Gaussian Regression-Driven Tensorized Incomplete Multi-View Clustering with Dual Manifold Regularization
Authors: Zhenhao Zhong
Zhibin Gu
Pengpeng Yang
Yaqian zhou
Ruiqiang Guo
Venue: NeurIPS 2025 poster ()
Keywords: Multi-view clustering
Primary area: general_machine_learning

Abstract: Tensorized Incomplete Multi-View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across multiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., $\ell_1$ or $\ell_{2,1}$), which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus on modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limitations, we propose a novel approach, GaUssian regressIon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model to characterize complex noise distributions in a more realistic and flexible manner. Meanwhile, a dual manifold regularization is introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the high-preservation $\ell_{\delta}$-norm tensor rank constraint, which applies differentiated penalties to the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demonstrate that our method outperforms SOTA approaches.

Gaussian Regression-Driven Tensorized Incomplete Multi-View Clustering with Dual Manifold Regularization
Zhenhao Zhong' Zhibin Gu Pengpeng Yang² Yaqian Zhou
Ruiqiang Guo!
"College of Computer and Cyber Security, Hebei Normal University, China Cooleee of computer and Information Technology, China Three Gorges University, China guzhibin @inibbnn@ian hebtu.edu.cn
Abstract
Tensorized Incomplete Multi View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across mul- tiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., & or 12,1). which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limi- tations, propose novel approach, GaUssian regresslon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model characterize complex noise distributions in flexible manner. Meanwhile, a dual manifold regularization introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the nigh-preservation Êg-norm tensor rank constraint, which applies differentiated penalties the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demon- strate that our method outperforms SOTA approaches. The code available https://githhr cww wwt.//occf.eee/e///iini..
realistic and
Introduction
With the rapid expansion of multi-view data across a wide range of domains, multi-view clustering (MVC) has emerged key unsupervised learning paradigm for integrating heterogeneous infor- mation [TS). By exploiting the complementarity and consistency among multiple views, MVC can significantly enhance clustering performance. However, real-world datasets often suffer from partially missing views due to sensor failures, privacy concerns, data corruption. Such incomplete- ness hinders the accurate modeling of inter-view relationships, thereby limiting the effectiveness of conventional MVC methods in assigning data points to their correct clusters. As a result, incomplete multi-view clustering (IMVC) has garnered growing attention for its potential exploit incomplete multi-view data and uncover their underlying structure [68
Incomplete multi-view clustering (IMVC) aims uncover correlations across multiple views in the presence of missing data by employing various strategies, thereby enabling more accurate data
Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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clustering. For example, Wen et al. [9] developed a confidence- neighborhood consensus graph model, which leverages the nearest-neighbor assumption to effectively extract group structure information. Wang et al. [10] integrated missing data imputation with bipartite graph learning in unified framework, leading to improved clustering accuracy and efficiency. Furthermore, Liu et al. [ proposed joint optimization framework for kernel matrix completion and multi-kernel alignment, enabling collaborative kernel and clustering optimization through alternating iterations. However, the methods mentioned above primarily focus on capturing linear correlations between views, neglecting the modeling of higher-order relationships, which limits clustering performance. To address this limitation, recent tensor- based approaches have been proposed to effectively capture higher-order correlations in multi-view data 11). For instance, Wen et al. [2] proposed a unified framework that seamlessly integrates missing- view inference with low-rank tensor learning, enabling joint recovery of latent information in missing views and modeling of high-order inter- view correlations. Zhang et al. [15] reformulated IMVC as a joint learning problem of incomplete similarity graphs and complete tensor representation, effectively capturing inter-view correlations and suppressing noise via structured tensor decomposition. In addition, EDISON (14 leverages an enhanced dictionary representation to infer missing data and build anchor graphs, enhancing robustness against data incompleteness.
Despite the impressive clustering performance achieved by TIMVC methods through exploiting high-order correlations across views, there remain three limitations that warrant further improvement. First, most existing TIMVC approaches rely on specific norms (c.g., 4 or l2,1) to model noise, which implicitly assumes that the noise follows predefined distribution. However, in rorl-world applications, noise often exhibits more complex characteristics, making it difficult for a single norm to accurately capture its nature, thus leading to suboptimal tensor representations. Second, the majority of TIMVC methods focus primarily on modeling the global Euclidean structure of the tensor representation, while neglecting the preservation of local manifold structures, which are often crucial for clustering tasks. Third, the commonly adopted Tensor Nuclear Norm (TNN) serves as a surrogate for tensor rank but is known to be biased estimator, which may result in suboptimal tensor recovery and limit the model's overall effectiveness.
To address the aforementioned challenges, we introduce novel model, Gaussian regression-driven tensorized incomplete multiview clustering with dual manifold regularization (GUITAR). Specificallyy first, GUITAR utilizes Gaussian regression model noise as Gaussian distribution, facilitating a more effective adaptation to diverse noise types and resulting in a more discriminative affinity matrix that better captures the true structure of the data. Second, we propose a dual Laplacian manifold regularization approach, which enables both the view-specific local manifold structures and the cross-view consensus manifold structure to jointly enhance the representational capacity of the affinity matrix. Additionally, we design a novel tensor rank regularization function that adaptively applies varying degrees of penalty to singular values of the tensor, allowing for the modeling of prior structural knowledge inherent in the tensor data. Figure [ illustrates the framework of GUITAR. Compared existing TIMVC methods, the contributions of this work can be summarized as follows:
We propose novel tensorized incomplete multi-view clustering framework that incorporates Gaussian regression-basee noise modeling strategy to adapt to diverse real-world noise distributions, enabling more discriminative affinity matrices and more accurate tensor representations.
A dual manifold regularization framework is introduced, which preserves local geometric structures within individual views while capturing cross-vies view consensus structures, thereby improving the affinity matrix's s capacity to model inter-sample relationships.
To better capture intrinsic low-rank structures, we introduce an adaptive tensor rank constraint that imposes differentiated penalties on singular values, thereby enhancing the robustness of tensor representations.
An efficient ADMM-based solver is developed with theoretical convergence guarantees. Extensive experiments demonstrate the superiority of our approach.
2 Related work
Incomplete Multi-view Clustering (IMVC) methods can be broadly categorized into matrix-based and tensor-based approaches, depending on whether they leverage high-order correlations across multiple views.
2

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Necwwry
vordre
W
Figure I: The proposed model consists of four main components: noise modeling, low-rank tensor learning, manifold alignment, and manifold fusion. Noise modeling captures complex noise caused by reconstruction errors and missing data. Low-rank tensor learning preserves essential structural information by imposing robust low-rank constraint. Manifold alignment and manifold fusion collaboratively align and integrate manifold structures across multiple views.
Natrix-based methods typically impose structural constraints or optimization strategies on feature or similarity matrices to integrate multi-view information. For instance, the DAIMC model [T6] proposes weighted semi-non- negaatve matrix factorization framework that incorporates 121 -orm regularization reduce the impact of missing views. Yu al. [77 propose constructing prototype- sample affinity matrices and cross-view prototypes to jointly unify representation learning and clustering under incomplete data. Recent deep learning- bbase matrix constraint methods have further advanced this area. Lin et al. [18] unify multi-view consistency learning and missing view recovery, maximizing mutual information through contrastive learning while minimizing conditional entropy to aid view completion. Tang and Liu 7 develop a dual optimization framework to dynamically interpolate missing views and select interpolated samples for training, thus reducing the impact of semantically inconsistent interpolations on clustering performance.
Tensor-based methods impose low-rank structural constraints on the dire-dimensional tensor recon- structed from incomplete multi-view data, leveraging cross cross-view high-order information to facilitate the completion of missing data [I5] 19 20]. Zhang al. [15] decompose the tensor into sparse tensor for noise modeling and a low-rank intrinsic tensor for capturing true similarities, enhancing discriminative power of similarity matrix. Wu et al.
[3] propose the use of kernel tensors to model inter-view correlations and impose low-rank constraints to enhance cross-view consistency, facilitating effective completion of missing kernel entries. Huang et (20) employ tensor decompo- sition jointly perform missing value imputation and feature selection, effectively capturing shared structures across multiple views.
3 Proposed method
3.1 The GUITAR model
Given a multi-view dataset (") consisting of m views and n samples, where X Rd. xx denotes the feature matrix of the w-th view with d, dimension, we build our method upon tensor-
based multi-view clustering framework 21 22 which can be generally formulated as follows:
min E mm
R(Z)
(P E" + BT(Z")
(I)
s.t. Ve, X
x = (Z z zz...., )...,,Z)),

---

where a and 5 are trade-off parameters. Z" R=x* denotes the coefficient matrix of the v-th view, and E" E Rd,x" represents the reconstruction error of the v-th view. The operator & stacks {Z") m into a third-order tensor Z whose rank is approximated by R(-). P(-) and (-)) are used to model the reconstruction error and regularize the coefficient matrices, respectively.
Model (I) is capable of capturing high-order correlations across multiple views. However, it has been shown that selecting all sample points to construct the dictionary is unnecessary and leads to increased computational cost. In contrast, selecting a subset of f representative samples-referre to as anchors- is sufficient to form an expressive dictionary, and these anchors can be learned adaptively during optimization [23 25]. In this setting, the sample data X for each view can be approximately reconstructed using an anchor matrix A Fd, xt and a coefficient matrix Z E R i.., X = A'Z". Furthermore, to address the common issue of missing data in multi-view settings, we introduce a diagonal indicator matrix W E RRxx to encode sample availability in the v-th view. Specifically, the i-th diagonal entry of W is set to 1 if the i-th sample is missing in view and 0 otherwise. Under this formulation, the missing data can be estimated via the reconstruction X = W in the optimization process, which selectively reconstructs only the missing entries. Accordingly, Model (1) can be naturally extended to a tensorized and anchor-based formulation that accommodates incomplete multi-view data. The resulting model is defined as:
min (B 2 pm
R(Z) + aP + 3T("")
(2)
s.t. Vv, X"
= A"Z" + E", 2 = $ ..... 2TH (A") II
A E IR denotes the anchor matrix for view 2. where each column represents an anchor point. The orthogonality constraint (A") A view clustering to enhance the discriminability and representativeness of the anchor points, thereby improving the clustering performance. The fundamental challenge in Model (2) lies in the principled design of regularization terms-Pl P(Z). R(E"), and T(Z") fully harness the complementary and heterogeneous information across multiple views for improved clustering performance. Although existing methods have proposed various constraints
commonly adopted in anchor-based multi-
the tensor representation Z, the error term E", and their affinity matrix Z", they often suffer from inherent limitations in expressiveness, flexibility, or robustness, particularly when dealing with complex, noisy, incomplete multi-view data.
Limitation 1: inaccuracy in reconstruction error modeling. Common reconstruction error models, such as the & norm, f2 norm, and Frobenius norm, each address specific types of noise- random, sample-specific, and Gaussian noise, respectively 26). However, these approaches have key limitations. They fail to explicitly model noise distributions, and while the Frobenius norm assumes Gaussian noise for E", does so imprecisely, potentially introducing bias. Furthermore, in the case of incomplete views, missing data makes reconstruction errors more complex, challenge these norms cannot adequately handle. To better model reconstruction error and handle complex noise, we introduce the Gaussian Regression Norm in tensor representation learning, which draws inspiration from the work of 27
Definition 1 (Gaussian Regression Norm) Consider the set of noise matrices {E"H" We assume that the noise within each view independently and identically distributed (f.i.d),, with each noise vector following multivariate Gaussian distribution N(e,, 1², )"). The Gaussian Regression Norm ( (GRN) is defined as:
m
M (E H JEIIGGRN
GRN
Σ
Σ In (N(e,, k², ,²,²"))
where ey E Rdd denotes the noise vector corresponding to the q-th sample in the v-th view, μº' e Rd is the mean vector of the noise distribution, and E E Rdd de is the view-specific covariance matrix.
The GRN represents the negative log- ligelikel of observing the residual noise under a multivariate Gaussian model. Minimizing this norm encourages the residuals to follow the assumed distribution, allowing for adaptive modeling of intra-view noise characteristics, including correlation structure and scale. The detailed procedure for constructing {E y || is provided in Appendix A.
Limitation 2: inadequate utilization of manifold information. For the term T(-), a commonly used constraint is the Laplacian manifold regularization, such (28-30). However, these methods

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typically construct the Laplacian matrix solely based on a consensus similarity matrix, thereby neglecting manifold alignment across different view pairs. This oversight introduces bias into the consensus manifold constraint and compromises its effectiveness. To address this issue, we propose novel constraint-Duaa Manifold Regularization-ddslee to precisely capture the intrinsic structure of the data.
Definition (Dual Manifold Regularization) Given set of coefficient matrices {Z") Jo=1- we de- fine its Dual Manifold Regularization (DMR) term follows:
KKZ") mm Jo=1 DMR
Ir L (Z)) + (TLZZLL(ZZ))
0=1
where Tr(.) denotes the matrix trace operator, and L" and Lg represent the normalized Laplacian matrices for the v-th view and the consensus across all views, respectively. Y is the balancing parameter. The first term in the DMR encourages mutual constraints among the manifolds of each view, thereby enhancing their consistency. The second term constructs a consensus Laplacian matrix that fuses the manifolds across all views, capturing unified manifold structure.
For each view v. the similarity S R is computed S 1 > where z E Rdd
denotes the feature vector of the i-th sample in view Each S is sparsified by retaining only the K-nearest neighbors. To integrate manifold information from multiple views, a consensus Laplacian Lg is constructed based on the averaged similarity S - - S", with the corresponding degree matrix D. The normalized shared Laplacian is given by Lg = D D 1/2, This construction provides a unified representation of manifold structures across all views. In the ideal case, the coefficient matrices Z" from all views are expected to share similar intrinsic structure of the data manifold. To this end, the consensus Laplacian matrix serves as regularizer that promotes unified manifold learning across views. As illustrated in the construction of the consensus Laplacian matrix, leverages a consensus similarity matrix to regularize fused manifold across multiple views, thereby enhancing the clustering performance. A thorough elaboration of the Dual Manifold Regularization (DMR) term is contained within Appendix A.2
Limitation 3: insufficient exploration of tensor prior information. Small singular values in tensor data typically correspond to noise, while large singular values capture the primary informa- tion. Traditional tensor rank approximation methods, such as the tensor nuclear norm [3]] fail to differentiate between these two aspects. In contrast, non-convex approximations, such the Logdet function 32 333, the Laplace function[34] (35), and the Eg fornomm (36] impose heavier penalties on small singular values and lighter penalties on larger ones, effectively removing noise while preserving critical information. Among these methods, the fa-nrrm offers a compact approximation of tensor rank; however, it tends to impose stronger penalties on larger singular values compared to other non-convex approximations, potentially leading to the loss of important components. To address this issue, we propose an improved version of the fs-norm, termed the figh-Prresevattinn fo-norm, which better balances noise removal and the retention of useful information under the low-rank constraint. The formal definitions of the three components are follows:
Definition (Figg--reservvation fy-norm) Given a thirl-order tensor Z E RR X222a,, the High- Preservation Es-norm (HPEs) of Z is defined as:
h (1 + 5) tanh (s)
1 73 k=
Rg
[1P6, =
HPE,
(5)
173
8 + tanh (i)
where h = min(ny, T22) and is a positive scalar that controls the flexibility of the norm. Here, S denotes the k-th frontal slice of the tensor S f, which is obtained through the tensor singular value decomposition (1-SVD (37 of Z's k-th frontal slice z = =V²))(()))) A full exposition of HP& is presented in Appendix A.3
5

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Overall objective function of GUITAR: Building upon 2 5), the overall objective function of the GUITAR model is as follows:
min (E
2 HPee + A E
E mm
To
IGRN + 2 Z IIDMR-1 + As IZ 1
|DDRR22
S.L. VU A E" 2= (Z z² 2"" (A")
(6)
where the parameter ur" in the GRN term is set to zero vector to simplify the optimization process. The term 2 [HHP,, imposes a low-rank constraint on the tensor 2. The employed HP& norm variant of the standard ls norm. penalizes small singular values similarly to the ls norm, while applying relatively milder penalties to larger singular values. This design helps to preserve more critical structural information for the reconstruction error model. Compared to traditional norms such as the & norm, &,, norm, and Frobenius norm, it has the ability to capture the underlying noise distribution to certain extent. Morcover, it incorporates learnable parameters that adaptively adjust during optimization, enabling more effective modeling of complex noise patterns, especially in scenarios involving incomplete views. The DMR term is explicitly decomposed into two complementary components for m
the data. [| Im |GRN introduces a novel formulation
better interpretability. Specifically, we define
[[Z")
H IDDMR-1 = Σ Σ
E.
m
Tr (Z'L (Z))".
=''''=1,''+
and | [Z")m |DMR-22 Σ Tr (Z),(Z"))) The combined effect of X2 and Ay can be regarded
as equivalent to adjusting both the value of and the weight of the DMR term. ( Ju=1 |I encourages the manifolds each view to mutually constrain each other, thus enhancing cross-vier consistency. [Z //=//22 constructs consensus Laplacian matrix that fuses the manifolds across all views, which helps capture unified and globally consistent manifold structure. After optimization, we compute the left singular vectors of _ [(-)) ..... (Zm) J. and then apply
<m
spectral clustering on these vectors obtain the final clustering result 38
3.2 Optimazition
To solve the proposed optimization problem, we adopt the Alternating Direction Method Multipliers (ADMM) 33). The corresponding augmented Lagrangian function is formulated as follows:
C(A o Jv=1:
E"")
m 1==1
Je=ı:
["")a> (Y") 9, Q)
||
Σ
Σ In(N(e)) 0, 00)")) + (2,
+
YY, X
A E + 11 X
A - -E
==1
m
+ L
TrIZ'L (O'L"(Z")T) +
LZ (Z
In the above formulation, {Y p=1 and Q are the Lagrange multipliers and > and > 0 are the penalty parameters. The detailed optimization procedure is provided in Appendix A.4
3.3 Convergence analysis
Theoretical guarantees for the convergence of the optimization algorithm are provided in Theorem [ while Appendix A.5 offers a detailed exposition of the underlying principles and implementation details.
Theorem The sequence {Jp A E. optimization algorithm satisfies the following properties:
9,, 2 generated by the proposed
The sequence (T))z is bounded;
Any accumulation point of {Tp) is stationary point that satisfies the KKT conditions.

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3.4 Complexity analysis
The computational complexity of the proposed GUITAR model mainly arises from variable optimiza- tion. Specifically, the optimization involves five groups of variables, namely A", E". Z", Σ", and g, whose respective computational complexities are denoted as O d,t), ((dd)) Ontdd, , + n²), ((de)), and (mmttlog (mn) + m²nt). Consequently, the overall computational complexity of GUITAR scales cubically with the number data samples.
Experiments
In this section, we evaluate the effectiivness and robustness of the proposed model through series of experiments. All experiments are conducted in MATLAB R2023b on machine equipped with a 2.30 GHz 17-12650H CPU and 16GB RAM. Due to space limitations, a subset of experimental results is presented in the main text; additional experiments can be found in Appendix A.6
4.1 Experimental settings
Datasets:
We conduct experiments six datasets: Yale3 40]
MSRC_vl vl
41 EYaleB10 42
COIL20MV, Mfeat [3). and Scene [44]. These datasets differ both sample size and the number of views. Specifically, Yale3 contains 165 samples with 3 views; MSRC_V v1 has 210 samples and views; Y 10 includes 640 samples with views; COIL20MV provides 1440 samples across views; Mfeat consists of 2000 samples with views; and Scene comprises 2688 samples described by 4 views.
Incomplete multi-view data construction: Incompleteness is introduced to the originally complete multi-view datasets by randomly setting a fraction of samples to zero, where the missing rate is chosen from {0.1, 1, 0.3, 0.5) in each view. To ensure that every sample remains present in at least one view, we restore the data in one randomly selected view for samples missing across all views. All experiments, except those in Section 4.2 are conducted with r 0.5.
Baselines:
We compare method with six baseline approaches: BSV (2001)
47 Con-
cat 46 47
PVC (2014) 48). IMVC-CBG (2022) 49). PSIMVC-PG (2024) 50, and SCSL 30 For each method requiring hyperparameter tuning, we adjust the parameters within the
(2024)
recommended ranges. For our method, we search for the optimal values of X1, X2, and X from the
set {10- 10
10-1 100 10²3, while is tuned over {10-3 10-2 1001 100).
Evaluation metries: Three evaluation metrics, Accuracy (ACC), Normalized Mutual Information (NMI), and Purity (PUR), are used to assess clustering performance. To ensure the reliability of the results, each method is executed five times during the evaluation process.
4.2 Clustering results
The performance comparison of clustering results is shown in Table [ with the top- nop-performing method in each dataset highlighted in bold and the recond-best method underlined. The analysis of the clustering results leads to the following three conclusions:
(1) The proposed GUITAR method consistently demonstrates strong performance across different missing rates, clearly outperforming the second-best method. For example, at a missing rate of 0.5, method achieves higher ACC scores than the runner-up by 16.89%. 12.86%, 5.35%, 33.51%, 24.12%, and 15.98% on the Yale3, 1, EYaleB 10, COIL20MV, Mfeat, and Scene datasets, respectively. Furthermore, even at lower missing rates, our method achieves competitive results. These findings demonstrate the robustness of our approach in the presence of complex noise and validate the effectiveness of the GRN component.
(2) Compared with recent matrix-based methods such as IMVC-CBG (2022), PSIMVC-PG (2024), and SCSL. (2024), our tensor-based approach consistently achieves superior performance. This highlights that the HPf, regularization enables the tensor low-rank constraint to effectively capture high-order correlations.
7

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Table Clustering performance comparison under different missing rates.
Da5
Methods
Missng RAC
ACC
NXI
PUK
ACC
KMJ
PUR
ACC
NMU
PCK
BSV
35G0E600
35.55:6555
35762335
36061204
353993366
11,76611:00
Yale3
PSIMVC-PGG
CBG
46.48:0.33
52.75-000
45.7560.00
56.34 10.00
45.09.0.35
53.94-0000
37,5820000
31 10
18.5520.00
13. 12.91-0.31
38.79:0000
22.9120.27
19.90 10.90100000
19442.0.229
00.00
31 83.40.00
23.52:0:27
SCSL
63:0-000
64.79 50000
63.10.0.00
55
0500000000
55.00 55.0120.00
55 15.7620.000
32. 12.1246:00
7577540000
33 13:94:000
GUITAR
64.8 64.8 4.19
65.92 65.92 X
64.61 4.42
61.04 1.54
57. $7.38.2266
59.78-2..1
57.58:3.12
BSY
60
30 80103:4711
00.00 05:00:13::5
11:8133000
31 11:3533:100
18:11:200
32.1913106
Concal
19:31-100 43
74.29-14330
54 54:25-7400
90-00-4 01
84 10421.5
44 W6:02-..9
71:2445324
59:26-3-20
53
52.2549.22
75::9-86
56 46
IMVC-CBG
12.10:0:4
36.07::000
17:02::0000
180:0000
2000
SCSL
64.000000
4.2620000
010020000
67.4400.0
GUITAR R
77.1 125
67.36 1:38
$1.441.55
$1.05 91.85-163
67.0
$1.88-1A3 YAA
SOUR MUNF 18.00
RSV
25 44: 100
21 10.56
1X.00 1009
188 16
11
323121335 35
Concat
23:2222 24
1910-245
18.99 11999115 157
19 19:47.5
99
16
17 17775-377 75
PVC
36 23:5547
35.07-7.90
37.2614.71
31 11:0::121
23
22.78:1
30
30.022244
25 35
31 $1.73-2.55
IMVC-UIG
15 M1:0111
4750
72-0 1.
27 09:-011
NO 20100
12225491 10
PSIMYC-PG
0.00:0000
2-0050000
122:0.00
02:0000000 00
17.0240000
SCSL
022:0000
00
70-7000000
B5V
PVC
0533000
0.00 0.00
3.23
505
63.08
0.00
5:20 3 600
47.47:1197
0.00
0.00
5.50
-0 000
585
0.00
0:00 1 060
5.65 0.00
COILXMV
PSIMYC-IG
IMYC-UIG
56 19:5
56 21 30
07 37.34.555
07 5K30 MM
60.88 1 25
59
500
50
50.6
550 20
35
41
3238136:57
1100411 mm
20 1048-11 10
36 36.4020.50
44 1h:1 2M
SESL
0000
(1)
21 1000
00091000
40 T14000
BSY
05
PVC
58.
35 05552440000
201-4-11
Micc
PSIMVC-PG
IMVC-UBG
48 06000.00
55.420.00
31:1000
40 12.6200000
31 11:84:000
$4:.0..000
33.3420.00
19 10.25:00.00
309540000
10
10070000
10 10.35:00.00
SUMI
S0.8 -0000
21 00)
55.55 1000
21 10:-0100
22 02:5040.00
26 10.00
GUITAR
78.05 78.0522.66
71.5541.10
78.07 2.65
31.30:00229
73.49-0.25
01.3220.22
$2.31:0.000
7189:0000
$2.31:0.00
BSY
11:12222
27 222222
$1.27 23095
45.0512245
199
326552275
34.42:2232
Concall
2.005-2..01
IMVC-CRG
10:000000
1000
PSIMYC-PG
31.00:0.00
35
00000:0000
0::00:000
15:72:1:000
20.19:0.00
5.19::.00
$6:10.00
SCSL
-1000
20-0000000
0000
18874000
1M.5740.00
6.05-0000
50.0000
GUITAR
L9:
44.8818.71
39.72-0.85
59.63:0000
45.79:0.00
09.89:0.00
5000:10.3
39.02:0.155
59.00:0.335
(3) Whether compared with methods without manifold constraints (BSV, Concat, PVC. IMVC-CBG, PSIMVC-PG) or the nanifold-constraing method SCSL, our approach maintains relatively stable performance across different datasets and missing rates. This can be attributed to the ability of DMR to accurately learn the underlying manifolds, even under high levels of missing data.
4.3 Parameters analysis
The GUITAR model involves three balancing parameters: Å1 Å2, and λ3. To evaluate the sensitivity of the model to these parameters, we perform grid search over two parameters while fixing the third, with search values drawn from (10-3, 10 10-1 100 10 ACC is used as the evaluation criterion. As illustrated in Figure - the performance on the Mfeat dataset remains consistently stable when \1, X2, and Ag chosen from (10-3, 10-2 10-1).
6001
9301
601
001
201
0.011
(a) AI vs. A2
(b) A As
(c) λ2 Às
Figure 2: Sensitivity analysis of balancing parameters in the GUITAR model on the Mfeat dataset.

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4.4 Anchor analysis
The proposed GUITAR model utilizes discriminative anchors from the original data as a dictionary to improve computational efficiency. The number of anchors is varied within the range (c, Tcl. where denotes the number of clusters. The detailed clustering results are presented in Figure 3 It can be observed that even with a number of anchors much smaller than the total number of samples, competitive and relatively stable clustering performance is consistently achieved across different datasets. However, results indicate that more anchors do not guarantee better performance. While insufficient anchors limit the dictionary's expressiveness, causing high reconstruction eπror, too many increase the risk of selecting low-quality anchors that introduce noise and degrade performance. The number of anchors should therefore be optimized empirically. In general, the GUITAR model yields the best performance when the number of anchors is 2c or 3c.
400
400
(a) Yale3
MSRC_v1
(c) Ba
Figure 3: The impact of anchor count the GUITAR model.
4.5 Analysis of the HP?; parameter 5
In this section, we analyze the impact of the HP?s parameter on the performance of our model. We search for an optimal value of å within the range (10-3, 10-2 10-1,1000 to make HPE, more effective and compact. As shown in Figure the performance metrics on the Yale3 dataset fluctuate as 5 increases, while the MSRC_v v1 dataset they decrease, and on the EYaleB 10 dataset they increase. For the other datasets, the performance remains relatively stable. Overall, the model achieves the best performance across all datasets when ó is set to 10
0.5
(a) Yale3
(b) MSRC_vl
(c) EYaleB10
Figure 4: The impact of 8 on the GUTTAR model.
4.6 Convergence behavior
We empirically validate the convergence of the GUITAR model using two metrics: the reconstruction error (RE), defined as min |XX' " E El and the match error (ME), given by | lloc-
The convergence processes on the Yale3, EYaleB 10, and COIL20MV datasets are illustrated in Figure 5 As shown, both RE and ME decrease rapidly and approach zero within 40 iterations, demonstrating the good convergence properties of the GUITAR model.

---

3003
20/3
(a) Yale3
(b) BYalcB10
(c) COIL200V
Figure 5: Convergence curves of the GUITAR model.
4.7 Ablation study
To study the effect of GRN and DMR on the model performance, we perform ablation by ting the balancing parameters Å₁. X2, and λ to zero in different combinations. DMR can be
decomposed into two smaller components: define Σ
Tr Z (Zz)T DMR-1,
#
and Ee= Tr (Z", DMR-2. Table reports the experimental results, where the best- performing entries are highlighted in bold. Removing GRN results in a substantial performance degradation, demonstrating its effectiveness in modeling complex noise. When GRN is present. incorporating either DMR-1 or DMR-2 2 leads to further improvements, The model achieves its optimal performance when GRN, DMR-I, and DMR-2 are all incorporated, indicating that the manifold learning capability of DMR also plays crucial role in enhancing GUITAR.
Table 2: Ablation results of the GUITAR model.
Components
Datusets
Yale3
MSRC_vI
EYaleB10
DMR-1
DMR-2
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
43.03
44.24
26.67
13.91
28.57
16.88
17.81
7.88
10.91
15.15
14.76
2.99
17.14
1.45
11.41
7.88
10.91
15.15
24.29
5.13
24.76
10.16
1.45
11.41
52.12
56.70
52.73
72.86
56.72
72.86
36.72
29.89
38.28
50.30
52.74
50.30
75.71
39.12
75.71
27.66
20.56
29.84
7.88
10.91
15.15
14.76
2.99
17.14
10.16
1.45
11.41
57.58
58.25
57.58
79.05
65.71
79.05
33.42
39.84
Conclusion
This paper proposes novel tensorized incomplete multi-view clustering framework that incorporates a Gaussian regression-bact based norm, along with two key enhancements: an improved, more compact and effective l norm, and dual Laplacian manifold constraint designed align and fuse view- specific manifolds. Our model introduces innovative formulations for noise modeling norms, rank functions for tensor low-rank regularization, and manifold constraints. Extensive experiments on six benchmark datasets demonstrate that our method consistently outperforms SOTA approaches, thereby validating the effectiveness and methodological novelty of GUITAR.
6 Limitations
The main limitation of the proposed model concerns its computational complexity. Specifically, the computational cost of GUTTAR increases cubically with the number of data samples, primarily due to the matrix inversion required during the update of the coefficient matrices Z". This complexity may limit the scalability of the model on large-scale datasets. Regarding hyperparameter sensitivity, our empirical analysis (see the corresponding chart) indicates that the model's performance exhibits moderate variation under different hyperparameter settings. This suggests that while the model relatively robust, hyperparameter sensitivity still has limited but non-negligible impact.
10

---

Acknowledgements
This work was supported by the Natural Science Foundation of Hebei Province (No. F2025205006), the Science Foundation of Hebei Normal University (No. L2025B38), and the Backbone Talent Program (Program for Returned Overseas Scholars) (No. A2025016).
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A
Technical Appendices and Supplementary Material
The supplementary material provides deeper insights into the GUITAR model through detailed optimization procedures, a convergence proof, additional experimental results, and further analyses.
A.1 Construction of the Gaussian Regression Norm
Mlee 1²", Σ") can be characterized by its probability density function, namely, (e 1=" "",""" = (2-717/2p--117 exp (c) " (("" - -²")). The Gaussian Regression Norm is derived by the negative log-likelihood of the noise under multivariate Gaussian model. Specifically, let e denote the noise vector of the g-th sample in the v-th view, which is assumed to follow a multivariate
Gaussian distribution:
p(e)) = -ee, 1 E")
(8)
where t² and D represent the mean vector and covariance matrix for the v-th view, respectively. Assuming that the noise vectors within each view independent, the likelihood of the entire noise matrix E" ..",... ,c]]] can be expressed as:
p E""
II N(C 11,,""
(9)
Taking the negative logarithm yields the negative likeliiid for the v-th view:
In Impp(E Σ In (N(c,) Σ"))
(10)
To regularize the noise across all views, we minimize the sum of negative log-likelihoods over all m views, which leads to the definition of the Gaussian Regression Norm:
E pm 1 IGRN
(- (mn)
Σ
Σ In (N W., ((,E"))
(I))
14

---

A.2 Detailed analysis of the Dual Manifold Regularization
The Dual Manifold Regularization has been introduced in the main text; however, certain details were not fully elaborated due to space limitations. This subsection will provide further analysis.
Detailed explanation of Dual Manifold Regularization The first term in the DMR. ΣE
Σ Σ Tr L ) is designed to enforce cross-view manifold alignment. Specifically, (
D L' it encourages the representation Z" of each view to conform the manifold structure captured by the Laplacian matrix L" of other views. This mutual regularization narrows the discrepancy between
views and enhances the overall consistency among them. The second term, Σ Tr (Z'L,(Z')),
m
==
incorporates consensus Laplacian matrix Lg that fuses the manifold structures from all views. plays a complementary role by guiding each view's representation toward a globally consistent manifold, which reflects the intrinsic geometry shared across views.
Distinctions between the two terms in DMR: The two terms the DMR serve complementary but distinct roles in promoting consistent manifold learning across views. When the manifold structures across different views differ significantly, enforcing a unified manifold directly may introduce bias.
This issue is addressed by the first term, Σ d'=l'e' constraints, encouraging the manifold of each view to align with those of the others. This mutual regularization helps to reduce discrepancies among siew-specific manifolds and improves inter-view
Tr (Z (Z*) which imposes cross-view
consistency. In contrast, the second term, Σ Tr (Z'), constructs a consensus Laplacian
matrix by integrating the manifold structures of all views. Its goal is to capture a globally consistent and representative manifold structure shared across views. The effectiveness of this consensus term enhanced when the individual view manifolds are already well-aligned, a condition facilitated by the first term. Together, these two terms enable the model first harmonize local structures and then learn a unified global manifold.
A.3 Analysis of the High-Presene Prigheressevttion f3-norm mechanism
Theoretical analysis: Let the function fure, (x) (1+6) tanh
5+tanh As - O, we have Sure, -
When x + +00, since tanh(x) - 3. the function converges to [HPI,( + 264- < 1.For comparison, consider (x) (1+8)r
8+x When x + 0, tanh(x) ss x, so SHPI, (x) v frg (z).
indicating that the penalization on small singular values remains almost unchanged. However, as I + +00, ft, (x) + 1, while fH (x) converges to a fixed value 264-7 strictly less than 1. This upper saturation effect effectively suppresses the penalization on large singular values, thus preserving more dominant components. As result, the Horm- penalizes small singular values effectively while reducing shrinkage on large ones, achieving a desirable balance between low-rankness and the preservation of critical information.
To empirically validate the effectiveness of the proposed HPC, norm, we conduct comparative experiments by replacing it with the LogDet function, the Laplace function, and the standard ls norm. All evaluations are carried out on the benchmark datasets with a missing rate of 0.5, and each experiment is executed five times during the evaluation process. As shown in Table 3 the proposed HP-f, norm achieves superior or competitive performance across most datasets, demonstrating its effectiveness.
Empirical analysis:
Table 3: Comparative experimental results of different methods.
Datasets
Yale3
MSRC v1
EYaleB10
COIL20MV
Mfeat
Scene
Det
56.97 + 2.94
76.19 1 0.00
35.78
1.10
71.65
2.67 81.83 + 0.00 54.47
0.46
Laplace
55.88 + 1.45
76.76 - 1.03
37.16 +
2.05
72.75
+ 3.89
82.11
+ 0.00
58.35 - 0.17
ts
54,91 + 2.29
79.52
= 0.58
74.50
1:00
3.44
81.47
+ 0.11 57.66 + 0.00
HP-&,
57.33 + 2.66
80.00 = 0.00
38.16
74.51
5.95
82.31
- 0.00
58.09 0.00
15

---

A.4 Optimization procedures
The augmented Lagrangian function to be optimized is formulated as follows:
1 ((
E 10=11
m
(Z"Je=
Je=1
{>" 10=1, 9. Q)
Ju=i
m
|
In(V 0, -0)")) + +2,
+
(Y",
A - E + 1 A" - E"
(12)
m=1
m
+ - 2
+
TH (Z*)T)+X) +
Tr Tr(Z'La(Z") (
Eq.
12
can be reformulated as set of the following subproblems.
" SSubprobeem
With other variables held constant, A can obtained by solving
org max Tr((A")TM) (A") A==1
(13)
where M" (Y" + μX" - 1 (Z")T. To obtain the optimal A", singular value decomposition (SVD) is performed M yielding UA and A., which are the left and right singular matrices of M respectively. The product U VA then gives the optimal solution for A
E" -SSbprobbeem With other variables fixed, E" Rd.xx is updated column-wise where the q-th column e represents the noise corresponding to the q-th sample of the v-th view, and can be obtained by solving the following optimization problem:
N(eejoo, Σ") + x" - Azz,, -e))
min - >1 In 6
(14)
x Az c/,22
The optimal solution is given by
e (1(2 + ul
y² m(A
(15)
In this context, ya, zy, and x correspond to the q-th column vectors of the matrices Y E xn z" Rox,, and X" Rdd. xn, respectively.
Ex SubSppobbelem
With other variables fixed, the update of " can be formulated
min D
A
Σ In
Wiee; 10,
(16)
9=1
This optimization problem admits a closed-fomm solution, resulting in the following update for the covariance matrix "
n n
Σ
" + +el
(17)
n
where el is small regularization term added ensure numerical stability.
16

---

Z" -SSSupoobleem With other variables fixed, the update of Z" is formulated as the following optimization problem:
Z arg min Tr(QuT (Z" G²) 2 0 G
X A E") 2 X A" -
(18)
Tr(Z'L' (Z') A TT')'L,
By setting the derivative of the objective with respect to Z" to zero, the following linear equation is obtained:
z" pl 11 2A2
L 2ABLe) = -pG" -p" QA") (X'--" (19)
Therefore, the closed-fome solution for Z" is
z" = (pG - Q" + (A") Y + ((A") - -E") (X--"")
(pI+uI++2)
Σ L +2d3l
(20)
G-Subproblem
With other variables fixed, g can be obtained by solving
G = arg min | + 2 g - (Z 2
(21)
The optimal solution of g can be obtained according to the following theorem:
Theorem Given tensor D E T Xm2Xna, whose tensor singular value decomposition (I-SVD) is denoted as D = u x S V our objective is to address the following minimization problem involving the High- Freee-Prennnvation f--norm:
min ElG + 1 + -
(22)
The optimal solution to Eq. (22 can be computed in closed-form
g' u ( V
(23)
In this formulation, (M (S (Sx), (,33 denotes tensor whose frontal slices are diagonal matrices. Each diagonal element 2 (S f)) is obtained by solving the following optimization problem:
1 } - ((,)))()))*++++ Ef(x)
D1.5 (S. = arg min
(24)
=20
where & 0 and the function fz) is defined
(1+-5) tanh 8-tanh
Eq. 24 comprises both convex and concave components, and can be addressed using Difference of Convex (DC) programming (51). leading to the following closed-form solution:
(t) af(citer)
çitert1
(25)
where f(x)
(1+4) tanha
< (S) (i, and iter denotes the iteration index.
8+tanb
17

---

Lagrange multipliers and penalty parameters The Lagrange multipliers Y", Q. and the penalty parameters pl, p are updated according to the following rules:
Y Y + 1(X" AA""" -E")
@ - e + p 9)
(26)
# nuH, F min(H,, Mmaz)
npp, p min(p; Pmaa)
With the ADMM-based optimization procedure concluded, the subsequent updates carried out independently of the ADMM scheme.
Update L
L' -D=
(27)
The Laplacian matrix L" is constructed from the similarity matrix S R for view v. Specifically, (x:) x
S | 12 " where z (R.d corresponds to the feature vector the i-th sample from view The similarity matrix S" is updated by keeping only the K K-nearest neighbors; following this, the degree matrix D is given by (Eag Sij)). The normalized Laplacian matrix for view v given
by Eq. (27).
Update L
Lg -- D 1DDSD 1/2
(28)
Following the construction in the main text, we compute the normalized shared Laplacian matrix Lg according to Eq. (28)
Impute X"
X W"
(29)
This equation utilizes the indicator matrix W to reconstruct the columns in X that correspond to missing samples. Algorithm provides summary of the complete optimization process of GUITAR.
Algorithm 1 Optimization Algorithm of GUITAR
Input: Incomplete multi-view data(X] ..... X"), cluster number c, trade-off parameter Å1, A2 As and anchor number t. Output: Clustering results
Initialize: Ve, Z
E. 0, Y 1.2, Pmax Pmax 10
0,9 0, 0.P 10-4,0 p -0 74 17p
10-7
2: while not converge do
3: Update {A mm
by Eq. 13
4: Update E [m
by Eq.
15
==1
5: Update "" Je=1 by Eq.
6:
Update "m by Eq.
20
7:
Update {g" 1m by Eq.
8:
Update YY'mm p==1 2.
by Eq. 26
9:
Update [L*) 0= by Eq. 27
10:
Update L, by Eq. 28
Update (X "== by Eq. (29
12:
Check the convergence conditions: X - A"Z" - -E < and Z" - g <c
13:
end while
14:
Output clustering results via performing k-means on the left singular vectors of
A.5
Convergence proof
In this section, we present the convergence analysis of the proposed model. We begin by introducing supporting lemma, and then proceed to prove Theorem I as stated in the main text.
18

---

Lemma [52/Assume funetion F; mmx - R is defined by the composition F(X) = (x)))), where xXX) (oi(X)...... G, (X))) denotes the vector of singular values of X E Rmxxn with
min(m, n). Let the singular value decomposition of X be X Udiag(<(Xi)) and assume the function f IR" - R is absolutely symmetric and differentiable at x()). Under these assumptions, the subdifferential of F(X) X is given by
OF(X) (ddig(0/(((X)))v
(30)
ØX
where 0f (k(())
[af(on (X))
Of(a,
0X
0x
Proof of the boundedness of the sequence {Jp)p=1: At the (p + 1)-th iteration, the column update for Ep+ is
yip Up(x; A (1t)tt + =1p1) -
(31)
The multiplier update is
Y 9+++1 = yy + px((X A A pxp+)
(32)
Substituting 4xpt1 into the multiplier update, we can factor terms obtain
Napt+ (1 1 -=,",(("")~~++,,))~~~==+-1)+ + up (I+ +pp1)
A Azz 1x
(33)
Taking the 62-norm and using submultiplicativity yields
bly 1 ll2 S Tı Fill"", 21l T2|1x" A Azz"" 2 1122
(34)
where Y, = - (1=" (pp)))
Y2= 1lup (T+ (E"") 1pp 1l. Given
that 2 is positive definite covariance matrix and the regularization Eq. 17 the inverse matrix (2")-1 possesses bounded spectral norm. With a constant and Up bounded, Ti and Tr are bounded constants. Finally, the initial multiplier Yo and the data term x A A2z,,t1 are bounded, the recursion implies sup, e < oc and therefore the sequence {Y,) is bounded.
The first-order optimality condition with respect 9p+1 iteration (p + 1) yields:
0 p 111+||eees + Pp(9 2 2p-1) 22
(35)
In conjunction with the update rule:
2 = 2p + Pp - 99p+1)
(36)
we obtain the following relationship:
0|| = 22+1
(37)
The tensor admits t-SVD decomposition of the form = S V., By invoking Lemma follows that
|aloo p+
11mS, 12=
1 u ifft (0f (8,), (.3)))) V
n3
min(n m2)
(38)
(0f(s))
(
Therefore, the Frobenius norm of the subgradient 0 Spt1 HPe, is upper-bounded by finite quantity, indicating that it remains bounded. In light of Eq. 37). this further implies that the sequence ( is also bounded.
100
19

---

Furthermore, based on the update rules described in Algorithm 1, we can derive the following inequality:
C(A p+1
E p 1 D
p+l pt1, Yp 2p Hp: Pp)
S S p: E 2,p, Ep 9 p. Y 2p Hp, Pp)
= LA E. 2, Dp 9 p.
Y p-1 1 2p p- Mp-1, Pp-1)
+ Pp Pp-1
2p 2 ||
(39)
2p
Mp + Hp-1 Y Y Σ
m
2 v=1
p-1 F
By recursively expanding the right-hand side of the inequality from p p= to n, we obtain:
(( E 7 Z 1+ : 1ptl. p: 2p. Pp. Pp)
CAY Ej. Z Ei, 11, Yo, Co. Po)
1 Pp + Pp-1
2p 2p-11 1|
2pp-1
(40)
p=1
Hp + 1p-1
Y
Y p- 11
2
v=1
is straightforward to verify that:
Σ Pp 1p Pp-1
Up + 1p-1 < <000
20,
(41)
2p
2
Given that the initial objective value L(A), Ei
Dy 9 Yū, Po, is finite, and the sequences n
" Σ
(Yp) (Op) along with the summations
P and Σ
Hatte-1 are all bounded,
20--1
2pz-1
p=1
p=1
we conclude that the augmented Lagrangian L(A p+1 E remains bounded throughout the iterations.
E Z 1
9 9ptp, Y 2p Mp Pp)
Recalling the following equality:
C(A 1 Ept1 Zp+1, Ep+1: pt1,, Y Pp)
199++1|HP2s A Σ
In (N(e "ppt1 00, 10+1))))) + (2p, 2p+1 9p+1)
+
Y X
15+1 E Ep-1> 1) + Up |
A p-
Z5+1
Ey 11
pz
p+
2
==1
1ptill + A2 m
m
m I
Pp +
1ppt1
Tr p+
L (Z)+1)
As
(Z(
2
p-
(42)
and each term on the right-hand side of Eq. is finite. Among all the components, particular attention is given to the term p |I which, being bounded, implies the boundedness of the associated singular values ().j) As result, we obtain the following relation:
1 ny min(ni.n2)
| p 1|
1 na
|
Σ
(i,)))))
(43)
n3
which further implies that the sequence ppp) bounded.
Moreover, it is readily observed from the update steps that the sequences {A
p
p- and {En) p=1 are also bounded. Therefore, we conclude that the entire sequence (J, A Eg. Z DV Y 9p, 2 ) remains within a finite range.
20

---

Establishing that the accumulation points converge to stationary KKT points: By invoking the Weierstrass Bolizan theorem [53], the bounded sequence p= is guaranteed to possess least one accumulation point, which we denote by J.. Accordingly, we have:
lim (Ap, pp Zp p: Yp 9 pp) - (A E, E. Ex, Y 2.)
(44)
p0000
In light of Eq.
26), we observe the following relationships:
Y p+1 Y
2p+1 2₂
x Ap+12 pp+
Bp+1
2p11 9pt1
(45)
Up
Pp
Given that both sequences (Y)) the accumulation point:
ply=1 and (pp) are bounded, we obtain the following constraints
X - A. E 0, 2, g- -
(46)
Furthermore, due to the fact that 1 and 9p+1 satisfy the first-order optimality conditions, follows that:
Y X E. GRN,
º. = = I1
(47)
Hence, the accumulation point J. satisfies all necessary conditions of stationarity and primal fea- pm
sibility. We thus conclude that any accumulation point of the sequence {fp]p= corresponds to stationary point that fulfills the KKT conditions of the proposed optimization problem.
A.6
Additional experimental results
Only a subset of the experimental figures was presented in the main text. In this subsection, we provide the remaining figures to offer more complete view of the experimental results. Figure 6 Figure and Figure illustrattes F the sensitivity analysis on the remaining datasets with respect to the balance parameter, the number of anchors, and the parameter 5 in the HPL, regularization. Figure shows the convergence behavior across the remaining datasets, while Table presents the ablation study results on those datasets.
Table 4: Ablation results of the GUITAR model across the remaining datasets.
Datasets
COIL20MV
Mfeat
Scene
Components
GRN DMR-1
DMR-2
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
38.47
52.33
42.36
29.90
21.67
30.25
26.19
13.47
29.02
5.07
1.38
6.32
12.80
0.82
13.10
15.29
0.26
15.51
5.07
1.38
6.32
10.05
0.45
10.45
15.29
0.26
15.51
70.76
80.86
73.33
81.85
71.43
81.85
58.11
39.34
58.11
70.28
76.64
70.90
81.20
70.63
81.20
42.45
29.31
44.23
5.07
1.38
6.32
10.05
0.45
10.45
15.29
0.26
15.51
73.89
82.44
74.58
82.35
71.86
82.35
58.18
39.88
58.18
21

---

500
0011
281
4
(a) COIL20MV
(b) COIL20MV
(c) COIL20MV
2.
001
201
A
(d) EYaeBB10
(c) EYaleB10
(f) EaleBB
0001
0.01
0007
MSRC_V
(h) MSRC_v1
MSRC
05
8 05
25
007
201
4
Scene
(k) Scene
(I) Scene
6601
0001
16
0301
(m) Yale3
(n) Yale3
(0) Yale3
Figure 6: Sensitivity analysis of balancing parameters in the GUITAR model on the other datasets.
22

---

(a) COIL20MV
(b) Mfeat
(c) Scene
Figure 7: The impact of anchor count the GUITAR model across the remaining datasets.
03
05
0.01
(a) COIL20MV
(b) Mfeat
(c)
Scene
Figure The impact on the GUITAR model across the remaining datasets.
070
16
(a) Mfeat
(b) MSRC_vl
(c) Scene
Figure 9: Convergence curves of the GUTTAR model across the remaining datasets.
23

---

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Reviews:
[{"review_id": "31lCGH0p5c", "reviewer": "Reviewer_ypNq", "summary": "This work introduces an advanced TIMVC framework designed to more effectively handle complex noise and preserve structural information across multiple views. By incorporating Gaussian regression, the method captures realistic noise characteristics beyond conventional norm-based assumptions. It further integrates dual-level manifold regularization to reinforce both intra-view and inter-view consistency. A tailored tensor rank constraint is employed to improve the quality of the tensor representation, thereby enhancing clustering performance.", "questions": "1. The manuscript does not clearly explain the Gaussian regression norm, especially the definition and role of the covariance matrix in Eq. (3). A more thorough explanation is needed to aid understanding.\n2. The Related Work section uses inconsistent tense when describing prior studies, which undermines the overall coherence.\n3. Eq. (4) lacks sufficient detail on how the consensus Laplacian matrix is constructed and how it contributes to the clustering task.\n4. The presentation of some equations is not fully standardized. For instance, Eqs. (3) and (4) omit summation symbols over multiple views on the left-hand side, which may lead to ambiguity.\n5. The proposed method incorporates an anchor-based subspace; however, the Complexity Analysis section indicates that the computational complexity is not clearly reduced compared to traditional approaches.", "limitations": "The authors are encouraged to address potential limitations regarding computational complexity and hyperparameter sensitivity to enhance the manuscript’s clarity and completeness.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1. The paper proposes a well-designed framework addressing key limitations of current TIMVC methods by integrating realistic noise modeling, dual-level manifold regularization, and robust tensor constraints.\n2.  Theoretical analysis with convergence guarantees is provided, supporting the validity of the optimization approach.\n3. The manuscript includes comprehensive experimental analyses of the proposed model from multiple perspectives.\n\nWeaknesses:\n1. The manuscript does not clearly explain the Gaussian regression norm, especially the definition and role of the covariance matrix in Eq. (3). A more thorough explanation is needed to aid understanding.\n2. The Related Work section uses inconsistent tense when describing prior studies, which undermines the overall coherence.\n3. Eq. (4) lacks sufficient detail on how the consensus Laplacian matrix is constructed and how it contributes to the clustering task.\n4. The presentation of some equations is not fully standardized. For instance, Eqs. (3) and (4) omit summation symbols over multiple views on the left-hand side, which may lead to ambiguity.\n5. The proposed method incorporates an anchor-based subspace; however, the Complexity Analysis section indicates that the computational complexity is not clearly reduced compared to traditional approaches.\n6. Some important related works are missing, such as [1] and [2].\n\n[1] On the Consistency and Large-Scale Extension of Multiple Kernel Clustering, TPAMI 2024.\n\n[2]  Large-scale Multi-view Tensor clustering with Implicit Linear Kernels, CVPR 2025.", "was_revised": true, "final_justification": "The authors have adequately addressed my concerns in the rebuttal. I am satisfied with their response and have decided to raise my score.", "rebuttal": "***\n> **Q1.** *Clarification needed on Gaussian regression norm and covariance matrix.*\n***\n**A1.** ① **A more thorough explanation of the Gaussian regression norm.** The Gaussian Regression Norm is derived by the negative log-likelihood of the noise under a multivariate Gaussian model. Specifically, let $\\mathbf{e}^v_q$ denote the noise vector of the $q$-th sample in the $v$-th view, which is assumed to follow a multivariate Gaussian distribution:\n$$\np(\\mathbf{e}^v_q) = \\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)\n$$\nwhere $\\boldsymbol{\\mu}^v$ and $\\boldsymbol\\Sigma^v$ represent the mean vector and covariance matrix for the v-th view, respectively.\nAssuming that the noise vectors within each view are independent, the likelihood of the entire noise matrix $\\mathbf{E}^v=[\\mathbf{e}^v_1,\\cdots,\\mathbf{e}^v_n]$ can be expressed as:\n$$\np(\\mathbf{E}^v) = \\prod_{q=1}^{n} \\mathcal{N} (\\mathbf{e}\\^v\\_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)\n$$\nTaking the negative logarithm yields the negative log-likelihood for the $v$-th view:\n$$ - \\ln p(\\mathbf{E}^v) = - \\sum\\limits_{q=1}^{n} \\ln \\left( \\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v) \\right)\n$$\nTo regularize the noise across all views, we minimize the sum of negative log-likelihoods over all $m$ views, which leads to the definition of the Gaussian Regression Norm:\n$$ \\\\| \\\\{ \\\\mathbf{E}^v \\\\}^m_{v=1}\\\\|_{ \\\\mathrm{GRN} } =  \\\\sum\\_{v=1}\\^{m}\\left( - \\ln p(\\mathbf{E}^v) \\right) = - \\sum\\_{v=1}\\^{m} \\left( \\sum\\limits\\_{q=1}\\^{n} \\ln \\left( \\mathcal{N} (\\mathbf{e}\\^v\\_{q}  \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v ) \\right) \\right) $$\n\n② **The definition and role of the covariance matrix in Eq. (3).** The covariance matrix $\\boldsymbol\\Sigma$ plays a key role in shaping the probability density function of a multivariate Gaussian distribution. In the GUITAR model, $\\boldsymbol\\Sigma^v$ is learnable during the optimization process, allowing the corresponding multivariate Gaussian distribution to be adaptively adjusted to better approximate the underlying noise distribution in each view.\n\n***\n> **Q2.** *Inconsistent tense.*\n***\n**A2.** Thank you, we will correct the tense errors.\n\n***\n> **Q3.** *Details on how the consensus Laplacian matrix is constructed and how it contributes to the clustering task.*\n***\n**A3.** ① **How is the consensus Laplacian matrix constructed?** The Laplacian matrix $ \\mathbf{L}\\^v $ is constructed from the similarity matrix $ \\mathbf{S}^v \\in \\mathbb{R}^{n \\times n} $ for view $ v $. Specifically, $ \\mathbf{S}\\^v\\_{ij} = \\\\frac{ {(\\mathbf{z}\\^v\\_i)}\\^\\top \\mathbf{z}\\^v\\_j }{ \\\\| \\mathbf{z}\\^v\\_i \\\\|\\_2 \\cdot \\\\| \\mathbf{z}\\^v\\_j \\\\|\\_2 } $, where $ \\mathbf{z}^v_i \\in \\mathbb{R}\\^{d_v} $ denotes the feature vector of the $ i $-th sample in view $ v $. The similarity matrix $ \\mathbf{S}^v $ is then sparsified by retaining only the $ K $-nearest neighbors, and the corresponding degree matrix is defined as $ \\mathbf{D}^v = \\mathrm{diag}(\\sum \\limits_{j=1}^n \\mathbf{S}^v_{ij}) $. The normalized Laplacian matrix for view $ v $ is given by $ \\mathbf{L}^v = \\mathbf{I} - {(\\mathbf{D}^v)}^{-1/2} \\mathbf{S}^v {(\\mathbf{D}^v)}^{-1/2} $.\nThe second term constructs a consensus Laplacian matrix that fuses the manifolds across all views, thereby capturing a unified manifold structure. The shared Laplacian matrix $ \\mathbf{L_s} $ is derived from the average similarity matrix $ \\mathbf{S_s} = \\frac{1}{m} \\sum \\limits_{v=1}^m \\mathbf{S}^v $, with the corresponding degree matrix $ \\mathbf{D_s} = \\mathrm{diag}(\\sum \\limits_{j=1}^n (\\mathbf{S_s})_{ij}) $. The normalized shared Laplacian matrix is then given by $ \\mathbf{L_s} = \\mathbf{I} - \\mathbf{D_s}^{-1/2} \\mathbf{S_s} \\mathbf{D_s}^{-1/2} $.\n\n② **How does the consensus Laplacian matrix $\\mathbf{L_s}$ contribute to the clustering task?** In the ideal case, the coefficient matrices $\\mathbf{Z}^v$ from all views are expected to share a similar intrinsic structure of the data manifold. To this end, the consensus Laplacian matrix serves as a regularizer that promotes unified manifold learning across views. As illustrated in the construction of the consensus Laplacian matrix, it leverages a consensus similarity matrix to regularize a fused manifold across multiple views, thereby enhancing the clustering performance. \n\n***\n> **Q4.** *The presentation of some equations is not fully standardized.*\n***\n**A4.** Thank you for your careful review. We will revise the notation for clarity. Specifically, we will modify $\\\\|\\mathbf{E}\\^v\\\\|\\_{\\mathrm{GRN}}$ to $\\\\|\\\\{\\mathbf{E}\\^v\\\\}\\^m\\_{v=1}\\\\|\\_{\\mathrm{GRN}}$, and $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR}}$ to $\\\\|\\\\{\\mathbf{Z}^v\\\\}^m_{v=1}\\\\|_{\\mathrm{DMR}}$, to explicitly indicate that these terms involve all views. This change helps to eliminate ambiguity and emphasizes that both constraint terms are applied across multiple views.\n\n***\n> **Q5.** *The proposed method incorporates an anchor-based subspace; however, the Complexity Analysis section indicates that the computational complexity is not clearly reduced compared to traditional approaches.*\n***\n**A5.** Actually, the majority of the computational cost arises from the update equation of $\\mathbf{Z}^v$:\n$$\n\\mathbf{Z}\\^v = \\left( \\rho \\mathbf{G}\\^v - \\mathbf{Q}\\^v + (\\mathbf{A}\\^v)\\^{\\top} \\mathbf{Y}\\^v + \\mu (\\mathbf{A}^v)^{\\top} (\\mathbf{X}^v - \\mathbf{E}^v) \\right)\\Big(\\rho \\mathbf{I} + \\mu \\mathbf{I} + 2\\lambda_2 \\\\sum_{\\substack{v'=1 \\\\ v' \\neq v}}^{m} \\mathbf{L}^{v'} + 2\\lambda_3 \\mathbf{L_s} \\Big)^{-1}\n$$\nThe matrix inversion involved in this update leads to a computational complexity of $\\mathcal{O}(n^3)$, which is inherently independent of the anchor matrix $\\mathbf{A}^v$ and therefore cannot be alleviated through its incorporation.\n\n***\n> **Weakness6.** *Some important related works are missing, such as [1] and [2].*\n>\n>[1] On the Consistency and Large-Scale Extension of Multiple Kernel Clustering, TPAMI 2024.\n>\n>[2] Large-scale Multi-view Tensor clustering with Implicit Linear Kernels, CVPR 2025.\n***\n**A6.** These important works will be cited in our paper to facilitate a thorough and comprehensive analysis.\n\n***\n> **Limitations.** *The authors are encouraged to address potential limitations regarding computational complexity and hyperparameter sensitivity to enhance the manuscript’s clarity and completeness.*\n***\n**A7.**  Thank you for your detailed and constructive review. \nThe main limitation of the proposed model concerns its computational complexity. Specifically, the computational cost of GUITAR increases cubically with the number of data samples, primarily due to the matrix inversion required during the update of the coefficient matrices $\\mathbf{Z}^v$. This complexity may limit the scalability of the model on large-scale datasets. In future work, we plan to investigate more efficient optimization strategies to alleviate this issue.\n\nRegarding hyperparameter sensitivity, our empirical analysis (see the corresponding chart) indicates that the model’s performance exhibits moderate variation under different hyperparameter settings. This suggests that while the model is relatively robust, hyperparameter sensitivity still has a limited but non-negligible impact. We will further elaborate on these aspects in the revised manuscript to improve its clarity and completeness."}, {"review_id": "oOACrTPCLC", "reviewer": "Reviewer_rBdX", "summary": "The manuscript tackles the shortcomings of current tensorized incomplete multi-view clustering approaches, which typically use oversimplified noise assumptions and neglect local manifold information. To address these issues, the authors develop GUITAR, a method based on Gaussian regression that employs dual manifold regularization to maintain structural consistency within and across views. Furthermore, they propose a high-preservation tensor rank constraint to enhance the robustness of low-rank representations.", "questions": "See the Weaknesses section in Strengths and Weaknesses.", "limitations": "The relatively high computational complexity should be acknowledged as one of the paper’s limitations.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n  1. The use of a Gaussian regression model allows the method to flexibly capture complex and realistic noise distributions, addressing the limitations of conventional norm-based approaches.\n2. The proposed tensor nuclear norm improves upon the traditional TNN by incorporating a more comprehensive modeling of the prior information embedded in tensor data, which contributes to a more robust representation.\n3. The experimental section is clearly structured, with implementation details and comparative results presented in an organized manner, which helps to illustrate the empirical effectiveness of the proposed approach.\n\nWeaknesses:\n  1. The description of the proposed model is not sufficiently detailed, which makes certain components difficult to understand. For instance, in Equation (2), the anchor matrix $A$ is introduced as a substitute for the original data in the dictionary. However, in Equation (6), an orthogonality constraint is imposed on $A$ without prior explanation. A more thorough justification and description of this constraint would improve clarity.\n2. The manuscript lacks a professional and in-depth comparison between the proposed tensor rank approximation method and existing approaches. Specifically, it is unclear why the proposed High-Preservation $\\ell_\\delta$-norm outperforms other commonly used tensor norms. Further theoretical insights or empirical analysis would strengthen this claim.\n 3. There is an inconsistency in the usage of hyperparameters. For example, Equation (6) involves $\\alpha$ and $\\beta$, while Section~4.3 refers to $\\lambda$. Similar inconsistencies are observed in other parts of the manuscript and should be corrected to avoid confusion.\n4. Equation (6) should be discussed in a more comprehensive manner, including its motivation and the roles of each term, to help readers better understand its formulation and contribution to the overall method.", "was_revised": true, "final_justification": "My concerns have been addressed, so I will maintain my positive rating.", "rebuttal": "***\n>**Q1.** *A more thorough justification and description of constraint $(\\mathbf{A}^v)^{\\top}\\mathbf{A}^v = \\mathbf{I}$ .*\n***\n**A1.** Thank you for raising this important point. Actually, the absence of the constraint $(\\mathbf{A}^v)^{\\top}\\mathbf{A}^v = \\mathbf{I}$ in Equation (2) is a flaw. The anchor-based model originally formulated in Equation (2) will be revised as follows:\n$$\n\\begin{aligned}\n&\\min_{\\\\{\\mathbf{E}^v,\\mathbf{Z}^v,\\mathbf{A}^v\\\\}_{v=1}^m,\\boldsymbol{\\mathcal{Z}}} \\mathcal{R}(\\boldsymbol{\\mathcal{Z}}) + \\alpha \\mathcal{P}(\\mathbf{E}^v) + \\beta \\mathcal{T}(\\mathbf{Z}^v) \\\\\\\\\n\\text{s.t. } \\forall v, \\mathbf{X}^v &= \\mathbf{A}^v \\mathbf{Z}^v+ \\mathbf{E}^v,\\boldsymbol{\\mathcal{Z}} = \\Phi(\\mathbf{Z}^1, \\mathbf{Z}^2, \\dots, \\mathbf{Z}^m), (\\mathbf{A}^v)^{\\top}\\mathbf{A}^v=\\mathbf{I}\n\\end{aligned}\n$$\nHere, $\\mathbf{A}^v \\in \\mathbb{R}^{d_v \\times t}$ denotes the anchor matrix for view $v$, where each column represents an anchor point. The orthogonality constraint $(\\mathbf{A}^v)^{\\top}\\mathbf{A}^v = \\mathbf{I}$ is commonly adopted in anchor-based multi-view clustering to enhance the discriminability and representativeness of the anchor points, thereby improving the clustering performance.\n\n***\n>**Q2.** *Theoretical Insights and Empirical Analysis of the High-Preservation $\\ell_\\delta$-Norm.*\n***\n**A2.** \n➀ **Theoretical analysis:** Let the function $ f_{HP\\ell_{\\delta}}(x) = \\frac{(1+\\delta)\\tanh x}{\\delta + \\tanh x} $. As $ x \\to 0 $, we have $ f_{HP\\ell_{\\delta}}(x) \\to 0 $. When $ x \\to +\\infty $, since $ \\tanh(x) \\to \\frac{\\pi}{2} $, the function converges to $ f_{HP\\ell_{\\delta}}(x) \\to \\frac{\\pi}{2\\delta + \\pi} < 1 $.For comparison, consider $ f_{\\ell_{\\delta}}(x) = \\frac{(1+\\delta)x}{\\delta + x} $. When $ x \\to 0 $, $ \\tanh(x) \\approx x $, so $ f_{HP\\ell_{\\delta}}(x) \\approx f_{\\ell_{\\delta}}(x) $, indicating that the penalization on small singular values remains almost unchanged. However, as $ x \\to +\\infty $, $ f_{\\ell_{\\delta}}(x) \\to 1 $, while $ f_{HP\\ell_{\\delta}}(x) $ converges to a fixed value $\\frac{\\pi}{2\\delta + \\pi}$ strictly less than 1. This upper saturation effect effectively suppresses the penalization on large singular values, thus preserving more dominant components. As a result, the HP$ \\ell_{\\delta} $-norm penalizes small singular values effectively while reducing shrinkage on large ones, achieving a desirable balance between low-rankness and the preservation of critical information.\n➁**Empirical analysis:** To empirically validate the effectiveness of the proposed HP$\\ell_{\\delta}$ norm, we conduct comparative experiments by replacing it with the LogDet function, the Laplace function, and the standard $\\ell_{\\delta}$ norm. All evaluations are carried out on the benchmark datasets with a missing rate of 0.5, and each experiment is executed five times during the evaluation process. \n\nAdditional theoretical analysis and experimental results will be provided in the supplementary material to further justify the effectiveness of the proposed High-Preservation $\\ell_\\delta$-norm over existing tensor norms.\n| Datasets       | Yale3           | MSRC\\_v1       | EYaleB10        | COIL20MV        | Mfeat           | Scene           |\n|----------------|------------------|----------------|------------------|------------------|------------------|------------------|\n| LogDet     | $56.97\\pm2.94$   | $76.19\\pm0.00$ | $35.78\\pm1.10$   | $71.65\\pm2.67$   | $81.83\\pm0.00$   | $54.47\\pm0.46$   |\n| Laplace    | $55.88\\pm1.45$   | $76.76\\pm1.03$ | $37.16\\pm2.05$   | $72.75\\pm3.89$   | $82.11\\pm0.00$   | **58.35$\\pm$0.17** |\n| $\\ell_{\\delta}$ | $54.91\\pm2.29$  | $79.52\\pm0.58$ | $35.84\\pm2.09$   | $74.50\\pm3.44$   | $81.47\\pm0.11$   | $57.66\\pm0.00$   |\n| HP$\\ell_{\\delta}$ | **57.33$\\pm$2.66** | **80.00$\\pm$0.00** | **38.16$\\pm$2.05** | **74.51$\\pm$5.95** | **82.31$\\pm$0.00** | 58.09$\\pm$0.00 |\n***\n>**Q3.** *Equation (6) involves $\\alpha$ and $\\beta$, while Section~4.3 refers to $\\lambda$.*\n***\n**A3.** To address this issue and improve the clarity and consistency of our presentation, we have revised Equation (6) by unifying all hyperparameter symbols to the form $\\lambda_i$, which is consistent with the notation used throughout Section~4.3 and the experimental settings.\nThe revised formulation of Equation (6) is given as follows:\n$$\n\\begin{aligned}\n&\\min\\_{\\\\{\\mathbf{E}^v,\\mathbf{Z}^v,\\mathbf{{A}}^v\\\\}\\_{v=1}^m,\\boldsymbol{\\mathcal{Z}}} \\\\|\\boldsymbol{\\mathcal{Z}}\\\\|\\_\\mathrm{HP\\ell_{\\delta}} + \\lambda_1 \\\\|\\mathbf{E}^v\\\\|\\_{\\text{GRN}} + \\lambda_2 \\\\|\\mathbf{Z}^v\\\\|_{\\mathrm{DMR\\text{-}1}}+ \\lambda_3 \\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}} \\\\\\\\ \n&\\text{s.t. } \\forall v, \\mathbf{X}^v = \\mathbf{A}^v \\mathbf{Z}^v+ \\mathbf{E}^v,\\boldsymbol{\\mathcal{Z}} = \\Phi(\\mathbf{Z}^1, \\mathbf{Z}^2, \\dots, \\mathbf{Z}^m), (\\mathbf{A}^v)^{\\top}\\mathbf{A}^v=\\mathbf{I}\n\\end{aligned}\n$$\nThe DMR term has been explicitly decomposed into two complementary components for better interpretability. Specifically, we define $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}1}}=\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, and $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}}=\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}\\_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$.\n***\n>**Q4.** *Discussion of equation (6) in a more comprehensive manner.*\n***\n**A4.** Building upon the improved formulation provided in **A3**, we perform a detailed analysis of each term, which will be presented in the supplementary material to aid comprehension:\n\nThe term $\\\\|\\boldsymbol{\\mathcal{Z}}\\\\|\\_\\mathrm{HP\\ell_{\\delta}}$ imposes a low-rank constraint on the tensor $\\boldsymbol{\\mathcal{Z}}$. The employed HP$\\ell_{\\delta}$ norm is a variant of the standard $\\ell_{\\delta}$ norm. It penalizes small singular values similarly to the $\\ell_{\\delta}$ norm, while applying relatively milder penalties to larger singular values. This design helps to preserve more critical structural information in the data.\n$\\\\|\\mathbf{E}^v\\\\|\\_{\\text{GRN}}$ introduces a novel formulation for the reconstruction error model. Compared to traditional norms such as the $\\ell_1$ norm, $\\ell_{2,1}$ norm, and Frobenius norm, it has the ability to capture the underlying noise distribution to a certain extent. Moreover, it incorporates learnable parameters that can adaptively adjust during optimization, enabling more effective modeling of complex noise patterns, especially in scenarios involving incomplete views.\n$\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}1}}$, defined as $\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, encourages the manifolds of each view to mutually constrain each other, thus enhancing cross-view consistency.\n$\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}}$, i.e., $\\sum\\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}\\_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$, constructs a consensus Laplacian matrix that fuses the manifolds across all views, which helps capture a unified and globally consistent manifold structure.\n$(\\mathbf{A}^v)^{\\top}\\mathbf{A}^v = \\mathbf{I}$ is a commonly adopted constraint in anchor-based multi-view clustering, aiming to enhance the discriminability and representativeness of the anchor points, which in turn facilitates improved clustering performance.\n***\n>**Limitations.** *The relatively high computational complexity should be acknowledged as one of the paper’s limitations.*\n***\n**A5.** Thank you for pointing this out. The main limitation of the proposed model concerns its computational complexity. Specifically, the computational burden of GUITAR increases at a cubic rate with respect to thte number of data samples. This is primarily due to the matrix inversion involved in the update of the coefficient matrices $\\mathbf{Z}^v$. Such complexity may hinder scalability when applied to large-scale datasets, and future work could explore more efficient optimization strategies to mitigate this issue."}, {"review_id": "gUfyEjxe9r", "reviewer": "Reviewer_n3re", "summary": "The authors address the insufficient noise modeling in existing tensor-based multi-view clustering methods by proposing a Gaussian regression–based clustering framework. Specifically, the approach employs Gaussian regression to more accurately characterize complex noise and incorporates dual manifold regularization to preserve both within-view and cross-view structural information. Additionally, an unbiased tensor constraint is designed to exploit the structural prior of the tensor data. Experimental results on six benchmark datasets demonstrate the effectiveness of the proposed method.", "questions": "1. The paper fails to clearly differentiate the proposed method from existing MVC approaches that also utilize Laplacian regularization, leaving its novelty unclear.\n2. In Table 1, the proposed method shows relatively large standard deviations at some missing rates, while at others the standard deviation is zero. The manuscript does not provide an explanation for this inconsistency, which raises questions about the stability of the results.\n3. The analysis of Figure 4 is limited; more detailed discussion is recommended to better demonstrate the effectiveness of the proposed tensor constraint.", "limitations": "Limitations and potential negative impacts are not discussed.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths：\n\n1. The motivation is well articulated, with clear presentation of key ideas and appropriate referencing.\n2. The paper includes comprehensive visualizations, such as flowcharts and experimental data plots.\n3. Ablation studies effectively demonstrate the contributions of individual components.\n\nWeaknesses:\n1. It remains unclear whether the Gaussian function used for noise modeling is shared across all views or defined separately for each view. Additionally, the paper lacks a clear description of how these functions are constructed.\n2. The interpretation of the balancing parameter $\\gamma$ in Equation (4) is unclear, and the paper lacks an analysis of its impact.\n3. The Proposed Method section is missing a clear and concise summary of the overall model, which makes it difficult to grasp the key contributions and structure of the approach.", "was_revised": true, "final_justification": "My concerns have been adequately addressed, and I appreciate the clarifications. I maintain my positive evaluation of the paper.", "rebuttal": "***\n>**Q1.** *The distinction between the proposed method and existing MVC approaches with Laplacian regularization is unclear.*\n***\n**A1.** Most existing Laplacian regularization methods typically involve only a single term, constructing the Laplacian matrix solely based on a consensus similarity matrix. However, when the manifold structures across different views differ significantly, such consensus can lead to bias. In contrast, our proposed DMR term introduces a more comprehensive regularization framework. One key component of DMR is $\\sum \\limits_{v=1}^m \\sum \\limits_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, which encourages the manifold of each view to be constrained by those of all other views, thereby enhancing cross-view consistency. This mutual regularization helps reduce manifold discrepancies among views. As a result, the consensus Laplacian term $\\sum \\limits_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$ which constructs a unified Laplacian matrix by fusing the manifolds of all views, can more effectively capture a globally consistent and representative manifold structure.\n***\n>**Q2.** *In Table 1, the proposed method shows relatively large standard deviations at some missing rates, while at others the standard deviation is zero.*\n***\n**A2.** In our model, we use a multivariate Gaussian distribution to model the noise. Since this distribution is relatively fixed, it may not fully capture all types of missing data, which could cause larger standard deviations in some scenarios while resulting in zero standard deviation in others.\n***\n>**Q3.** *The effectiveness of the proposed tensor constraint.*\n***\n**A3.** This is a detailed theoretical analysis of the proposed tensor constraint: Let the function $ f_{HP\\ell_{\\delta}}(x) = \\frac{(1+\\delta)\\tanh x}{\\delta + \\tanh x} $. As $ x \\to 0 $, we have $ f_{HP\\ell_{\\delta}}(x) \\to 0 $. When $ x \\to +\\infty $, since $ \\tanh(x) \\to \\frac{\\pi}{2} $, the function converges to $ f_{HP\\ell_{\\delta}}(x) \\to \\frac{\\pi}{2\\delta + \\pi} < 1 $.For comparison, consider $ f_{\\ell_{\\delta}}(x) = \\frac{(1+\\delta)x}{\\delta + x} $. When $ x \\to 0 $, $ \\tanh(x) \\approx x $, so $ f_{HP\\ell_{\\delta}}(x) \\approx f_{\\ell_{\\delta}}(x) $, indicating that the penalization on small singular values remains almost unchanged. However, as $ x \\to +\\infty $, $ f_{\\ell_{\\delta}}(x) \\to 1 $, while $ f_{HP\\ell_{\\delta}}(x) $ converges to a fixed value $\\frac{\\pi}{2\\delta + \\pi}$ strictly less than 1. This upper saturation effect effectively suppresses the penalization on large singular values, thus preserving more dominant components. As a result, the HP$ \\ell_{\\delta} $-norm penalizes small singular values effectively while reducing shrinkage on large ones, achieving a desirable balance between low-rankness and the preservation of critical information.\n***\n>**Weakness1.** *Is the noise-modeling Gaussian function shared across views or view-specific? Construction of Noise Modeling Functions.*\n***\n**A4.** ➀**Is the noise-modeling Gaussian function shared across views or view-specific?** Each view is associated with its own multivariate Gaussian distribution; therefore, a distinct Gaussian function is employed independently for each view. ➁**How are these functions constructed?** $\\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)$ can be characterized by its probability density function, namely, $\\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)=\\frac{1}{(2\\pi)^{d_v/2} |\\boldsymbol{\\Sigma}^v|^{1/2}} \\exp\\left( -\\frac{1}{2} (\\mathbf{e}^v_{q} - \\boldsymbol{\\mu}^v)^\\top (\\boldsymbol{\\Sigma}^v)^{-1} (\\mathbf{e}^v_{q} - \\boldsymbol{\\mu}^v) \\right)$.\n\nThe Gaussian Regression Norm is derived by the negative log-likelihood of the noise under a multivariate Gaussian model. Specifically, let $\\mathbf{e}^v_q$ denote the noise vector of the $q$-th sample in the $v$-th view, which is assumed to follow a multivariate Gaussian distribution:\n$$\np(\\mathbf{e}^v_q) = \\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)\n$$\nwhere $\\boldsymbol{\\mu}^v$ and $\\boldsymbol\\Sigma^v$ represent the mean vector and covariance matrix for the v-th view, respectively.\nAssuming that the noise vectors within each view are independent, the likelihood of the entire noise matrix $\\mathbf{E}^v=[\\mathbf{e}^v_1,\\cdots,\\mathbf{e}^v_n]$ can be expressed as:\n$$\np(\\mathbf{E}^v) = \\prod_{q=1}^{n} \\mathcal{N} (\\mathbf{e}\\^v\\_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v)\n$$\nTaking the negative logarithm yields the negative log-likelihood for the $v$-th view:\n$$ - \\ln p(\\mathbf{E}^v) = - \\sum\\limits_{q=1}^{n} \\ln \\left( \\mathcal{N} (\\mathbf{e}^v_{q} \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v) \\right)\n$$\nTo regularize the noise across all views, we minimize the sum of negative log-likelihoods over all $m$ views, which leads to the definition of the Gaussian Regression Norm:\n$$ \\\\| \\\\{ \\\\mathbf{E}^v \\\\}^m_{v=1}\\\\|_{ \\\\mathrm{GRN} } =  \\\\sum\\_{v=1}\\^{m}\\left( - \\ln p(\\mathbf{E}^v) \\right) = - \\sum\\_{v=1}\\^{m} \\left( \\sum\\limits\\_{q=1}\\^{n} \\ln \\left( \\mathcal{N} (\\mathbf{e}\\^v\\_{q}  \\mid \\boldsymbol{\\mu}^v,\\boldsymbol{\\Sigma}^v ) \\right) \\right) $$\n\nWe will modify $\\\\|\\mathbf{E}^v\\\\|\\_{\\mathrm{GRN}}$ to $\\\\|\\\\{\\mathbf{E}^v\\\\}^m_{v=1}\\\\|\\_{\\mathrm{GRN}}$, to explicitly indicate that GRN involves all views.\n***\n>**Weakness2.** *The interpretation of the balancing parameter $\\gamma$ in Equation (4) is unclear, and the paper lacks an analysis of its impact.*\n***\n**A5.** The DMR term has been explicitly decomposed into two complementary components for better interpretability. Specifically, we define $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}1}}=\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, and $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}}=\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$. The parameter $\\gamma$ allows manual adjustment of the relative weight between $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}1}}$ and $\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}}$. The analysis of $\\gamma$ can actually be inferred from the experimental results and discussions on hyperparameters in Section 4.3. To improve the clarity and consistency of our presentation, we have revised Equation (6) by unifying all hyperparameter symbols to the form $\\lambda_i$, which is consistent with the notation used throughout Section 4.3 and the experimental settings.\nThe revised formulation of Equation (6) is given as follows:\n\n$$\n\\begin{aligned}\n&\\min\\_{\\\\{\\mathbf{E}^v,\\mathbf{Z}^v,\\mathbf{{A}}^v\\\\}\\_{v=1}^m,\\boldsymbol{\\mathcal{Z}}} \\\\|\\boldsymbol{\\mathcal{Z}}\\\\|\\_\\mathrm{HP\\ell_{\\delta}} + \\lambda_1 \\\\|\\mathbf{E}^v\\\\|\\_{\\text{GRN}} + \\lambda_2 \\\\|\\mathbf{Z}^v\\\\|_{\\mathrm{DMR\\text{-}1}}+ \\lambda_3 \\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}} \\\\\\\\ \n&\\text{s.t. } \\forall v, \\mathbf{X}^v = \\mathbf{A}^v \\mathbf{Z}^v+ \\mathbf{E}^v,\\boldsymbol{\\mathcal{Z}} = \\Phi(\\mathbf{Z}^1, \\mathbf{Z}^2, \\dots, \\mathbf{Z}^m), (\\mathbf{A}^v)^{\\top}\\mathbf{A}^v=\\mathbf{I}\n\\end{aligned}\n$$\nThe combined effect of $\\lambda_2$ and $\\lambda_3$ can be regarded as equivalent to adjusting both the value of $\\gamma$ and the weight of the DMR term.\n***\n>**Weakness3.** *The interpretation of the balancing parameter $\\gamma$ in Equation (4) is unclear, and the paper lacks an analysis of its impact.*\n***\n**A6.** Building upon the improved formulation provided in **A5.**, we perform a detailed analysis of the overall model, which will be presented in the supplementary material to aid comprehension:\nThe term $\\\\|\\boldsymbol{\\mathcal{Z}}\\\\|\\_\\mathrm{HP\\ell_{\\delta}}$ imposes a low-rank constraint on the tensor $\\boldsymbol{\\mathcal{Z}}$. The employed HP$\\ell_{\\delta}$ norm is a variant of the standard $\\ell_{\\delta}$ norm. It penalizes small singular values similarly to the $\\ell_{\\delta}$ norm, while applying relatively milder penalties to larger singular values. This design helps to preserve more critical structural information in the data.\n$\\\\|\\mathbf{E}^v\\\\|\\_{\\text{GRN}}$ introduces a novel formulation for the reconstruction error model. Compared to traditional norms such as the $\\ell_1$ norm, $\\ell_{2,1}$ norm, and Frobenius norm, it has the ability to capture the underlying noise distribution to a certain extent. Moreover, it incorporates learnable parameters that can adaptively adjust during optimization, enabling more effective modeling of complex noise patterns, especially in scenarios involving incomplete views.\n$\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}1}}$, defined as $\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, encourages the manifolds of each view to mutually constrain each other, thus enhancing cross-view consistency.\n$\\\\|\\mathbf{Z}^v\\\\|\\_{\\mathrm{DMR\\text{-}2}}$, i.e., $\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$, constructs a consensus Laplacian matrix that fuses the manifolds across all views, which helps capture a unified and globally consistent manifold structure.\n$(\\mathbf{A}^v)^{\\top}\\mathbf{A}^v = \\mathbf{I}$ is a commonly adopted constraint in anchor-based multi-view clustering, aiming to enhance the discriminability and representativeness of the anchor points, which in turn facilitates improved clustering performance.\n***\n>**Limitations.**\n***\n**A7.** The main limitation of the proposed model is its cubic computational complexity due to matrix inversions in updating $\\mathbf{Z}^v$, which hinders scalability on large datasets. Future work should explore more efficient optimization methods."}, {"review_id": "yiTgKiTwMX", "reviewer": "Reviewer_P3Lv", "summary": "The paper presents a tensorized framework for incomplete multi-view clustering, incorporating a Gaussian regression-based norm, a compact tensor norm for low-rank tensor regularization, and a dual Laplacian manifold constraint to align view-specific structures. The method introduces new formulations for noise modeling, rank approximation, and manifold regularization. Experimental results on six benchmark datasets show competitive performance compared to existing state-of-the-art methods.", "questions": "See Weaknesses for details.", "limitations": "The paper does not discuss its limitations or potential negative impacts. Including a brief discussion on these aspects is recommended.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1. The manuscript is logically structured and clearly written.\n2. The proposed method integrates Gaussian regression with dual manifold regularization into a unified framework in a principled manner. This design is conceptually interesting and effectively improves the quality of tensor representations for clustering tasks.\n3. The source code is provided in the supplementary material, which facilitates reproducibility.\n\n\nWeaknesses:\n1. The explanation of Dual Manifold Regularization is insufficient, with unclear distinctions between the two terms in Equation (4) and their roles in the model.\n2. Figure 1 lacks clarity—“Manifold Alignment” is not well defined, and its link to the objective is unclear. A brief description of the model pipeline below the figure is needed.\n3. The procedure for constructing incomplete multi-view data, as described in the Experimental Settings section, is ambiguous. In particular, the mechanism for ensuring that each sample is present in at least one view is not clearly specified. The statement regarding restoring data in one randomly selected view for completely missing samples requires further clarification.\n4. In Figure 3, the results indicate that increasing the number of anchors does not always lead to improved performance. The manuscript should provide a more in-depth analysis of this phenomenon, including potential reasons why a larger number of anchors may not consistently benefit the clustering results.", "was_revised": true, "final_justification": "Thank you for the authors’ detailed response. My concerns have been adequately addressed, and I appreciate the clarifications. I maintain my positive evaluation of the paper.", "rebuttal": "***\n>**Q1.** *The explanation of Dual Manifold Regularization. Distinctions between the two terms in DMR and their roles in the model.*\n***\n**A1.** ➀**Explanation of Dual Manifold Regularization:** The first term in the DMR, $\\sum \\limits_{v=1}^m \\sum \\limits_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, is designed to enforce cross-view manifold alignment. Specifically, it encourages the representation $\\mathbf{Z}^v$ of each view to conform to the manifold structure captured by the Laplacian matrix $\\mathbf{L}^{v'}$ of other views. This mutual regularization narrows the discrepancy between views and enhances the overall consistency among them.\nThe second term, $\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}\\_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$, incorporates a consensus Laplacian matrix $\\mathbf{L}\\_\\mathbf{s}$ that fuses the manifold structures from all views. It plays a complementary role by guiding each view’s representation toward a globally consistent manifold, which reflects the intrinsic geometry shared across views. ➁ **Distinctions between the two terms in DMR:** The two terms in the DMR serve complementary but distinct roles in promoting consistent manifold learning across views. When the manifold structures across different views differ significantly, enforcing a unified manifold directly may introduce bias. This issue is addressed by the first term, $\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{v'=1, v' \\neq v}^m \\mathrm{Tr}\\left( \\mathbf{Z}^v \\mathbf{L}^{v'} {(\\mathbf{Z}^v)}^\\top \\right)$, which imposes cross-view constraints, encouraging the manifold of each view to align with those of the others. This mutual regularization helps to reduce discrepancies among view-specific manifolds and improves inter-view consistency.\nIn contrast, the second term, $\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\mathbf{Z}^v \\mathbf{L}_\\mathbf{s} {(\\mathbf{Z}^v)}^\\top \\right)$, constructs a consensus Laplacian matrix by integrating the manifold structures of all views. Its goal is to capture a globally consistent and representative manifold structure shared across views. The effectiveness of this consensus term is enhanced when the individual view manifolds are already well-aligned, a condition facilitated by the first term. Together, these two terms enable the model to first harmonize local structures and then learn a unified global manifold.\n***\n>**Q2.** *Figure 1 lacks clarity—“Manifold Alignment” is not well defined, and its link to the objective is unclear. A brief description of the model pipeline below the figure is needed.*\n***\n**A2.** ➀**The meaning of “Manifold Alignment”:** The concept of manifold alignment is realized through the term$\\sum \\limits_{v=1}^m \\sum \\limits_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, which imposes geometric constraints on each view using the Laplacian matrices derived from all other views. This cross-view regularization drives the alignment of view-specific manifolds, ensuring a more consistent and integrated representation across views. ➁ **A brief description of the model pipeline:** As illustrated in the figure, the proposed model consists of four main components: noise modeling, low-rank tensor learning, manifold alignment, and manifold fusion. Noise modeling is achieved through $\\\\|\\mathbf{E}^v\\\\|\\_{\\text{GRN}}$, which captures the complex noise introduced by reconstruction error and missing data. Low-rank tensor learning corresponds to $\\\\|\\boldsymbol{\\mathcal{Z}}\\\\|\\_\\mathrm{HP\\ell_{\\delta}}$, where the HP$\\ell_{\\delta}$ norm imposes a smaller penalty on large singular values compared to the $\\ell_{\\delta}$ norm. Manifold alignment is represented by the first term in the DMR, $\\sum \\limits\\_{v=1}^m \\sum \\limits\\_{\\substack{v'=1, v' \\neq v}}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}^{v'} {(\\textbf{Z}^v)}^\\top \\right)$, which aligns each view’s manifold structure to those of the other views. Manifold fusion corresponds to the second term in the DMR, $\\sum \\limits\\_{v=1}^m \\mathrm{Tr}\\left( \\textbf{Z}^v \\textbf{L}\\_\\textbf{s} {(\\textbf{Z}^v)}^\\top \\right)$, promoting global fusion of manifold structures across all views.\n***\n>**Q3.** *The procedure for constructing incomplete multi-view data, as described in the Experimental Settings section, is ambiguous. In particular, the mechanism for ensuring that each sample is present in at least one view is not clearly specified. The statement regarding restoring data in one randomly selected view for completely missing samples requires further clarification.*\n***\n**A3.** Thank you for your valuable comment. In cases where a sample is missing across all views, one view is randomly selected with equal probability to retain its data. This ensures that, in the incomplete multi-view dataset used for clustering, each sample has at least one observed view.\n***\n>**Q4.** *Increasing the number of anchors does not always lead to improved performance.*\n***\n**A4.** The number of anchor points can affect clustering performance, but the quality of the anchor points is also a critical factor. When the number of anchor points is small, the dictionary may lack sufficient expressive power, leading to large reconstruction errors. As the number increases, the dictionary becomes more expressive, but the likelihood of learning low-quality anchor points also rises. These low-quality anchors may introduce noise and degrade clustering performance. Therefore, more anchor points do not necessarily lead to better results, and an appropriate number should be chosen based on experimental outcomes.\n***\n>**Limitations.**\n***\n**A5.** We will discuss and incorporate the limitations into the revised manuscript.\n\nThe main limitation of the proposed model concerns its computational complexity. Specifically, the computational burden of GUITAR increases at a cubic rate with respect to thte number of data samples. This is primarily due to the matrix inversion involved in the update of the coefficient matrices $\\mathbf{Z}^v$. Such complexity may hinder scalability when applied to large-scale datasets, and future work could explore more efficient optimization strategies to mitigate this issue."}]

Author rebuttal:

Meta-review: The paper proposes a novel gaussian regression-driven tensorized incomplete multi-view clustering. The method integrates realistic noise modeling, dual-level manifold regularization, and robust tensor constraints in a unified framework. The method can effectively capture realistic noise characteristics beyond conventional norm-based assumptions and preserve structural information across multiple views. Sufficient experiments are conducted. All reviewers provided positive comments and recommendations for this paper. The final decision is to accept.
Decision: Accept (poster)