98
55.83
IMDC-DIA
91.27
92.22
86.03
85.08
83.02
87.52
80.92
82.50
70.95
69.28
64.59
73.65
24


Reviews:
[{"review_id": "Gi5SMce2nY", "reviewer": "Reviewer_aouo", "summary": "Existing incomplete multi-view deep clustering methods typically encode each data view into an independent latent representation, overlooking the intrinsic uniqueness of the underlying data representation across views. Moreover, they fail to sufficiently exploit the pair-wise similarities among missing data instances. To address these limitations, this paper proposes a novel incomplete multi-view deep clustering approach that jointly imputes missing data and aligns the reconstructed views using a proposed linear alignment mechanism. The method enforces consistency across views by assuming a shared latent representation for each sample and projects it to each view via independent neural networks. Extensive experiments on four benchmark datasets demonstrate that the proposed approach consistently outperforms state-of-the-art methods across a wide range of missing ratios, validating its effectiveness in both representation learning and clustering accuracy.", "questions": "Please find in *Strengths and Weaknesses* section.", "limitations": "yes, at the end of *Conclusion* section.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "# Strength\n\n1. The proposed linear alignment measurement is simple but effective and efficient (linear complexity) to incorporate the pair-wise similarities of missing data.\n\n2. The proposed IMDC-DIA achieves promising clustering results compared to the existing methods.\n\n3. The limitations are discussed at the end of *Conclusion* section.\n\n# Weaknesses\n\n1. The authors are expected to doubly check the Equation (1). This paper argues that the latent representation is unique to all data views. But $z_i^{(v)}$ in Equation (1) indicates that each data view corresponds a latent representation. The authors are encouraged to clarify this ambiguity and revise the notation accordingly. It is also recommended to carefully proofread the entire manuscript to eliminate typos and inconsistencies.\n\n2. Although the paper reports accuracy and normalized mutual information (NMI), purity is another standard metric in clustering evaluation. Including purity results (if available) would provide a more comprehensive performance comparison.\n\n3. In ablation study, \"Three settings are designed ...\". However, only two settings are designed and tested.\n\n4. The convergence should be analyzed empirically at least.\n\n5. The paper focuses on data imputation as a core component, yet recent related works on imputation for incomplete multi-view clustering are not cited, e.g., Incomplete Multi-view Clustering via Prototype-based Imputation, IJCAI 2023, Decoupled Contrastive Multi-view Clustering with High-order Random Walks, AAAI 2024.\n\n6. Theorem 1 plays a central role in the paper’s theoretical foundation, but its statement lacks clarity. Specifically, key terms such as \"consistency\" and \"pair-wise linear similarities\" are not formally defined, making the theorem difficult to interpret or evaluate.", "was_revised": true, "final_justification": "I thank the authors for their detailed rebuttal. I believe they have adequately addressed the main concerns I raised in my initial review, and their clarifications have improved my understanding and appreciation of the work. As a result, I have decided to raise my score.", "rebuttal": "Thanks so much for your recognition on the proposed linear alignment measurement and the effectiveness of experiment results!\n\n**Q1. Typos and inconsistencies**\n\nThanks. So sorry for the typos! $\\mathbf{z}_ i^{(v)}$ should be revised to $\\mathbf{z}_ i$, where Eq. (1) should be\n$$\\hat{\\mathbf{x}}_i^{(v)} = g _{\\Theta_v}(\\mathbf{z}_i).$$\nAlso, we have proofread the whole manuscript to eliminate all typos and inconsistencies. \nSpecifically, we have added the bracket of $v$ in Eq. (3) to keep consistency of all equations, i.e.\n$$\\bar{\\mathbf{x}}_i^{(v)} = \\begin{cases}\n    \\mathbf{x}_i^{(v)} & \\text{ if } \\mathbf{a} _{i,v} = 1, \\\\\\\\\n    \\hat{\\mathbf{x}}_i^{(v)} & \\text{ if } \\mathbf{a} _{i,v} = 0.\n  \\end{cases}$$\n\n**Q2. Purity results**\n\nThanks. After running the experiments again, we have obtained not only the purity results but also the ARI results additionally. In the following are those on Handwritten dataset, while the others will be provided in Appendix. It can be seen that the purity and ARI results follow the same trend with the ACC and NMI results.\n\n| Metric |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | DITA-IMVC | 77.85 | 80.90 | 81.38 | 81.02 | 55.00 | 75.23 | 66.61 | 70.78 | 70.87 | 68.67 | 35.92 | 62.57 |\n|  | DSIMVC | 81.13 | 80.73 | 79.88 | 77.50 | 51.18 | 74.08 | 71.69 | 70.19 | 67.27 | 63.91 | 32.36 | 61.08 |\n|  | DCP | 83.97 | 78.08 | 79.40 | 73.40 | 13.42 | 65.65 | 75.32 | 61.27 | 62.61 | 53.62 | 0.02 | 50.57 |\n|  | DVIMC | 86.53 | 83.12 | 45.53 | 25.27 | 19.45 | 51.98 | 82.38 | 77.91 | 35.65 | 14.20 | 5.74 | 43.18 |\n|  | CPSPAN | 90.42 | 91.25 | 91.08 | 90.27 | 87.82 | 90.17 | 80.83 | 82.12 | 81.69 | 80.46 | 78.02 | 80.62 |\n|  | IMDC-DIA | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 93.68 | 91.80 | 90.65 | 87.93 | 91.23 |\n\n\n| Metric |  |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | w/o imp. | avg | 78.12 | 68.13 | 59.27 | 53.78 | 44.48 | 60.76 | 62.70 | 44.29 | 24.49 | 18.14 | 11.49 | 32.22 |\n|  |  | zero | 83.98 | 70.98 | 62.73 | 51.35 | 46.63 | 63.14 | 71.39 | 47.75 | 32.75 | 21.58 | 15.48 | 37.79 |\n|  |  | rand | 80.18 | 71.13 | 59.95 | 55.62 | 46.58 | 62.69 | 70.79 | 55.61 | 32.89 | 25.63 | 15.86 | 40.16 |\n|  |  | none | 96.13 | 84.73 | 89.28 | 79.67 | 56.68 | 81.30 | 91.59 | 77.60 | 80.11 | 69.16 | 37.18 | 71.13 |\n|  | w/o align. |  | 93.62 | 88.18 | 90.57 | 83.77 | 84.12 | 88.05 | 86.73 | 78.23 | 80.55 | 71.71 | 69.92 | 77.43 |\n|  | IMDC-DIA |  | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 86.37 | 82.60 | 80.53 | 75.42 | 83.40 |\n\n\n**Q3. Three settings**\n\nThanks. Sorry for the inconsistency. In ablation study, three settings are considered, i.e.\n1. The *avg.*, *zero* and *rand* of *w/o imp.* substitute the data imputation into completing the missing data with averages of available data observations, zeros and random values, respectively. \n2. The *none* of *w/o imp.* refers to only using the available data observations in data alignment module rather than completing the missing.\n3. *w/o align.* removes the data alignment module, which can be easily implemented by setting parameter $\\beta$ to $0$.\n\n**Q4. Empirical convergence analysis**\n\nThanks. We have recorded the loss value at each training epoch. Since the figures cannot be uploaded in Rebuttal period, we list the loss values on HandWritten dataset at each 40 epochs in the following: \n\n`\n1.4718, 0.4360, 0.1024, 0.0549, 0.0281, -0.0070, -0.0433, -0.0717, -0.0925, -0.1082, -0.1203, -0.1298, -0.1375, -0.1437, -0.1489, -0.1534, -0.1573, -0.1607, -0.1637, -0.1663, -0.1687, -0.1708, -0.1726, -0.1743, -0.1757, -0.1769, -0.1780, -0.1790, -0.1799, -0.1807, -0.1814, -0.1821, -0.1828, -0.1834, -0.1839, -0.1845, -0.1850, -0.1854, -0.1859, -0.1863, -0.1867, -0.1870, -0.1874, -0.1877, -0.1880, -0.1883, -0.1886, -0.1888, -0.1891, -0.1893\n`\n\nIt can be observed that the loss value continuously decreases and finally converges to the minimum. In next version, we will plot them and provide the loss value variation on all datasets in Appendix.\n\n**Q5. Related work**\n\nThanks. The two researches present classical incomplete multi-view clustering methods. Specifically, \n- The first one proposes a novel dual-stream model by performing data recovery using the prototypes in the missing view and the sample-prototype relationship inherited from the observed view.\n- The second one proposes a novel robust method by leveraging random walks to progressively identify data pairs globally and performing inter-view and intra-view contrastive learning in different embedding spaces.\n\nWe will introduce them in the Related Work section of next version.\n\n**Q6. Clarity of Theorem 1**\n\nThanks. Sorry for the missing of these two concepts! They are introduced as follows. Also, we polish Theorem 1 and its proof carefully.\n\n\nDenoting vector $\\mathbf{x}_ i$ to the $i$-th row of an arbitrary matrix $\\mathbf{X}$, the **pair-wise linear similarity** between its $i$-th and $j$-th rows is measured by their dot-products that \n\\begin{equation}\n  k_{i,j} = \\mathbf{x}_i\\mathbf{x}_j^\\top, \\quad w.r.t.\\quad i, j\\in \\{1, 2, \\cdots, N\\}\n\\end{equation}\n\nWith considering two arbitrary matrices $\\mathbf{X}_ 1$ and $\\mathbf{X}_ 2$ coherently, their pair-wise linear similarities should be \n\\begin{equation}\n  k^1_ {i,j} = \\mathbf{x}^1_ i\\mathbf{x}^{1\\top}_ j \\quad \\text{and} \\quad k^2_ {i,j} = \\mathbf{x}^2_ i\\mathbf{x}^{2\\top}_ j\n\\end{equation}\nOn this basis, the similarity **consistency** of these two matrices can be measured by the sum of their dot-products as \n\\begin{equation}\n  c = \\frac{\\sum_ {i,j=1}^N k^1_ {i,j}k^2_ {i,j}}{\\sqrt{\\sum_{i,j=1}^N k^1_ {i,j}k^1_ {i,j}}\\sqrt{\\sum_ {i,j=1}^N k^2_ {i,j}k^2_ {i,j}}}\n\\end{equation}\nwhere the denominator is a scaler term to ensure the obtained consistency in range $[-1, 1]$. \n\n**Theorem 1**. *The linear alignment of two arbitrary matrices measures the consistency of the pair-wise linear similarities of their rows.*\n\n**Proof**. \nThe consistency can be transformed to \n$$\nc  = \\frac{\\sum_ {i,j=1}^N k^1_ {i,j}k^2_ {i,j}}{\\sqrt{\\sum_ {i,j=1}^N k^1_ {i,j}k^1_ {i,j}}\\sqrt{\\sum_ {i,j=1}^N k^2_ {i,j}k^2_ {i,j}}} = \\frac{\\sum_ {i,j=1}^N k^1_ {i,j}k^2_ {j,i}}{\\sqrt{\\sum_ {i,j=1}^N k^1_ {i,j}k^1_ {i,j}}\\sqrt{\\sum_ {i,j=1}^N k^2_ {i,j}k^2_ {i,j}}}\n$$\n$$\n = \\frac{<\\mathbf{K}_1, \\mathbf{K}_2>_F}{\\sqrt{<\\mathbf{K}_1, \\mathbf{K}_1>_F<\\mathbf{K}_2, \\mathbf{K}_2>_F}} = \\frac{\\mathrm{Tr}[(\\mathbf{X}_1\\mathbf{X}_1^\\top)(\\mathbf{X}_2\\mathbf{X}_2^\\top)]}{\\sqrt{\\mathrm{Tr}[(\\mathbf{X}_1\\mathbf{X}_1^\\top)(\\mathbf{X}_1\\mathbf{X}_1^\\top)]\\cdot\\mathrm{Tr}[(\\mathbf{X}_2\\mathbf{X}_2^\\top)(\\mathbf{X}_2\\mathbf{X}_2^\\top)]}}\n$$\n$$\n= \\frac{\\mathrm{Tr}[(\\mathbf{X}_1^\\top\\mathbf{X}_2)^\\top(\\mathbf{X}_1^\\top\\mathbf{X}_2)]}{\\sqrt{\\mathrm{Tr}[(\\mathbf{X}_1^\\top\\mathbf{X}_1)(\\mathbf{X}_1^\\top\\mathbf{X}_1)]\\cdot\\mathrm{Tr}[(\\mathbf{X}_2^\\top\\mathbf{X}_2)(\\mathbf{X}_2^\\top\\mathbf{X}_2)]}} = \\frac{\\|\\mathbf{X}_1^\\top\\mathbf{X}_2\\|_F^2}{\\|\\mathbf{X}_1^\\top\\mathbf{X}_1\\|_F\\cdot\\|\\mathbf{X}_2^\\top\\mathbf{X}_2\\|_F} = LA,\n$$\n\n  in which the second equation holds for \n  \\begin{equation}\n    k^2_ {j,i} = \\mathbf{x}_ {2,j}\\mathbf{x}_ {2,i}^\\top = \\mathbf{x}_ {2,i}\\mathbf{x}_ {2,j}^\\top = k^2_ {i,j},\n  \\end{equation}\n\n  while the third holds for \n\n\\begin{equation}\n \\mathbf{K}_ 1 = \\begin{bmatrix}\n    \\mathbf{x}_ {1,1}\\mathbf{x}_ {1,1}^\\top & \\mathbf{x}_ {1,1}\\mathbf{x}_ {1,2}^\\top  & \\cdots & \\mathbf{x}_ {1,1}\\mathbf{x}_ {1,N}^\\top \\\\\\\\\n    \\mathbf{x}_ {1,2}\\mathbf{x}_ {1,1}^\\top & \\mathbf{x}_ {1,2}\\mathbf{x}_ {1,2}^\\top  & \\cdots & \\mathbf{x}_ {1,2}\\mathbf{x}_ {1,N}^\\top \\\\\\\\\n    \\vdots & \\vdots  & \\ddots & \\vdots \\\\\\\\\n    \\mathbf{x}_ {1,N}\\mathbf{x}_ {1,1}^\\top & \\mathbf{x}_ {1,N}\\mathbf{x}_ {1,2}^\\top  & \\cdots & \\mathbf{x}_ {1,N}\\mathbf{x}_ {1,N}^\\top \\\\\\\\\n  \\end{bmatrix} = \\begin{bmatrix}\n    k^1_ {1,1} & k^1_ {1,2} & \\cdots & k^1_ {1,3} \\\\\\\\\n    k^1_ {2,2} & k^1_ {2,2} & \\cdots & k^1_ {2,3} \\\\\\\\\n    \\cdots & \\cdots & \\ddots & \\cdots \\\\\\\\\n    k^1_ {N,1} & k^1_ {N,2} & \\cdots & k^1_ {N,N}\n  \\end{bmatrix}\n\\end{equation}\n\nand\n\n$$\n\\mathbf{K}_ 2 = \\begin{bmatrix}\n    \\mathbf{x}_ {2,1}\\mathbf{x}_ {2,1}^\\top & \\mathbf{x}_ {2,1}\\mathbf{x}_ {2,2}^\\top  & \\cdots & \\mathbf{x}_ {2,1}\\mathbf{x}_ {2,N}^\\top \\\\\\\\\n    \\mathbf{x}_ {2,2}\\mathbf{x}_ {2,1}^\\top & \\mathbf{x}_ {2,2}\\mathbf{x}_ {2,2}^\\top  & \\cdots & \\mathbf{x}_ {2,2}\\mathbf{x}_ {2,N}^\\top \\\\\\\\\n    \\vdots & \\vdots  & \\ddots & \\vdots \\\\\\\\\n    \\mathbf{x}_ {2,N}\\mathbf{x}_ {2,1}^\\top & \\mathbf{x}_ {2,N}\\mathbf{x}_ {2,2}^\\top  & \\cdots & \\mathbf{x}_ {2,N}\\mathbf{x}_ {2,N}^\\top \\\\\\\\\n  \\end{bmatrix} = \\begin{bmatrix}\n    k^2_ {1,1} & k^2_ {1,2} & \\cdots & k^2_ {1,3} \\\\\\\\\n    k^2_ {2,2} & k^2_ {2,2} & \\cdots & k^2_ {2,3} \\\\\\\\\n    \\cdots & \\cdots & \\ddots & \\cdots \\\\\\\\\n    k^2_ {N,1} & k^2_ {N,2} & \\cdots & k^2_ {N,N}\n  \\end{bmatrix}\n$$\n\nIn summary, $c = LA$, illustrating that the linear alignment of two arbitrary matrices equals to the consistency of the pair-wise linear similarities of their rows.\nThis completes the proof."}, {"review_id": "AQEXHE5pzE", "reviewer": "Reviewer_Awrn", "summary": "This paper proposes an incomplete multi-view deep clustering method with data imputation and alignment named IMDC-DIA. It assumes that the latent representations are unique to a fixed set of data samples in all views. Moreover, it utilizes the pair-wise similarities of missing data observations in latent representation learning. In experiments, the authors compare it with the existing methods on four datasets. It can be seen that the IMDC-DIA method obtains state-of-the-art performances.", "questions": "See strengths and weaknesses.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. The proposed method assumes that the latent representations are unique to a fixed set of data samples in all views, which is different from that of the most existing methods. This is rational and more consistent to real-world practice.\n\n2. The proposed linear alignment considers but does not require to compute the pair-wise similarities of data samples between different views, hence is of linear complexity to sample number. This is novel and practical, especially in large-scale problem. \n\n3. The proposed method is only composed of three simple and direct modules, i.e. data reconstruction, imputation and alignment. No sophisticated techniques are derivations are involved. But it achieves impressive performances in the comparison experiments. So the method is elegant and effective. \n\n4. The paper is well-organized and the writing is easy to follow.\n\n**Weaknesses**\n\n1. In Eq. (9), the trade-off parameter is $\\alpha$, but the parameter is written to $\\beta$ mistakenly in Fig. 2 and corresponding analysis. Please keep them consistent. \n\n2. In experiment, the performance and loss to training epoch are supposed to be presented and analyzed, at least for validating the rationality of the loss design. \n\n3. It is claimed that PUR and ARI are adopted in experiments in Section 4.1. However, they are missing in Table 1 and 2.\n\n4. Fig. 2 presents the accuracy variation to parameter $\\beta$. Also, the other evaluation measurements should be provided, including NMI, PUR and ARI.\n\n5. The optimization should be enhanced. At least, the optimization order and logic should be clarified.\n\n6. Please eliminate all typos and grammar errors.\n\n7. In Theorem 1, the authors say \"The linear alignment of two arbitrary matrices measures the consistency of the pair-wise linear similarities of their rows,\" but they do not define what \"consistency\" means or \"pair-wise linear similarities.\" So, Theorem 1 does not make sense at all in the current manuscript.", "was_revised": true, "final_justification": "The authors' response have addressed most of my concerns, thus I will raise my score.", "rebuttal": "Thanks so much for your recognition on the novelty, rationality, effectiveness and paper writing!\n\n**Q1. Typos**\n\nThanks. Sorry for the typos! we have replaced $\\alpha$ with $\\beta$ in the whole manuscript. \n\n\n**Q2. Performance and loss variation in training process**\n\nThanks. \nWe have recorded the performance and loss value at each training epoch. Since the figures cannot be uploaded in Rebuttal period, we list the accuracy values on HandWritten dataset at each 40 epochs in the following: \n\n`\nAccuracy: 12.80, 18.60, 50.50, 75.10, 85.90, 88.70, 89.75, 89.10, 79.00, 90.30, 92.15, 92.90, 92.70, 92.10, 94.20, 95.00, 94.95, 94.60, 84.80, 93.85, 93.45, 95.60, 95.70, 93.95, 95.95, 95.90, 95.85, 94.30, 82.20, 96.40, 96.35, 96.35, 96.20, 96.55, 83.45, 96.50, 96.50, 96.25, 96.65, 96.70, 96.65, 96.40, 96.75, 96.55, 97.00, 96.85, 96.80, 82.80, 96.90, 96.65\n`\n\n`\nLoss value: 1.4718, 0.4360, 0.1024, 0.0549, 0.0281, -0.0070, -0.0433, -0.0717, -0.0925, -0.1082, -0.1203, -0.1298, -0.1375, -0.1437, -0.1489, -0.1534, -0.1573, -0.1607, -0.1637, -0.1663, -0.1687, -0.1708, -0.1726, -0.1743, -0.1757, -0.1769, -0.1780, -0.1790, -0.1799, -0.1807, -0.1814, -0.1821, -0.1828, -0.1834, -0.1839, -0.1845, -0.1850, -0.1854, -0.1859, -0.1863, -0.1867, -0.1870, -0.1874, -0.1877, -0.1880, -0.1883, -0.1886, -0.1888, -0.1891, -0.1893\n`\n\nIt can be observed that the loss value continuously decreases and finally converges to the minimum, while the accuracy increases to the top and fluctuate around their top values.\nThese observations well illustrate the effectiveness of loss design in Eq. (9) and the proposed IMDC-DIA method.\n\nIn next version, we will plot them and provide the loss value variation on all datasets in Appendix.\n\n\n**Q3. Missing PUR and ARI results**\n\nThanks. After running the experiments again, we have obtained the PUR and ARI results. In the following are those on Handwritten dataset, while the others will be provided in Appendix. It can be seen that the purity and ARI results follow the same trend with the ACC and NMI results.\n\n| Metric |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | DITA-IMVC | 77.85 | 80.90 | 81.38 | 81.02 | 55.00 | 75.23 | 66.61 | 70.78 | 70.87 | 68.67 | 35.92 | 62.57 |\n|  | DSIMVC | 81.13 | 80.73 | 79.88 | 77.50 | 51.18 | 74.08 | 71.69 | 70.19 | 67.27 | 63.91 | 32.36 | 61.08 |\n|  | DCP | 83.97 | 78.08 | 79.40 | 73.40 | 13.42 | 65.65 | 75.32 | 61.27 | 62.61 | 53.62 | 0.02 | 50.57 |\n|  | DVIMC | 86.53 | 83.12 | 45.53 | 25.27 | 19.45 | 51.98 | 82.38 | 77.91 | 35.65 | 14.20 | 5.74 | 43.18 |\n|  | CPSPAN | 90.42 | 91.25 | 91.08 | 90.27 | 87.82 | 90.17 | 80.83 | 82.12 | 81.69 | 80.46 | 78.02 | 80.62 |\n|  | IMDC-DIA | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 93.68 | 91.80 | 90.65 | 87.93 | 91.23 |\n\n\n| Metric |  |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | w/o imp. | avg | 78.12 | 68.13 | 59.27 | 53.78 | 44.48 | 60.76 | 62.70 | 44.29 | 24.49 | 18.14 | 11.49 | 32.22 |\n|  |  | zero | 83.98 | 70.98 | 62.73 | 51.35 | 46.63 | 63.14 | 71.39 | 47.75 | 32.75 | 21.58 | 15.48 | 37.79 |\n|  |  | rand | 80.18 | 71.13 | 59.95 | 55.62 | 46.58 | 62.69 | 70.79 | 55.61 | 32.89 | 25.63 | 15.86 | 40.16 |\n|  |  | none | 96.13 | 84.73 | 89.28 | 79.67 | 56.68 | 81.30 | 91.59 | 77.60 | 80.11 | 69.16 | 37.18 | 71.13 |\n|  | w/o align. |  | 93.62 | 88.18 | 90.57 | 83.77 | 84.12 | 88.05 | 86.73 | 78.23 | 80.55 | 71.71 | 69.92 | 77.43 |\n|  | IMDC-DIA |  | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 86.37 | 82.60 | 80.53 | 75.42 | 83.40 |\n\n\n\n**Q4. NMI, PUR and ARI results on parameter study**\n\nThanks. After running the experiments again, we have computed the NMI, PUR and ARI results when parameter $\\beta$ varies in range $\\\\{0.01, 0.1, 1, 10, 100\\\\}$. Since the figures cannot be uploaded in Rebuttal period, we list them in the following table.\n\n- The NMI results with respect to different $\\beta$ in different missing ratios.\n| $\\beta$ | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |\n|---|---|---|---|---|---|\n| 0.01 | 90.54 | 85.32 | 83.31 | 82.05 | 76.77 |\n| 0.1 | 91.80 | 86.68 | 83.67 | 81.05 | 77.39 |\n| 1 | 86.99 | 77.55 | 72.86 | 67.22 | 66.71 |\n| 10 | 83.42 | 75.21 | 68.92 | 61.40 | 57.90 |\n| 100 | 81.64 | 71.65 | 62.97 | 55.85 | 43.97 |\n\n- The PUR results with respect to different $\\beta$ in different missing ratios.\n| $\\beta$ | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |\n|---|---|---|---|---|---|\n| 0.01 | 95.65 | 90.62 | 91.80 | 90.65 | 85.23 |\n| 0.1 | 96.37 | 93.68 | 89.38 | 90.37 | 87.93 |\n| 1 | 88.72 | 80.08 | 76.95 | 71.30 | 72.72 |\n| 10 | 84.58 | 77.75 | 73.57 | 67.98 | 64.47 |\n| 100 | 83.55 | 76.48 | 69.17 | 62.22 | 49.47 |\n\n- The ARI results with respect to different $\\beta$ in different missing ratios.\n| $\\beta$ | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |\n|---|---|---|---|---|---|\n| 0.01 | 90.61 | 83.15 | 82.60 | 80.53 | 72.80 |\n| 0.1 | 92.09 | 86.37 | 81.86 | 79.84 | 75.42 |\n| 1 | 83.70 | 71.08 | 63.92 | 54.18 | 53.81 |\n| 10 | 78.90 | 66.68 | 55.82 | 44.31 | 37.59 |\n| 100 | 76.86 | 63.46 | 48.54 | 37.57 | 24.23 |\n\nIt can be observed that those metrics follows similar trend to the ACC. Specifically, they decrease with a larger $\\beta$ in almost all missing ratios on all benchmark datasets, while the best are obtained mostly when setting $\\beta$ to 0.01 and sometimes when setting $\\beta$ to 0.1. Therefore, we recommend to set parameter $\\beta$ from 0.01 to 0.1 in first priority.\n\n\n**Q5. Clarity of optimization**\n\nThanks. We re-organize the optimization section and add the optimization pseudo-code which will be provided in Appendix. Meanwhile, they are provided in the following. \n\nAccording to the overall loss of Eq. (9), there are three variables to optimize in model training, including the neural network parameter $\\\\{\\Theta_v\\\\}_ {v=1}^V$, the unique latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and weight parameter $\\\\{w_v\\\\}_ {v=1}^V$. \nEach of them can be optimized as follows:\n- *Optimization of neural network parameter $\\\\{\\Theta_v\\\\}_ {v=1}^V$*. Same to most of deep learning methods, the neural network parameter can be optimized with gradient descent strategy. In experiment, we adopt the popular Adaptive Moment Estimation (Adam) optimizer. \n- *Optimization of latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$*. Different from the existing multi-view clustering methods, such as [10], the proposed IMDC-DIA method is difficult to find the close-form solution of data latent representation. Therefore, the gradient descent strategy with Adam optimizer is adopted in its optimization. \n- *Optimization of weight parameter $\\\\{w_v\\\\}_ {v=1}^V$*. With fixing the others, $L_a^{(v)}$ is given and minimizing the overall loss of Eq. (9) equals to \n$$\n  \\max_ {\\\\{w_v\\\\}_ {v=1}^V} \\sum_ {v=1}^V w_v(-L_a^{(v)}), \\quad s.t. \\sum_ {v=1}^V w_v^2 = 1.\n$$\nAccording to o Cauchy–Schwarz inequality [31], \n$$\n  \\sum_{v=1}^V w_v(-L_a^{(v)}) \\leq \\sqrt{\\left(\\sum_{v=1}^Vw_v^2\\right)\\left(\\sum_{v=1}^VL_a^{(v)2}\\right)} = \\sqrt{\\sum_{v=1}^VL_a^{(v)2}},\n$$\nwhere the equality holds for when\n$$\n  \\frac{w_1}{-L_a^{(1)}} = \\frac{w_2}{-L_a^{(2)}} = \\cdots = \\frac{w_V}{-L_a^{(V)}}.\n$$\nUnifying the constraint $\\sum_ {v=1}^V w_v^2 = 1$ in Eq. (10), the solution can be computed to \n$$\n  w_v^* = -L_a^{(v)} / \\sqrt{\\sum_{v'=1}^V L_a^{(v')2}}.\n$$\nOverall, the aforementioned three parameters are optimized alternately and the latent representations can be achieved until the convergence or maximal epoch. \nNext, $k$-means algorithm is applied on the computed latent representations $\\\\{\\mathbf{z}_i\\\\} _ {i=1}^N$ to group multi-view data into categories.\nFurthermore, to specify the optimization procedure more clearly, corresponding pseudo-code is summarized in Alg. 1.\n\n\n**Algorithm 1. Incomplete Multi-view Deep Clustering with Data Imputation and Alignment**  \n**Input**: incomplete multi-view data $\\\\{\\mathbf{x}_ i^{(v)}\\\\}_ {i,v=1}^{N,V}$ with availability indicator $\\\\{\\mathbf{a}_ i\\\\}_ {i=1}^N$, cluster number $k$  \n**Output**: data labels  \n1. initialize latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and network parameters $\\\\{\\Theta_ v\\\\}_ {v=1}^V$;\n2. $t=0$;\n3. **while** $t<epochs$\n    - *\\# forward*\n    - compute $L_r$ with Eq. (2);\n    - complete multi-view data with Eq. (3);\n    - compute $\\\\{L_a^{(v)}\\\\}_ {v=1}^V$ with Eq. (7);\n    - update the view weights $\\\\{w_v\\\\}_ {v=1}^V$ with Eq. (13);\n    - compute the overall loss $L$ with Eq. (9);\n    - *\\# back propagation*\n    - update latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^{N}$ and network parameters $\\\\{\\Theta_v\\\\}_ {v=1}^V$;\n    - $t = t + 1$;\n4. **end while**\n5. compute the data labels with $k$-means on latent representations $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$;\n\n\n**Q6. Typos and grammar errors**\n\nThanks. We have carefully proofread the whole manuscript and tried our best to eliminate all typos and grammar errors. For example, the bracket is added on $v$ of Eq. (3) to keep consistency of all equations. More are not listed.\n\n**Q7. Clarity of Theorem 1**\n\nThanks. Sorry for the missing of these two concepts! They are introduced in detail. Also, we polish Theorem 1 and its proof carefully. Due to the space limit, please refer to the **Q6** of **Reviewer aouo** (*the same question*)."}, {"review_id": "NQIKCLtnMS", "reviewer": "Reviewer_ZBHB", "summary": "To consider the uniqueness of data representation of all data views and the pair-wise similarities of missing data observations, the authors propose an incomplete multi-view deep clustering method by imputing the missing data and aligning them iteratively. Moreover, they conduct experiments on the method and achieve state-of-the-art performances.", "questions": "Most issues have already been mentioned in Weaknesses. One additional problem is as follows:\n- In Theorem 1, the authors say \"The linear alignment of two arbitrary matrices measures the consistency of the pair-wise linear similarities of their rows,\" but they do not define what \"consistency\" means or \"pair-wise linear similarities\". The authors should clearly define \"pair-wise linear similarities\" and \"consistency\" in Theorem 1 and Proof 1.", "limitations": "Yes.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- The authors propose a new measurement (linear alignment) similar to kernel alignment which reduces the computation complexity to O(n). Also, the linear alignment is validated to be effective in experiments, especially in ablation study of Table 2. This will have a broader impact on the future research. \n\n- The experiment design of ablation study is impressive. Insides, the w/o imp. and w/o align. settings well validate the functions of data imputation and data alignment components respectively. Also, the w/o imp. setting considers four strategies, i.e. the average-filling, zero-filling, rand-filling and no-filling, which is complete. \n\n- The IDMC-DIA method achieves state-of-the-art results compared with the existing methods in literature, well validating its effectiveness.\n\n- The limitations are discussed. Also, the possible future work is also provided, which is appreciated. \n\nWeaknesses\n\n- As seen from Fig. 1 and corresponding descriptions, the $z_i^{(v)}$ in Equation (1) is supposed to be $z_i$ probably. The authors should check this.\n\n- In Equation (3), $v$ lacks the bracket. Please keep consistent in the whole paper.\n\n- In optimization section, the authors provide the method to optimize the neural network parameter, latent representation and weight parameter. But how to combine them in order is not illustrated clearly. The authors are encouraged to provide the pseudocode. \n\n- The convergence should be analyzed. \n\n- Table 1 and 2 only present the ACC and NMI results, but miss the PUR and ARI. Although the paper length is limited, the authors may provide them in Appendix.", "was_revised": true, "final_justification": "Thank the author for their rebuttal. My concerns have been resolved. I will raise my score to 'Borderline accept'.", "rebuttal": "Thanks so much for your recognition on the proposed alignment measurement, experiment design and effectiveness!\n\n**Q1 and Q2. Typos**\n\nThanks. So sorry for the typos! $z_i^{(v)}$ should be revised to $z_i$, where Eq. (1) should be\n$\\hat{\\mathbf{x}}_i^{(v)} = g _{\\Theta_v}(\\mathbf{z}_i)$\nAlso, we have added the bracket of $v$ in Eq. (3) to keep consistency of all equations, i.e.\n$$\\bar{\\mathbf{x}}_i^{(v)} = \\begin{cases}\n    \\mathbf{x}_i^{(v)} & \\text{ if } \\mathbf{a} _{i,v} = 1, \\\\\\\\\n    \\hat{\\mathbf{x}}_i^{(v)} & \\text{ if } \\mathbf{a} _{i,v} = 0.\n  \\end{cases}$$\nNevertheless, we have proofread the whole manuscript to eliminate all typos and inconsistencies.\n\n**Q3. Algorithm pseudocode**\n\nThanks. We have re-organized the optimization section and added the corresponding pseudocode, which are provided in the following.\n\nAccording to the overall loss of Eq. (9), there are three variables to optimize in model training, including the neural network parameter $\\\\{\\Theta_v\\\\}_ {v=1}^V$, the unique latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and weight parameter $\\\\{w_v\\\\}_ {v=1}^V$. \nEach of them can be optimized as follows:\n- *Optimization of neural network parameter $\\\\{\\Theta_v\\\\}_ {v=1}^V$*. Same to most of deep learning methods, the neural network parameter can be optimized with gradient descent strategy. In experiment, we adopt the popular Adaptive Moment Estimation (Adam) optimizer. \n- *Optimization of latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$*. Different from the existing multi-view clustering methods, such as [10], the proposed IMDC-DIA method is difficult to find the close-form solution of data latent representation. Therefore, the gradient descent strategy with Adam optimizer is adopted in its optimization. \n- *Optimization of weight parameter $\\\\{w_v\\\\}_ {v=1}^V$*. With fixing the others, $L_a^{(v)}$ is given and minimizing the overall loss of Eq. (9) equals to \n$$\n  \\max_ {\\\\{w_v\\\\}_ {v=1}^V} \\sum_ {v=1}^V w_v(-L_a^{(v)}), \\quad s.t. \\sum_ {v=1}^V w_v^2 = 1.\n$$\nAccording to o Cauchy–Schwarz inequality [31], \n$$\n  \\sum_{v=1}^V w_v(-L_a^{(v)}) \\leq \\sqrt{\\left(\\sum_{v=1}^Vw_v^2\\right)\\left(\\sum_{v=1}^VL_a^{(v)2}\\right)} = \\sqrt{\\sum_{v=1}^VL_a^{(v)2}},\n$$\nwhere the equality holds for when\n$$\n  \\frac{w_1}{-L_a^{(1)}} = \\frac{w_2}{-L_a^{(2)}} = \\cdots = \\frac{w_V}{-L_a^{(V)}}.\n$$\nUnifying the constraint $\\sum_ {v=1}^V w_v^2 = 1$ in Eq. (10), the solution can be computed to \n$$\n  w_v^* = -L_a^{(v)} / \\sqrt{\\sum_{v'=1}^V L_a^{(v')2}}.\n$$\nOverall, the aforementioned three parameters are optimized alternately and the latent representations can be achieved until the convergence or maximal epoch. \nNext, $k$-means algorithm is applied on the computed latent representations $\\\\{\\mathbf{z}_i\\\\} _ {i=1}^N$ to group multi-view data into categories.\nFurthermore, to specify the optimization procedure more clearly, corresponding pseudo-code is summarized in Alg. 1.\n\n\n**Algorithm 1. Incomplete Multi-view Deep Clustering with Data Imputation and Alignment**  \n**Input**: incomplete multi-view data $\\\\{\\mathbf{x}_ i^{(v)}\\\\}_ {i,v=1}^{N,V}$ with availability indicator $\\\\{\\mathbf{a}_ i\\\\}_ {i=1}^N$, cluster number $k$  \n**Output**: data labels  \n1. initialize latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and network parameters $\\\\{\\Theta_ v\\\\}_ {v=1}^V$;\n2. $t=0$;\n3. **while** $t<epochs$\n    - *\\# forward*\n    - compute $L_r$ with Eq. (2);\n    - complete multi-view data with Eq. (3);\n    - compute $\\\\{L_a^{(v)}\\\\}_ {v=1}^V$ with Eq. (7);\n    - update the view weights $\\\\{w_v\\\\}_ {v=1}^V$ with Eq. (13);\n    - compute the overall loss $L$ with Eq. (9);\n    - *\\# back propagation*\n    - update latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^{N}$ and network parameters $\\\\{\\Theta_v\\\\}_ {v=1}^V$;\n    - $t = t + 1$;\n4. **end while**\n5. compute the data labels with $k$-means on latent representations $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$;\n\n\n**Q4. Convergence analysis**\n\nThanks. we analyze the convergence of the proposed algorithm as follows.\n\nIn the optimization, the proposed IMDC-DIA method aims to minimize the loss $L$ of Eq. (9).\nInsides, three variables are optimized alternately, including the neural network parameter $\\\\{\\Theta_v\\\\}_ {v=1}^V$, the unique latent representation $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and weight parameter $\\\\{w_v\\\\}_ {v=1}^V$.\nWith a little abuse of notation, let the loss be represented by \n\\begin{equation}\n  L = \\ell(\\\\{\\Theta_ v\\\\}_ {v=1}^V, \\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N, \\\\{w_v\\\\}_ {v=1}^V).\n\\end{equation}\nTaking the loss at $t$ epoch to be \n\\begin{equation}\n  L^{(t)} = \\ell(\\\\{\\Theta_ v^{(t)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V), \n\\end{equation}\nBy fixing $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and $\\\\{w_v\\\\}_ {v=1}^V$ at $\\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N$ and $\\\\{w_ v^{(t)}\\\\}_ {v=1}^V$, optimizing $\\\\{\\Theta_ v\\\\}_ {v=1}^V$ at $t+1$ epoch induces to \n\\begin{equation}\n  \\ell(\\\\{\\Theta_ v^{(t)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V) \\leq \\ell(\\\\{\\Theta_ v^{(t+1)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V).\n\\end{equation}\nSo do the optimizations of $\\\\{\\mathbf{z}_ i\\\\}_ {i=1}^N$ and $\\\\{w_ v\\\\}_ {v=1}^V$, resulting in\n\\begin{equation}\n\\begin{split}\n  & \\ell(\\\\{\\Theta_ v^{(t)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V) \\leq \\ell(\\\\{\\Theta_ v^{(t+1)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V) \\\\\\\\ \n  & \\leq \\ell(\\\\{\\Theta_ v^{(t+1)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t+1)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t)}\\\\}_ {v=1}^V) \\leq \\ell(\\\\{\\Theta_ v^{(t+1)}\\\\}_ {v=1}^V, \\\\{\\mathbf{z}^{(t+1)}_ i\\\\}_ {i=1}^N, \\\\{w_ v^{(t+1)}\\\\}_ {v=1}^V),\n\\end{split}\n\\end{equation}\nwhich can be simplified to \n\\begin{equation}\n  L^{(t)} \\leq L^{(t+1)}.\n\\end{equation}\nNevertheless, \n\\begin{equation}\n  L = L_r + \\beta L_a \\geq 0 + (-1) = -1.\n\\end{equation}\nTo be summarized, the former equation indicates that the loss monotonically decreases, while the latter illustrates that the loss is lower bounded. \nTherefore, the optimization algorithm is convergent. \n\n**Q5. PUR and ARI results**\n\nThanks. After running the experiments again, we have obtained the PUR and ARI results. In the following are those on Handwritten dataset, while the others will be provided in Appendix. It can be seen that the purity and ARI results follow the same trend with the ACC and NMI results.\n\n| Metric |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | DITA-IMVC | 77.85 | 80.90 | 81.38 | 81.02 | 55.00 | 75.23 | 66.61 | 70.78 | 70.87 | 68.67 | 35.92 | 62.57 |\n|  | DSIMVC | 81.13 | 80.73 | 79.88 | 77.50 | 51.18 | 74.08 | 71.69 | 70.19 | 67.27 | 63.91 | 32.36 | 61.08 |\n|  | DCP | 83.97 | 78.08 | 79.40 | 73.40 | 13.42 | 65.65 | 75.32 | 61.27 | 62.61 | 53.62 | 0.02 | 50.57 |\n|  | DVIMC | 86.53 | 83.12 | 45.53 | 25.27 | 19.45 | 51.98 | 82.38 | 77.91 | 35.65 | 14.20 | 5.74 | 43.18 |\n|  | CPSPAN | 90.42 | 91.25 | 91.08 | 90.27 | 87.82 | 90.17 | 80.83 | 82.12 | 81.69 | 80.46 | 78.02 | 80.62 |\n|  | IMDC-DIA | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 93.68 | 91.80 | 90.65 | 87.93 | 91.23 |\n\n\n| Metric |  |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | w/o imp. | avg | 78.12 | 68.13 | 59.27 | 53.78 | 44.48 | 60.76 | 62.70 | 44.29 | 24.49 | 18.14 | 11.49 | 32.22 |\n|  |  | zero | 83.98 | 70.98 | 62.73 | 51.35 | 46.63 | 63.14 | 71.39 | 47.75 | 32.75 | 21.58 | 15.48 | 37.79 |\n|  |  | rand | 80.18 | 71.13 | 59.95 | 55.62 | 46.58 | 62.69 | 70.79 | 55.61 | 32.89 | 25.63 | 15.86 | 40.16 |\n|  |  | none | 96.13 | 84.73 | 89.28 | 79.67 | 56.68 | 81.30 | 91.59 | 77.60 | 80.11 | 69.16 | 37.18 | 71.13 |\n|  | w/o align. |  | 93.62 | 88.18 | 90.57 | 83.77 | 84.12 | 88.05 | 86.73 | 78.23 | 80.55 | 71.71 | 69.92 | 77.43 |\n|  | IMDC-DIA |  | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 86.37 | 82.60 | 80.53 | 75.42 | 83.40 |\n\n\n**Q6. Clarity of Theorem 1**\n\nThanks. Sorry for the missing of these two concepts! They are introduced in detail. Also, we polish Theorem 1 and its proof carefully. Due to the space limit, please refer to the **Q6** of **Reviewer aouo** (*the same question*)."}, {"review_id": "0TVq03hwss", "reviewer": "Reviewer_kzHN", "summary": "Existing multi-view deep clustering methods encode the data observations into latent representations but ignore their uniqueness to all views. Also, they fail to consider the pair-wise similarities of missing data observations. To address the two problems, this paper proposes an incomplete multi-view deep clustering method with data imputation and alignment named IMDC-DIA.", "questions": "1. In the experiment setting, the authors claim that four metrics are adopted to evaluate the method. But there are only two of them, i.e. ACC and NMI, in the tables. So the authors are supposed to provide the results of PUR and ARI.\n\n2. The missing data setting should be illustrated more clearly. \n\n3. More details of experiment settings are expected to be provided, such as the neural network structure, learning rate, optimizer, etc. \n\n4. The code should be released publicly for reproductivity.", "limitations": "Yes, at the end of the Conclusion section.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 2, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strength\n\n1. Novelty. Different from the existing methods of encoding the data observation into latent representation, this paper assumes the latter is unique and projects it to reconstruct the former. This is rational and novel. \n\n2. Writing. This paper is well-organized and easy to follow. Also, the framework of Fig. 1 provides a good overview of the method and is appreciated.\n\n3. Effectiveness. The proposed method achieves the best performances over those in literature in almost all missing ratios. Also, the ablation study well validates effectiveness of the data imputation and alignment modules.\n\n\nWeakness\n\n1. Completeness of experiment. This paper lacks some experiment results. \n\n2. Clarity of experiment setting. Some of the important experiment settings, such as details of deep learning structure, are missing. \n\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": "Thanks so much for your recognition on the novelty, writing and effectiveness. \n\n\n**Q1. PUR and ARI results**\n\nThanks. After running the experiments again, we have obtained the PUR and ARI results. In the following are those on Handwritten dataset, while the others will be provided in Appendix. It can be seen that the purity and ARI results follow the same trend with the ACC and NMI results.\n\n| Metric |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | DITA-IMVC | 77.85 | 80.90 | 81.38 | 81.02 | 55.00 | 75.23 | 66.61 | 70.78 | 70.87 | 68.67 | 35.92 | 62.57 |\n|  | DSIMVC | 81.13 | 80.73 | 79.88 | 77.50 | 51.18 | 74.08 | 71.69 | 70.19 | 67.27 | 63.91 | 32.36 | 61.08 |\n|  | DCP | 83.97 | 78.08 | 79.40 | 73.40 | 13.42 | 65.65 | 75.32 | 61.27 | 62.61 | 53.62 | 0.02 | 50.57 |\n|  | DVIMC | 86.53 | 83.12 | 45.53 | 25.27 | 19.45 | 51.98 | 82.38 | 77.91 | 35.65 | 14.20 | 5.74 | 43.18 |\n|  | CPSPAN | 90.42 | 91.25 | 91.08 | 90.27 | 87.82 | 90.17 | 80.83 | 82.12 | 81.69 | 80.46 | 78.02 | 80.62 |\n|  | IMDC-DIA | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 93.68 | 91.80 | 90.65 | 87.93 | 91.23 |\n\n\n| Metric |  |  | PUR |  |  |  |  |  | ARI |  |  |  |  |  |\n|---|---|---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n| Missing ratio |  |  | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | avg. |\n| HandWritten | w/o imp. | avg | 78.12 | 68.13 | 59.27 | 53.78 | 44.48 | 60.76 | 62.70 | 44.29 | 24.49 | 18.14 | 11.49 | 32.22 |\n|  |  | zero | 83.98 | 70.98 | 62.73 | 51.35 | 46.63 | 63.14 | 71.39 | 47.75 | 32.75 | 21.58 | 15.48 | 37.79 |\n|  |  | rand | 80.18 | 71.13 | 59.95 | 55.62 | 46.58 | 62.69 | 70.79 | 55.61 | 32.89 | 25.63 | 15.86 | 40.16 |\n|  |  | none | 96.13 | 84.73 | 89.28 | 79.67 | 56.68 | 81.30 | 91.59 | 77.60 | 80.11 | 69.16 | 37.18 | 71.13 |\n|  | w/o align. |  | 93.62 | 88.18 | 90.57 | 83.77 | 84.12 | 88.05 | 86.73 | 78.23 | 80.55 | 71.71 | 69.92 | 77.43 |\n|  | IMDC-DIA |  | 96.37 | 93.68 | 91.80 | 90.65 | 87.93 | 92.09 | 92.09 | 86.37 | 82.60 | 80.53 | 75.42 | 83.40 |\n\n\n**Q2. Missing data setting**\n\nThanks. We generate incomplete datasets by following the common strategy [36] in literature.\nSpecifically, assuming the missing ratio to be $m$, $m$ percent of data samples are selected to remove at least one views randomly. \nIn the experiments, $m$ is set in $\\\\{0.1, 0.3, 0.5, 0.7. 0.9\\\\}$.\nNevertheless, we provide the corresponding pseudocode and will add it in Appendix. \n\n**Algorithm 2. Generation of Incomplete Multi-view Data**  \n**Input**: incomplete multi-view data $\\\\{\\mathbf{x}_ i^{(v)}\\\\}_ {i,v=1}^{N,V}$, missing ratio $m$  \n**Output**: availability indicator $\\\\{\\mathbf{a}_ i\\\\}_ {i=1}^N$  \n1. obtain the numbers of data samples and views, i.e. $N$ and $V$;\n2. random sample incomplete data index $\\mathcal{S}$ with missing ratio $m$; \n3. initialize availability indicator $\\mathbf{a}_i = \\\\{1, 2, \\cdots, V\\\\}$ w.r.t. $i\\in \\\\{1, 2, \\cdots, N\\\\}$;\n4. **for** $p\\in\\mathcal{S}$ **do**\n    - random sample missing index $\\mathbf{m}_p \\subset \\\\{1, 2, \\cdots, V\\\\}$ and $\\mathbf{m}_p = \\emptyset$;\n    - set availability indicator $\\mathbf{a}_p = \\\\{1, 2, \\cdots, V\\\\} - \\mathbf{m}_p$;\n5. **end for**\n\n\n**Q3. More experiment setting**\n\nThanks. We provide the details of experiment setting in the following and will add them in Appendix. \n\nIn the experiments, we adopt fully-connected neural networks on all datasets where different numbers of neurons are adopted according to different feature dimensions, as shown in the following table. \nMeanwhile, the unique data latent representation and parameters of neural networks are both optimized with gradient descent strategy with Adam optimizer whose learning rate is set to 0.001. \nAdditionally, the codes of the proposed method and recent advances in comparison are executed on a server with 40 *Intel(R) Xeon(R) Silver 4210R CPU @ 2.40GHz* CPUs and 2 *NVIDIA GeForce RTX 3090* GPUs. \nThe software environment includes *Python 3.10.13* and *PyTorch 1.12.1* optimized with *CUDA 11.4*.\n\n|  | HandWritten | Caltech5V | Flower17 | MSRCV1 |\n|---|---|---|---|---|\n| 1st-view | (60, 64, 216) | (21, 16, 40) | (34, 512, 5376) | (21, 256, 1302) |\n| 2nd-view | (60,64,76) | (21, 64, 254) | (34, 256, 512) | (21, 32, 48) |\n| 3rd-view | (60, 32, 64) | (21, 128, 928) | (34, 512, 5376) | (21, 64, 512) |\n| 4th-view  | (60, 16, 6) | (21, 128, 512) | (34, 512, 5376) | (21, 32, 100) |\n| 5th-view | (60, 64, 240) | (21, 256, 1984) | (34, 256, 1239) | (21, 64, 256) |\n| 6th-view | (40, 32, 47) | - | (34, 512, 5376) | (21, 64, 210) |\n| 7th-view | - | - | (34, 512, 5376) | - |\n\n\n**Q4. Code release**\n\nThanks. The code will be released once the paper is accepted."}]

Author rebuttal:

Meta-review: The manuscript proposes an incomplete multi-view deep clustering method with data imputation and alignment.
Reviewers agree that the proposed approach is novel, the motivation and technical details are well-written, and the overall design of experiments including ablation study is thorough.
While the original manuscript had an issue in providing some experimental results and complete theoretical statements, they have been solved through the author-reviewer discussion.
Decision: Accept (poster)