Trusted Multi-View Classification  with Expert Knowledge Constraints
Authors: Xinyan Liang
Shijie Wang
Yuhua Qian
Qian Guo
Liang Du
Bingbing Jiang
Tingjin Luo
Feijiang Li
Venue: ICML 2025 spotlightposter (2025)
Keywords: multi-view classification
trusted multi-view classification
trusted  fusion
distribution-aware subjective opinion
Primary area: general_machine_learning->supervised_learning

Abstract: Multi-view classification (MVC) based on the Dempster-Shafer theory has gained significant recognition for its reliability in safety-critical applications. However, existing methods predominantly focus on providing confidence levels for decision outcomes without explaining the reasoning behind these decisions. Moreover, the reliance on first-order statistical magnitudes of belief masses often inadequately capture the intrinsic uncertainty within the evidence.  To address these limitations, we propose a novel framework termed Trusted Multi-view Classification Constrained with Expert Knowledge (TMCEK). TMCEK integrates expert knowledge to enhance feature-level interpretability and introduces a distribution-aware subjective opinion mechanism to derive more reliable and realistic confidence estimates. The theoretical superiority of the proposed uncertainty measure over conventional approaches is rigorously established. Extensive experiments conducted on three multi-view datasets for sleep stage classification demonstrate that TMCEK achieves state-of-the-art performance while offering interpretability at both the feature and decision levels. These results position TMCEK as a robust and interpretable solution for MVC in safety-critical domains. The code is available at https://github.com/jie019/TMCEK_ICML2025.

Trusted Multi-View Classification with Expert Knowledge Constraints
Xinyan Liang' Shijie Wang'
Yuhua Qian
Qian Guo
Liang Du'
Bingbing Jiang Tingjin Luo
Feijiang Li
Abstract
1. Introduction
Sleep disorder is related to lots of diseases like insom- nia, narcolepsy, obstructive sleep apnea syndrome (OSA) (Jahrami et al., 2022). Sleep stage classification (SSC) is the primary diagnostic tool for sleep disorder (Guillot et al., 2020; Wulff et al., 2010). Multi-view learning (MVL) is a powerful paradigm that leverages diverse data representa- tions to improve model performance and robustness (Zhang et al., 2020; Liang et al., 2022; Wei et al., 2025; Yuan et al., 2025), making it particularly valuable in SSC that is mainly based multi-view polysomnography signals such as EEG, EOG and EMG (Phan et al., 2020). By leveraging data from multiple perspectives, MVL not only enhances diagnostic accuracy but also offers better generalization across diverse patient populations.
Trusted multi-view classification (TMVC) based on the Dempster-Shafer theory has gained sig- nificant recognition for its reliability in safety- critical applications. However, existing meth- ods predominantly focus on providing confidence levels for decision outcomes without explaining the reasoning behind these decisions. Moreover, the reliance on first-order statistical magnitudes of belief masses often inadequately capture the intrinsic uncertainty within the evidence. To address these limitations, we propose a novel framework termed Trusted Multi-view Classifi- cation Constrained with Expert Knowledge (TM- CEK). TMCEK integrates expert knowledge to en- hance feature-level interpretability and introduces distribution-awe subjective opinion mecha- nism to derive more reliable and realistic confi- dence estimates. The theoretical superiority of the proposed uncertainty measure over conven- tional approaches is rigorously established. Ex- tensive experiments conducted on three multi- view datasets for sleep stage classification demon- strate that TMCEK achieves ofth-oofthhe-rt per- formance while offering interpretability at both the feature and decision levels. These results po- sition TMCEK as a robust and interpretable so- lution for MVC in safety-critical domains. The code is available at https: / tiub..uu..... com/ jie019/ /M111//////CCCC. TTTC//CCCCCCCCCCCEEEEE ICML2025.
While MVL addresses many challenges in SSC, trustwor- thiness and interpretability remain critical concerns (Wang et al., 2023; Zou et al., 2023). Trusted multi-view learning aims to improve the reliability of predictions by incorporat- ing uncertainty estimation (Han et al., 2023). However, two significant limitations persist: (1) feature-level opacity: Cur- rent trusted learning methods often function as black boxes at the feature level, failing to clarify which features are criti- cal and how they contribute to the decision-making process. The lack of transparency reduces trust and interpretability for clinicians and patients. (2) Inaccurate confidence esti- mates at decision level: Existing methods primarily rely on the quantity of evidences for uncertainty estimation, with- out considering their distribution. As a result, confidence estimates may deviate significantly from expected values, particularly in scenarios involving ambiguous or conflicting data, undermining their practical utility.
'Inttiutee of Big Data Science and Industry. Key Laboratory of Evolutionary Science Intelligence of Shanxi Province, Shanxi Uni- versity. Taiyuan, China "Shanxi Key Laboratory of Big Data Analy- sis and Parallel Computing, School of Computer Science and Tech- nology, Taiyuan University of Science and Technology. Taiyuan, China SScoool of Information Science and Technology, Hangzhou Normal University, Hangzhou, China "College of Science, Na- tional University Defense Technology, Changsha, China. Corre- spondence to: Yuhua Qian <jinchengqyh@ 126.com>.
In this paper, we propose novel trusted multi-view learn- ing framework that combines interpretability at both the feature and decision levels. Specifically, we firstly utilize Gabor functions in the initial layers of the model to embed expert knowledge into feature extraction, enabling explicit representation of critical features. This approach allows for better understanding of which features contribute clas- sification decisions, improving transparency and reliance. Second, we improve uncertainty estimation by introducing the distribution of evidence as an additional factor, moving
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Trusted Multi- Classification with Expert Knowledge Constraints
beyond traditional reliance on the quantity of evidence. By capturing both the magnitude and distribution of evidence, our method provides more reliable confidence estimates, especially in scenarios with ambiguous or conflicting data. These innovations enhance the interpretability, reliability, and robustness of multi-view learning in high-stakes appli- cations like automated sleep stage classification.
alone.
2.2. Automatic Sleep Stage Classification
Existing work on automatic sleep staging can be catego- rized three main categories based on the types of signal input representation of the network. The first uses raw one-dimensional (ID) signals directly as input to capture sequential features by one-dimensional convolutional neural networks (ID CNNs) (Chambon et al., 2017), recurrent neu- ral networks (RNNs) (Dong et al., 2016) and attention mech- anism (Phan et al., 8b). The second converts raw signals into -wo-dimensional (2D) spectrograms using techniques such as the continuous wavelet transform (Kuo et al., 2022) or short-time Fourier transform (STFT) (Guillot et al., 2019). Two awo-dimensional convolutional neural networks (2D CNNs) are then used to process these spectrograms, which capture essential frequency characteristics linked to each sleep stage. The third combines both temporal and fre-ffeuyyncy repre- sentations which employs a dual-stream architecture. In this structure, each branch of the model processes different view. Then integrating the outputs from each view to pro- duce fusion output by concatenate operation. XSleepNet (Phan et al., 2020) uses the outputs of three branches to compute losses. SleepPrintNet (Jia et al., 2020) only uses the fusion output to compute losses. Compared with the above methods that focuses on classification performance, our method focuses on trustworthiness and interpretability besides classification performance.
Our main contributions are summarized as follows: (1) We propose novel trusted multi-view learning framework that enhances feature-level interpretability by embedding ex- pert knowledge, enabling explicit identification of critical features contributing to classification decisions. (2) We in- troduce an improved uncertainty estimation mechanism by incorporating the distribution of evidence, providing more reliable and realistic confidence estimates. (3) Due to the rich expert knowledge available in the sleep domain, we instantiate our method on the sleep datasets, and the experi- ments show that our approach improves both interpretability and reliability, while also outperforming baseline methods in terms of accuracy.
2. Related Work
2.1. Trusted Multi- View Learning
Multi-view learning has become a powerful approach for integrating complementary information from multiple data representations, leading to more robust and accurate models across a range of applications (Liang et al., 2024; Wen et al., 2024; Zhang et al., 2024). However, these methods often fail to capture the uncertainty of their predictions. Evidential deep learning (EDL) (Sensoy et al., 2018) uses subjective logic-based approaches to avoid sampling by explicitly mod- eling uncertainty, making them computationally efficient. Recent work extends EDL into multi-view learning (Liang et al., 2025). A notable approach, trusted multi-view clas- sification (TMC) (Han et al., 2023), employs Dempster's s combination rule (Josang & Hankin, 2012), assigning lower weights to views with high uncertainty, thereby prioritizing more reliable views. Building on this foundation, several aggregation methods have advanced uncertainty handling by refining how views are integrated (Liu et al., 2023; Zhang et al.. 2023). These methods commonly exhibit the prop- erty that adding another opinion reduces overall uncertainty. Since data of different views are might not aligned, RCML (Xu al., 2024) proposes a new aggregation method en- sure that integrating confficting views appropriately raises uncertainty. Despite these advances, current methods hibit notable limitations: feature-level opacity and Inaccu- rate confidence estimates at decision level. In light of these shortcomings, this work proposes a novel framework to ad- dress these gaps by enhancing interpretability at the feature level and introducing a more comprehensive uncertainty estimation method that moves beyond evidence magnitude
3. The Proposed Method
In this study, we propose a method that integrates both time- domain and time- frequeeyy (T-F) domain representations of biosignals to establish robust multi-vien learning frame- work. We design two subnetworks independently process the two types of input signals and adopt late fusion at the decision level, where the classification outputs of the two subnetworks are combined to produce the final prediction. The overall architecture of the model is illustrated in Fig. 1.
3.1. The Interpretation of Feature Level
Filter parametrization has become a frequently-used tech- nique for designing interpretability deep neural networks (Xie ct al., 2023; Zheng et al., 2024). The Gabor function is often used as filters in signal processing tasks (Chang & Morgan, 2014). To explicitly examine the features that con- tribute to decision-making we follow the strategy (Niknazar & Mednick, 2024) to parameterize Gabor function, and use them to fit specific signal patterns that align with expert knowledge such as slow oscillations (~1 Hz), alpha (8-13 13 Hz), theta (3-7 Hz), spindles (15-18 Hz bursts of activity in a spindle shape), K-complexes (large biphasic waves). Specifically, some Gabor functions are first embedded into
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Trusted Multi-Viee Classification with Expert Knowledge Constraints
DM
signal
32M256
Differentiable parametrized
(256,2801)
(3072)
Exidence
(3000) Time domain: X;
Gaber kernels:
Feature mapping F
Classifier CL'
DMP
Classffication result
STFT
(512)
Evidenee
by
(2.24.129) Frequency domali: Ny
Feature mapping F2
Classifier CL2
GeLAU
ReLU:
Dropout:
Max pooling and BN:
Conv:
Reshape:
Figure 1. The whole framework of model.
the first convolutional layer as its kernels KG, and then convolution operation is performed between the input sig- nal X, and Kg. The outputs of the convolution operation reflect the correlation between both of them. At the end of the training, the kernel Kg optimized to be pattern which facilitates decision makinn... The process can be mathemati- cally expressed as follows:
Itf is also realized by convolutional neural networks (CNNs). The processed frequency domain features shaped into one-dimensional feature vector by adaptive av- erage pooling. Then the vector Iı = F²(),)) E 12522 is passed to three fully connected layers, we get the prob- ability distribution evidence e² (z,( E R in the time-frequene domain. Details on the network architecture are provided in the Appendix A.3.
KG(T) = (-=") cos (2
3.2. The Interpretation Decision Level
Output = KG * Xt.
(2)
In the previous process, we learn view-specific evidence by F1, CL3, F2 and CL2, which could be termed as the amount of support the classification collected from data, Then the view-specific distributions of the class probabil- ities are modeled by Dirichlet distribution, parameterized with view-specific evidence. From the distributions, we can construct mass consisting of the belief quality of each category and the overall uncertainty. We also combine a conflicting mass aggregation strategy based on trusted fu- sion reduce decision conflicts caused by view-specifie Fl and F?.
where u is center of the kernel function (temporal or spatial location), a is controls the width of the Gaussian envelope, frequency of the oscillations in the cosine part of the kernel, T' is the time variable used in evaluating the kernel (-18 < T & 18), and is convolution operator.
Feature mapping Fl and Classifier CL In order to trans- form a raw signal X2 into a high-level feature Ie, the feature mapping Fl: X, + 24 is realized by convolutional neural networks (CNNs). The output of the Gabor convolutional layer (GCL) represents the magnitude of the specific wave- forms (Gabor kernels KG) across the time. Then the result- ing Gabor features are used input to the one-dimensional CNNs to further extract discriminative features. Then flatten and randomly discard some of the processed features to form epoch-wise (30s) feature vector x; =F (KG * X,) E 3R3072 In the end, through three fully connected layers, we get the probability distribution evidence el (x+( RR5 in the time domain.
View-Specific Evidencial Deep Learning. In decision layer, it is essential to ensure accurate and trustworthy pre- dictions. Traditional methods like softmax layers often over- estimate confidence, particularly in incorrect predictions (Wang al., 2021). Due to their reliance on single-point probability estimates, this limits their ability capture true model confidence and risk. To overcome the limitation, ev- idential deep learning (EDL) which is based on evidence theory under the framework of subjective logic (SL) has been introduced (Sensoy et al., 2018). Evidence e here refers to the information extracted from the input data that supports the classification decision, and is used derive belief mass by each class label and overall uncertainty mass u to the whole frame based the evidence theory.
Feature mapping F2 and Classifier CL Simultancously, the EEG raw signals X; in the time domain is transformed into the fime-frequency (T-F) domain using the Short-Time Time Fourier Transform (STFT), yielding time-frequency repre- sentation Xzy E F) where F is frequency bins and is time steps. Same as Fl. the feature mapping F2: Xzf
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Trusted Multi- Classification with Expert Knowledge Constraints
Definition 3.1. (Subjective opinion (Han et al., 2023)): Let == e2, 1 ,ek] be the evidences where Eg denotes the k-th category evidence. The parameter a of the Dirichlet distribution is defined by a = e + 1. Then the subjective opinion can be denoted as M = [b,, h2,.. ... bx, u) derived by the Dirichlet distribution Dir(plax) where p is the class probability vector on a simplex.
concentration e. A larger d indicates more concentrated evidence distribution, which corresponds to greater uncer- tainty. And then distribution-aware subjective opinion is defined as DM- = [b1, b2.... bg d, 2i,, we redefine the calculation of by and u" as follows:
b9
ek u s.
Kd
gdd=
(1 + Gini(e))
(3)
5
For the vth view, then the belief mass by and the uncertainty u are computed as: by 3r. u = gr. where S Ef + 1) = ビ oz is the Dirichlet strength.
where == K coefficient where pk:
= (eg + d), Gini(e) = =1 - kk=1 P is Gini probability of class k.
K
Ck
2ラ=1
In contrast to conventional subjective opinion frameworks, our approach determines the uncertainty measure u through a dual consideration of both the cumulative evidence sum and its distribution characteristics, represented by e. This enhanced formulation is formally characterized by the the- oretical analysis in Subsection 3.3, which demonstrates its superior sensitivity uncertainty quantification compared to existing methods.
The core of this framework is that the more evidence there is, the higher the quality of belief in a category, and the more confident the model is in predicting that category. Conversely, when there is less evidence, the overall uncer- tainty increases. The mean of the corresponding Dirichlet distribution p" for the class probability 0 is computed as
PJ Se. In subjective opinion, the uncertainty mass is detined as u" K
K 5 (ey which implies that u
Evidential Multi- Fusion via Distributed Mass Ag- gregation. After obtaining V independent sets of prob- ability masses assignments (DM"), where DM" d", u²) under each view, we next need to com-
depends solely on the aggregate sum of evidences e. So, it is unsensitive to distribution of evidences e. The problem, which is called as Evidence Distribution-unawarr Problem, can be illustrated using the below example.
Example 3.2. Given an input we feed it into a network to obtain evidence nnorma/[[,,1,1 and uncertainty Unormal =5/12. Now, if we add noise to x, the evidence (22221-12.,,,211.0,,, leading to -3333,21333 and Unoisy=5512 Normally, as the distribution becomes more concentrated, the uncer- tainty should increase. Interestingly, after adding noise, the uncertainty u remains constant, which is counterintuitive and clearly unreasonable. We present this problem in Fig. 2, the complete presentation is in Fig. 10 Appendix A.8.
bine them to obtain a joint mass DM- = [b,} d. u Misalignment of multi-view data in feature mapping can cause conflicts. We would diminish their impact in the fusion stage.
From this, we com-
pute (5.0rma
The joint mass DM- = [101)/ : d, u is calculated from
the two sets of masses DM = [0]], d,, u² and
DM = [103]
K d,, u² in the following manner:
DM = DM DDM = 1b uu 102 1022.'' .2 (4)
10
Normal datasets
6ju² + bzu²
2u u2
dl 2d d2
Noisy datasets
0,00
u¹ + uu² -u 1002_
u² + 2
d' + d2
Density
6-
(5)
The averaging belief fusion can be computed simply by d² e +-d eq in Appendix A.2. We can fusion the final joint +
4-
mass DM from different views with the following rule:
0.0
0.2
Uncertainty
0.4
0.6
0.8
DM = DM DMM .DMM..
(6)
Figure 2. Density uncertainty before and after adding noise.
Based on the above combination rule, we can obtain the estimated multi-view joint evidence e and the corresponding parameters of joint Dirichlet distribution to produce the final probability of each class and the overall uncertainty.
To overcome the limitation inherent in Definition 3.1, we propose a novel distribution -awrriiionaaaaaaaaaeeeeee subjective opinion frame- work that extends the conventional model through the incor- poration of an evidence distribution concentration measure. Its definition is as follows.
Loss Function. For instance {XF]}
V e = CL" (F"(F((XX)) represent the evidence vector predicted by the network for the classification. To ensure that the network outputs non- negative values, we need to replace the softmax layer of the
Definition 3.3. (Distribution-awaree subjective opinion): Let e- [e1, 62, "* ,ex] be the evidences, d denote the
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Trusted Multi- Classification with Expert Knowledge Constraints
traditional neural network based classifier with the activation function layer (ReLU). Different from the typical cross- entropy loss used in traditional neural networks below:
V-1
Loo V(V 1) m= n=m++1
e
e"
Loon = [Coon1 + >/oonnn2
(10)
Lee
Σ ==1
Vij Poj
To sum up, the overall loss function for specific instance {XT]== can be calculated as:
where Pij is the predicted probability of the ith sample for class j. For our model, we can get the parameter a; of the Dirichlet distribution by a; e, + d. Based on Eq. (7), we have the adjusted cross-entropy loss using evidence-based approach:
L L= Lace (a;; + Σ Lace (af)) + YCoon
(II)
3.3. Theoretical Analysis
K
K II Psi
Lace(as))
/
Σ
Wis Pij
cas-1 dp:
To demonstrate the superiority of the distribution sub- jective opinion framework, we conduct a comprehensive theoretical analysis. This examination reveals several key advantages: (1) enhanced modeling capability for uncer- tainty quantification through explicit distribution considera- tion, (2) the relation between distribution-awarr subjective opinion aggregation and evidence aggregation, and (3) ag- gregation properties. The theoretical framework establishes rigorous mathematical foundation that not only justifies its practical effectiveness but also provides insights into its relationship with conventional subjective logic approaches.
B(ass)
j=l
K
Σ
vis (V(S)) - +b(a)))),
(13)
where v-) is the digamma function. The above loss func- tion does not guarantee that the evidence generated by the incorrect labels is lower. To address this issue, we can in- troduce additional term in the loss function, namely the Kullback-Leibler (KL) divergence:
LKI((a)) (o:s = KL (((r)la)) || D(P(11)
(8)
Proposition 3.4. Given two evidences el le].e], .ek. and e² = e Σ K c) = Σ3 ez and d(e!) s d(e?). then u I u²
ekl.
If
T TE Ris)
= loog
I(K) ((K)II} I(āss)
Proposition 3.4 establishes that our modified opinion frame- work properly captures the uncertainty quantification of evi- dence through its dispersion characteristics. The complete mathematical proof is provided in Appendix A.
K
K Σ
(oi 1) ((ārs)) -
ōij
where 11) 1 is the uniform Dirichlet distribution, o; y: + (1 y/) O a; is the Dirichlet parameters after removal of the non mon-miilea evidence from predicted parameters og for the i-th instance, and T(-) is the gamma function.
The distribution-awarr subjective opinion aggregation operation DM = DM is mathe- matically equivalent to the weighted evidence pooling:
Proposition 3.5.
e02 de' d
(12)
Therefore, given the Dirichlet distribution with parameter a; for the i-th instance, the loss is:
d + d2
Proposition 3.5 demonstrates that the proposed distribution- aware aggregation mechanism can be effectively imple- mented through a dispersion-weiggheed evidence pooling scheme. The detailed proof is available in Appendix A.2. Proposition 3.6. Let DM [b] ,b....,bbk dt u²) and 2 = l........ .bx,, d2, u² represent distribution- aware subjective opinions from two distinct views, with ul < u? The aggregation process exhibits the following properties:
Laco(a:) (a:) = Lace (ax;) + Xa:)
(9)
where de mii E [0, 1] is the annealing coeffi cient, t is the index of the current training epoch, and T is the annealing step. By gradually increasing the influence of KL divergence in loss, premature convergence of misclassi- fied instances to uniform distribution can be avoided.
In order to ensure the consistency of results between differ- ent mass during training, minimizing the conflicts between mass was adopted. The consistency loss for the instance ( Te=1
When DM is aggreguted into DM 2 the resulting uncertainty mass decreases: uhen u²:
V is calculated as (Xu et al., 2024):
Lconl
Σ
V
Σ
1TTh
p9 (1 - - -11 )
When 2M is aggregated into DM 1 the resulting uncertainty mass increases: u. > w!.
2. 2. (V -1)
m
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Trusted Multi-Viee Classification with Expert Knowledge Constraints
Sleep-EDF
Sleep-EDP 78
SHISS
N2 N1 W
0.88
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REM N3 Artual
Actual
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W
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Predicted
Predicted
Predicted
Figure 3.
The normalized confusion matrix.
Proposition 3.6 reveals that the proposed aggregation method naturally accounts for potential conflicts between different opinions through its uncertainty-awan fusion mechanism. Based on Eq. 5, its proof is obvious.
Table I. Results comparison between the proposed method and some other deep learning methods.
DATASET STUDY
ACc
MF1
KAPPA
DEEPSLEEPNET
81.9
76.6
0.760
4. Experiments
ARNN+SVM
79.1
69.8
0.700
MULTITASKCNN
83.1
75.0
0.77
4.1. Experimental Setups
EDF20
DFSC
84.44
78.25
0.784
RESATTEN
84.3
79.0
0.78
Datasets. In this experiments, we use three public datasets including Sleep-EDF 20, Sleep-EDF 78 and Sleep Heart Health Study (SHHS) as shown in Appendix A.4. For each dataset, we use a single EEG channel for various models in our experiments.
MISC
81.9
74.4
0.75
TMCEK (OURS)
85.0
80.2
0.80
DEEPSLEEPNET
77.8
73.9
0.73
SLEEPEEGNET
74.2
69.6
0.66
RESNET
78.9
71.4
0.71
EDF78
MULTITASKCNN
79.6
72.8
0.72
ATTNSLEEP
81.3
75.1
0.74
Compared Methods. We compared model with the several representative methods three datasets includ- ing DeepSleepNet (Supratak et al., 2017), ARNN+SVM (Phan et al., 201 SleepEEGNet (Mousavi et al., 2019), ResNetLSTM (Sun et al., 2018), MultiTaskCNN (Phan et al., 80), DFSC (Liu et al., 2018), ResAtten (Qu et al., 2020), AttSllepp (Eldele et al., 2021) and MISC (Niknazar & Med- nick, 2024). For detailed description of these methods, please refer to Appendix A.5.
MISC
77.4
0.68
TMCEK (OURS)
81.4
77.5
0.75
DEEPSLEEPNET
81.0
73.9
0.73
SLEEPEEGNET
73.9
68.4
0.65
RESNETLSTM
83.3
69.4
0.76
SHHS
MULTITASKCNN
81.4
71.2
0.74
ATTNSLEEP
84.2
75.3
0.78
MISC
79.1
72.6
0.71
TMCEK (OURS)
84.3
78.0
0.79
Evaluation Metrics and Implementation Details. To eval- uate the performance of the proposed method of sleep stage scoring. We used accuracy (Acc), macro Fl-score (MF1), and Cohen's i kappa (Kappa). Among these measures, FI- score showed the performance of the method with respect each sleep stage separately. The experimental setups are detailed in Appendix A.6
datasets. The evaluation metrics include Ace, MF1 and Kappa. The rxperimental results on the three datasets are reported in Table 1, (1) TMCEK achieves the best results in terms of all met- rics. This indicates that the proposed method which deeply integrates time-domain and frequency domain features ef- fectively improve performance. (2) Compared with methods which focus on either temporal or frequency modeling, our method achieved better results, which further verified this effectivity of fusing complementary information. (3) Com- pared to DFSC, superior performance may be attributed to fusion method leverages preliminary feature interaction and post-fusion, ensuring deeper integration of complemen- tary information.
draw the following conclusions:
-euunney-domain
4.2. Experimental Results
In the section, conduct the following experiments eval- uate model from three aspects: performance comparison, confusion matrix analysis and hypnogram visualization.
Performance Comparison. To verify the superiority of the proposed sleep scoring system, we compare the three evaluation metrics of our model with the baseline on two
Confusion Matrix Analysis. The classification results of the confusion matrix are shown Fig. 3. From the results,
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Trusted Multi-Viee Classification with Expert Knowledge Constraints
Ground Truth Hypnogram (Subject 0)
REM
first night
second night
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52-
S1
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REM
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Second Predicted Hypnogram (Subject 0)
REM
SWS
S2
S1
250
500
750
1000
1250
1500
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Figure 4. Example of ground truth (expert's scoring) and predicted hypnogram for one fold. The red dots indicate that the network misclassified the 30 epoch.
can be observed that TMCEK has the best classification results on W and N3 stages. The classification performance of the NI stage is the worst among all sleep stages. The tran-
and increased the classification performance significantly.
4.3. Interpretation
reasons of the results may be that the N1 stage, sitional state between wakefulness and deeper sleep stages like N2, exhibits overlapping features with both. For ex- ample, EEG characteristics NI, such as low-amplitude theta waves and occasional alpha waves, are also present in wakefulness and N2, leading to blurred boundaries. This feature ambiguity makes it difficult for traditional feature extraction methods and deep learning models to distinguish NI from other stages, particularly W and N2. In addition, the NI stage is typically underrepresented in sleep staging datasets: NI accounts for approximately 5% of night's 's sleep, much lower than other stages like N2 REM. This imbalance biases classification models towards dominant stages, thereby degrading the performance for the N1 stage.
increase the system's interpretability and reliability, we introduce the Gabor kernel at the first convolution layer in time domain. In addition, can know whether the decision is credible by uncertainty estimation. Next, analyze these two aspects respectively.
1. INTERPRETABILITY AT FEATURE-LEVEL
In terms of interpretability. the trainable Gabor kernels in the first layer are used to learn meaningful waveform pat- temns that are directly associated with sleep stages. These kernels are adjusted during training capture representa- tive time- fime-frreunncy structures within the EEG signals. The outputs of this Gabor layer reflect how prominently each learned waveform appears in the input, effectively highlight- ing characteristic features relevant to sleep staging. The calculation
Hypnogram Visualization. In Fig. 4 we present an origi- nal manually scored hypnogram and its corresponding esti- mated sleep hypnogram using the trained single-epoch and multi-epoch networks for one fold on Sleep-EDF 20. score is approximately equal to the mean score across the entire dataset. From Fig. 4, can be observed that there are many misclassified points in the single epoch network out- put. Using the multi-epoch network to model transition rules between epochs can eliminate partial misclassified points
overall qualitative impact each kernel waveform given Appendix A.7.
In Fig. 5, show the top eight EEG optimized Gabor waveforms along with their frequency domain by overall im- portance (the complete figure is shown in Fig. 8 in Appendix A.8). Some of the optimized kernels were perfectly matched to well-known EEG waveforms including slow waves (SW,

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Trusted Multi- Classification with Expert Knowledge Constraints
Kernol 8
Kornel 17
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S0
25 Frequency (H3))
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50
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Frequency (Hz)
Frequency (Ha)
Figure 6. Density of uncertainty.
Figure 5. Waveform and frequency domains of important opti- mized Gabor kemels.
related with the quality of the instances, thereby validating the capability of our method in uncertainty estimation.
1H2), deta waves(I to 4Hz), theta waves(3 to 8Hz). Opti- mized Gabor kernels 8 and 17 is similar SW and deta waves, kernels 5, 24 and 25 are fitted to theta waves.
4.4. Robustness
The robustness of the model can be improved through trusted learning. In order to verify the robustness improve- ment brought by trusted learning. we select the first fold (the first subject is used as the test set, and the others are used as the training set) for robustness testing compare the evaluation indicators of the model trained with trusted learning and the model without trusted learning by adding the Gaussian noise with different levels of standard deviations (6) to time domain view on the test set. From Fig. 7, it can be observed that models using trusted learning are more robust than those without it, which highlights the importance of the reliability of decision results.
Fig. 9 in Appendix A.8 displays the importance of the cor- responding Gabor waveforms in the overall sleep staging process and different sleep stages of the single-epoch net- work. The results in this figure are compatible to the experts' knowledge and the sleep scoring manuals. For example, Ga- bor kernels 8 and 17 which represent SW and deta waves have highest impact in stage S2 and SWS. On the other hand, the results in Fig. 9 show that some Gabor kernels are not important because the training process could not optimize them or they had redundant information, and other opti- mized kernels produced enough information for decision making. To improve kernel optimization, our subsequent work considers to apply diversity regularization for explic- itly penalizing similarity among kernels and encouraging each to capture distinct patterns.
Bleep-EDF<u 20. We
Trusted Acc
No-Trusted MFL
No-Trusted Acc
Trusted Kappa
0.9
No-Trasted Kappa
4.3.2. UNCERTAINTY ESTIMATION AT DECISION LEVEL
0.8
To further evaluate the estimated uncertainty, we visualize the distribution of normal and noisy data on the Sleep-EDF 20 dataset in Fig. 11 in Appendix A.8. To construct noisy test sets, we introduce Gaussian noise with standard de- viation 10, 30, 50, 100 of the test instances. The experimental results are presented in Fig. 6. The results reveal that, when the noise intensity is low (a 10), the dis- tribution curve of the noisy instances closely aligns with that of the normal instances. However, as the noise intensity in- creases, the uncertainty of the noisy instances also increases. This finding indicates that the estimated uncertainty cor-
0.7
10
30
50
100
Standard deviation (5)
Figure 7. Comparison on Slecp-EDF 20 with different noise levels. 4.5. Comparison with Trusted Multi-view Methods
To validate the effectiveness of the proposed trustworthy multi view learning method, we conducted experiments on several benchmark multi-view datasets, including the Hand-
8

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Trusted Multi- Classification with Expert Knowledge Constraints
Table Classification accuracy (%) on different datasets. indicates results from CCMI. (Liu et al., 2024).
DATA
EDL'
DCCAE"
CAML
ETMC²
RCML*
CCML
TMCEK (OURS)
HANDWRITTEN
97.00 = 0.16 97.05 + 0.24 98. 18.10+ 0.12 98.32 + 0.22 98.70 = 0.19 98.75 = 0.27
98.80 + 0.76
SCENE15
60.60 = 0.13 64.26 - 0.42
70.17 0.13 66.87 + 0.29 71.28 = 0.32 72.60 0.87
74.84 - 0.39
CUB
89.51 = 0.24 85.39 + 1.36 94.33 + 0.73 91.05 + 0.63
93.28 2.75 94.58
1.30
94.67 1.55
PIE
87.99 + 0.56 81.96 + 1.04 93.38 1 0.80 93.82 1 0.82 93.89 + 2.46 94.56 = 1.83
97.06 1 1.80
Written (HW) and Sc, CUB and PIE datasets (details in Appendix A.4). We compare methods with EDL (Sensoy et al., 201 8), DCCAE (Wang et al., 2015), CALM (Zhou et al., 2023), ETMC (Han et al., 2023), RCML (Xu et al., 2024) and CCML (Liu et al., 2024). Among them, EDL, ETMC, RCML, and CCML are four widely trusted multi-view methods. Detailed descriptions of the compared methods and implementation specifics are provided in Ap- pendix A.5 and A. From Table 2, one can get that TM- CEK achieves the best classification accuracy across all datasets. To further demonstrate the superiority of TMCEK, we select a sample from Scene15 and show its classifica- tion performance and uncertainty estimate before and after adding noise. The result is illustrated Fig. 12. From Fig. 12, it can be observed that (1) RCML misclassifies the noisy sample, whereas our method correctly classifies it. (2) RCML shows decrease in uncertainty after noise injection due overall increase in the amount of evidence. In contrast, TMCEK provides a more accurate uncertainty esti- mation. This improvement stems from our method's novel dual consideration of both the cumulative evidence and its distributional properties during uncertainty quantification.
Acknowledgements
This work was supported by National Natural Science Foun- dation of China (Nos. 62306171, T2495251, 62406218 88, 62376281, T2495253), the Science and Technology Ma- jor Project of Shanxi (No. 202201020101006), and Fundamental Research Program of Shanxi Province (No. 202203021222183).
Impact Statement
The results demonstrate that our framework bridges the gap between interpretability and performance, making it promising tool for sleep disorder diagnosis and other healthcare applications where trust and transparency are paramount. Future work could extend this approach to broader domains, further enhancing its utility in diverse multimodal diagnostic settings.
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Trusted Multi- View Classification with Expert Knowledge Constraints
A. Appendix
In the supplemental material:
A.1. Proof of Proposition 3.4.
A.2. Proof of Proposition 3.5.
A.3. Sleep Model Architecture.
A.4. Datasets,
A.5. The Compared Methods.
A.6. The Implementation Details and Evaluation Metries.
A.7. The Quantification of Gabor Kernel Influence.
A.8. Supplementary Figures.
A.1. Proof of Proposition 3.4
Proof.
Kd
Kd²
u1 2
Σ (ef + d ()= P))
Kd 2z=1 [e -
K
Kd. E Ee
Σjs(ee) (e) + d' (x)
K(d ΣØ=1 & 6 1 d
R E +
K(d Li=1 +d d
/ &
(Kd
d2)
K(d' Ej=1 of - 8 >K K (
K
Ej (e) + d Σ E (e) +d)
K(d d2) EØ=1
(: > o
[j=(ee) + ) Σ )= (e) + P))
Ø=1
K( ((2tinniee))
Linile C)=1 Ej
2 E + d') Ej=1 + d2)
K(Gini(e') - Gini(e2) 10
S 0 (: Gini(e")) < Gini(e?))
2 (c) + d') E (e) + d2)
K
Hence, v S u² holds.
12

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Trusted Multi- Classification with Expert Knowledge Constraints
A.2. Proof of Proposition 3.5 Proof. Based on Eqs. 3 and we have
by = 6k
Kd
u =
S
s
by b u + 6 u
u + v
2u u²
u
u + 12
2d dd
d d + d
Hence,
ek ek S (:: by 5
by Kd
Kd
(:: u
s
uguu² + bluu
u² u²
2Kd d²
uguu + blut
2=²
d 2d
(:: bb
2
ul + u²
u2
d' +
ul + u²
u + u
+ d
Kd dl
03,u² + BLu
d' d
u'u2
Keld
S1 + Keld
Kd d
g1
d' 1 d²
Kd Kdl
81 8
Lej + d'e c d + d2
A.3. Sleep Model Architecture
Single-Epoch Network. The proposed model consists of two main modules: the time-domain module and the frequency- domain module. The time-domain module processes raw signals through series of one-dimensional convolutional layers. These include five convolutional layers with kernel size 3, gradually increasing the number of filters (64, 128, 128, 256, 256) and applying strides to reduce temporal resolution while maintaining key features. Batch normalization is applied after each layer, and ReLU activation is used throughout. The output is flattened, and three fully connected layers with dropout (p=0.6) are employed to map features to a final probability distribution. In the frequency-domain module, the raw signals are first transformed into time- freeueer representations X,s using Short-Time Fourier Transform (STFT). The window size is set as 256, with 50% overlap between adjacent frames. 256-point FFT is utilized, leading 256 to 129-D in the feature axis. These representations passed through convolutional layers with wider kernels (3x9) to capture complex spectral patterns. Filters progressively increase from 64 to 512, with strides along the frequency axis to ensure real-time processing capability. Adaptive average pooling is applied to reshape the features, producing one- mee-imensional feature vectors for classification. This design leverages complementary information from both time and frequency domains, enhancing feature extraction and ensuring robust and accurate classification.
Multi-Epoch Network. As the consideration of transition rules between epochs can effectively improve the performance of sleep scoring (Supratak et al., 2017), we use the multi-epoch network analyze the inter-epoch temporal context. We obtain the classification results of each epoch (O₃ to O,)) through the above network. Based on the experts suggestion (Iber et al., 2007), we take ten epochs input of the multi-epoch network (O, 4 to O, and O, to On+4). The multi-epoch network consists of two long short-term memory (LSTM) layers and fully connected layer (FC) for classification. The first LSTM feeds the output of the first level network in the forward direction and the second LSTM feeds the output of the first level network in the backward direction. The LSTM layers in the multi-epoch network consist of two layers with a hidden state size of 10. We use the cross-entropy loss function train the multi-epoch network.
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Table 3. Details of three datasets used in experiments((acch sample is 30-second epach).
DATASETS
SUBJECTS
EEG CHANNEL
SAMPLING RATE
W
N1
N2
N3
REM
TOTAL
EDF20
20
Frz-CZ
100 Hz
8285
2804
17799
5703
7717
42308
EDF78
78
FpZ-CZ
100 Hz
65951
21522
69132
13039
25835
195479
SHHS
329
C4-A1
125 Hz
46319
10304
142125
60153
65953
324854
A.4. Datasets
Multi-view Datasets. HandWritten' comprises 2000 instances of handwritten numerals ranging from '0" to '9', with 200 patterns per class. It is represented using six feature sets. Scene152 includes 4485 images from 15 indoor and outdoor scene categories, We extract three types of features HOG, LBP, and GIST. CUB' consists of 1 11788 instances associated with text descriptions of 200 different categories birds, we focus on the first 10 categories and extract image features using GoogleNet and corresponding text features using doc2vec. PIE contains 680 facial instances belonging to 68 classes. We extract intensity, LBP, and Gabor as three views.
Sleep Datasets. We used three public datasets, namely, Sleep-EDF 20, Sleep-EDF 78 and Sleep Heart Health Study (SHHS) as shown in Table 3.
1) The Sleep-EDF dataset, sourced from PhysioBank (Goldberger et al., 2000), includes two subsets: Sleep-EDF 20 (EDF-20) and Sleep-EDF 78 (EDF-78). Sleep-EDF 20 contains data from 20 subjects, while Sleep-EDF 78 extends this to 78 subjects. These datasets originate from two distinct studies. The first study, Sleep Cassette (SC* files), examines the effects of aging on sleep and involves healthy participants aged 25 to 101 years. The second study, Sleep Telemetry on
(ST* files), investigates the impact of temazepam sleep, focusing on 22 Caucasian males and females who any other medications. For both studies, each polysomnography (PSG) file includes two EEG channels (Fpz-Cz, Pz-Oz) sampled at 100 Hz, as well as one EOG channel and one chin EMG channel. We select the Fpz-Cz channel as the input for our experimental models.
2) The SHHS dataset (Zhang et al., 2018), (Quan et al., 1997) a large-scale, multi-center cohort study designed to explore cardiovascular and other health impacts of sleep-disordered breathing. Participants this study presented a range of medical conditions, including pulmonary and cardiovascular diseases. To reduce the influence of these conditions, we followed the subject selection criteria outlined in (Fonseca al., 2017), focusing on individuals with relatively normal sleep patterns (Apnea Hypopnea Index or AHI below 5). This resulted in subset of 329 participants from the original pool of 6,441 subjects. For this dataset, we utilized the C4-A1 EEG channel with sampling rate of 125 Hz.
Across all datasets, the following preprocessing steps were applied. First, any UNKNOWN stages not corresponding to specific sleep stages were excluded. Second, N3 and N4 stages were merged into a single N3 stage following the AASM standard. Finally, only minutes of wakefulness before and after the primary sleep periods were retained to better emphasize the sleep stage classification. We use per-subject 20-fold cross validation, dividing the subjects in each dataset into 20 groups. The recordings in one group were considered as test data, and the rest were used training data. This process was repeated until all folds were iterated.
A.5. The Compared Methods
Multi-view Methods. There are six compared multi-view methods:
EDL (Sensoy et al., 2018) quantifies classification uncertainty by placing a Dirichlet distribution on the class probabili- ties. It models the evidence for each class and uses this evidence to compute the Dirichlet distribution parameters. The Dirichlet distribution provides measure of uncertainty, which used make more reliable predictions.
DCCAE (Wang et al., 2015) is a deep multi-view representation learning method that uses autoencoders to learn a common representation across multiple views. It maximizes the correlation between the views to extract shared
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Trusted Multi- Classification with Expert Knowledge Constraints
information.
CALM (Zhou et al., 2023) is an enhanced encoding and confidence evaluating framework for trustworthy multi-view classification. combines early and late fusion strategies to leverage the complementarity of multiple views and improve classification reliability.
ETMC (Han et al., 2023) extends the Trusted Multi-view Classification (TMC) method by introducing pscudo-view to enhance interaction between different views. It dynamically evaluates the quality of different views and makes trusted decisions based on uncertainty.
RCML (Xu et al., 2024) proposes a conflictive opinion aggregation strategy to handle conflictive multi-view data, ensures the consistency of results between different views during training and quantifies the conflictive degree between views.
CCML (Liu et al., 2024) constructs view-specific evidential DNNs to learn view-specific evidence. dynamically decouples the consistent and complementary evidence and processes them according to different principles.
Sleep Staging Methods. We compared our model with the following nine baselines:
DeepSleepNet (Supratak al., 2017) is model based on two-stage neural network architecture, combining ID CNNs and Bi-LSTMs. It extracts time-freee frequency features through ID CNNs and then uses Bi-LSTMs for sequence modeling, and is good at processing long-term sleep stage data.
ARNN+SVM (Phan et al., 2018b) utilizes bidirectional RNN with an attention mechanism to extract sequential features from EEG, combined with an SVM classifier for sleep staging. Performance is enhanced through learned filter banks.
MultitaskCNN (Phan et al., 2018 first converts the original EEG signal into a power spectrum image, and then optimizes the main task (classification) and the related auxiliary task (prediction) by sharing the feature extraction layer, thereby improving the generalization ability of the model.
DFSC (Liu et al., 2018) applies diffusion geometry fuse EEG raw signal and spectral information for sleep dynamics visualization and stage prediction, with automatic annotation using SVM.
ResAtten (Qu et al., 2020) uses CNNs to extract multi-band features and employs the multi-head attention module of the Transformer to model global temporal context, achieving efficient sleep staging.
SleepEEGNet (Mousavi et al., 2019) focuses on processing specific features of EEG signals. It uses ID CNNs combined with lightweight design to achieve efficient sleep staging in environments with limited device resources.
ResnetLSTM (Sun et al., 2018) combines residual networks (ResNet) and LSTM, first extracting spatial features through ResNet and then using LSTM for time series modeling, thereby improving the accuracy and robustness of model.
AttnSlcep (Eldele et al., 2021) first extracts and optimizes features through a multi-resolutin convolutional neural network (MRCNN) and an adaptive feature recalibration module. In addition, the temporal dependency of the signal can be captured through the temporal context encoder (TCE) of the multi-head attention mechanism.
MISC (Niknazar & Mednick, 2024) integrates domain knowledge and data-driven methods through multi-level structural design. The model injects expert knowledge into deep neural networks to improve the interpretability and performance of the model.
A.6. The Implementation Details and Evaluation Metrics
Multi-view Classification. We briefly introduce the details of the experiment. We utilize fully connected networks with a ReLU layer to extract view-specific evidence. The Adam optimizer is used to train the network, where L2-norm regularization is set to 1e-5, 5, We employ 5-fold cross- validation to select the learning rate from the options of -3 In all datasets, 20% the instances are allocated as the test set. The average performance is reported by running each test case five times.
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Sleep Staging. To extract the time-frequency input, the window size is set 12 ms, with 50% overlap between adjacent frames. 256-point FFT is utilized, leading 129-D in the feature axis. The model is trained on Pytorch platform with NVIDIA RTX 4090 GPU. We use the Adam optimizer with a batch size of 16 to train the proposed model, and the learning rate is initialized as 3. 12.e 5 (0.0005/batch size) and 6.25e-4 (0.01/batch size) in single-epoch network and multi-epoch network, respectively. In addition, the frequency f of the Gabor kernels was clamped between 0 to 35 Hz. In the training, batch samples were randomly selected from the train subset with normalized probability equal to inverse of the number of samples in each class to overcome an unbalanced distribution of classes.
Evaluation Metries. To evaluate the performance of the proposed sleep stage classification method. We use accuracy (Acc).
macro Fi-score (M F1), and Cohen's 's kappa (K Kappa). They are defined as follows:
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Rec TP+FN- Pre- = TP+FP- Here, P denotes the proportion of observed agreements, and Pe represents the expected agreement by chance. N denotes the number of all samples and M denotes the number of sleep stage classes. For a specific sleep stage S, TP refers to the number of 30-second epochs correctly classified as stage S, FN is the number of epochs that truly belong to stage S but are misclassified as other stages, and FP denotes the number of epochs incorrectly classified as stage S when they actually belong to a different stage.
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A.7. The Quantification of Gabor Kernel Influence
Since the output of the Gabor convolutional layer (GCL) can not be directly used to estimate the contribution of each Gabor kernel to the final decision, we compute the sensitivity of the decision layer output with respect to the output of the Gabor convolutional layer and use it as the normalization weights. Specifically, the sensitivity is quantified by computing the local gradient of the decision output Olclass] with respect the time series output of the ith GCL filter, defined as:
d0 cclas)]
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This sensitivity reflects how changes in the GCL output at time influence the decision. We compute the functional effect of each kernel by combining its output with the corresponding positive sensitivity (Ancona et al., 2019). Then the positive contribution of each Gabor kernel quantified as the squared sum of its output modulated by the corresponding positive sensitivities:
Eff GCt ooddaaa (t) GCT (CT
x ((Sen(t)acc::-xooaa))
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(18)
where 0(-) is the Heaviside step function, and EfJC (Eff) denotes the positive functional effect of the ith Gabor kernel on the classth element of the output given input X, (EEG). By averaging Eff across all test samples, the overall impact of each kernel on sleep stage classification is summarized by Effe
ESS= Σ ΣN, N₁
Σ
Bi j): Xx
(19)
where N, total number of the test epochs in sleep stage j. 8(-) the unit impulse function and Ofclassx] is the real sleep stage of the relative input signals X,, Effe which is the average of the positive functional effect the real output class, can represent the overall qualitative impact of each of the Gabor kernels the decision making process.
A.8. Supplementary Figures
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18


Reviews:
[{"review_id": "HAzMo7EmVf", "reviewer": "Reviewer_8nsw", "summary": "This study proposes an expert knowledge-guided trusted multi-view classification framework that achieves dual advancements in interpretability and uncertainty quantification. Specifically, the proposed method introduces expert knowledge as a tool of the feature-level interpretability and defines distribution-aware subjective logic for more sensitive uncertainty estimation. The experimental results show its superior performance on three public datasets.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your detailed feedback and thoughtful questions. Below are our responses.\n\n**Q: Could you clarify why certain Gabor kernel outputs are considered redundant during the training process? Are there any strategies for improving kernel optimization?**\n\nA: Some Gabor kernels become redundant during training because the training process could not optimize them or their learned waveforms overlap significantly with others. In our framework, the first convolutional layer uses Gabor kernels whose parameters (center, width, frequency) are tuned via gradient descent. When multiple kernels converge to capture similar EEG characteristics (for example, several may approximate slow‐wave or theta patterns), only a subset is needed to sufficiently cover the most discriminative features. The training loss naturally down‐weights kernels that do not contribute additional information to the final decision, making some kernels effectively redundant.\n\nTo improve kernel optimization, strategies such as incorporating diversity regularization can be employed to explicitly penalize similarity among kernels and encourage each to capture distinct patterns. Additionally, using domain-informed initialization schemes that span a broader range of frequencies and scales, as well as regularization techniques like adding penalty terms or employing dropout to discourage redundancy, can promote a more distributed set of feature extractors.\n\n**Q: It would be beneficial to include ablation experiments where different components of the model are removed or modified, such as removing the Gabor layer or other key modules. This would help quantify the contribution of each part of the model to the overall performance.**\n\nA: We agree that ablation studies are essential for quantifying the contribution of each module.\nIn our ablation experiments on one fold of the Sleep-EDF 20 dataset, we evaluated the impact of removing the Gabor layer and the Distribution-Aware Fusion Module. The results are as follows:\n| Gabor | Distribution | acc    | f1    | kappa  |\n|-------|-------------|--------|-------|--------|\n| ✔     | ✔           | 0.8673 | 0.7953| 0.8266 |\n| ✔     | ✘           | 0.8613 | 0.7735| 0.8173 |\n| ✘     | ✔           | 0.8618 | 0.7683| 0.8179 |\n\nThese results demonstrate that the complete model—integrating both the Gabor layer and the Distribution-Aware Fusion Module—achieves higher overall performance. This indicates that the two components work: the Gabor layer enhances interpretability by learning EEG features aligned with expert knowledge (such as slow, delta, or theta waves), while the Distribution-Aware Fusion Module optimizes uncertainty estimation by considering the distribution of evidence. Together, they not only improve classification accuracy but also make the model’s decision-making process more transparent.\n\n**Q: It might be beneficial to further explore the hyperparameters involved in the loss function. Could you provide additional insight or analysis regarding how different hyperparameter settings might impact the performance of the model?**\n\nA: Our overall loss function is composed of three components. The first component is the accuracy loss computed from the aggregated evidence. The second component is the accuracy loss computed for each individual view, which is then weighted by β. The third component is the consistency loss, which combines two sub-losses that measure the differences in probability outputs across views and the cosine similarity of the evidence, weighted by ζ and η, and then scaled by γ in the overall loss. We conducted hyperparameter experiments on ζ and η as follows.\n| ζ | η | HD | Scene15 | CUB | PIE |\n|  ----  | ----  |  ----  | ----  |  ----  |  ----  |\n| 0.3 | 0.7 | 97.70$\\pm$0.37 | 73.47$\\pm$1.44 | 92.50$\\pm$2.17 | 96.32$\\pm$1.04 |\n| 0.4 | 0.6 | 98.00$\\pm$0.47 | 72.73$\\pm$1.37 | 94.33$\\pm$1.33 | 96.47$\\pm$1.50 |\n| 0.5 | 0.5 | 98.40$\\pm$0.37 | 72.60$\\pm$0.99 | 95.33$\\pm$1.25 | 96.47$\\pm$0.98 |\n| 0.6 | 0.4 | 98.35$\\pm$0.51 | 72.60$\\pm$1.24 | 94.67$\\pm$1.55 | 97.06$\\pm$1.80 |\n| 0.7 | 0.3 | 98.05$\\pm$0.80 | 73.22$\\pm$1.34 | 93.67$\\pm$1.80 | 95.59$\\pm$1.32 |\n\nBased on the experimental results, we can observe that the values of ζ and η do not have a significant impact on the overall performance. This indicates that while these hyperparameters play a role in balancing the consistency loss components, their precise values can be flexibly chosen according to specific application requirements without drastically affecting the results.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes, the proposed method and evaluation criteria make sense for the trusted multi-view classification.", "theoretical_claims": "Based on my check, the theoretical claims made in this paper are underpinned by a solid mathematical foundation. The authors successfully demonstrate, through rigorous proofs in Propositions 3.4 and 3.5, how their novel distribution-aware subjective opinion framework offers improved uncertainty estimation.", "experimental_designs_or_analyses": "I have checked all the experiments in the experimental section.", "relation_to_broader_scientific_literature": "The paper has a close relation to multi-view learning and uncertainty estimation.  It makes a significant contribution at enhancing interpretability and uncertainty estimation.", "essential_references_not_discussed": "The paper has included the main related works that are crucial for understanding the context and significance of their contributions.", "other_strengths_and_weaknesses": "Strengths:\n\n1. The novel integration of expert knowledge and uncertainty estimation offers clear advantages.\n\n2. The paper provides strong experimental validation and achieves the SOTA results.\n\n3. The deficiency of existing trusted multi-view methods and the superiority of the proposed method is illustrated by example. Overall, the organization of paper is coherent and easily understood.\n\nWeaknesses:\n1. Could you clarify why certain Gabor kernel outputs are considered redundant during the training process? Are there any strategies for improving kernel optimization?\n2. It would be beneficial to include ablation experiments where different components of the model are removed or modified, such as removing the Gabor layer or other key modules. This would help quantify the contribution of each part of the model to the overall performance.\n3. It might be beneficial to further explore the hyperparameters involved in the loss function. Could you provide additional insight or analysis regarding how different hyperparameter settings might impact the performance of the model?", "other_comments_or_suggestions": "See weaknesses", "questions_for_authors": "See weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ItgBhwvx37", "reviewer": "Reviewer_YxMg", "summary": "This paper proposed a novel trusted multi-view classification method, called TMCEK. Compared with the existing trusted multi-view classification methods, TMCEK embeds the Gabor function into the first convolutional layer as its kernel to enhance feature-level interpretability. Moreover, it introduces a distribution-aware subjective opinion mechanism to derive more reliable and realistic confidence estimates. The TMCEK obtains state-of-the-art results against compared SOTA methods, especially providing an interpretability feature map aligned with humans.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are sincerely grateful to the reviewer for dedicating their time and effort to review our work. Below are our responses.\n\n**Q: The use of Gabor kernels for feature extraction at the first convolutional layer is a key feature of the model. Could you provide further details on how the Gabor kernels are optimized during training and how they compare to other common feature extraction techniques regarding their impact on sleep stage classification?**\n\nA: We are sincerely grateful to the reviewer for dedicating their time and effort to review our work. The Gabor kernels are embedded in the first convolutional layer, where their parameters are jointly optimized with the rest of the network via backpropagation. Their design aligns with expert knowledge of EEG waveforms, with some kernels learning to match critical patterns such as slow waves, delta, or theta rhythms that are key in sleep staging.\n\nIn contrast to standard convolutional kernels that are learned from scratch without any explicit domain bias, Gabor kernels offer enhanced interpretability—since their waveform shapes can be directly compared to known EEG characteristics—and guided feature extraction by acting as filters tuned to critical frequency bands. \n\nExperimental results indicate that this guided approach not only yields competitive classification performance but also improves the model’s interpretability, as demonstrated by our attribution analysis.\n\n**Q: The paper employs attribution maps to analyze the importance of the Gabor kernels. Clarify and extend the explanation of the saliency map method. A more detailed background on this attribution technique would help readers, particularly those not familiar with this approach, to fully appreciate its significance in your model’s interpretability.**\n\nA: We use saliency maps to interpret the role of individual Gabor kernels in decision making by computing the gradient of the output (or evidence) with respect to the feature maps from the Gabor layer. This approach relies on two key ideas: sensitivity analysis, where regions or kernels that cause large changes in the output when perturbed are deemed more important, and visual attribution, which allows us to directly visualize which kernel responses contribute most to a specific classification. \n\nAttribution maps are generated by backpropagating the gradient information through the network, effectively highlighting the areas that have the highest impact on the final decision. This method not only enhances transparency by linking specific kernel activations to decision outcomes but also bridges the gap between black-box deep learning models and expert interpretability requirements. \n\nFor readers less familiar with attribution methods, this technique is well-documented (see, e.g., Ancona et al., 2019) and serves as a powerful tool to validate that kernels corresponding to critical EEG patterns—such as slow waves or theta waves—are indeed influential in the sleep staging decision.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes, the proposed method makes sense for the problem at hand.", "theoretical_claims": "I have checked the correctness of all proofs for theoretical claims. The theoretical claims regarding the uncertainty estimation mechanism are solid and well-supported by mathematical analysis. The authors present a rigorous derivation that clearly shows how their distribution-aware subjective opinion framework enhances uncertainty quantification compared to traditional methods. The proofs provided for Propositions 3.4 and 3.5 are mathematically sound and logically consistent. Overall, there are no apparent issues with the correctness of these proofs.", "experimental_designs_or_analyses": "The experimental designs for evaluating the proposed model involve five aspects: performance comparison, each module effectiveness, hyper-parameter sensibility, interpretation and robustness. I think that the experimental designs are solid and the results are sufficient for supporting their claims.", "relation_to_broader_scientific_literature": "This work improves the trusted multi-view classification from two aspects: (1) feature-level interpretability by embedding expert knowledge and (2) more reliable and realistic confidence estimate by incorporating the distribution of evidence. These contributions are completely innovative.", "essential_references_not_discussed": "The paper has covered and discussed the essential references.", "other_strengths_and_weaknesses": "Strengths:\n1. The expert knowledge is applied to the trusted multi-view classification, which is a fresh view to trusted multi-view classification. \n2. The work finds a new problem that the subjective opinion is distribution-unaware and defines distribution-aware subjective opinion by incorporating the distribution of evidence.\n3. Compared with exiting methods, the paper not only achieves state-of-the-art results, but also provides a confident degree and Gabor kernel aligned with human domain experts for decision results.\n\nWeaknesses:\n1. The use of Gabor kernels for feature extraction at the first convolutional layer is a key feature of the model. Could you provide further details on how the Gabor kernels are optimized during training and how they compare to other common feature extraction techniques regarding their impact on sleep stage classification?\n2. The paper employs attribution maps to analyze the importance of the Gabor kernels. Clarify and extend the explanation of the saliency map method. A more detailed background on this attribution technique would help readers, particularly those not familiar with this approach, to fully appreciate its significance in your model’s interpretability.", "other_comments_or_suggestions": "Please See the Weaknesses", "questions_for_authors": "Please See the Weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bws9B93KAg", "reviewer": "Reviewer_YgiK", "summary": "This paper introduces an innovative trusted multi-view classification approach designed to tackle the significant shortcomings of existing methods, namely, opacity at the feature level and imprecise confidence assessments at the decision level. Its primary contribution resides in advancing current trusted multi-view classification techniques by bolstering interpretability at the feature level and refining uncertainty estimation. This enhanced framework is subsequently applied to sleep stage classification tasks. The proposed methodology demonstrates superior performance compared to state-of-the-art (SOTA) methods across multiple sleep stage classification datasets.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the feedback and suggestions. Below are our responses.\n\n\n**Q: In regards to the lower classification performance observed for the N1 stage (Figure 4), have the authors investigated methods to mitigate class imbalance or improve classification accuracy for this specific stage?**\n\nA: Regarding the lower classification performance observed for the N1 stage, our paper takes sampling strategy to alleviate the challenges posed by the unbalanced distribution of classes (in Appendix A.6). During training, batch samples are randomly selected from the training subset using normalized probabilities that are inversely proportional to the number of samples in each class. This ensures that underrepresented classes such as N1 are more likely to be included in each batch, thereby mitigating class imbalance.\nOn the Sleep-EDF20 dataset, we use one fold to verify the effectiveness of the sampling strategy.\n| Method    | acc    | f1     | kappa  | wake_f1 | n1_f1  | n2_f1  | n3_f1  | rem_f1 |\n|----------|--------|--------|-------|--------|-------|-------|-------|-------|\n| Sample   | 0.8674 | 0.7953 | 0.8266 | 0.9254 | 0.4035 | 0.8883 | 0.9246 | 0.8347 |\n| No Sample| 0.8725 | 0.7672 | 0.8312 | 0.9288 | 0.2532 | 0.8943 | 0.9313 | 0.8285 |\n\n\nFrom the results, we can observe that the sampling strategy effectively mitigates the class imbalance issue by significantly boosting N1 classification performance, leading to a better overall balance (as reflected by the macro F1-score), even though there is a slight reduction in overall accuracy and kappa.\n\n**Q: The paper utilizes the Gini coefficient to measure evidence concentration. Have the authors considered alternative methods, and what potential implications might these alternatives have on the overall results?**\n\nA: Regarding the Gini coefficient used for measuring evidence concentration, we recognize that alternative measures—such as entropy or variance—could be explored. Each measure might bring different sensitivity characteristics in uncertainty estimation. For instance, entropy may offer a more nuanced view of dispersion; however, the theoretical properties of the Gini coefficient, as analyzed in our propositions, provide clear advantages in our framework. Future work will examine these alternatives to assess their potential impact on both uncertainty quantification and overall performance. We replaced the method on the multi-view dataset. In the experiment, we fixed the loss weight $\\\\beta$ to 0.5 and $\\\\gamma$ to 0.5. The experimental results are as follows.\n| Method | HD| Scene | CUB | PIE |\n|  ----  | ----  |  ----  | ----  |  ----  |\n| Gini      | 98.40 $\\pm$ 0.37 | 72.60 $\\pm$ 0.99 | 95.33 $\\pm$ 1.25 | 96.47 $\\pm$ 0.98 |\n| Var       | 98.15 $\\pm$ 0.51 | 72.42 $\\pm$ 1.24 | 93.00 $\\pm$ 2.56 | 96.76 $\\pm$ 1.19 |\n| Entropy| 97.75 $\\pm$ 0.65 | 67.09 $\\pm$ 1.21 | 94.00 $\\pm$ 1.62 | 94.41 $\\pm$ 2.01 |\n\nThese results suggest that the theoretical properties of the Gini coefficient offer a robust measure for capturing evidence dispersion, which in turn contributes to better uncertainty estimation and overall performance.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "I have checked the correctness of all proofs for Propositions 3.4 and 3.5 in Sec. A.1 and A.2. They are clearly articulated and mathematically rigorous, leaving little room for doubt about the soundness of the theoretical claims.", "experimental_designs_or_analyses": "I have verified the robustness and validity of the experimental designs and analyses. The designs encompass a thorough evaluation, including performance benchmarks against previous state-of-the-art (SOTA) methods, assessments of individual module effectiveness, an analysis of hyperparameter sensitivity, interpretability, and robustness.", "relation_to_broader_scientific_literature": "The paper is related to trusted multi-view learning‌. Its core contribution lies in ‌enhancing existing trusted multi-view classification through improved feature-level interpretability and uncertainty estimation‌, ‌and extending it to sleep stage classification task.", "essential_references_not_discussed": "The paper has discussed the essential references.", "other_strengths_and_weaknesses": "Strengths:\n\n--The paper provides enhancements in both performance and interpretability.\n--The integration of expert knowledge with uncertainty estimation represents a notable contribution. To my knowledge, this is the pioneering work in applying trusted multi-view classification to sleep stage classification, marking a practical application.\n\nWeaknesses:\n\n--In regards to the lower classification performance observed for the N1 stage (Figure 4), have the authors investigated methods to mitigate class imbalance or improve classification accuracy for this specific stage?\n--The paper utilizes the Gini coefficient to measure evidence concentration. Have the authors considered alternative methods, and what potential implications might these alternatives have on the overall results?", "other_comments_or_suggestions": "I have not any other comments or suggestions here. see Strengths and Weaknesses", "questions_for_authors": "see weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EFIHhSrTjE", "reviewer": "Reviewer_x8HD", "summary": "This paper proposes Trusted Multi-View Classification with Expert Knowledge Constraints (TMCEK). There are core contributions: (1) Integrating expert knowledge into multi-view learning to enhance both interpretability and uncertainty estimation, and (2) proposing a novel distribution-aware subjective opinion framework that extends the conventional model through the incorporation of an evidence distribution concentration measure. Finally, the effectiveness of TMCEK is validated on sleep stage classification, outperforming existing models in both classification accuracy and interpretability.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive and encouraging comments. Below are our responses.\n\n**Q: The paper presents the method primarily for sleep staging, but there is limited discussion on how this method might generalize to other domains.**\n\nA: Thanks for your professoional question. While our method is demonstrated for sleep stage classification, the underlying framework of integrating expert knowledge through Gabor-based feature extraction and a distribution-aware subjective opinion mechanism is **general**. \nIn any application where domain-specific patterns are critical (e.g., medical imaging, speech recognition, or remote sensing) , one could parametrize them and tailor the initial kernel functions or expert constraints accordingly. \n\nFor example, our framework can be effectively applied to image classification by adapting its core components to process image data. In this setting, the first convolutional layer is replaced with 2D Gabor filters, which are designed to capture edges, textures, and other structural patterns in images. These Gabor kernels can be initialized with parameters informed by expert knowledge—such as preferred orientations, scales, and frequencies that are known to highlight important features in images—and then fine-tuned through backpropagation during training. This results in a feature extraction process that is both interpretable and closely aligned with domain-specific patterns.\nAdditionally, our framework employs a distribution-aware subjective opinion mechanism to estimate uncertainty. In image classification, this mechanism quantifies not only the overall evidence supporting each class but also the dispersion of that evidence, allowing for a more reliable estimation of confidence in the predictions. \n\nHowever, we acknowledge that in certain domains lacking sufficient domain-specific expert knowledge or clearly defined feature representations, our framework may not be fully applicable.\n\n**Q: The paper compares the proposed TMCEK model to various existing multi-view methods like EDL and RCML. Could you provide more details on how the distribution-aware subjective opinion mechanism improves uncertainty estimation compared to traditional methods?**\n\nA: Traditional uncertainty estimation methods, such as those based on Evidential Deep Learning (EDL), rely primarily on the overall sum of evidence, making them insensitive to its distribution across classes. To address this, our distribution-aware subjective opinion mechanism incorporates an explicit measure of evidence concentration using the Gini coefficient. This dual consideration of both magnitude and distribution improves sensitivity by assigning higher uncertainty when evidence is more concentrated, even if the total sum remains constant, and enhances conflict resolution by adjusting the fusion rule to weight each view’s contribution based on evidence dispersion. \n\nMorever, theoretical analysis (see Propositions 3.4 and 3.5 in our paper) and experimental results demonstrate that this approach leads to more reliable confidence estimates, particularly in scenarios with ambiguous or noisy data.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes. The proposed method and evaluation criteria make sense for the problem.", "theoretical_claims": "I have checked the correctness of Proposition 3.4 and Proposition 3.5. The algebraic steps in Appendices A.1–A.2 are clear and free of errors, demonstrating the framework’s mathematical validity. This theoretical foundation directly supports the empirical results, reinforcing the method’s reliability.", "experimental_designs_or_analyses": "The experimental setup is comprehensive, with evaluations on multiple datasets and comparisons against a variety of baseline models. The experiments are well-designed, but the testing data distribution and the specifics of how the datasets were divided could benefit from more clarity.", "relation_to_broader_scientific_literature": "The paper contributes to the broader field of multi-view learning and uncertainty estimation. It builds on previous work in trusted learning and expert knowledge integration. The authors effectively position TMCEK within the context of related literature, referencing key studies on multi-view learning, evidence theory, and sleep stage classification.", "essential_references_not_discussed": "The authors have cited the essential related works for understanding the key contributions of the paper.", "other_strengths_and_weaknesses": "Strengths:\n1.The framework is innovative, combining interpretability and performance improvement.\n2.The use of expert knowledge through Gabor kernels enhances model transparency.\n3.The promising results, particularly in the context of sleep disorder diagnosis, are crucial in areas where trust and transparency are essential. The paper's strong demonstration of the method's performance across multiple datasets further adds to its impact. \n4.The paper is well-written and structured, offering a clear and thorough explanation of both the methodology and results. \nWeaknesses:\n1.The paper presents the method primarily for sleep staging, but there is limited discussion on how this method might generalize to other domains.\n2.The paper compares the proposed TMCEK model to various existing multi-view methods like EDL and RCML. Could you provide more details on how the distribution-aware subjective opinion mechanism improves uncertainty estimation compared to traditional methods?", "other_comments_or_suggestions": "Some symbols like d lack a proper explanation in the context.", "questions_for_authors": "1.The paper presents the method primarily for sleep staging, but there is limited discussion on how this method might generalize to other domains.\n2.The paper compares the proposed TMCEK model to various existing multi-view methods like EDL and RCML. Could you provide more details on how the distribution-aware subjective opinion mechanism improves uncertainty estimation compared to traditional methods?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a framework that enhances multi-view classification by integrating expert knowledge (via Gabor filters) and a novel distribution‐aware subjective opinion mechanism. The proposed method is motivated by theoretical proofs and is validated on sleep stage classification datasets. All four reviewers provided an overall recommendation of 4 (Accept), with their feedback converging on the novelty of the contributions, the clarity of the experimental design, and the potential impact on both interpretability and uncertainty estimation in safety-critical applications.

Overall, this work represents an advancement in both trusted multi-view classification and interpretable uncertainty estimation, with potential impact on safety-critical applications. Based on the strength of the contributions, the comprehensive experimental validation, and the satisfactory addressing of all major concerns during the rebuttal phase, the meta-review recommends acceptance of the submission. Minor revisions are encouraged to further refine the kernel optimization explanations and broaden the generalizability discussion.
Decision: Accept (spotlight poster)