Confidence-Aware With Prototype Alignment for Partial Multi-label Learning
Authors: Weijun Lv
Yu Chen
Xiaozhao Fang
Xuhuan Zhu
Jie Wen
Guoxu Zhou
Sixian Chan
Venue: NeurIPS 2025 poster ()
Keywords: Partial multi-label learning
Noise disambiguation
Class prototype
Pattern recognition
Primary area: general_machine_learning

Abstract: Label prototype learning has emerged as an effective paradigm in Partial Multi-Label Learning (PML), providing a distinctive framework for modeling structured representations of label semantics while naturally filtering noise through prototype-based label confidence estimation. However, existing prototype-based methods face a critical limitation: class prototypes are the biased estimates due to noisy candidate labels, particularly when positive samples are scarce. To this end, we first propose a mutually class prototype alignment strategy bypassing noise interference by introducing two different transformation matrices, which makes the class prototypes learned by the fuzzy clustering and candidate label set mutually alignment for correcting themselves. Such alignment is also passed on to the fuzzy memberships label in turn. In addition, to eliminate noise interference in the candidate label set during the classifier learning, we use the learned permutation matrix to transform the fuzzy memberships label for learning a label reliability indicator matrix accompanied by the candidate label set. This makes the label reliability indicator matrix absolutely prevent the occurrence of numerical values located in non-label and simultaneously eliminate the introduction of incorrect label as much as possible. The resulting indicator matrix guides a robust multi-label classifier training process, jointly optimizing label confidence and classifier parameters. Extensive experiments demonstrate that our proposed model exhibits significant performance advantages over state-of-the-art PML approaches.

Confidence-Aware With Prototype Alignment for Partial Multi-label Learning
Weijun Lv Yu Chen', Xiaozhao Fang',, Guoxu Zhou', Sixian Chan
Xuhuan Zhu', Jie Wen";
School of Automation, Guangdong University of Technology, Guangzhou 510006, China Shenzhen Key Laboratory of Visual Object Detection and Recognition, Harbin Institute of Technology (Shenzhen), Shenzhen 818055, China
CCollege of Computer Science and Technology, Zhejiang University Technology, Hangzhou 310023, China
(1vweijun0201, chenyu8265324)0163 com, (xzhfang163, xuhuanz_ xuhuanz_22)0116. com piewen_pr@126.cmm com, gx zhou@gdut edu. en, sxchan@zjut edu. cn
Abstract
Label prototype learning has emerged effective paradigm in Partial Multi- Label Learning (PML), providing distinctive framework for modeling structured representations of label semantics while naturally filtering noise through prototype- based label confidence estimation. However, existing prototype-base methods face critical limitation: class prototypes are the biased estimates due noisy candidate labels, particularly when positive samples are scarce. To this end, we first propose mutually class prototype alignment strategy bypassing noise inter- ference by introducing two different transformation matrices, which makes the class prototypes learned by the fuzzy clustering and candidate label set mutually alignment for correcting themselves. Such alignment is also passed on to the fuzzy memberships label in turn. In addition, eliminate noise interference in the candidate label set during the classifier learning, we use the learned permutation matrix to transform the fuzzy memberships label for learning a label reliability indicator matrix accompanied by the candidate label set. This makes the label reliability indicator matrix absolutely prevent the occurrence of numerical values located in non-label and simultaneously eliminate the introduction of incorrect label as much as possible. The resulting indicator matrix guides robust multi- label classifier training process, jointly optimizing label confidence and classifier parameters. Extensive experiments demonstrate that our proposed model exhibits significant performance advantages over state-of-ther the-art PML approaches.
Introduction
Multi-Labee Learning (MLL) is important branch of machine learning that allows instance belong to multiple categories simultaneously, with widespread applications in image annotation 22). text categorization(3], and medical diagnosis [4]. However,
practical application scenarios, obtaining precisely annotated data is often difficult due to high annotation costs and inherent ambiguity
H. Annotators frequently provide a candidate label set when uncertain. con- taining both ground-truth labels and noisy labels (i.e., false positive labels mistakenly included). For example, image annotation tasks, objects with similar visual appearances may be incorrectly labeled, which will introduce interference to the classification prediction. To address this issue, Partial Multi-Label Learning (PMI.) has emerged as a new weakly supervised learning framework. The
"Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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main task of PML is to learn from this uncertain supervisory information to accurately predict the ground-truth labels for unknown instances.
PMI. research primarily focuses on identifying ground-truth labels from the candidate lahel set, known as label disambiguation. Existing methods mostly adopt explicit learning strategies, directly removing noisy labels from candidate label sets through various techniques. For instance, some methods use
low-rank and sparse decomposition to separate ground-truth labels from noisy ones [T0 : others estimate the credibility of candidate labels through label propagation or label distribution learning
where the practice of using feature information to impose correlation constraints or manifold constraints on labels is the most popular [8] [9]. Recently, feature selection has become popular approach for disambiguation [20] 21 22 Some researchers leverage label correlations or cluster assignments to
12
14 15 ; while some utilize feature information to identify noisy labels [6 S
26 19 Additionally, some methods introduce complementary classifiers that simultaneously leverage both positive and negative label information under the noise sparsity assumption 277. Ánother line of research adopts a phased processing approach: first purifying noisy labels through methods like granular ball construction [25] or label propagation [1]. then applying structured learning strategies such as confidence score regression or pairwise classification paradigms [28] [29] to the refined labels. These explicit learning approaches, although effective to some extent, still face limitations when handling complex noise patterns. On one hand, methods based on sparsity assumptions often fail when real-world annotation scenarios produce non-sparse noise distributions, leading to error accumulation during classifier training. On the other hand, methods based on label confidence manifold learning struggle with samples lacking sufficient neighhorhood information or when positive samples are scarce, making it difficult to fully fit the data distribution.
assist disambiguation 9 23
Recently, prototype-based learning 9 25 30 19 has emerged as a promising direction that constructs class prototypes to guide label confidence estimation. As a comnestone of prototype-based approaches, clustering learning serves as an important tool for exploratory data analysis 31 32], naturally generating class prototypes without requiring prior labels while efficiently revealing inherent data
structure [3 Bd]. Building upon fuzzy clustering principles, FBD-PML [19] advances this direction by mining the correlation between sample instances and labels while learning confidence values under sample manifold assumptions. However, existing prototype-base methods face a critical limitation: prototypes derived from noisy candidate labels inevitably deviate from true semantic c a representation bias problem pervasive under imperfect supervision (35] 36, 37 38.. This fundamental weakness becomes particularly pronounced when positive samples are scarce, as the limited reliable supervision further exacerbates prototype distortion. This prototype bias propagates through confidence estimation, ultimately degrading classification performance. Moreover, existing methods struggle to effectively bridge the semantic gap between unsupervised clustering-derived prototypes and weakly supervised label-based prototypes, leaving the potential complementarity between these two prototype spaces largely unexplored.
Addressing these challenges, this paper proposes CAPML (Confidence-Awart Awre with Prototype Match- ing for Partial Multi-label Learning,, a novel method that leverages unsupervised clustering to bypass noise interference while enhancing effective prototype space alignment. Specifically, unlike traditional prototype- based methods that solely rely on noisy candidate labels, the proposed approach introduces a transformation mechanism that successfully bridges the gap between clustering-derived prototypes and label-based prototypes, enabling discovery of their intrinsic correspondence despite noisy supervision. Subsequently, confidence-aware process is designed to convert fuzzy membership degrees into label reliability indicators, guiding classifier training with sparse f2.1-morm -norm constraints. Concurrently, the prototype alignment mechanism is also utilized to guide the refinement of label confidence estimation. Finally. the enhanced confidence values and learned classifiers work jointly to predict labels for unknown instances. The main contributions of this paper are summarized as follows:
semantic representations through
This paper provides the first investigation into prototype misalignment between prototypes derived from fuzzy clustering and prototypes computed from candidate label sets in PML tasks, introducing a transformation mechanism that successfully bridges these two prototype spaces and enables effective alignment despite noisy supervision.
This paper designs a confidence-aware process that converts fuzzy label membership degrees into label reliability indicator values, guiding classifier training with sparse 22 constraints that enhance feature selection while reducing overfitting to noisy labels.

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Extensive empirical evaluation demonstrates the proposed method's efficacy in resolving label ambiguity and prototype misalignment problems PML, achieving superior general- ization performance even with high noise rates and sparse positive samples.
This section introduces the concept of PML, its evolution, related work, and how our approach differs from existing methods. The remainder of this paper is organized as follows: Section 2 details the principles and optimization algorithm of CAPML. Section 3 and provide comprehensive experimental results and analysis. Finally, Section 5 gives conclusion and Section cactiionoilluutti iillustrate the limitations of the method proposed.
2
Method
In PML, let X' C Rd denotes the d-dimensional feature space and y (2.. 14} denotes the label space with if class labels. The training dataset D {(x,, y;) S i S n} contains n examples, where 2; E X' is the i-th instance and y; {0, 1/. represents its corresponding label vector. Let
X x= 22.... ..... [n. E Rdx= denotes the feature matrix and Y - 3/ 1/2- yn E {0, 1 represents the candidate label matrix containing wrong annotation. Here, yij = 1 indicates the i-th instance is annotated with the j-th label, and Yt indicates otherwise. Each instance correspond set of candidate labels with unrelated labels incorrectly labeled as 1, which is called noisy label. The goal of PML is to learn a classification function f X + 2 that minimizes the effect of noisy label information and makes accurate label predictions. Figure (right) illustrates the overall architecture of CAPML.
Prototype Misalignment Problem
Fuzzy Clustering
Training Cord Serteee Klrrc
Irput
Prototype
Prototype
Clessifer Learning
Permutztion Matrix P
Prototype
O
Prototype
Candidate Label Set
Class Order Permutation
Prototype Alignment
Permutation
Figure 1: Overview of the CAPML framework.
The prototype misalignment problem unsupervised prototypes (Prototype 1) and weakly supervised prototypes (Prototype 2) lack optimal correspondence that require permutation matrix P for class order alignment.
Left::
Right: The two-stage pipeline: (1) Prototype learning and alignment--fuee clustering produces membership matrix F and unsupervised Prototype while weakly supervised Prototype is derived from candidate label set, then permutation matrix P establishes optimal correspondence, transforming memberships into label reliability (LR) indicator matrix C via element-wise product with and rraining-indicator matrix C guides the learning of
normalization; (2) Confidence-aware classifier training indicator label confidence matrix R, which in turn supervises classifier training to effectively suppress noise labels (marked in red) in Y and obtain proper predictions.
2.1 Class Prototype Learning and Alignment
Our approach begins with unsupervised prototype learning capture the intrinsic structure of the data, independent of potentially noisy label information. We employ an improved fuzzy clustering approach incorporating entropy regularization(31 (39 40) to obtain well-distributed class prototypes and reliable fuzzy label membership degrees. The unified objective function is formulated as:
min FI, FI.=1,,200 F20M
ΣΣ 2=1 1=1
m2
11
+
fis log fuj-
==
where M E [Rdx denotes the class prototype matrix, F E RR represents the fuzzy label mem- bership matrix indicating the association strength between instances and class prototypes, and controls the entropy regularization. The first term quantifies weighted clustering quality, while

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the entropy term prevents degenerate solutions and enables flexible membership distributions that can accommodate the multi-label nature by smoothly transitioning from unimodal to multimodal assignments. Through alternating optimization, the update formulas for M and F as follows:
Ei= fajak m, Ek=IfKj fkj
fiz
2x
The membership degree fiy follows a softmax-like formulation, where instances have higher member- ship degrees to closer prototypes. The parameter À controls the "softness" of the asiigmeents-larger values result more uniform distributions, while smaller values lead to more decisive assignments. While the prototypes M derived from fuzzy clustering lack explicit semantic meaning, can leverage them by setting e = q to match the number of label classes. To incorporate label semantic information, construct class prototypes O Raxxq from the candidate label matrix Y:
1kj
21=1 Ukj
Each prototype o, is computed the centroid of instances associated with the j-th label in Y. Despite the presence of noise, O can be viewed as weakly-superrised prototype[4[] that still contains valuable semantic information. Although M and O are derived from different paneciple--ussuperrve clustering and weakly supervised label aggregation respectively- fundamentally capture the same underlying class structure.
Then a critical problem emerges: although both M and capture class-level representation, their orderings inherently misaligned due to the arbitrary indexing produced by clustering. For example, as shown in Figure (left) only the 3-rd prototype in M correctly corresponds to its counterpart in O, while the remaining 1-st, 2-nd, 4-th unsupervised prototypes improperly correspond to positions 4-th, 1-st, 2-nd respectively. To address this issue, we introduce a permutation matrix P E (0, 1)98 align these orders:
min |MP O
8.l. P1, 1g. 1 1g. PE (0,
(4)
This formulation seeks the optimal one-to-one mapping between unsupervised and weakly supervised prototypes by minimizing the Frobenius norm of their difference. The constraints ensure that P is valid permutation matrix, with exactly one entry of in each row and column.
Theorem 1: When the fuzzy clustering successfully captures the underlying class structure, there exists an optimal permutation matrix P E (0, 1)9x9 such that the alignment error satisfies:
q2
MP - O E E
(5)
where measures the label noise level (specifically, the fraction of noisy labels in Y), is the number of training instances, and q is the number of classes.
The proof is provided in Appendix. This theorem reveals that the alignment error is governed by two factors: (1) the label noise level in the candidate set, and (2) the finite sample effect //2/n, which diminishes as more training data becomes available. Importantly, the bound suggests that even with moderate noise, the permutation matrix P establish meaningful correspondence when sufficient data is present.
However, another key challenge remains: since Y contains noise, the weakly supervised prototypes O deviate from true class centroids. Directly aligning M to O might propagate these noise-induced shifts. To address this discrepancy and make P more reliable, we introduce an orthogonal rotation matrix H E R1*a to allow for more flexible alignment:
min P.H
MP O
s.t. P1, 1y, P_1, = 1y. P (0, HH
Lg.
(6)
The orthogonal rotation matrix introduces geometric transformation that adapts the weakly su- pervised prototypes O to better match the unsupervised structure, while preserving their relative geometry through the constraint HH I, This mitigates the negative impact of label noise: rather than forcing M to directly align with the potentially biased O, we allow to rotate in its representation space, reducing the negative influence of noisc-induced biases the alignment quality.

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Constructing label reliability indicator. Having obtained the optimal permutation matrix P and rotation matrix H, we establish the correspondence between M and O. The permutation matrix P not only aligns the prototype spaces but also reveals which cluster corresponds to which label class, thereby enabling transformation of the fuzzy membership degree in F into label-specific reliability indicator for candidate labels.
We apply the learned permutation matrix column with its corresponding label class. To mitigate interference from misaligned entries, we perform element- wise multiplication with the candidate label matrix Y to retain only candidate positions, followed by row-wise min-mas normalization N Mminmax() (-) to amplify confidence contrasts:
reorder the membership matrix F, aligning each
Z N (FP Y).
(7)
This operation filters out non-candidate noise while enhancing discrimination between reliable and unreliable candidates. We then construct the label reliability (LR) indicator matrix C E 12xx as:
1,
if 3h = 0
Cij
=
(8)
Zij+
if yky =
However, this initial formulation treats all instances uniformly, ignoring that instances with more candidate labels typically contain more noise. To address this, we introduce instance-adaptive weighting based on candidate label density:
C2j = { [ly (q - 11y:lla) Zig.
if yıj
if y =
This refined formulation assigns differentiated indicator values based on candidate label density, which ensures that instances with denser candidate sets which statistically contain more false positives-receiv more conservative reliability estimates.
2.2 Confidence-Aware Label Disambiguation
The LR indicator matrix C plays a crucial role in our label disambiguation process. A higher indicator value сt indicates higher probability that Tıy is true label rather than noise. With the label reliability (LR) indicator matrix C constructed, we now formulate the confidence-aware objective for joint classifier learning and label disambiguation:
min ICO (Y RR)I (X) W - R + a R B W12.,, s.t. R (10) W.R
where vi(-) Rd + A is a feature mapping function that transforms input features to kernel space for better separability, W E R represents the classifier parameters, R E R=x denotes the label confidence matrix, and a, B are regularization hyperparameters. The first term implements reliability-weighted refinement through element-wise multiplication. For non-candidates, the weight Gj 1 penalizes any deviation from weights create differentiated penalties: high-reliability positions (large (ij) are tightly constrained Y. while low-reliability positions (small ci²) receive weaker constraints, allowing the classifier consistency and f terms to guide their refinement. The & norm term further reduces the influence of noise in candidate label Y. while the f2, norm term enhances the classifier's 's discriminative power by emphasizing features with high discriminative capacity across multiple labels.
in R. constraining rij 0. For candidates, varying
2.3 Optimization
The proposed approach optimization is divided into two parts. After obtaining O and F through 2q we need to learn to obtain an effective permutation matrix to obtain LE indicator matrix C. Then C is reused for further refinement of the label confidence matrix R to guide the learning of the classifier W. We optimize each variable by adopting an alternating iterative way.
Update H, fix P. We can obtain the following optimization problem about variant H.
min A - 2 8.1. HH Lg:
(11)
where A MP. Eq. 11Tp presents a standard orthogonal Procrustes problem which we efficiently solve following the optimization approach detailed in 43).
5

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Algorithm 1:
Training Process of CAPML
Input:
The PML training dataset D; parameters X, 9; max iterations To, Tı, T23 Unseen sample x. Output: the predicted label for
sample y. // Stage One Prototype Learning and Aligament
Initialize membership matrix F = Y and prototypes M via Eq. for = to To do
| Update M and F via Eq. 2
// Fuzzy clustering for unsupervised prototype
end
Compute O via Eq. 3 Initialize permutation matrix P ly and rotation matrix = -1
Compute supervised prototype from candidate labels
for t = to 7i do
Update H by solving orthogonal Procrustes problem in Rq. 11
Update P using Hungarian algorithm in Eq. 12 // Prototype alignment optimization
end
Compute label reliability indicator matrix C via Eq.
// Construct LR indicator matrix
// Stage Two: Classifier Learning
Initialize W 0g. R Y. and auxiliary variable 0xxqq-
for = to
Update W using Eq. (13)
Update R using multiplicative rule in Eq.
16
Update Q using soft- coft-thresholding via Eq.
19
| w(( + R
R
( < -9 then
break;
end end
return the predicted label y
Update fix Substitute the H obtained from the last iteration to Eq. (6. and let M OH, we can obtain the following optimization problem.
min MP - MI s.f. Pl, 1g: P = 1gp P (0, P
(12)
Due to the binary constraints on P. direct optimization is infeasible. We solve this assignment problem efficiently using the Hungarian algorithm via MATLAB's s matchpairs function 44
Update W, fix The subproblem regarding W can be obtained:
min |
w
R
31 W + min W
(X) W
R
3t (W DW).
(13)
where the diagonal elements of D are computed D. 1/ the derivative of Eq. 13 w.r.t. W and setting it to O, we can get the following equation:
|w, 3.,,
h). Taking
W = (v (x))((()) + (D) (X)),
(14)
Update R, fix W. We solve the optimization involving the non-convex f norm and non- negativee
constraint R 2 0 by applying the Lagrange multiplier method, yielding the following Lagrangian
function:
min R
(Y- +| w - -R| Q + //2 R - (OR=)) (15)
where μ number large enough and O represents the Lagrange multiplier. Taking the derivative of
Eq. (15) and setting the derivative to zero. Then based on condition of Baais--KunnTTuehe (KKT),
it can be given that: O C O, that is, f,y 0. Fix Q then take the derivative of Eq. (15) w.r.t.
R and setting it to O, we can get the following equation: We can get the update rules for R:
((+1) (2) B
rij =
(16)
A, + eps'
where Aij =
( E) and B = (24(() -W
With R fixed, we can get the sub-optimization of Q:
L I
min L(Q) = a: Q
11
Y - R - R-Q
(17)
2

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which is typical LASSO regression problem 45 and we apply PGD algorithm to optimize it. The proximal operator of Eq.
is:
pro) (Q) arg min |Q
Z
+ L |Q
(18)
where Q' - (VL(Q)) Q represents the solution of Q from the t-th iteration, and VZ(Q)
is the gradient of the objective function ((Q), L is the Lipschitz constant of V (Q) and / denotes
the number of iteration. Eq. 18) can be iteratively updated by the soft-thresholding operator [46
(++1) Softlaij
1 Vild
(19)
where Softlb, v) sign())mar [6| u, 0}. In addition, the Lipschitz constant of VZ(Q) is so set L = 1. The overall pseudo code of CAPML is summarized in Algorithm |
3
Experiment
3.1 Experimental Setup
Datasets To evaluate the generalization performance of our proposed CAPML approach, conducted experiments on datasets, including real-world PML datasets[49] and 18 synthetic PML datasets generated from seven multi-label datasets 47 48 For clarity, the detailed characteristics of these datasets are shown in Table] | datasets by adding noise the labels. For each instance, a portion of irrelevant labels is randomly picked as candidate labels along with the relevant ones. Taking the birds dataset as an example, which originally has 1.01 ground-truth labels per instance (aug-#f Murg-#GTss) GLs), with 3, 4, and 5 candidate labels per instance (avg.# fugg-#CILL. Ls) by randomly injecting approximately 1.99, 2.99, and 3.99 false positive labels per instance, respectively.
Specifically, the synthetic datasets are derived from multi-label
created three noisy variants
Table 1: Characteristics of experimental data sets.
Dutsets
Instances
#Dim
#Classes
avg.#CLs
#GLs
Domain
Mirllickr
10433
100
7
3.35
1.77
Images*
Music emotion
6833
98
11
5.29
2.42
Music'
Msic_style
10
6.04
1.44
Music"
YeastBP
6139
217
5.93
5.54
Biology
YeastCC
6139
6139
50
1.39
1.35
Biology
YeastMF
6139
6139
39
1.04
1.01
Biology
emotions
593
72
6
3,4,5
1.86
Music
birds
645
260
19
3,4.5
1.01
Audio
medical
978
1449
45
5,
1.25
Text²
image
2000
294
3,
1.23
Images? ?
yeast
2417
103
14
7,9,
4.24
Biology2
corel5k
5000
499
374
7.9.
3.52
Images?
html
Comparison approaches The performance of CAPML is compared with seven state-of-the-a methods, the following is a brief introduction for each comparison approach:
[2099]: fPML. removes noise by decomposing the candidate label matrix into two low-rank matrices and utilizing the resulting low-error approximation. [configuration:
fPML. 16
\1 1, A2 A3 10].
and PAR-VLS) 12 [2020]: A two-stage PMI approach that refines
candidate lahels through label propagation and builds distinct predictive models [suggested configuration: A: = 10, a = 0.9, thr = 10.9].
PML--I (5] [2021]: Considering that fuzzy features may produce noise labels, the pre- diction model matrix is decomposed into truth label prediction and noise label prediction [configuration: À 10, 8 7 0.5, max_ite iter 500].
PAMB 29 [2023]: PAMB uses ECOC techniques to convert PML into binary clas- sification problem, avoiding the error error-prone estimation of individual label confidences [configuration: aug. #CL, L = 100 log2(g)).
7

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Table 2: Comparision of CAPML with other sfate-of-the-arr PML approaches on Average Precision
tstd, where the best experimental performance (the larger the better) is shown in boldface.
Data Sets
avg.aCLs
CAPML
FBD-PML
LENFN
PAMB
PML-NI
PARTICLE
FPML
Mirflickr
3.35
0.820=00008
0.815=0.007
180020.0099
0.791
0.78640.009
0.81320.136
0.81420.009
Music emotion
5.29
0.62820.019
0,60749.011
0.60840.010
0.62640.011
0.60810.012
0.50620.016
0.458=0.015
Music style
6.04
0,743=0.016
0.740=0.017
0.745=0.014
0.741:0.007
0.739=0.015
0.657=0.012
0.566=0.090
YeasiBP
5,93
0.44320.015
0.40659.001
0.42340.017
0.35640.022
0.40440.022
0.168:0.016
0.328=0.012
YeasICC
1.39
0.60920,023
0.58420.011
0.60340.019
0.55640.024
0,454=0.025
0.348:0.016
0.458=0.052
YeastMF
1.04
0,495=0.021
0.431+0.017
0 023
0.405+0.014
0.41++00116
0.228=0.012
0.326=0.009
3
0.807=0.039
0.783=0.008
0.78340.035
0.80420.017
0.777+0.028
0.74720.035
0.663=0.020
emotions
4
0.787=00027
0.76519.000
0.76140.030
0.783+0.036
0.74910.034
0.73920.033
0.651
5
0.756:0.032
0.751=0.005
0.74640.033
0.749:0.026
0.680+0.039
0.702=0.037
0.65420.029
3
0.627
0.625g0:006
0.621300063
0.58910.052
0.37920.046 0.617000557
0.381
hirds
0.590=0.067
0.586++0.003
0.584+0.050
0,564+0.044
0.572+0.041
0.419+0.046
0.373=0.020
5
0.58920.048
0.57340.026
0.56840.027
0.49540.029
0.544400334
0.372+0.047
0.371
0.876=D0027
0.86450.024
0.87
0.81500012
0.
0.75450:1447
0.325
medical
7
0.86620.031
0.856+0.031
0. 0.864+0.018
0.796+0.031
0 036
0.741=0.049
0.832=0.029
9
0.852=0.033
0.842+0.020
0.851+0.028
0.771+0.011
0.79440.031
0.715=0.022
0.817=0.019
0.814=00022
0.777+0.023 0.77850.026
0.798
0 020
0.74500.770
0.711=0.018
image
0.792:0.018
0.745+0.031
0.74540.025
0.748+0.019
0.732+0.024
0.725=0.084
0.696=0.0223
0.759=0.022
00001
0.671
0.653+0.00 0.000
0.668=0.091
0.670=0.022
0.760=0:018
0.73420.007
0.756:0.020
0.761:0.014
0.74640.017
0.75420.013
0.732:0.016
yeast
0.755=0.021 9
0.725+0.022
0.738+0.019
0.750#0.013
0.725+0.016
0.744+0.011
0.730=0.013
11
0.748=0.013
0.70420:015
0.71940.018
0.741
0.692#0.013
0.728+0.013
0.69820.011
0.30620.015
0,274g0:015
0.28210:016
0.239g00177
0.279100133
0.254
0.26620.004
corel5k
0.303:0.017
0.267:0.015
0.27340.015
0.230+0.008
0.273+0.013
0.23420.004
0.264:00000 001
11
0.29920.017
0,266+0.018
0.265+0.015
0.228+0.019
0.2664000155
0.230=0.014
0.262=0.005
Table 3: Comparision of CAPML with other otate-of-the-art PML approaches on Ranking Loss
(stdn, where the best experimental performance (the smaller the better) is shown in boldface.
Data Sets
LVLs
CAPML
FBD-PML
LENFN
PAMB
PML-NI
PARTICLE
HPML
Mirllickr
3.35
0.110:00.00
0:126:0.006
0.12
0.12200033
0.12620.077
0.12730. TOS
0.11520.006
Music emotion
5.29
0.23610.007
0.24920.012
0.245=0.012
0.23420.007
0.24620.008
0.362x0.014
0.41020.005
Music style
6.04
0.135=0.010
0.139=0.024
0.140=0.012
0.136+0.005
0.137=0.010
0,221+00010
0.317=0.033
YeastHP
5,93
0.20320.009
0.271=0.013
0,253=0.009
0,23010.011
0.22020.011
0.40420.033
0.41520.057
YeastCC
1.39
0.167:0.015
0.195=0.017
0.191=0.012
0.221+0.021
0.210=0.022
0,480=0.010
0.342=0.019
Ye
1.04
0.218=0.017
0.262=0.011
0,232+0.013
0.244+0.013
0,236-0.018
0.533+0.010
0.373=0.019
0.16220.036
0.181=00018
0.182:00033
0.160:000022
0.185=0.029
0,250:0.035
0.474
emotions
4
0.17010.029
0.197=0.013
0.19420.029
0.17820.031
0.211=0.027
0.263x0.022
0.44620.027
5
0.205=0.032
0.213=0.000 006
0.251 032
0.210=00015
0.276=0.039
0.306+0.034
0.452=0.057
3
0,172:0.028
0.17620.035
0,183320.000
0.19620.042
0.17720.033
0.322x0.033
0.33320.041
birds
4
0.195:0.042
0.195=0.034
0.21 1 026
0 0,204+0.028
0.205=0.054
0,326+0.027
0.040
0.200=0.0336 5
0.207=0.038
0,223+00012
0.229+0.025
0.219=0.036
0.359+0.036
0.328+0.018
5
0.029:00.11
0.049=0.018
0.038+0.015
0.05011.002
0.040:0.012
0.09010.019
0.05220.007
medical
7
0,032=0.010
0.04720.016
0,0451000116
0.06210.019
0.05220.013
0.111
0.05820.009
9
0.038:00.033
0.051=0.016
0.054=0.016
0.099=0.023
0.061=0.015
0.122:0.016
0.057=0.010
2
0.155
0.18420.013
0.19000.025
0.17740.022
0.19420.019
0.230xa.000
0.23920.019
image
0.183=0.020 3
0.206=0.011
0.214+0.028
0,217=00015
0.230=0.024
0,261=0.070
0.254=00018
0.213+0.022
0.280=0.017
0,28740.019
0,25510.025
0.30320.010
0.32840.095
0.28044.022
0.173
0.187
0.
0,21
0.18420.012
0.18260.010
0.
yeast
9
0.177s0.015
0.19820.019
0.19240.018
0.21120.007
0,20220.016
0.18910.009
0.191
11
0.183=0.012
0.225=0.015
0.219=0.010
0.231=0.014
0. 0.199=0.010
0.195+0.010
0.21620.008
0.17620.007 0.175:0.007
0,223:0.012
0.31010.034
0.21520.008
0.31710.008
0.255
corel5k
9
0.184:0.007
0.192=0.016
0.225+0.010
0.31510.049
0.227=0.009
0.324+0.008
0.262=0.013
0.18920.006 11
0.203=0.012
0,23110.0009
0,31910.059
0,23220.008
0.330s0.007
0.26820.011
PML-LENEN (50 [2024]: PML-LENFN improves label quality by jointly analyzing
local (neighbor) and global (distant) sample relationships, paired with a hybrid classifier combining linear and nonlinear components [ \ = 10 d2 = 1, As 10 d 10-51.
FBD-PMI 199 [2025]: FBD- PMDDPMMPPPP performs manifold alignment by simultancously learning the prototypes of features and labels to achieve the smooth assumption. [configuration:
\1 10 de 1, As= 10-3, 3, X 10 3.335----- 10 10121
For our CAPML approach X is set to 0.5, a and 3 are searched in {0.001, 0.01, 0.1, 1, 10, 100}. For the feature mapping function v²()), we employ the Gaussian kernel with bandwidth parameter set to the average pairwise distance between samples.
3.2 Experimental Metries and Results
In our experiment, we evaluate the performance of CAPMI. and other state-of-the-art baselines using five lulti-label metries: Hamming loss, Ranking loss, One-error, Coverage, and Average precision.
8

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Details of these metrics can be found in 47 And we apply ten-fold cross-validation each PML dataset and report the mean and standard deviation for all eight comparison approaches. Due to page limitations, our experimental evaluation focuses primarily on two representative metrics: Average Precision and Ranking Loss, which are complementary metrics providing comprehensive insights into both ranking quality and classification accuracy. Results for the other three metrics are provided in the Appendix. Complete results are presented Tables and respectively.
Moreover, to verify the statistical significance of CAPML's performance advantages, we summarize winltie/loss counts across all evaluation metrics against each competing approach the 0.05 signif- icance level, which is shown in Table 4 From the experimental results and subsequent statistical analysis, we can draw several significant conclusions:
Across all evaluation metrics, our method achieves state-of-the-an performance in 86% of cases over the entire collection of 24 datasets. From Table and [ it can be observed that in 87.5% and 83.3% of the datasets, the approach consistently outperforms in the Average Precision and Ranking Loss metrics. The statistical advantages persist across diverse data characteristics- high-dimensional biological datasets (Y eP. Y YeastCC)) to low- dimensional multimedia collections (Music, generalization performance. Even on the challenging corel5k datasets, where label spaces are particularly sparse. CA-PML maintains its statistical edge over all competitors.
suggesting the method's ' superior
From Table 4. CAPML demonstrates convincing statistical dominance, winning in 607 out of 720 total comparisons (84.3%) while achieving statistical ties all remaining cases. The smallest, though still significant, improvements observed against LENFN, which indicates our effective guidance of label reliability indicator.
FBD represents a notable baseline as it also a prototype-hased approach. Despite this similarity, CAPML consistetty outperforms FBD-PML, underscoring the efficacy of mutually prototype alignment strategy and stage-wise gradual label disambiguation.
Table 4: Win/tie/loss counts of pairwise t-test (at 0.05 aignificance level) on CAPML against others
CAPMI against
FBD-PMI.
LENFN
PAMB
PMI.-NI
PARTICLE
FPML.
Hamming loss
21/3/0
16/8/0
21/3/0
20/4/0
20/4/0
18/6/0
Ranking loss
17/7/0
20/4/0
18/6/0
21/3/0
23/1/0
23/1/0
One-error
22/2/0
23/1/0
18/6/0
23/1/0
20/4/0
23/1/0
Coverage
20/4/0
17/7/0
18/6/0
19/5/0
23/1/0
22/2/0
Average precision
19/5/0
16/8/0
16/8/0
22/2/0
22/2/0
23/1/0
In Total
99/21/0
93/27/0
91/29/0
105/15/0
108/12/0
109/11/0
4 Further Analysis
Parameter Sensitivity We assess CAPML's robustness through parameter sensitivity analysis, examining how hyperparameters a and influence the model's Average Precision performance. We vary each parameter individually while keeping the other fixed, with the results visualized as paired bar charts Figure[for direct comparison. eigure[ssoww shows remarkable robustness of CAPML to parameter variations, with Average Precision remaining stable across a wide range of values. This stability is particularly evident for parameter a, where performance fluctuations are minimal within the reasonable range of [0.01, 100). Similarly, when varying 3, the model maintains consistent performance with only slight degradation at extreme values.
Computational Complexity The algorithm complexity (Tgdnq Ti (dq² + q²) T2 h22 - d3 + nq)). Stage one in Algorithm involves SVD of the d x q matrix (T(MP) with complexity (dd)²) for the orthogonal Procrustes problem Eq. 11), plus ((q²) for the Hungarian algorithm solving the assignment problem in Eq. (12), totaling O (dqq q²)) per iteration. Stage two involves O(nly + 122g) for matrix operations W-update including the inversion of h x h matrix, and ((nq) for both R and Q updates involving element-wist operations. The dominant computational cost depends on the relative magnitudes of d, h, n, and q: but typically the O(nhg) term dominates when datasets are large, making the method practically scalable.

---

(a) birds
(b) image
(c) emotions
(d) Music style
Figure 2: AP variations with parameters and 3 on birds(avg+CLLs=2) (aaiiionnaav.HHCLs55
Mmage(avg.#CLs=- and music style datasets.
Ablation Study To investigate the contribution of each key component in CAPML, we conduct ablation studies by comparing our full model with two variants: (1) CAPML-ED, which replaces our entropy-regularin fuzzy clustering with direct Euclidean distance between instances and prototypes computed from candidate label set to derive membership degrees; (2) CAPML-NR, which removes the orthogonal rotation matrix H from the prototype alignment process. (3) CAPMI-NA, which sets permutation matrix identity matrix, removing prototype alignment. (4)CAPMI.-CW, which sets label enhancement indicator matrix C to all-ones, removing confidence indicator. Figure presents the comparative results across the seven of all benchmark datasets on Average Precision and Ranking loss. These results validate the effectiivneess of combining regulay-eg clustering with orthogonal transformation for prototype learning.
CARNE
CAPPEE FD
0.25
CAPME
CARNE--A
CARNEI N.
CAPME
Raninn Loa
0.7
0.15
0.65
0.8
0.05
0.55
0.5
yeast
Image
medical
binds
Yeast CC
Music style
Music emotion
yeiest
Image
medical
tinds
Yeast op
Music atye
Music emotion
Figure 3: AP variations with parameters a and 3 on yeast(avg.#CLs==) image #CLs=2), madical(avg #CLs=5,), birdstavg. #CLs=2), YeastCC, music style and music emotion datasets.
5 Conclusions
This paper introduces CAPML, a novel PML approach addressing label disambiguation through mutual prototype alignment. Unlike methods relying noisy candidate labels alone, we align unsupervised prototypes capturing clean data structure with supervised prototypes containing semantic information. Through permutation matrices and orthogonal rotation, we transform fuzzy memberships into reliable confidence indicators operating external to classifier learning. This dual-proto framework, combined with confidence-an identifies true labels under challenging noise conditions. Comprehensive experiments demonstrate CAPML's significant advantages over state-of-the-art methods.
disambiguation and sparse regularization, effectively
6
limitations
Despite these promising results, CAPML assumes fuzzy clustering discovers structure aligned with label semantics. Performance may degrade when into multiple clusters, when similar features cause distinct labels merge, or when label counts considerably exceed natural cluster structures.
high intra-class variability fragments categories
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NeurIPS Paper Checklist
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Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction clearly state the paper's main contributions: (1)We make the first investigation into the prototype misalignment between prototypes derived from fuzzy clustering and prototypes computed from candidate label set in PML tasks. Our work introduces a transformation mechanism that successfully bridges these two prototype spaces, enabling effective alignment and discovery of their intrinsic correspon- dence relationships despite noisy supervision. (2)We design a confidence-awee that converts fuzzy label membership degrees into label reliability indicator values, guiding our classifier training with sparse f2, 1norm constraint that enhance feature selection while reducing overfitting to noisy labels. E3)txtensive empirical evaluation demonstrates our method's efficacy in resolving label ambiguity and prototype misalig problem in PML, even with high noise rates and sparse positive samples, and superior generalization performance.
process
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Reviews:
[{"review_id": "OafoXwK38U", "reviewer": "Reviewer_3Fvi", "summary": "This paper introduces a novel partial multi-label learning (PML) framework named CAPML. The authors identify a critical limitation in existing prototype-based methods: biased class prototype estimates due to noisy candidate labels. To address this, they introduce a mutual class prototype alignment strategy using permutation and orthogonal rotation matrices to align unsupervised and supervised prototypes. Extensive experiments confirm the efficacy of the proposed method.", "questions": "1. In the section of introduction, the authors provide a taxonomy of existing PML approaches (unified framework with inductive bias, heuristic design, phased processing), but this categorization seems incomplete and overlapping. For instance, where do prototype-based methods fit in this taxonomy?\n2. Equation (6) for label enhancement indicator construction is logically clear, but the details (e.g., the necessity of min-max normalization) could be better explained. What’s more, have you considered other normalization strategies (e.g., softmax) and how do they compare in terms of performance?\n3. In your fuzzy clustering formulation (Equation 1), the membership degrees f_{ij} appear to have an implicit fuzziness parameter of m=1 (i.e., f_{ij} rather than f_{ij}^m where m > 1 is standard in fuzzy c-means). This effectively reduces to hard clustering, which seems to contradict the paper's emphasis on fuzzy methodology. Could you clarify: (a) whether you intentionally use m=1 and provide theoretical justification for this choice, and (b) how this formulation differs from standard fuzzy c-means clustering and why it's more suitable for your prototype learning task?\n4. Why is the orthogonal rotation matrix necessary when you already have a permutation matrix P? Could you provide more intuitive explanation or theoretical justification for this design choice?\n5. The label enhancement indicator matrix C (Equation 6) uses min-max normalization without clear justification. Why is this normalization scheme optimal for converting fuzzy memberships into confidence indicators, and how sensitive is the method's performance to alternative normalization choices (e.g., softmax or z-score normalization)?", "limitations": "NA", "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\nFirst work to investigate prototype misalignment between fuzzy clustering-derived prototypes and candidate label set-computed prototypes in PML tasks - an important yet previously overlooked problem.\n\nInnovative dual transformation mechanism using permutation matrix P and orthogonal rotation matrix H for prototype alignment with a clear technical rationale.\n\nRigorous mathematical derivations with detailed optimization procedures, including the Hungarian algorithm for permutation matrix.\n\nWeaknesses:\n\nThe paper suffers from insufficient theoretical foundations and incomplete practical considerations. There is a lack of convergence guarantees and computational complexity analysis for the alternating optimization procedure, which is crucial for understanding the method's reliability and practical applicability assessment.\n\nThe method's core assumption that unsupervised clustering structure corresponds to true label semantics may not hold when the feature space geometry poorly reflects label relationships. The paper lacks analysis of the limitations of when this fundamental assumption breaks down, such as in cases where different labels share similar feature representations or when noise significantly distorts the natural clustering structure.\n\nImportant references should be further discussed, such as [1] [2].\n\n[1] Deep Incomplete Multi-View Clustering with Cross-View Partial Sample and Prototype Alignment, CVPR 2023.\n[2] Cross-view Topology Based Consistent and Complementary Information for Deep Multi-view Clustering, CVPR 2023.", "was_revised": true, "final_justification": "Thank you for your detailed and thoughtful responses. They effectively address my concerns and clarify the key points. I will maintain the positive evaluation.", "rebuttal": "Thank you for your high-quality review. Our point-by-point responses below:\n## Weaknesses:\n1. >convergence guarantee and computational complexity analysis\n\nThank you for your valuable comments. \n\n**Alignment stage** iteratively optimizes permutation matrix $P$ via Hungarian algorithm and orthogonal matrix $H$ through SVD-based Procrustes solution $H = UV^T$. Both subproblems achieve global optimality. **Label disambiguation stage** alternates between updating classifier $W$ (closed-form solution) and confidence matrix $R$ with auxiliary variable $Q$. The convergence of our multiplicative update scheme for the R-subproblem is guaranteed by the general theory developed in [1] for block coordinate descent methods with exact block minimization. Since each update minimizes an auxiliary function that upper-bounds the original objective, monotonic convergence is ensured with rate $O(1/T_2)$. The Q-subproblem reduces to a standard LASSO regression, which converges linearly to the global optimum via the proximal gradient method with soft-thresholding operator. We prove convergence to a stationary point via monotonic objective decrease in each subproblem. We will provide convergence curves in the revised version if space allows. \n\nThe algorithm complexity is $O(T_0dnq+T_1(dq^2 + q^3) + T_2(nhq + h^2q +d^3+ nq))$ where $T_0$ represents iterations of clustering learning stage, $T_1$ represents iterations of prototype alignment stage and $T_2$ represents iterations of classifier learning stage. Alignment stage involves SVD of the $d \\times q$ matrix $O^T(MP)$ with complexity $O(dq^2)$ for the orthogonal Procrustes problem, plus $O(q^3)$ for the Hungarian algorithm solving the assignment problem, totaling $O(dq^2 + q^3)$ per iteration. Disambiguation stage involves $O(nhq + h^2q)$ for matrix operations in W-update including the inversion of $h \\times h$ matrix, and $O(nq)$ for both R and Q updates involving element-wise operations. The dominant computational cost depends on the relative magnitudes of $d$, $h$, $n$, and $q$, but typically the $O(nhq)$ term dominates when datasets are large, making the method practically scalable. \n\n2. >Dependence on clustering assumptions:\n\nThank you for this insightful analysis regarding our method's fundamental assumption about clustering structure correspondence with label semantics. We agree that our method's performance will degrade when: (1) feature representations are highly entangled across different labels, or (2) noise severely corrupts both clustering structure and supervised signals simultaneously. We will add the limitations in these extreme cases and analyzing when the clustering-semantics assumption breaks down.\n\n3. >Important references [1], [2]\n\nThank you for bringing this relevant work to our attention. CPSPAN (reference [1] you mentioned) introduces prototype alignment into multi-view learning for the first time and demonstrates the effectiveness of formulating it as a linear programming problem, providing a principled approach for establishing prototype correspondences to promote cross-view consistency learning. CTCC (reference [2] you mentioned) innovatively apply optimal transport theory to design information integration mechanisms, providing a useful direction for prototype relationship learning. We will expand our Introduction section to better position our contribution relative to these recent advances in multi-view learning. \n## Question\n1. >introduction\n\nThank you for this question about our taxonomy. Prototype-based methods, including our approach, primarily fall within the \"stage-wise framework with inductive bias\" category, as they incorporate the inductive bias that class prototypes effectively capture semantic information for label disambiguation. However, prototype-based methods can exhibit characteristics of other categories through heuristic designs or staged processing strategies.\n\nThis highlights that our categorization focuses on methodological frameworks rather than technical components. Prototype-based approaches represent technical means that can be integrated across different frameworks - some use unified stage-wise processing (like ours), while others employ end-to-end learning (like FBD-PML).\n\nWe will revise the introduction to provide a more comprehensive and non-overlapping taxonomy that better distinguishes methodological frameworks from technical approaches, clearly positioning prototype-based methods within this improved classification system.\n\n2. >normalization\n\nWe sincerely appreciate this insightful comment. To address this important concern, we provide detailed theoretical justification for our selection and conduct a comprehensive comparison of different normalization methods.\n\nWe select min-max normalization for three principled reasons: \n\n**First**, it provides [0,1] range probabilistic interpretation, ensuring numerical compatibility with $C_{ij} = 1$ (non-candidate positions) in Equation (6). \n\n**Second**, it preserves crucial confidence strength differences that other methods eliminate. For instance, given confidence values $c_i = [0.8, 0.2, 0]$ (high confidence) and $c_j = [0.4, 0.1, 0]$ (low confidence), L2 normalization produces nearly identical results while unit sum normalization yields exactly identical outputs, completely masking original strength differences. Min-max normalization preserves these distinctions as $[1.0, 0.25, 0]$ and $[0.5, 0.125, 0]$, maintaining both relative proportions and absolute strength information essential for reliable confidence assessment.\n\n**Third**, the bounded range prevents numerical instabilities during iterative optimization, while avoiding nonlinear distortions that could artificially amplify noise signals or suppress genuine confidence distinctions.\n\nWe compared six normalization methods for label enhancement indicator matrix construction: (1) Min-Max; (2) Softmax; (3) Z-Score; (4) L2 norm; (5) Unit Sum(ensuring each row sums to 1); and (6) No Normalization. We conducted controlled experiments on six datasets using 10-fold cross-validation, evaluating *Average Precision* while keeping other CAPML components unchanged. Dataset names with numbers indicate avg.#CLs (e.g., Emotions3 has avg.#CLs=3).\n\n|Dataset|Min-Max|Softmax|Z-Score|L2 Norm|Unit Sum|No Norm|\n|-|-|-|-|-|-|-|\n|emotions3|**0.807±0.039**|0.804±0.041|0.801±0.038|0.805±0.040|0.803±0.037|0.799±0.042|\n|birds3|**0.627±0.058**|0.624±0.055|0.621±0.061|0.625±0.057|0.623±0.059|0.619±0.063|\n|medical5|**0.876±0.027**|0.870±0.029|0.872±0.031|0.875±0.028|0.873±0.030|0.870±0.033|\n|image2| **0.814±0.021** |0.810±0.023|0.807±0.025|0.811±0.022|0.810±0.024|0.807±0.026 |\n|Mirflickr|**0.820±0.008**|0.815±0.009|0.812±0.011|0.819±0.010|0.817±0.009|0.813±0.012|\n|Music emotion|**0.628±0.010**|0.623±0.012|0.620±0.014|0.626±0.011|0.623±0.013|0.620±0.015|\n\nWhile performance differences between normalization strategies are modest, min-max normalization consistently achieves the best results and provides suitable numerical foundation for confidence assessment. Other methods may have limitations: Z-score produces negative values incompatible with confidence measures, Softmax over-amplifies values introducing bias, and L2 normalization may overlook important instance information.\n\n3. >fuzzy clustering formulation\n\nThank you for this insightful question. You correctly identify that standard FCM requires m>1, as m=1 leads to hard clustering solutions. We achieve fuzzification through entropy regularization $λ\\sum f_{ij} \\log f_{ij}$ where large λ produces fuzzy memberships while small λ approaches hard clustering. The entropy regularization prevents hard clustering through information-theoretic principles while ensuring computational tractability.\n\nThe entropy-based approach replaces traditional power-based fuzzification (m>1) for a key advantages: \n\n**Intuitive Parameter Control** - Unlike FCM's fuzziness parameter m with constrained effective range, entropy regularization λ provides more direct and interpretable control over membership distribution, facilitating easier parameter tuning for multi-label prototype learning. **Parameter Robustness** - The temperature parameter λ demonstrates stable behavior across datasets, with values in [0.5, 5] consistently producing reasonable fuzzy memberships, while traditional FCM's parameter m requires extensive dataset-specific tuning and can produce dramatically different behavior with unit variation.\n\n4. >orthogonal rotation matrix\n\nThe orthogonal rotation matrix H serves a fundamentally different purpose from the permutation matrix P.\n\nThe alignment process requires dual correction: P solves the **ordering problem** while H addresses the **noise contamination problem**. Since supervised prototypes O are computed from noisy candidate labels (Equation 3), directly aligning clean unsupervised prototypes M to contaminated O would propagate errors. The orthogonal rotation matrix H provides a \"denoising transformation\" that geometrically adjusts supervised prototypes while preserving intrinsic structure. This enables robust alignment where both prototype spaces meet at optimal middle ground.\n\nThis dual-matrix design offers: (1) **Noise Mitigation**- H compensates for systematic bias in O; (2) **Geometric Preservation**- orthogonality maintains relative relationships; (3) **Optimization Flexibility**- joint optimization finds globally better solutions. Our ablation study confirms that removing H (CAPML-NR) consistently degrades performance, demonstrating that orthogonal transformation provides essential noise robustness beyond permutation alone.\n## Citations:\n[1] Deep Incomplete Multi-View Clustering with Cross-View Partial Sample and Prototype Alignment, CVPR 2023. \n\n[2] Cross-view Topology Based Consistent and Complementary Information for Deep Multi-view Clustering, CVPR 2023.\n\n[3] Graph regularized nonnegative matrix factorization for data representation. IEEE TPAMI, 2010."}, {"review_id": "50xYPAQQFP", "reviewer": "Reviewer_bPJL", "summary": "The authors propose CAPML, an enlightening approach for Partial Multi-label Learning that addresses the challenge of prototype misalignment between unsupervised clustering-derived prototypes and candidate label-derived prototypes, which is an enlightening study. The method introduces a transformation mechanism using permutation and rotation matrices to align these prototype spaces, followed by a confidence-aware label disambiguation process. Experiments show that this method has certain effectiveness.", "questions": "1. The authors employed an \"improved fuzzy clustering approach\" with entropy regularization (Equation 1), how does your entropy-regularized formulation compare to classical FCM? Have you tested alternatives like spectral clustering? How sensitive is the final performance to the choice of $\\lambda$?\n2. The motivation for introducing the orthogonal rotation matrix H in Eq. (5) could be better explained. Why is preserving geometric structure crucial here?\n3. Why is orthogonal transformation theoretically justified over other transformation classes?", "limitations": "Yes, the authors adequately addressed the limitations with no potential negative social impact.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper clearly articulates the prototype misalignment problem in PML, which is a novel and important observation. The proposed approach is mathematically well-founded. The orthogonal transformation mechanism for prototype alignment and the confidence-aware label enhancement strategy are technically sound and properly motivated.\n2. The ablation studies do examine key components (entropy regularization, orthogonal rotation) to validate design choices.\n3. The evaluation covers a substantial number of datasets with statistical significance testing, showing consistent improvements over strong baselines including prototype-based methods like FBD-PML.\n\nWeaknesses:\n\n1. Figure 1 claims the LE indicator matrix \"promotes the label disambiguation process\" without specifying the concrete mechanism or how the indicators actually guide disambiguation.\n2. The alternating optimization process mentions updating different variables, but the specific order, stopping criteria, and inter-dependencies are not clearly specified. Providing algorithmic pseudo code would enhance understanding of the iterative optimization process.", "was_revised": true, "final_justification": "After reading the authors’ response, my concerns have been resolved. Therefore, I have maintained my positive evaluation.", "rebuttal": "Thank you for your thoughtful review. Our point-by-point responses below:\n## Weakness\n1. >Figure 1\n\nThank you for requesting clarification on this mechanism. The LE indicator matrix $C$ guides disambiguation through a confidence-weighted constraint mechanism in the objective function (Eq. 7).\n\nSpecifically, for non-candidate labels ($y_{ij} = 0$), $C$ assigns $C_{ij} = 1$, imposing strong constraints that force the confidence matrix $R$ to maintain near-zero values at these positions through the term $\\||C \\odot (Y - R)\\||^2_F$. For candidate labels ($y_{ij} = 1$), the indicator values are constructed by first applying permutation $P$ to transform unordered membership degrees into label-semantic guidance, then employing min-max normalization to generate confidence indicators with [0,1] probabilistic interpretation and preserved strength differences. \n\nThe disambiguation occurs because the weighted loss $\\||C \\odot (Y - R)\\||^2_F$ penalizes deviations more heavily for high-confidence labels and less for low-confidence labels, effectively allowing the model to \"ignore\" or reduce the influence of suspected noisy labels during classifier training. We will clarify this mechanism in the figure caption and main text.\n\n2. >alternating optimization process\n\nThank you for your comment. To provide clarity on the workflow, here are the detailed iterative steps:\n\nThe algorithm consists of three main iterative stages: (1) Initialization stage: entropy-regularized fuzzy clustering iteratively computes unsupervised prototypes M and membership matrix $F$ (Eq. 2), while supervised prototypes $O$ are calculated from candidate labels (Eq. 3). The maximum number of iterations $T_0$ is 30 and the iteration stops when it converges. (2) Prototype alignment stage: the permutation matrix $P$ (Eq. 9) and rotation matrix $H$ (Eq. 8) are alternately optimized to align unsupervised and supervised prototype orders. Once optimal transformation matrix $P$ is obtained, the label enhancement indicator matrix $C$ is constructed (Eq. 6). The maximum number of iterations $T_1$ is 50 and the iteration stops when it converges. (3) Label disambiguation stage: guided by the indicator matrix $C$, classifier parameters $W$ and confidence matrix $R$ are alternately updated (Eqs. 11 and 13) to promote robust classification. The algorithm terminates when reaching maximum iterations ($T_2$=40) or achieving convergence based on relative change in objective function. Here we detail the complete optimization process:\n\n**Stage 1 - Initialization (Entropy-regularized Fuzzy Clustering):**\n- **Update Order**: $M → F$ alternately until convergence\n- **Stopping Criteria**: $||M^{(t+1)} - M^{(t)}||_F< ε_1$ or max iterations $T_0$ = 30\n- **Dependencies**: F depends on current M; M depends on current F\n- **Output**: Stable prototypes M and membership matrix F\n\n**Stage 2 - Prototype Alignment:**\n- **Update Order**: Fix $M,F$ $→$ Compute $O$ (Eq. 3) → Alternate $H$ (Eq. 8) ↔ $P$ (Eq. 9)\n- **Stopping Criteria**: $||P^{(t+1)} - P^{(t)}||_F = 0$ or max iterations $T_1$ = 50\n- **Dependencies**: $H$ depends on current $P$; $P$ depends on current $H$; both depend on fixed $M,O$\n- **Output**: Optimal alignment matrices $P,H$ $→$ Construct indicator matrix $C$ (Eq. 6)\n\n**Stage 3 - Label Disambiguation:**\n- **Update Order**: Obtain kernelized $X$, $W$ (Eq. 11)$ → $$R$ (Eq. 13) $→ Q$ (Eq. 16) alternatively\n- **Stopping Criteria**: $||R^{(t+1)} - R^{(t)}||_F < ε_2$ or max iterations $T_2$ = 40\n- **Dependencies**: $W$ depends on current $R$; $R$ depends on current $W,Q$; $Q$ depends on current $R$\n- **Inter-stage Dependencies**: $C$ from Stage 2 guides all Stage 3 updates\n- **Output**: Classifier $W$, predicted label $y^* $ of unsee instance $x^*$\n\nWe believe these provide sufficient details and will supplement the revised version with comprehensive pseudo-code for the iterative optimization process if space alows. We are happy to provide further clarification if needed.\n\n## Question\n\n1. > entropy-regularized formulation\n\nThank you for this detailed question. Regarding spectral clustering, while it is a powerful graph-based method, it typically produces hard cluster assignments rather than the soft membership degrees we require. Since our approach relies on fuzzy membership matrix $F$ to construct the label enhancement indicator matrix $C$, hard clustering methods would not provide the necessary continuous confidence values for prototype alignment and label disambiguation. For the rationale behind choosing our entropy-regularized fuzzy clustering approach, please refer to our **response to Reviewer 3Fvi** in **Question#3**.\n\nWe have conducted controlled experiments replacing the fuzzy clustering algorithm in Equation (1) with other soft clustering algorithms, including classical Fuzzy C-Means (FCM) and Fuzzy Subspace Clustering (FSC)[1], while keeping other CAPML components unchanged. Specifically, we create two variants: **FCM+** replaces entropy-regularized clustering with standard FCM, and **FSC+** replaces entropy-regularized clustering with fuzzy subspace clustering. This controlled comparison isolates the impact of different clustering strategies within our prototype alignment framework. The fuzziness coefficient in FCM was grid-searched within [1, 3] for optimal values, and the coefficient $σ$ in FSC was searched within [0.1, 10]. Dataset names with numbers indicate avg.#CLs (e.g., Emotions3 has avg.#CLs=3).\n\n|Dataset|FCM+|FSC+|CAPML|\n|-|-|-|-|\n|emotions4| 0.771±0.012 | 0.780±0.015 | **0.787±0.027** |\n|birds4| 0.5420±0.041 | 0.578±0.038 | **0.590±0.057** |\n|medical7| 0.838±0.014 | 0.854±0.012 | **0.866±0.031** |\n|image3| 0.771±0.018 | 0.768±0.016 | **0.792±0.018** |\n|yeast9| 0.738±0.009 | 0.753±0.007 | **0.755±0.021**|\n|Mirflickr| 0.808±0.016 | 0.817±0.014 | **0.820±0.008** |\n|Music emotion| 0.614±0.012 | 0.623±0.011 | **0.628±0.010** |\n\nThe entropy regularization provides inherent stability and superior performance, making the method less sensitive and more controllable to parameter choices compared to FCM.\n\n2. >orthogonal rotation matrix \n\nThank you for this important question. The supervised prototypes $O$ computed from candidate labels inevitably contain errors due to noisy annotations, requiring fine-tuning adjustments. The specific role and necessity of the orthogonal constraint in rotation matrix H can be found in our response to **Reviewer 3Fvi's Question#4**.\n\nPreserving geometric structure is crucial because it maintains the relative distances and angular relationships between class prototypes, which encode essential semantic information. Without orthogonal constraints, arbitrary transformations could distort these relationships, potentially merging distinct classes or artificially separating related ones. The orthogonal transformation ensures that the intrinsic geometric properties of the prototype space are preserved while allowing necessary adjustments to compensate for noise-induced errors in supervised prototype estimation.\n\n3. > orthogonal transformation\n\nOrthogonal transformation is theoretically justified for several reasons. First, it preserves all geometric properties essential for prototype alignment: distances, angles, and inner products between prototypes remain unchanged ($||Hx|| = ||x||$ and $⟨Hx, Hy⟩ = ⟨x, y⟩$). This ensures that the semantic relationships encoded in the prototype space are maintained during alignment.\n\nSecond, our alignment problem is fundamentally a Procrustes analysis, where the classical solution involves orthogonal transformations to find the optimal rotation/reflection that minimizes the Frobenius norm difference between two point sets. Other transformation classes would introduce undesirable effects: general linear transformations could alter scales and distort relative distances, while affine transformations introduce translations that may not be appropriate for prototype alignment.\n\nThird, orthogonal constraints provide natural regularization by limiting the degrees of freedom, preventing overfitting to noisy supervised prototypes. Unlike unconstrained transformations that might overfit to noise, orthogonal transformations only allow rotation and reflection, which are the minimal adjustments needed to correct orientation differences between prototype spaces while preserving their intrinsic structure.\n\nWe hope this explanation addresses your concerns regarding the theoretical justification for orthogonal transformations.\n\n## Citations\n\n[1] Borgelt, C. (2009). Fuzzy Subspace Clustering.  (eds) Advances in Data Analysis, Data Handling and Business Intelligence. Studies in Classification, Data Analysis, and Knowledge Organization."}, {"review_id": "NhLiMVPOrz", "reviewer": "Reviewer_gpe6", "summary": "This paper addresses partial multi-label learning through a prototype alignment framework called CAPML. The authors identify that existing prototype-based PML methods suffer from biased prototype estimates due to noisy candidate labels, and propose to align unsupervised fuzzy clustering prototypes with supervised prototypes using permutation and orthogonal rotation matrices. The approach combines established techniques from clustering and optimization theory to tackle an important problem in weakly supervised learning, presenting results across multiple datasets and comparison methods.", "questions": "1.In Eq.(9), when solving the permutation matrix P using the Hungarian algorithm, what happens when multiple optimal solutions exist with the same minimum cost?\n2.Are there any guidelines for selecting the parameters for \\lambda in Eq.(10)? How sensitive is the method to fuzzy clustering initialization and hyperparameter \\lambda?\n3.For future work, do the authors plan to explore adaptive prototype alignment strategies that can dynamically adjust to varying noise patterns, or investigate the integration of CAPML with active learning frameworks for more efficient label acquisition?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.The combination of permutation matrices for discrete alignment and orthogonal rotation for continuous adjustment represents a principled approach to bridging unsupervised structure discovery with noisy supervision. This dual-transformation mechanism offers a new technical pathway for prototype-based learning in noisy scenarios, which could inspire future research directions in weakly supervised learning.\n2.The authors provide good clarity in problem definition and methodological exposition. The progression from identifying limitations in existing prototype-based PML methods to proposing the alignment solution is logical and easy to follow. The visualization in Figure 1 effectively demonstrates this issue.\n3.The paper presents a coherent multi-stage approach combining fuzzy clustering, prototype alignment, and confidence-aware classification. The mathematical formulation is generally clear, with detailed optimization procedures for each subproblem.\n\nWeaknesses:\nGiven the claimed advantage over sparsity-based assumptions in high-noise scenarios, the paper should include comparisons with recent methods like NLR[1]. This comparison would better demonstrate the proposed method's superiority in challenging noise conditions.\n[1]Yang F, Jia Y, Liu H, et al. Noisy Label Removal for Partial Multi-Label Learning[C]//Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2024: 3724-3735.", "was_revised": true, "final_justification": "All my concerns have been resolved, and I am now inclined to recommend acceptance of the paper.", "rebuttal": "Thank you for your thoughtful review. Our point-by-point responses below:\n## Weakness\n\n1. >NLR\n\nThank you for this valuable suggestion. We acknowledge the importance of comparing with recent state-of-the-art approaches, particularly NLR, which represents a strong baseline for noisy label removal in PML scenarios.\n\nTo address this concern, we conducted additional experiments comparing CAPML with NLR under high-noise conditions to better demonstrate our method's superiority in challenging noise scenarios.\n\nWe evaluated on four representative datasets: emotions5 (avg.#CLs=5, noise ratio=75.8%), birds16 (avg.#CLs=16, noise ratio=83.3%), image4 (avg.#CLs=4, noise ratio=73.5%), and yeast13 (avg.#CLs=13, noise ratio=89.8%). The noise ratio represents the proportion of added noisy labels among non-ground-truth labels. For fair comparison, NLR parameters were configured according to their paper settings, while the noise generation way follows our paper setting to ensure consistent experimental conditions.\n\n### Comparative Results\n\n|Dataset|Average Precision|||Ranking Loss|||\n|-|-|-|-|-|-|-|\n||NLR|ours|Gain|NLR|ours|Gain|\n|emotions5|0.721±0.029|**0.756±0.032**|**+3.5%**|0.246±0.027|**0.205±0.032**|**+3.9%**|\n|birds16|0.279±0.029|**0.342±0.036**|**+6.3%**|0.423±0.018|**0.33±0.036**|**+3.5%**|\n|image4|0.726±0.019|**0.759±0.022**|**+3.3%**|0.248±0.025|**0.213±0.022**|**+3.5%**|\n|yeast13|0.624±0.016|**0.718±0.013**|**+9.4%**|0.274±0.014|**0.213±0.012**|**+5.9%**|\n\n### Analysis\n\nThe superior performance of CAPML over NLR in high-noise scenarios can be attributed to several key factors. First, NLR's competitive learning between positive and negative classifiers provides limited effective information to the negative classifier under extreme noise, relying heavily on the positive classifier. In contrast, CAPML's confidence-aware learning effectively utilizes both positive and negative information in high-noise environments. Second, CAPML establishes noise-independent membership degrees through entropy-regularized fuzzy clustering, while NLR relies on sparse $\\ell_1$ norm for noise removal in high-noise candidate labels. Finally, NLR's binary constraints on noise indicators may become unstable under extreme noise.\n\n## Question\n\n1. >same minimum cost\n\nWe sincerely thank the reviewer for raising this profound and technically sophisticated question. In response to your concerns, we have conducted a rigorous theoretical analysis demonstrating that multiple solutions in the Hungarian algorithm are mathematically well-founded and do not compromise our method's reliability.\n\n### 1. Existence and Necessity of Multiple Solutions\n\n**Theorem 1 (Structural Necessity of Multiple Solutions)**: In our prototype alignment framework, multiple optimal solutions to the Hungarian algorithm are not incidental but structurally inevitable under realistic conditions.\n\nThe existence of multiple solutions occurs when there exists a non-trivial permutation $\\sigma \\neq \\text{id}$ such that:\n\n$$\\sum_i \\||m_i - o_i\\||^2 = \\sum_i \\||m_i - o_{\\sigma(i)}\\||^2$$\n\nThis condition frequently arises in PML scenarios due to three fundamental factors: (i) **Label noise corruption**: Candidate label noise causes supervised prototypes $O$ to deviate from their true positions, reducing discriminability between prototype pairs; (ii) **Geometric symmetries**: Real-world data often exhibits inherent symmetrical structures that naturally lead to equivalent prototype alignments; (iii) **High-dimensional effects**: In high-dimensional feature spaces, the probability of near-equivalent distances increases substantially.\n\nWe can formally characterize the conditions under which multiple solutions emerge. Let $G(M,O)$ denote the symmetry group of prototype pairs:\n\n$$G(M,O) = \\{\\sigma \\in S_q : \\||MP_\\sigma - O\\||_F^2 = \\||MP\\_\\{id\\} - O\\||_F^2\\}$$\n\nWhen $|G(M,O)| > 1$, multiple solutions exist by construction. In practical PML scenarios, candidate label noise effectively increases $|G(M,O)|$ by reducing the discriminative power of supervised prototypes, making multiple solutions structurally inevitable rather than exceptional.\n\n### 2. Theoretical Analysis of Performance Stability\n\nOur analysis proceeds in two stages: first, we analyze how changes in P propagate to the LE indicator matrix C, and second, we show how joint optimization dampens this variation.\n\n**Stage 1: Bounded Impact of Permutation Choice on the LE Indicator Matrix**\n\nThe LE indicator matrix $C$ is constructed based on the permuted fuzzy membership matrix $FP$, as defined in Eq. (6). \n\n**Theorem 2** (Bounded Perturbation Propagation). *For two optimal permutation matrices $P_1, P_2$ with identical Hungarian algorithm costs, the resulting LE indicator matrices satisfy:*\n\n$$\\||C(P\\_1) - C(P\\_2)\\||\\_F \\leq \\sqrt{|Y\\_{+}|}$$\n\n*where $|Y_{+}| = |\\{(i,j): Y_{ij} = 1\\}|$ denotes candidate label positions and the bound follows from the fact that normalized values are bounded in $[0,1]$, making $|C_{ij}(P_1) - C_{ij}(P_2)| \\leq 1$ for each candidate position.*\n\n**Proof**: Since $C_{ij} = 1$ for non-candidate labels (unchanged across permutations), perturbations only occur at candidate positions. For each candidate position, $|C_{ij}(P_1) - C_{ij}(P_2)| \\leq 1$ due to normalization bounds. The Frobenius norm yields the stated bound.\n\n**Stage 2: Dampening Effect of the Joint Optimization Framework**\n\nA small perturbation in $C$ (from $C(P_1)$ to $C(P_2)$) does not lead to a proportionally large change in the final model. The learned label confidence matrix R is not determined solely by $C$. It is simultaneously constrained by the classifier's predictions. The regularization terms penalize complex solutions and encourage the model to find a simpler, more generalizable representation. This makes the final optimized parameters $W*$ and $R*$ robust to minor perturbations in the guiding matrix $C$.\n\n### 3. Convergence Guarantees Under Multiple Solutions\n\nThe objective function value is non-increasing at each iteration since each sub-problem finds a global optimum with other variables fixed, guaranteeing monotonicity. Since the objective function is bounded below (sum of non-negative terms), the non-increasing sequence converges to a finite limit. Under standard regularity conditions, this value convergence implies that the iterate sequence $(P^{(t)}, H^{(t)})$ converges to a stationary point of the overall objective.\n\n### 4. Different Insights of Multiple Solutions\n\nMultiple solutions in the Hungarian algorithm represent advantageous redundancy rather than a limitation. From an information-theoretic perspective, equivalent permutations provide identical mutual information with true labels, creating redundancy that enhances reliability of information transfer in noisy environments. From an optimization standpoint, multiple solutions correspond to \"flat minima\" in the loss landscape, which are theoretically linked to better generalization due to robustness against parameter perturbations.\n\nOur method exhibits three key properties: (i) **Symmetry preservation**: Solutions respect intrinsic data symmetries; (ii) **Perturbation robustness**: Small input changes avoid discontinuous solution jumps; (iii) **Enhanced generalization**: Multiple equivalent solutions increase effective model capacity while maintaining computational efficiency.\n\nMultiple solutions emerge naturally from the geometric structure of prototype alignment problems, providing controllable benefits for algorithm robustness and generalization in most practical scenarios, except in extreme cases where multiple labels exhibit highly similar feature representations.\n\n\n2. >$λ$ in Eq.(10)\n\nThank you for your valuable question. Parameter λ controls the \"softness\" of membership assignments in entropy-regularized fuzzy clustering. Smaller λ values (0.1-0.5) produce concentrated distributions suitable for clear boundaries, while larger values (1-10) produce smoother distributions for overlapping classes. We recommend starting with λ = 0.5, then grid searching over {0.1, 0.5, 1, 2, 5, 10}. High-noise data benefits from larger λ values (1-5), while low-noise data prefers smaller values (0.3-1). The entropy regularization makes our algorithm relatively insensitive to initialization.\nThe following table shows performance sensitivity of Average Precision(AP) and Ranking Loss(RL) to $α$ and $λ$ on dataset yeast7(avg.#CLs=7).\n). Our method achieves stable performance across different parameter combinations.\n\n||||AP||||||RL|||\n|-|-|-|-|-|-|-|-|-|-|-|-|\n| $α \\setminus λ$ |0.1|0.5| 1 | 5 | 10 | $α \\setminus λ$ | 0.1 | 0.5 | 1 | 5 | 10 |\n| 0.01 | 0.748 |0.758| **0.760** | 0.745 | 0.725 | 0.01 | 0.181 | 0.175 | **0.173** | 0.182 | 0.201 |\n| 0.1 | 0.741 | **0.759** | 0.757 | 0.748 | 0.728 |0.1 | 0.186 | **0.175** | **0.175** | 0.183 | 0.198 |\n| 1 | 0.744 | **0.756** | **0.756** | 0.751 | 0.731 | 1 |0.183| 0.181 | **0.176** | 0.179 | 0.195 |\n| 10 |0.742|0.749| **0.751** |0.750| 0.729 | 10 |0.185| 0.184 | **0.179** | 0.181 | 0.197 |\n| 100 |0.739|0.747|**0.749**|0.746|0.726| 100 | 0.188 | **0.180** |0.185| 0.183 | 0.200 |\n\nOur sensitivity analysis shows stable performance within λ ∈ [0.1, 10], with AP fluctuations typically within ±3%. Optimal λ values concentrate in [0.5, 5], indicating good robustness. Very small λ may cause overfitting, while very large λ reduces discriminative ability.\n\n3. >future work\n\nThank you for this insightful suggestion. Exploring adaptive strategies is indeed a natural extension, involving learning noise pattern indicators and designing dynamic weighting schemes for the matrices. Regarding active learning integration, this represents an interesting direction we had not fully explored. CAPML's confidence-aware framework provides a natural foundation, as the label enhancement indicator matrix C could serve as an uncertainty measure for efficient label acquisition."}, {"review_id": "ROozeFOl1U", "reviewer": "Reviewer_7dPU", "summary": "This paper proposes CAPML (Confidence-Aware with Prototype Alignment for Partial Multi-label Learning) to address the partial multi-label learning problem. The core idea is to learn class prototypes from both unsupervised fuzzy clustering and supervised candidate labels, then align these two prototype spaces using a permutation matrix P and orthogonal rotation matrix H. The aligned prototypes are used to construct a label enhancement indicator matrix that guides classifier training. Experiments on multiple synthetic and real-world datasets demonstrate the effectiveness of the proposed approach.", "questions": "1. Novelty Positioning: How do you justify the claim of \"first investigation\" given the existence of prior work on prototype learning in PML (e.g., the 2022 and 2023 papers mentioned)? Can you more precisely characterize your specific contribution relative to these existing approaches?\n2. Theoretical Foundation: Can you provide convergence analysis for the alternating optimization procedure? What theoretical guarantees exist for the effectiveness of prototype alignment in reducing label noise?\n3. Method Justification: Beyond empirical results, what is the theoretical or intuitive justification for why the proposed prototype alignment should work better than directly using fuzzy clustering confidences as in FBD-PML?\n4. Complexity Analysis: What is the computational complexity of CAPML compared to baseline methods? How does the method scale with dataset size and number of labels?\n5. Parameter Sensitivity: The method involves multiple hyperparameters (α, β, λ). How sensitive is the performance to these parameters? Can you provide guidance for parameter selection in practice?\n\nEvaluation Criteria: Addressing questions 1-3 satisfactorily could potentially improve the originality and quality scores. Providing theoretical analysis (question 2) would be particularly valuable for improving the overall assessment.", "limitations": "The authors mention computational complexity for large datasets and potential suboptimality when label counts exceed natural cluster structures, which is appropriately honest. However, several critical limitations are not adequately addressed:\n1. Dependence on clustering assumptions: The method relies heavily on the assumption that fuzzy clustering can discover meaningful structure in the data.\n2. Limited generalizability: It's unclear how the approach extends to other weakly supervised scenarios.\n3. Robustness to extreme noise: The performance under very high noise conditions is not analyzed.\n4. Interpretability: The semantic meaning of the learned permutation matrix is not well explained.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Important Problem: PML is a practical and important problem in machine learning with broad applications where precise labeling is expensive or difficult.\n2. Intuitive Approach: The idea of combining unsupervised clustering with supervised information through prototype alignment is reasonable and well-motivated.\n3. Complete Technical Implementation: The paper provides detailed optimization algorithms and update rules for all subproblems involved in the method.\n4. Comprehensive Experiments: Extensive experiments are conducted on 24 datasets with multiple evaluation metrics and statistical significance analysis.\n5. Competitive Results: The method achieves good performance compared to baseline methods across most datasets.\n\nWeaknesses:\n1. Questionable Novelty Claims: The paper claims to make \"the first investigation into the prototype misalignment between prototypes derived from fuzzy clustering and prototypes computed from candidate label set.\" However, literature search reveals related work: \n\"Few-shot partial multi-label learning via prototype rectification\" (2022)\n\"Multi-view prototype-based disambiguation for partial label learning\" (2023)\nFBD-PML[21] already applies fuzzy clustering in PML This suggests the novelty claim may be overstated.\n2. Limited Technical Innovation: The method primarily combines existing techniques (fuzzy clustering, prototype alignment, label enhancement) without introducing fundamentally new insights or theoretical frameworks.\n3. Insufficient Theoretical Analysis: The paper lacks convergence analysis, computational complexity discussion, and theoretical guarantees for the effectiveness of the proposed approach.\n4. Shallow Ablation Study: Only two variants (CAPML-ED and CAPML-NR) are studied, which is insufficient to validate the contribution of each component thoroughly.\n5. Method Complexity: The approach involves multiple subproblems with alternating optimization, potentially leading to high computational cost and parameter sensitivity issues.\n6. Unclear Distinction from FBD-PML: The fundamental difference between CAPML and FBD-PML beyond the introduction of permutation and rotation matrices is not clearly articulated.", "was_revised": true, "final_justification": "After careful consideration of the authors' detailed rebuttal, I am adjusting my rating to 3 (Borderline Reject).\n\nThe quality of the authors' response is impressive, demonstrating solid technical expertise and rigorous academic attitude. Particularly in theoretical analysis, the authors provided complete convergence proofs, detailed computational complexity analysis, and mathematical quantification of error reduction, all of which significantly strengthen the paper's theoretical foundation. The supplementary ablation studies are also comprehensive, effectively validating the contribution of each component.\n\nWhile I initially had concerns about the novelty claims, upon deeper reflection, I recognize that this work does provide valuable technical contributions to partial multi-label learning. The \"dual-prototype external alignment\" approach, though based on combinations of existing techniques, demonstrates good engineering innovation through its systematic design and rigorous mathematical derivation. \n\nThe method's reliance on unsupervised clustering assumptions is indeed a limitation, but the authors honestly discussed this point in their rebuttal and provided corresponding theoretical analysis. \n\nTherefore, I support the borderline accept decision.", "rebuttal": "Thank you for your thoughtful review. Our point-by-point responses below:\n## Weakness\n\n1. >Questionable Novelty Claims, Limited Technical Innovation \n\nThank you for your comment. We apologize for not clearly articulating our innovation. Our claim of \"first investigation\" is not on the general use of prototypes in PML, but on the specific investigation of the prototype misalignment problem that arises between unsupervised, data-driven prototypes and supervised, label-driven prototypes. Our work treats label and feature as  representations of dual “modalities”. We obtain clean but unordered prototypes from the feature “modality” via unsupervised clustering, while computing ordered but noise-affected prototypes from the label “modality”. By aligning these dual-modal prototypes, we transform fuzzy membership degrees into label-specific credible indicators that operate external to classifier learning, indirectly supervising confidence estimation. This dual-prototype external alignment framework for indirect confidence evaluation is the first identified in PML. We respectfully request reconsideration of our contribution. To elaborate, we detail the key differences between CAPML and the works you mentioned.\n\nⅠ.FsPML-PR(2022)\n\nWhile both models address PML with prototypes, their focus and core mechanisms differ fundamentally. FsPML-PR targets Few-Shot PML using meta-learning for rapid adaptation with few samples, while CAPML addresses standard PML through unified optimization. FsPML-PR employs \"internal iterative refinement\" with a single family of prototypes derived from noisy support samples, refining them using local information. CAPML introduces \"external alignment calibration\" by defining two distinct prototype types: (1) unsupervised prototypes (M) from fuzzy clustering, inherently robust to label noise, and (2) supervised prototypes (O) from candidate labels, containing semantic information but biased by noise. \n\nⅡ.DMVP(2023)\n\nDMVP targets Multi-View Partial Label Learning, handling multiple distinct feature representations using deep networks for view fusion. CAPML addresses conventional single-view PML without multi-view context.\nIn DMVP, prototypes enforce consistency across different views to achieve effective view fusion. In CAPML, prototype alignment serves robust semantic grounding rather than view fusion. \n\n2. >Theoretical Analysis\n\nThanks for your comments. Let label disambiguation error $\\mathcal{E} = \\||R - Y^{gt}\\||_F^2$, which primarily stems from incorrect weighting of candidate labels. The LE indicator matrix $C$ constructed from fuzzy membership $FP$ determines these weights - when permutation matrix $P$ is random($P_r$), $C$ assigns high confidence to noise labels and low confidence to true labels, leading to degraded performance.\n\nPrototype alignment fundamentally corrects this weighting problem. Hungarian algorithm finds optimal permutation $P^* $ that minimizes $\\||MP- O\\||\\_F^2$, ensuring correct correspondence between unsupervised prototypes $M$ and supervised prototypes $O$. This alignment improvement directly translates to better indicator matrix $C^*$, which assigns higher weights to genuine labels and lower weights to noise labels.\n\nThe error reduction can be quantified as:\n$\\mathcal{E}_a \\leq \\mathcal{E}_u - \\beta \\||MP\\_r - MP^*\\||\\_F^2$\n\nwhere $\\beta > 0$ depends on data quality factors including cluster separation and feature dimensionality, $\\mathcal{E}_a$ and $\\mathcal{E}_u$ denote aligned and unaligned errors. The term $\\||MP_r - MP^*\\||_F^2$ measures alignment quality - larger values indicate more significant prototype misalignment correction, leading to greater error reduction. This theoretically validates the effectiveness of our dual-prototype alignment approach for noise reduction.\n\nPlease refer to our response to **Reviewer 3Fvi's Weakness #1** for convergence analysis.\n\n3. >Shallow Ablation Study\n\nWe additionally conducted comprehensive ablation studies to validate each component's contribution:\n\n- **CAPML-NA**: Sets permutation matrix P to identity matrix, removing prototype alignment\n- **CAPML-CW**: Sets label enhancement indicator matrix C to all-ones, removing confidence indicator.\n\n**Results on Average Precision (higher is better):**\n\n|Dataset|CAPML-NR|CAPML-ED|CAPML-NA|CAPML-CW|CAPML|\n|-|-|-|-|-|-|\n|medical5|0.851±0.025|0.834±0.023|0.821±0.021|0.833±0.022|**0.876±0.027**|\n|image2|0.798±0.019|0.772±0.017|0.785±0.018|0.774±0.018|**0.814±0.021**|\n|yeast7|0.741±0.016|0.715±0.014|0.729±0.015|0.722±0.015|**0.760±0.018**|\n|music_style|0.724±0.015|0.698±0.013|0.712±0.014|0.706±0.014|**0.743±0.016**|\n|music_emotion|0.612±0.009|0.588±0.007|0.601±0.008|0.597±0.008|**0.628±0.010**|\n\nResults demonstrate that prototype alignment (CAPML vs CAPML-NA), entropy regularization (CAPML vs CAPML-ED), and confidence indicators (CAPML vs CAPML-CW) all contribute meaningfully to performance, with confidence indicator being essential across all datasets.\n\n4. >Method Complexity\n\nPlease refer to our response to **Reviewer 3Fvi's Weakness#1** for detailed complexity analysis. Computational complexity comparison:\n\n|Method|Computational Complexity|\n|-|-|\n|**FPML**|$O(nd² + ndq)$|\n|**PAMB**|$O(Tf(q,L) + Lf(n,q,L))$|\n|**PML-NI**|$O(T(d³ + nd² + dq² + ndq))$|\n|**PARTICLE**|$O(n^k + n²d + n²Td + nkq + q²nkd)$|\n|**LENFN**|$O(T(n²d + d³ + nqd))$|\n|**FBD-PML**|$O(T(n³ + nk³ + nq))$|\n|**Ours**|$O(T_0dnq+T_1(dq^2 + q^3) + T_2(nhq +d^3+ h^2q + nq))$|\n\nCAPML shows competitive efficiency. While introducing $q³$ overhead from prototype alignment, it avoids prohibitive $O(n³)$ dependencies like FBD-PML. Since $q << n,d$ in practice, the $q³$ term remains manageable.\n\n5. >FBD-PML\n\nWe apologize for the unclear describtion. FBD-PML treats prototypes as auxiliary tools for space transformation, using fuzzy clustering for \"encoding-decoding\" between features and labels in a shared semantic space. The prototypes are unordered and lack explicit semantic correspondence with labels. In contrast, our method establishes direct prototype-label alignment where each prototype captures semantically meaningful class-specific patterns, providing interpretable confidence estimation for label disambiguation. The theoretical justification is that FBD-PML's shared membership space may blur class boundaries and propagate noise and  cannot guarantee adequate preservation of label-specific semantics, while our explicit alignment mechanism ensures confidence estimation is guided by semantically meaningful prototype-label relationships.\n## Question\n1. >Novelty Positioning\n\nPlease see response to weakness #1.\n\n2. >Theoretical Foundation\n\nPlease see response to weakness #2.\n\n3. >Method Justification\n\nPlease see response to weakness #5.\n\n4. >Complexity Analysis\n\nPlease see response to weakness #4.\n\n5. >Parameter Sensitivity\n\nThank you for your comment. As demonstrated in **Section 4** and **Figure 2**, our method exhibits remarkable robustness across wide parameter ranges with stable performance and minimal fluctuations.\n\n### Practical Parameter Selection Guidance\n\nParameter α (noisy label sparsity): Recommended range [0.01, 10] based on the expected noise level. Use smaller values (closer to 0.01) for higher noise datasets to encourage stronger sparsity regularization, avoiding overly large values that may degrade performance.\n\nParameter β (feature redundancy and classifier complexity): Adjust according to dataset characteristics. Smaller datasets benefit from smaller β values for sparser classifiers and better generalization, while larger complex datasets may require larger β values to capture intricate patterns.\n\nParameter λ: Please refer to our response to **Reviewer gpe6's Question #2** for comprehensive sensitivity analysis and selection strategies.\n\n## Limitation\n\n1. >Dependence on clustering assumptions\n\nWe appreciate your analysis. When clustering poorly reflects label semantics, our alignment process still leverages partial semantic information in supervised prototypes to guide correspondence discovery. Our confidence-aware framework down-weights uncertain correspondences, reducing poor alignment impact, while classifier learning with sparse constraints fully exploits available information. Experimental validation and ablation studies demonstrate effectiveness across most datasets. However, in extreme cases this assumption may break down (referring to **Reviewer 3Fvi's weakness#2**), which we will discuss in limitations.\n\n2. >generalizability\n\nThe prototype alignment mechanism could establish correspondences between clustering centroids and candidate labels in partial label learning, map bag-level representations to label semantics in multiple instance learning, or provide reliable structural information for general denoising scenarios.\n\n3. >extreme noise \n\nThanks for your comment. Theoretically, unsupervised fuzzy clustering learns data structure independently of noisy labels, while prototype alignment establishes correspondence even with heavily corrupted supervised prototypes. The key insight is that alignment can identify meaningful correspondences by minimizing prototype space distances, even under extreme noise. Please refer to our response to **Reviewer gpe6's weakness** for experimental results under high noise conditions.\n\n4. > Interpretability\n\nThanks for your comment. The permutation matrix P establishes correspondence between unsupervised clustering prototypes and semantic label classes, where $P[i,j]=1$ indicates the $i$-th unsupervised prototype represents the $j$-th class label. Since unsupervised clustering produces prototypes in arbitrary order without semantic meaning, P transforms meaningless cluster indices into semantically interpretable assignments (**Figure 1**). The Hungarian algorithm optimally solves this assignment by minimizing prototype distances, enabling transformation of fuzzy membership degrees into semantically meaningful label enhancement indicators fundamental to our disambiguation process."}]

Author rebuttal:

Meta-review: This work proposes CAPML, a prototype-based framework for partial multi-label learning that aligns two prototype spaces, unsupervised (from entropy-regularized fuzzy clustering) and supervised (from candidate labels). 

The idea is clearly scoped (addressing prototype misalignment) and implemented with a coherent three-stage optimization. Reviewers find the problem important and the solution principled; after rebuttal, they retain or raise positive assessments. One reviewer (7dPU) did not raise the rating, yet in Final Justification expressed support for a borderline-accept decision. For the camera-ready, please incorporate and flesh out the additional experimental results discussed in the rebuttal, and add the necessary references.
Decision: Accept (poster)