Trusted Multi-View Classification via Evolutionary Multi-View Fusion
Authors: Xinyan Liang
Pinhan Fu
Yuhua Qian
Qian Guo
Guoqing Liu
Venue: ICLR 2025 Poster (2025)
Keywords: Trusted multi-view classification
NAS-based multi-view classification
evolutionary multi-view fusion
multi-view learning
Primary area: other topics in machine learning (i.e., none of the above)

Abstract: Multi-view classification based on the Dempster-Shafer theory is widely recognized for its reliability in safety-critical domains with multi-view data. However, the adoption of a late fusion strategy constrains information interaction among views, thereby leading to suboptimal utilization of multi-view data. A recent advancement addressing this limitation involves generating a pseudo view by concatenating individual views. Yet, the efficacy of this pseudo view may diminish when incorporating underperforming views like noisy views. Additionally, the integration of a pseudo view exacerbates the issue of imbalanced multi-view learning, as it contains a disproportionate amount of information compared to individual views.  To address these issues, we propose the enhancing Trusted multi-view classification via Evolutionary multi-view Fusion (TEF) approach. TEF employs an evolutionary multi-view architecture search method to create a high-quality fusion architecture serving as the pseudo view, facilitating adaptive view and fusion operator selection. Furthermore, TEF enhances each view within the fusion architecture by concatenating the fusion architecture's decision output with its respective view. Our experimental results demonstrate the effectiveness of this straightforward yet powerful strategy in mitigating imbalanced multi-view learning issues, particularly on complex many-view datasets exceeding three views. Extensive evaluations across 13 multi-view datasets validate the superior performance of our proposed method compared to other trusted multi-view learning approaches. The code is available at https://github.com/fupinhan123/TEF.

Published as a conference paper at ICLR 2025
TRUSTED MULTI-VIEW CLASSIFICATION VIA EVOLU- TIONARY BULTI-VIEW FUSION
Xinyan Pinhan Fu', Yuhua Qian' Qian Guo?, Guoqing Liu'
1 Institute of Big Data Science and Industry, Key Laboratory of Evolutionary Science Intelligence of Shanxi Province, Shanxi University
2 Shanxi Key Laboratory of Big Data Analysis and Parallel Computing,
School of Computer Science and Technology. Taiyuan University of Science and Technology {1 1liangxinyan48, fupinhan15 68, ezquoqian, guw.inguiiigggoo e 63. com jinchengqyh@ 126. com
ABSTRACT
Multi-view classification based on the Dempster-Shafer theory widely recog- nized for its reliability in safety-critical domains with multi-view data. However, the adoption of a late fusion strategy constrains information interaction among views, thereby leading to suboptimal utilization of multi-view data. A recent ad- vancement addressing this limitation involves generating a pseudo view by con- catenating individual views. Yet, the efficacy of this pseudo view may diminish when incorporating underperforming views like noisy views. Additionally, the in- tegration of pseudo view exacerbates the issue of imbalanced multi-view learn- ing, as it contains disproportionate amount of information compared to individ- ual views. To address these issues, we propose the enhancing Trusted multi-view classification via Evolutionary multi-view Fusion (TEF) approach. TEF employs an evolutionary multi-view architecture search method to create a high-quality fu- sion architecture serving the pseudo view, facilitating adaptive view and fusion operator selection. Furthermore, TEF enhances each view within the fusion archi- tecture by concatenating the fusion architecture's 's decision output with its respec- tive view. Our experimental results demonstrate the effectiveness of this straight- forward yet powerful strategy in mitigating imbalanced multi-view learning is- sues, particularly on complex many-view datasets exceeding three views. Exten- sive evaluations across 13 multi-vier datasets validate the superior performance of our proposed method compared to other trusted multi-view learning approaches. The code is available at
com/
INTRODUCTION
Multi-view classification (MVC) endeavors to construct classifiers utilizing multi-view data, wherein each sample is characterized by multiple groups of feature sets (Liang et al. 2022; Wen et al. 2024| Jiang al. 2024 Zhang al. [2024a] Lyu et al. 2022bb Jiang et al. 2021) Notably, plethora of methodologies has been proposed in this domain. Among these, trusted multi-view clas- sification (TMVC) methods (Xu et al. 2024 Liu et al. 2023) deviate from conventional approaches by leveraging distinct views at the level of evidence rather than focusing solely on features. They have garnered significant application across various safety-criticll medical diagnostic fields, includ- ing retinal anomaly identification (Wang et al. 2023), eye disease screening (Zou et al. 2023). and
medical image classification (Xu al.] 2022).
However, the adoption of a late fusion strategy restricts the interaction of information among views, leading to suboptimal utilization of multi-view data. To address this limitation Haaitaationaannnnn al. (2023) proposed an enhanced trusted multi-view classification (ETMC). ETMC augmented their pioneering work on Trusted Multi-view Classification (TMC) (Han et al.) (02T) by introducing pseudo view obtained through the concatenation of individual views, thereby enriching it with complementary
Equual contribution Corresponding author

---

Published as a conference paper at ICLR 2025
Existing methods
Ours
Suhoptimized
(e)
Pacudo view gencration
Perado view
pseudo view
View
View
New
NAS
View
View
View
View
Imbalameed views
(d)
guided by pocadd view
View
View 1
View
Trusted
View Pahance men
View
View 2
View 3 View
TAKC
TNVC
View 3
View 4
Vieen 4
(Pxendn
Pseudo view.
klow
view
Higher-quality views
Lower-quality views
Enhanced views
Fusion operators (differrnt colors denote different fusion operaturs)
Figure 1: Two issues of existing trusted multi-view learning and our solutions.
information. Yet, real-world multi-view data often suffer from noise or uncertainty due to complex- ities in data collection and transmission (Zhou et al., 2023). Additionally, each view may have its own feature or distribution, in some cases, the data in each separate view may not be compatible with the other. Obviously, if fusion approach is unable to cope appropriately with multiple views, the obtained pseudo view may be suboptimized when incorporating underperforming views. This issue is illustrated in Fig. aa) where the classification accuracy of the pseudo view is lower than the view 3. The similar results on experimental multi-view datasets can be observed by comparing the accuracy of pseudo views from Table with one of best view (BV) from Table 3 Regrettably, the pseudo view generation strategy of ETMC is susceptible to negative influences from noisy or corrupted views in certain real-world scenarios.
Morcover, as shown in Fig. [bb, the pscudo view inherently contains a disproportionate amount of information compared to individual views. The phenomenon referred to as imbalanced views. Recent study (Peng et al.) (202)) has shown that the multi-view models learn on imbalanced views may be suboptimized evens fail outperform its uni-view counterpart due to view with better per- formance contributes to lower whole loss then dominates the optimization progress via propagating limited gradient over the other view. To our knowledge, the exiting pseudo- seaudo-view-guee view-guided trusted multi-view learning have not yet paid attention this issue, limiting their performance. In addition, the predominant approach to tackling imbalanced multi-view learning involves the manipulation of
gradients and they are often challenging technique use (Wei et al. 2024 Wang al. 2020).
To address these issues, we propose the enhancing Trusted multi-view classification via Evolu- tionary multi-view Fusion (TEF) approach. Specifically, as shown in [ig TEF introduces an evolutionary multi-view architecture search method to generate high-quality fusion architecture serving as the pseudo view, enabling adaptive selection of views and fusion operators. To mitigate the imbalanced multi-view learning problem, each view within the fusion architecture is enhanced by concatenating the decision output of the fusion architecture with its respective view shown in d). With the two simple but effective techniques, the potential of trusted multi-view classifi- cation significantly unleashed, particularly on complex many-view datasets featuring more than three views compared to its counterparts. Notably, compared to gradient-basee NAS that requires predefined search space and substantial memory, and reinforcement learning- NAS that relies on extensive computational resources, evolutionary NAS offers advantages such as global search ca- pability, flexibility, and parallelization (Liang et al. 2021 Fu et al. 2025). This makes it particularly suitable for handling complex multi-view tasks and large search spaces. The issue of time consump- tion for TEF will be discussed and addressed in the experimental section 4.2 The contributions of this paper are:
2

---

Published as a conference paper at ICLR 2025
The pseudo view generation is formulated as population- based multi-view neural archi- tecture problem where the higher-quality views can be automatically selected and fused with selected some fusion operators from candidate fusion operator set.
From the perspective of view enhancement, we propose simple yet effective strategy to deal with the issue of imbalanced multi-view learning that is raised by a disproportionate amount of information between pseudo view and individual views.
Extensive evaluations across 13 multi-view datasets validate the superior performance of our proposed method compared to other trusted multi-view learning approaches.
2 RELATED WORK
Multi-view classification (MVC): MVC methods can be divided into early fusion and late fusion
Guo et al. 2024); Lyu et al. 2024a Zhang et al. (2024b). Early fusion combines data from dif- ferent views at the initial stage to form a unified representation before inputting it to the classifier. Techniques include element- wise addition, multiplication, and feature concatenation, along with ad- vanced operators like MLB (Kim et al. 2017), MFB (Yu et al., 2018), TEN (Zadeh et al.) (017), LMF (Liu et al. 2018), and PTP. This approach fully utilizes information from all views but may suffer from dimensionality issues and redundancy. Late fusion processes each view independently and merges the outputs of multiple classifiers using methods like majority voting and weighted av- eraging- It offers strong model flexibility and reduces view interference but has higher decision fusion complexity. Early fusion focuses on feature-level integration, while late fusion emphasizes decision-level integration, each with its own strengths and weaknesses. As shown in Fig. [ our TEF possesses their strengths by achieving early fusion and late fusion at the stage and the stage respectively.
Trusted multi-view classification (TMVC) TMVC, a late-fusion method, stands out for its ability integrate diverse views based on their respective trustworthiness,, quantified through the Dempster- Shafer theory (Xu et al., 2024 Liu et al. 2023). A typical example is TMC (Han et al. 202T) which involves Dempster's 's combination rule that assigns smaller weights to highly uncertain views. Fol- lowing this approach, various opinion aggregation methods have been proposed (Liu et al.) [202]] Han et al. 2023). Recent studies have highlighted that a significant feature of previous methods that the uncertainty mass decreases after integrating another opinion into the original one. Re- cently, RCML. introduced the idea that uncertainty should increase when incorporating unreliable conflicting opinions. To address this, RCML (Xu al. 2024) proposed a conffictive opinion aggregation strategy and thcoretically proved that uncertainty increases for confficting instances. TMVC methodologies differ from traditional approaches by leveraging distinct views at the idence level rather than focusing solely on features. The utilization of the variational Dirichlet distribution is pivotal in modeling the distribution of class probabilities. This distribution, parame- terized with evidence gleaned from diverse views, facilitates the integration of evidence through the interpretable framework of the Dempster-Shan Shafer theory. This strategic shift yields more stable and reasonable estimation of uncertainty, thereby enbancing the reliability and robustness of classifica- tion outcomes. Although they have shown great potential for widespread adoption -afetty-rriiccl domains, they sometimes fail to outperform non-trusted multi-view classification method even uni- view counterpart due the limited interaction among views and imbalanced issue among views.
3 METHOD
The enhancing trusted multi-view classification via evolutionary multi-view fusion (TEF) approach consists of two stages: (1) obtaining high-quality fusion architecture as pseudo view with neu- ral architecture search, and (2) balanced and trusted fusion driven by enhanced pseudo view. Its overview is illustrated in Fig.
3.1 PSEUDO VIEW GENERATION
The research conducted by Han et al. 2023 underscores the significance of pseudo views in aug- menting the performance of TMC method. Particularly, early interaction among views is identified critical factor in this enhancement. To refine the quality of pseudo views, we advocate for
3

---

Published as a conference paper at ICLR 2025
Stage 1: Pscudo view generation
Mutation
Berrinariedd
Fuilon
svaliation
Iniiiakze pegulation
Pojulaiion
Selection
Evidence multi-view neural network
Ar MK MTai,, Baure Bao
Evidence Kejel tol
Pscudo View
cennraain
Subjection opinious
Sorktierdistibutie o' dhl
DE Subjection spiainus
Evidence DNN
Viaw 2
Evidence DNN
f cominini
Mi N² "ib,, Baoros Buo
View
Subjection opiniam:
Dirihlet distribtiin chujelenhmeel
[2) D2
View set:
Stage Balunced trusted fasion
Figure 2: The overview of TEF
an automated approach. Our proposition involves framing the pseudo view generation process as multi-view neural architecture search task within the evolutionary computation paradigm. This methodological framework holds promise for eliciting superior pseudo views, thus offering a path- way further elevate the efficacy of the trusted multi-view learning.
Specifically, let V denote the of views and F represent the of fusion operators (see A.2). These sets collectively define multi-view neural architecture space, denoted as H. Within our framework, each multi-view classi- fication model h from H corresponds an individual the evolutionary computation framework. It can be encoded multiple forms like tuple or tree. The study on individual encode is out of scope of our work. Here, we take a tuple form for example to illustrate the process of encoding and de- coding. Comparable results between different forms can be found in Section (A.5 in the appendix. Notably, h can be encoded as tuples = [U. f], where e = jui, U2 ... [7]] represents / used views, [f1, f2.... fi-1] denotes the utilized fusion schemes, and and fi are element from V and F, respectively.
Multi-view classification model encoding and individual decoding:
Each individual chromosome vector be decoded to multi-view classification model h that takes V = [U,, 022- ... my] as its input. Specifically, each o; first transferred to u, by a fully connected layer and then Relu function. Next fuse 21, 22, 21 in simple yet effective behavior:
(1(1)))))
if 1, 11-
ifie 2,, 2......... G = (4)))1)44))
To alleviate the issue of wide fluctuations in the fused vector values due to different fusion operator usage in the process of fusion, we normalize with the following process (Liang et al. 2021)
f- sigu(c) Vll
(2)
c - T
(3)
where sign denotes the sign function. Eq. (2) represents Power Law Normalization, while Eq. denotes L2 Normalization. The effectiveness of this strategy has been validated many works (Liang et al. 2021). Lastly, transfer to probability vector by fully connected layer and softmax function. The optimization objective adopts cross entropy loss and is defined as:
N
K
Loe
Yek log yik-
(4)
N

---

Published as a conference paper at ICLR 2025
where N is the number of the examples, K is the number of the categories, Yik is if the 1th example belongs to ktth category, otherwise, and yix is the prediction probability that the 7th example belong to hthh category, which is the output of the softmax layer.
Optimization: Our pseudo view, conceived as a multi-view neural architecture rather than a sin- gular fusion vector, serves pivotal element in approach. The optimal pseudo view can be autonomously searched via an evolutionary computation method. This search method, detailed in Alg. | encompasses population initialization, fitness evaluation, offspring generation, and selection, facilitating the systematic exploration and refinement of multi-view neural architectures.
In the initial stage of our evolutionary algorithm, population initialization involves randomly gen- erating N individual chromosome vectors, each potentially having a distinct value for k. Subse- quently, the fitness of each chromosome vector p within the population assessed by decoding into a multi-view classification model. This model is trained on multi-view dataset and its classi- fication accuracy is measured on separate validation set, serving as the fitness metric for p. More details can be found in Section A.7 in the appendix.
3.2 BALANCED AND TRUSTED FUSION
This part aims to make better trusted making-decision by jointly fusing the all views and the generated pseudo view. nature idea directly pass each view into an evidence-basee classi- fier (Sensoy et al. 2018). Yet, the pseudo view inherently contains a disproportionate amount of information compared to individual views. Thus, its integration exacerbates concerns regarding im- balanced multi-view learning (Peng et al., (022). We proposed a very effective solution by adding the output into the selected views. Specifically, our trusted fusion works as follows:
(1) View enhancement: Let h be the optimal multi-view fusion model searched via Alg, and its output is denoted as houe. We enhance each view in h by concatenating it with houe, denoted as [u,, hout], producing T = [[v hont], (02, h hou]] .... [bk, houf]]
(2) Evidence collection: Let E = [e1, 62. .e]] be the evidences where each element eg is the k- th category evidence and its value is larger than O. Then it can be obtained by replacing the softmax activation function with the Softplus activation function:
E Softplu((Fou),
(5)
where pouu is the last layer of the backbone. It is noted that the backbone of the enhanced pscudo view is h but its takes 6P input instead of v.
(3) Dirichlet distribution calculation: Let a = [an, ....... axk be the concentration parameters of one Dirichlet distribution where each element 0g is the k-th catagory Dirichlet distribution parame- ter and can be obtained via
a ek + 1.
J = [M1, U2: .K]] be the mean of the corresponding Dirichlet distribution, its each element J computed as
S
where S= E ag is the Dirichlet intensities. Then the probability density function of the Dirich- let distribution is given by:
K
Dir(ula) = B(a)
1
a-1
(8)
where B(a) is the K-dimensional multinomial beta function.
(4) Subjective opinions calculation. Let be set of belief masses and u is its corresponding uncertainty score. Then the subjective opinion M can be represented as
M = [b. u),
where b b2,, b.. bx) where each element by is the belief mass. Let S -EK ag be the Dirichlet intensities. Then b, and be obtained by
5

---

Published as a conference paper at ICLR 2025
OK
K S
bg
16
(10)
5
S
can seen from Eq. evidence for category k.
10 the probability assigned to category k is proportional to the observed
(5) Fusion: Let M M M M and M be (V+ opinions obtained from V views and the pseudo view. Then the trusted fusion is conducted via
M = e Y M' M
(11)
where @ denotes the Dempster's combination operator for K -Class classification. Various imple- mentation modalities are available like (Xu et al. 2024 Liu al. 2023 Han al. 2023). To show the advantage of our framework, we adopt its one simple implementation form from (Han et al. 2023). Specifically, given two opinions M [b], 02....... .ix, w"I and M = |/ b2
bg u DK uj:
we do the following fusion calculation to generate the combination opinion M [b,, b2
1 C u'u?
bE
(bbbg b/u² bgu' ) u
(12)
where Eitf 6..33.
(6) Probability of each class induction: With the Eq. class and the overall uncertainty via
10 we can get the final probability of each
K S
Ck by x S.
(13)
Optimization: The objective function is
N
M
N
N
L
m
Un)
+
Dpscddo ( (Irm m= Vn)
Σ
M fused ((2m Im=1 Un),
(14)
1=1
1=1
1M where T. (." ,y). peeeddo (-e 1m=11 Vn.) and Iufused are the variational loss functions for the m-th view, the pseudo view and final decision, and their definition are follows
I. Fay (am) poseuoo (in (ogg - X, (,.,,, (15)
"d""
1])]
fased Le (ogg -Dtpa////oooiiii----DDDDDDUUUAnD (DDDDDi
where de balances the expected classification error and KL regularization,
K
(ogppylll F logrlull)" =
Σ
yk (s (16)
TOCK K k= 2x)
K
K
DKL [Dir(p" [ [1.... 1))] log( [(K) ITK [(āu)
)+ ++
(d)=1)((b(a))
-b6
Σ
a,)]
Am
==1
(17)
where 43 (1""">>"" a probabilistic encoder with parameters d (.)) and T(.) are the digamma
function and gamma function, respectively; yk is the k-th element of that is onehot vector. 5 Ek= of is the Dirichlet distribution (1"")""))) âmm y + (1 y) @ " is the adjusted parameter of the Dirichlet distribution to prevent penalizing evidence of the groundtruth class to 0.
K
The optimization process for the proposed model is summarized in Alg.

---

Published as a conference paper at ICLR 2025
4 EXPERIMENTS
In this section, we aim to validate the effective of TEF from six aspects: (1) Comparison with trusted multi-view classification methods, (2) comparison with other state-of-the methods, (3) impact analysis of different fusion strategies on pseudo-view quality, (4) impact analysis of different pseudo-view generation methods on TEF, (5) impact analysis of different strategies to address view imbalance, and (6) computation time analysis. Moreover, we offer more in-depth analysis for our TEF by conducting more ablation experiments. These results can be found in the appendix A.5
4.1 SETUP
We briefly present the experimental setup here, including the experimental datasets, evaluation met- rics, model selection, and comparison methods.
Datasets. In our experiments, we cover six datasets with multiple views, namely Animals with Attributes (AWA), NUS-WIDES 128 (NUS). Reuters, MVoxCeleb, and YoutubeFace. For the Reuters dataset, we generate two versions by adding Gaussian noise, named Reuters5 and Reuters3. AWA and NUS contain seven views each, while Reuters, VVxCelee, and YoutubeFace have five views. For more detailed descriptions of the datasets, please refer the appendix [A.3]
Evaluation metrics. In the experiment, to avoid the randomness caused by data partitioning and network initialization, we adopted a 5-fold cross-validation strategy within the overall framework, dividing each dataset into training and testing sets. Notably, during the evolutionary search for the pseudo-view architecture, the training set was further split into a training set and a validation set to prevent data leakage. We reported the average performance and standard deviation across five data partitions. To evaluate the performance of TEF, we used five commonly used evaluation metrics: accuracy (AC), precision (PF), recall (RE), F1 score, and Kappa (K). Higher values of these evaluation metrics indicate better performance. All metrics were measured on single P100 GPU. For more detailed information about the experimental environment, please refer to Appendix A.4
Comparison methods. We compare TEF with three categories of multi-view classification meth- ods (MVCs): (1) Trusted MVCs: For example, TMC, which integrates multi-view information at an evidence level using the Dempster-Shafer theory in learnable manner. TMOA integrates multi- view information at an evidence level using opinion aggregation. ETMC improves upon previous methods by adding a pseudo view containing complementary information from multiple views and simply concatenating the original features. RCML fuses view-specific opinions consisting of deci- sion results and reliability using conflictive opinion aggregation strategy and simple and effective average pooling fusion. (2) Other nate-of-theear MVCs: such as BV, SSV, MR, EmbraceNet, AWDR, RMA., and DC-NAS (Liang al.) 2024). (3) Various multi-view fusion strategies include- ing five basic fusion operators: sum, mean, max pooling, product, and concatenation as well as five advanced fusion operators: MLB, MFB, TFN, LMF, and PTP. For detailed description of these methods, please refer to the appendix A.
4.2 EXPERIMENTAL RESULTS
Comparison with trusted multi-view classitication methods. According to the results in Table 1 TEF demonstrates significant advantages over various advanced trusted fusion methods across live metries on six datasets. For instance, in the AWA, NUS, and VoxCeleb datasets, TEF achieves approximately 4.09%, 2.07%, and 3.71% accuracy improvements, respectively, compared to the second-ranked model. This is attributed the effective implementation of feature-level information interaction achieved by the high-quality pseudo views obtained through adaptive selection. This approach addresses the issue of view imbalance caused by high-quality fusion views, thereby en- hancing the model's learning capability. This has been validated in the ablation study.
Comparison with other state-of- sfate-of-the-art (SOTA) methods. We further compare the TEF with other SOTA methods including BV, SSV, MR, EmbraceNet, AWDR, RMAR, and DC-NAS (Liang et al.) 2024). The conclusion can be made based on the results in Table I (1) Performance superiority: While these SOTA methods outperform previous trusted fusion methods in terms of raw performance metrics, they fall short in providing trustworthy decisions at the view fusion level. thus lacking in security and reliability. (2) Trustworthy decision: TEF, trusted fusion architecture, not only

---

Published as a conference paper at ICLR 2025
Table 1: Accuracy comparison results with trusted MVCs and other SOTA MVCs (mean + standard
deviation), where the best performance is highlighted in bold. The other four metries are provided Table 12 in the appendix.
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb YoutubeFace
TMC (ICLR22)
88.59::0.25 72.73+ 88.5990..2572..333000...... 79.60=0.56 74000000000000543353533337733333 13.12:3300.333533333 71.18+2.27
TMOA (AAA122)
79.1 65177HGH777...000000000000444110 84.72 84.35=00225
ETMC (TPAMI23)
88.00 1.86
RCML (AAA124)
89.06:10.21
97650221722S500S5511908888888800 80.1
81.95+0.20
BV SSV MR EmbraceNet
82.01=0.18
84.43++0.31
84.78=0.21
10.90=1.04
85.11
85.21+0.17
005.0666660777450000333300000350 05.28+0.144
TEF (Ours)
86.02.10.41
achieves superior performance metrics but also ensures trustworthy decisions at the view fusion level. This dual advantage sets TEF apart from other advanced methods. For instance, on the AWA and NUS datasets, TEF achieves approximately 2.6% and 0.77% accuracy improvements compared the second-best model. These improvements highlight the significant advantage of TEF in ensuring both high performance and security in decision making. (3) The trustworthiness is derived from - 44 where u is the uncertainty score in Eq. y Compared to TMC and ETMC, we have significant advantages in making trustworthy decisions shown in Table 2 For example, achieved improvements of 26.9% and 15.6% on the AWA and NUS datasets, respectively. This is because the quality of pseudo-view data after sufficient feature interactions is high, leading to more reliable decisions and strengthening the overall architecture.
Table 2: Trustworthiness comparison across different datasets for TMC, ETMC and TEF.
Datasets
TMC
ETMC
TEF (Ours)
AWA
0.46180.008
0,49410.013
0.76310.046
NUS
0.684
0.793+10.044
0.001
Reuters5
0.908
0.842+0.015
0.059-0.002
Reuters3
0.923+0.010
0.879:00.21
0.9861100002
YoutubeFace
0.621
0,901
0.96310.004
Impact analysis of different fusion strategies on pseudo-view quality. To investigate the impor- tance of adaptive view selection for pseudo-vies quality (PV), compare our PV with five basic fusion operators and five advanced fusion operators. Tsble their respective performances. It can be observed that each operator has its own advantages, with single operator performing excel- lently across all datasets. For instance, except for PV, the Max fusion operator performs hest on the AWA dataset, but performs mediocrely on other datasets. Additionally, although advanced fusion operators involve complex fusion operations, they sometimes perform lower than basic fusion oper- ators in terms of performance. The strategy of adaptive view fusion achieves the best performance. These findings highlight the importance of adaptive view selection and fusion operators.
Impact analysis of different pseudo-view generation methods on TEF. This section aims vali- date the impact of different pecudo-view generation methods on trusted multi-view learning. Specif- ically, five basic fusion operators are used as the pseudo views generation method at first stage of the proposed TEF, respectively. From Table 4 it is evident that the pseudo views using the sin- gle fusion operator are significantly inferior to the high-quality pseudo views obtained through our adopted NAS strategy. For instance, on the YoutubeFace dataset, our approach outperforms the second- best performing method by 7.66%, and similar improvements of at least one percentage point are observed the remaining datasets. This fully demonstrates the importance of introducing high-quality pseudo views and underscores the necessity of adaptively selecting views and fusion operators compose high-quality pseudo views.
8

---

Published as a conference paper at ICLR 2025
Table 3: Accuracy comparison results with five basic fusion operators and five advanced fusion operators, the best performance is highlighted in boldface. "PV" denotes our pseudo view generation the first stage in TEF. The other four metries provided Table [3 the appendix.
Basic fusion operators
Methods Add
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
88.56=0.008
72801=0.70
79.70::..25
83.4610.28
87.53+0.41
82.40=0.23
Mul
86.53=0.41
64.58=0.63
77.02=#0.38
81.89=0.70
72.31
83.18=0.14
Cat
88.22:10117
72.32=0.50
79.91
83.6610.17
87.98+10200
83.05=0.56
Max
88.82-10.32
71.36::0.47
80.02:10.20
84.01-10.28
81.57+0..1
81.49
Avg
88.83++0.32
73.00+0.51
0..69+00.0
83.58
87.27+L0.33
82.23 0.17
Advanced fusion operators
MLB
87.6910.21
70.60=0.29
80.1610.115
83,8011022
87.11:0.67
85.20-0.28
MFB
88.8710.34 7..34=0.40
79.28
83.25+0.18
85.23+0.20
82185=0.17
TFN
81.02=#0.33 63.66=1.22
79.95+0.30
83.73+0.31
57.53+00.2
81.33=0.19
LMF
88.66:10.43 0.77
80.02:10.20
84.01110.28
81.57:L0.41
81.49=0229
PTP
87.78 7.50
80.10.10.10
84.06-10.20
88.61
PV (Ours)
91.43
74.44 0.69
80.9740.34
85.30
92.25 0..20
85.60 0.16
Table 4: Accuracy comparison results (mean + standard deviation) with pseudo-views formed by
different fusion strategies introduced in trustworthy fusion framework, the best performance is highlighted in boldface. Among them, Cat is the direct concatenation of all original features, while Cat unifies all views to the same dimension before concatenation.
Methods AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
Cat 88.24:10.17
73.05-10.67
79.80-F0.41
84.25-10.42
88.70-00.15
79.63
Add
90.29++0.06
73.05++0.62
0..9
84.42+0066
90.65+0008
78.36+
Mul
89.13++0.24
71.85+00.50
77.70+0.58
83.00++0488
77.83++.29
64.09++1110
Cat
89.22++0.09
73.29++063
79.25+0049
84.11+0.59
77.82=0.29
1..6
Max
90.5411012
72.29:10.55
78.53-10.63
84.03-10.52
84.02-1.008
74.80+2.91
Avg
90.63-10.18
72.1240.84
79.86:10.72
84.93
89.49
76.40:10.99
TEF (Ours)
13.26
75.12 + 0.57
10.26
86.49-1.110
92.41
86.02
Impact analysis different strategies to address view imbalance. This section aims to validate the effectiveness of view enhancement strategy for addressing view imbalance by comparing TEF with its three degraded versions. (1) TEF;: Stage is removed from TEF, i.e., degrading into TMC (Han et al.] 2021), without introducing pseudo-views.
(2) TEF;; View Enhancement is removed from the TEF, i.c., only a high-quality pseudo-view generation architecture is introduced. (3) TEF2: Directly using the decisions output of the fusion architecture generated by the evolutionary algorithm
95 10.00%
95
23.22
TEF ((seudo-view)
$1.30
TERpseude-vviww)
TEF
15:18
$6.21
02.02
55 33
30.42
60.00%
70.24
03
79.93
75-12
15.00%
75 25.00%
73.71
10.00%
70.00%
15.00%
YoufubeFace
Reuterss
Reuters3
AIA
NUS
YoutubeFace Reafers5
Reufers3
AWA
NUS
Figure 3: The accuracy comparison before and after solving the pseudo-view imbalance problem. The left chart shows the accuracy of pseudo-views in TEF, and the right chart shows the overall accuracy of TEF. The results other metrics are shown Fig. glin in the appendix.

---

Published as a conference paper at ICLR 2025
Table 5: Comparison results (mean + std) addressing the imbalance problem using feature
hancement versus directly using decision results, with the best performance highlighted in boldface.
Accuracy
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TEF
88.5910.25
72.73-10.30
79.60
84.2310.33
73.13=0.15
71.1812.27
TEF
91.60-:0.20
73.71=0.48
79.9310.54
85.3340.41
91.44=0.14
7..68
TEF2
09.2
73.93+0.52
80.11=0.51
84.79+0.46
62.74=0.20
74.47
TET
93.26.11.25
75.12 0.57
82.2610.23
86.49.1.10
92.4120.11
86.02.10441
Table 6: Time comparison of TEFs armed with different acceleration strategies on NUS dataset.
Methods
FC
CS
Time
TEFI
False
False
13.21h
TEF2
True
False
10.35h
TEF3
False
True
4.43h
TEF4
True
True
2.46h
for trustworthy fusion, i... the decision output of* Alg. 1 as the pseudo view. Observing Table 5 reveals the following findings: TEF; significantly outperforms TEFo, highlighting the importance of introducing high-quality pseudo-views. The performance differences between TEF, and TEF indicate the presence of the view imbalance problem. For example, as shown in Fig. 3 introducing high-quality pseudo-view generation architecture can significantly exacerbate imbalance issues, where the pseudo-views are not sufficiently trained. However, concatenated fusion decisions can significantly resolve this issue. For instance, in the YoutubeFace dataset, the performance improved from 75.1 % without concatenation to 85.18 18% with concatenation. Similarly, TEF's performance increased from 76.68% to 86.02% with the introduction of concatenation. The results of TEF2 indicate that directly introducing the decisions of the fusion architecture is ineffective. Despite its high individual accuracy, it cannot make significant contribution to the overall trusted decision- making process, did not participate in the training of the entire trusted architecture.
Computation time. is well known that evaluating the fitness of all N chromosome vectors re- quires too much computing time at each generation. Fortunately, evolutionary multi-view learning has provided many accelerated solutions. In this part, we arm the TEF with two acceleration strate- gies. The first one is fitness caching (FC) (Liang et al. (021) ) where previously evaluated vectors are recorded, avoiding redundant evaluations of individual chromosome vectors that have already been assessed. The second one is search guided by core structures are first found from a shrunk space, and then the optimal MMC model is found with the guidance of CSs from the expanded space. The results are shown Table where "True" and "False" denote that the corresponding acceleration strategies is used or not, respectively. One can see that the TEF4 that is the version of TEF armed with FC and CS is very high-efficiency. Obvi- ously, new developments of the acceleration techniques in the evolutionary computation community can be readily integrated into the TEF, achieving a more higher-efficiency implementations TEF if more effort is made.
structure (CS) (Fu et al., 2024a ()) where
CONCLUSION
In this paper, we have proposed an innovative approach to enhance the performance of the trusted multi-view classification. Our method has contributed to the advancement of trusted multi-view classification in two key dimensions. Firstly, we introduced a powerful mixture fusion framework that seamlessly integrates both early and late fusion techniques, with the early fusion process being automated for enhanced efficiency. Secondly, we addressed the challenge of imbalanced multi- view learning in large-scale datasets through a straightforward yet highly effective solution. By enriching the results of trusted multi-view learning through these novel strategies, approach offers promising avenues for improved classification accuracy and scalability in complex real-world scenarios.
10

---

Published as a conference paper at ICLR 2025
ACKNOWLEDGMENTS
This work was supported by National Natural Science Foundation of China (Nos. 62306171, T2495251, 62406218), the Science and Technology Major Project of Shanxi (No. 202201020101006,, and Fundamental Research Program of Shanxi Province (No. 202203021222183).
REFERENCES
MassihReza Amini, Nicolas Usumier, and Cyril Goutte.
Learning from Multiple Partially Observed Views an Application to Multilingual Text Categorization. In Advances in Neural Information Processing Systems, pp. 28-36, Vancouver, Canada, 2009.
Junho Choi and Jongseok Lec. Embracenet: A robust deep learning architecture for multimodal classification. Information Fusion, 51:259-2700 2019.
Tat-Seng Chua, Jinhui Tang, Richang Hong, Haojie Li, Zhiping Luo, and Yantao Zheng. NUS- WIDE: real-world web image database from national university of singapore. In Proceedings of the ACM International Conference on Image and Video Retrieval, 2009.
Pinhan Fu, Xinyan Liang, Tingjin Luo, Qian Guo, Yayu Zhang, and Yuhua Qian. Core-structures- guided multi- classification neural architecture search. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, pp. 3980-3988, 2024a.
Pinhan Fu, Xinyan Liang. Yuhua Qian, Qian Guo, Zhifang Wei, and Wen Li. CoMO-NAL Core- structures-guice guided multi-objective neural architecture search for multi-modal classification. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 9126-9135, 2024b.
Pinhan Fu, Xinyan Liang. Yuhua Qian, Qian Guo, Yayu Zhang, Qin Huang, and Ke Tang. Multi- scale features effective for multi-modal classification: An architecture search viewpoint. IEEE Transactions on Circuits and Systems for Video Technology, 1570 2025.
Akira Fukui, DongHuk Park, Daylen Yang, Anna Rohrbach, Trevor Darrell, and Marcus Rohrbach. Multimodal compact bilinear pooling for visual question answering and visual grounding. pp- 457-468, 2016.
Yu Geng, Zongbo Han, Changqing Zhang, and Qinghua Hu. Uncertainty multi-view repre- sentation learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pp. 7545-7553 2021.
Qian Guo, Xinyan Liang, Yuhua Qian, Zhihua Cui, and Jie Wen. A progressive skip reasoning fusion method for multi-modal classification. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 429-437, 2024.
Zongbo Han, Changqing Zhang, Huazhu Fu, and Joey Tianyi Zhou. Trusted multi-view classifica- tion. In International Conference on Learning Representations, pp. 1-11, 2021.
Zongbo Han, Changqing Zhang, Huazhu Fu, and Joey Tianyi Zhou. Trusted multi-view classi- fication with dynamic evidential fusion. IEEE Trunsactions on Puttern Analysis and Machine Intelligence, 45(2):2551-22
2023.
Ming Hou, Jiajia Tang, Jianhai Zhang. Wanzeng Kong, and Qibin Zhao. Deep multimodal multilin- ear fusion with high-order polynomial pooling. In Proceedings of the 32th Advances in Neural Information Processing Systems, pp. 12136-12145, 2019.
Haojian Huang, Chuanyu Qin, Zhe Liu, Kaijing Ma, Jin Chen, Han Fang, Chao Ban, Hao Sun, and Zhongjiang He. Trusted unified neighorneig dynamics for multi-view classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume abs/2409.00755. 2025.
Bingbing Jiang. Junhao Xiang, Xingyu Wu, Wenda He, Libin Hong, and Weiguo Sheng. Robust aalaptive-eeightte multi-view classification. In Proceedings of the 30th ACM International Con- ference Information & Knowledge Management, pp. 31 17-3122, 2021.

---

Published as a conference paper at ICLR 2025
Bingbing Jiang, Junhao Xiang, Xingyu Wu, Yadi Wang, Huanhuan Chen, Weiwei Cao, and Weiguo Sheng. Robust multi-view learning via adaptive regression. Information Sciences, 610:916-9311 2022.
Zhangqi Jiang, Tingjin Luo, and Xinyan Liang. Deep incomplete multi-view learning network with insufficient label information. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 12919-12927, 2024.
Jinhwa Kim, Kyoung Woon On, Woosang Lim, Jeonghee Kim, Jungwoo Ha, and Byoungtak Zhang. International Conference on Learning Representations, pp. 1-10, 2017.
Shu Kong and Charless Fowlkes. Low-rank bilinear pooling for fine-graines classification. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, pp. 7025-7034, 2017.
Christoph H. Lampert, Hannes Nickisch, and Stefan Harmeling. Aitribute-based classification for zero-shot visual object categorization. IEEE Transactions on Patlern Analysis and Machine In- telligence, 36(3):553446) 2014.
Xinyan Liang, Qian Guo, Yuhua Qian, Weiping Ding, and Qingfu Zhang. Evolutionary deep fusion method and its application in chemical structure recognition. IEEE Trunsactions on Evolutionary Computation, 25(5):883- 893, 2021.
Xinyan Liang, Yuhua Qian, Qian Guo, Honghong Cheng, and Jiye Liang. AF: An association- based fusion method for Machine Intelligence, 44 44(12)9923--9254, 2022.
classification. IEEE Transactions on Pattern Analysis and
Xinyan Liang, Pinhan Fu, Qian Guo, Keyin Zheng, and Yuhua Qian. DC-NAS: Divide-and-conquer neural architecture search for multi-modal classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 13754-13762, 2024.
Wei Liu, Xiaodong Yue, Yufci Chen, and Thierry Denoeux. Trusted multi-view deep learning with opinion aggregation. In Association for the Advancement of Artificial Intelligence, volume 36, pp. 7585-7593, 2022.
Wei Liu, Yufei Chen, Xiaodong Yue, Changging Zhang, and Shaorong Xie. Safe multi-view deep classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp- 8870-8878, 2023.
Zhun Liu, Ying Shen, Varun Bharadhwaj Lakshminarasimhan, Paul Pu Liang, AmirAli Bagher Zadeh, and Louis-Philippe Morency. Efficient low-rank multimodal fusion with modality- specific factors. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics, pp. 2247-2256, 2018.
Gengyu Lyu, Weiqi Kang, Haobo Wang, Zheng Li, Zhen Yang, and Songhe Feng. Common- individual semantic fusion for multi-view multi-label learning. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligene, pp. 4715 2024a.
Gengyu Lyu, Zhen Yang, Xiang Deng, and Songhe Feng. L-VSM: Label-driven view-specific fusion for multiview multilabel classification. IEEE Transactions on Neural Networks and Learning Systems, pp. 1-15, 2024b. doi: 10.
Arsha Nagrani, Joon Son Chung, Weidi Xie, and Andrew Zisserman. Voxceleb: Large-scale speaker verification in the wild. Computer Speech Language, 60:101027, 2020.
Xiaokang Peng, Yake Wei, Andong Deng, Dong Wang, and Di Hu. Balanced multimodal learning via on- gradient modulation. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 8238-8247, June 2022.
Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classifica- tion uncertainty. In Advances in Neural Information Processing Systems, volume 31, pp. 1-11, 2018.
Shaojun Shi, Feiping Nie, Rong Wang, and Xuelong Li. When multi-view classification meets ensemble learning. Neurocomputing, 490:17-29, 2022.
12

---

Published as a conference paper at ICLR 2025
Jinhui Tang, Xiangbo Shu, Guojun Qi, Zechao Li, Meng Wang. Shuicheng Yan, and Ramesh Jain. Tri-clustered tensor completion for social-aware image tag refinement. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(8):6622116777 2017.
Meng Wang. Tian Lin, Lianyu Wang. Aidi Lin, Ke Zou, Xinxing Xu, Yi Zhou, Yuanyuan Peng, Qingquan Meng. Yiming Qian, Guoyao Deng, Zhiqun Wu, Junhong Chen, Jianhong Lin, Mingzhi Zhang, Weifang Zhu, Changqing Zhang, Daoqiang Zhang, Rick Siow Mong Goh, Yong Liu, Chi Pui Pang, Xinjian Chen, Haoyu Chen, and Huazhu Fu. eepertaint--nnspier open set learning for retinal anomaly identification. Nature Communications, 14(6757):1-11 2023.
Siwei Wang. Xinwang Liu, Li Liu, Wenxuan Tu, Xinzhong Zhu, Jiyuan Liu, Sihang Zhou, and En Zhu. Highly-efficient incomplete largescale multiview clustering with consensus bipartite graph. In 2022 IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 9766- 9775, 2022.
Weiran Wang, Raman Arora, Karen Livescu, and Jeff Bilmes. On deep multi-view representation learning. In Proceedings of the 32nd International Conference Machine Learning, volume 37, pp. 1083-1092, 2015.
Weiyao Wang, Du Tran, and Matt Feiszli. What makes training multi-modal classification networks hard? In Proceedings the 2020 IEEE/CVF Conference on Computer Vision and Pattern Recog- nition, pp.
2020.
Yake Wei, Ruoxuan Feng, Zihe Wang, and Di Hu, Enhancing multimodal cooperation via sample- level modality valuation. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), pp. 27338-27347, 2024.
Jie Wen, Chengliang Liu, Shijie Deng, Yicheng Liu, Lunke Fei, Ke Yan, and Yong Xu. Deep double incomplete multi-view multi-label learning with incomplete labels and missing views. IEEE Transactions on Neural Networks and Learning Systems, 35(8):11396- 1408, 2024.
Cai Xu, Jiajun Si, Ziyu Guan, Wei Zhao, Yue Wu, and Xiyue Gao. Reliable conflictive multi-view learning. Proceedings of the AAAI Conference on Artificial Intelligence, 38(14);16129-1613 2024.
Shaoxun Xu, Yufei Chen, Chao Ma, and Xiaodong Yue. Deep evidential fusion network for medical image classification. International Journal of Approximate Reasoning, 150: 1 188-198, 2022.
Muli Yang, Cheng Deng, and Feiping Nic. Adaptive-weighting discriminative regression for multi- view classification. Pottern Recognition, 88(4):236-244 245, 2019.
Zhou Yu, Jun Yu, Chenchao Xiang, Jianping Fan, and Dacheng Tao. Beyond bilinear: Generalized multimodal factorized high-order pooling for visual question answering. IEEE Transactions on Neural Networks and Learning Systems, 29(12):5947-537 2018
Xiaodong Yue, Zhicheng Dong, Yufei Chen, and Shaorong Xie. Evidential dissonance measure in robust multi-view classification to resist adversarial attack. Information Fusion, 1 113: 102605, 2025a.
Xiaodong Yue, Zhicheng Dong, Yufei Chen, and Shaorong Xie. Evidential dissonance measure in robust multi-view classification to resist adversarial attack. Information Fusion, 1 103:00 2025b. ISSN 1566-2535.
Amir Zadeh, Minghai Chen, Soujanya Poria, Erik Cambria, and Louisphilippe Morency. Tensor fusion network for multimodal sentiment analysis. Proceedings of the 2017 Conference on Empirical Methods Natural Language Processing, pp. 1103-1114, 2017.
Changqing Zhang, Zongbo Han, yajie Cui, Huazhu Fu, Joey Tianyi Zhou, and Qinghua Hu. CPM- Nets: Cross partial multi-view networks. In Advances in Neural Information Processing Systems, volume 32, pp. 1-11, 2019.
13

---

Published as a conference paper at ICLR 2025
Chenglong Zhang, Yang Fang, Xinyan Liang, Han Zhang, Peng Zhou, Xingyu Wu, Jie Yang. Bing- bing Jiang. and Weiguo Sheng. Efficient multi-view unsupervised feature selection with adaptive structure learning and inference. In Proceedings of the Thirty-Third International Joint Confer- ence on Artificial Intelligence (ICCAI-24), pp. 5443-5452, 2024a.
Chenglong Zhang, Xinyan Liang, Peng Zhou, Zhaolong Ling, Yingwei Zhang, Xingyu Wu, Weiguo Sheng, and Bingbing Jiang. Scalable multi-view unsupervised feature selection with structure learning and fusion. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 5479-5488, 2024b.
Hai Zhou, Zhe Xue, Ying Liu, Boang Li, Junping Du, Meiyu Liang, and Yuankai Qi. CALM: enhanced encoding and confidence evaluating framework for trustworthy vuew learning. In Proceedings of the 31st ACM Interaational Conference on Multimedia, pp. 3108-3116, 2023.
Ke Zou, Tian Lin, Xuedong Yuan, Haoyu Chen, Xiaojing Shen, Meng Wang, and Huazhu Fu. Reliable multimodality eye disease screening via mixture of student's distributions. In Medical Image Computing and Computer Assisted Intervention MICCA/ 2023, pp. 596-606, 2023.
14

---

Published as a conference paper at ICLR 2025
A APPENDIX
In the supplemental material:
A.1: We describe the basic information of all comparative methods.
A.2: We describe the five basic fusion operators used in evolutionary NAS.
A.3: We give detailed descriptions of the datasets.
A.4: We explain the implementation details.
A.5: We present supplementary results.
A.6: Comparison on benchmark datasets used by other TMVC methods.
A.7: We describe the detailed algorithm steps of the TEF framework.
A.8: We describe the drawbacks of TEF and future work.
A.1 BACKBONE MODEL
To ensure a fair comparison, we downloaded the source codes of the compared methods from the authors' websites and followed the experimental settings and parameter tuning steps outlined in each paper. For the trusted fusion methods TMC, TMOA, ETMC, and RCML, as well as other non-trusted fusion methods, we meticulously tuned them each dataset to ensure fully fair comparison. The main comparison methods are briefly introduced below.
EmbraceNet (Choi & Lee 2019): This is random method where each component of the fused vector comes from one view determined by multinomial distribution. The proba- bility value p of view selection set to [V]
AWDR Yang al. 2019): An adaptive-weighting discriminative regression method. The parameter is selected from {10-3, 33, 10-2. ,,,,,,,,,,,,... 110),, and takes values from (1.3,5,.....)
RMAR (Jiang al.) 2022): It adopts the L2,1- loss function learn joint weighted projection subspace across all views, preserving correlation and diversity among views via self-supervised weighting manner. The parameter À is selected from {10-3 (10-3,10-2 10-2.-22... 10 and k takes values from (1,3,5,...,, ....,.
DC-NAS (Liang et al. 2024): It is method that searches for the optimal multi-view fusion strategy through evolutionary neural architecture search. The divide-and-conuuer approach used during the search process greatly improves efficiency while ensuring enhanced per- formance without sacrificing effectiveness.
Simple Soft Voting (SSV) (Liang et al. 2021 : simply averages the outputs of each single view method, treating each view equally.
Best View (BV) (Liagg et 2021): A winner-take-all weighted strategy at the view level, selecting the best method among all single view methods.
Maximum Rule (MR) (Liang et al. 2021): : A winner-take-all weighted strategy at the example level, selecting the highest confidence score among the outputs all single view methods.
TMC (Han et al.
2021): Integrates multi-view information evidence level using the Dempster-Shafer theory in a learnable way.
TMOA (Liu et al.
2022): Integrates multi-view information at an evidence level using
opinion aggregation.
ETMC (Han et al. 2023): An improved version that adds a pseudo view containing com- plementary information from multiple views by simply concatenating the original features.
RCML (Xu et al. 2024): Fuses view-specific opinions consisting of decision results and reliability via the conflictive opinion aggregation strategy, employing simple and effective average pooling fusion.
15

---

Published as a conference paper at ICLR 2025
RMVC (ue et al. 2025bb: It proposes robust multi-view classification method based on an evidential inconsistency measure, which effectively quantifies view confficts, designs a belief fusion strategy, and introduces gradient penalties to resist adversarial attacks.
TUNED (Huang et al. 2025 :II integrates feature structures, employs MRF to manage
dependencies, and generates consensus evidence address fusion uncertainties in multi-
view data.
We review bilinear-based fusion (Fukui et al. 2016) and tensor-based fusion (iu et al. 2018) as representative of advanced fusion methods. Recently, they widely applied many small-scale applications such as fine-grained classification (two views) (Kong & Fowlkes) 2017), visual question answering (two views) Yu al. 2018) and multimodal sentiment analysis (three views) (Zadch
et al. 2017)
Compared with linear methods, bilinear methods can yield richer representation by modeling all pairwise interactions among features from different views. Two typical methods are multi-modal low-rank bilinear pooling (MI.) approach (Kim et al. 2017) and multimodal factorized bilinear pooling (MFB).
MLB Kim et al. 2017) is to solve the dimension curse feature fusion by using V matrix multiplication approximate the outer product. The fusion process can be formalized as follows.
IV MLB(UI, 02, U2. .Iv1) = U U vs) +b,
(18)
V where A V; 31 Z2 o 2ivi U, Rd and RT where d and are hyper- parameters to determine the dimension of joint embeddings and the output dimension of low-rank bilinear models, respectively.
Noting that MLB could result in insufficient representation, (Yu et al. 2018) proposed an enhanced version MFB of MI.B MFB, the features from different views are first expanded to high- dimensional space and then integrated the expanded vectors with Hadamard product. Then sum pooling followed by the normalization layers conducted to squeeze the high-dimensional feature into the compact output feature. The fusion process can be formalized as follows.
IVI
MFB(U1, ..p]) = SumPool A (Tu, k,,
(19)
==1
where the function SunPool k) uses a one-dimensional non-overlap window with size k to do sum pooling over
Tensor-based methods model interactions among different view features by using a V -fold Carte- sian product from view embeddings. Typical methods include tensor fusion network (TFN) (Zadeh) et al. 2017). low-rank multimodal fusion method (LMF) (Liu et al. 2018) and polynomial tensor pooling (PTP) (Hou et al. 2019).
TFN (adeh al. 2017) introduce a tensor fusion layer. Given [V] view vectors {u; R
VV 1=r
they are fused as follows:
2 U1
02
(20)
1
where 8 is the Kronecker product operator, namely R. (mm +1) (mm))))((()))))))) xx (m)vi++) is an order- V| tensor.
outer product, and 2 E
Then the tensor is mapped into vector by linear transformation as follows:
== WZ + b,
(21)
where W E (mm++ (m ()x (m)
R and c E R.
Noting that in TFN the number of parameters to learn in the weight tensor W will increase exponen- tially with the number of views, Liu et al. (Liu et al. 2018) proposed a low-rank multimodal fusion method (LMF). The fusion process be formalized follows.
16

---

Published as a conference paper at ICLR 2025
IVI
c= (M1 02, ",,,,,, ,vr) A == [
(w
1/
(22)
where denotes the rank or the decomposition factors of a tensor; w (m)(m++1) and c R
Noting that tensor-based multimodal fusion methods simply fuse features all at once, ignoring the complex local intercorrelations, Hou al. (Hou et al. 2019) proposed a polynomial tensor pooling (PTP) by considering high-order moments, followed by a tensorized fully connected layer. Given [V] view vectors {v; E Rm (MM
N=1 they are fused as follows:
F
8 f 1 00.00
P-onder
where f = [1, 01, 02 ... Vivll E R and Raxax a a=
E my +
Then the tensor F is mapped into vector by linear transformation as follows:
IV
C PTP("1, mv)) WFF
( FF,
(23)
where W Raxax-xaxx and R
Despite achieving promising performance, the manual multi-view fusion might be sub-optimal for message propagation between views. Moreover, the dimensionality of the fused vector that some of them produce increases exponentially as the number of view increases and are unsuitable for many-view data. Hence, we adopt an evolutionary strategy for automatically discovering well- suitable many-view fusion scheme. For a good computational efficiency in fusing many-view data, the evolved fusion scheme only includes the basic fusion operators.
A.2 FIVE BASIC FUSION OPERATORS
To better illustrate the fusion process of multiple fusion operators, we define x; as the vector feature, represents the quantity of vector features be fused, where the superscript indicates the index of the fused vector feature. In this context, the fusion operator set F encompasses the following operations (Liang et al. 2021 Fu al. 2025).
Concatenation: The information from vector features is fused as follows:
o [x] x² 22/11 |n]
(24)
where [ is the concatenation operator.
Element-wise fusion operators require that the dimensions of input vectors are the same, hence different vector features need be mapped into the same dimension space by linear function before fusing. This can be achieved using fully-connected layer (FC) without any activation function.
Addition: The information from vector features is fused as follows:
o(x;) FC(x)) + FC(x?) + +... + (1!!)
(25)
Multiplication: The information from vector features is fused follows: o(x;)= FC(=)) FC(2²) ..... FC(x)")),
(26)
where o denotes Hadamard product, namely element- wise multiplication.
Max: The information from vector features is fused as follows:
o(x;) mmx(FC(x)) where max element-wise max, also called max- max-pooling.
FF((=!") )),
(27)
Average: The information from vector features is fused as follows:
o( 1
n (FC(x)) FC(=)) .... FC(
(28)
where denotes element-wise addition, also called average-pooling.
17

---

Published as a conference paper at ICLR 2025
Table 7: Statistic information of datasets
View
AWA
NUS
Reuters
MVoxCeleb
YouTube Faces
CH(2,688)
CH(64)
EN(21,531)
2capa(192)
Vi(64)
V2
LSS(2,000)
CM(225)
FR(24,893)
resnet(512)
V2(512)
V/
PHOG(252)
CORR(144)
GR(34,279)
fbank(160)
V3(64)
V1
SIFT(2,000)
EDH(73)
IT(15,506)
mfcc(80)
Vg(647)
VG
SURF(2.000)
WT(128)
SP(11,547)
spec(514)
V3(838)
VB
rgSIFT((20000)
BoW(500)
V7
ResNet101(2,048)
Tags1k(1,000)
#Sample
30,475
23,438
111,740
153,516
101,499
#Label
50
1,251
A.3 DATASETS DETAILS
We describe the datasets used in the experiments in detail and summarize the datasets in Table 7
Animals with Attributes (AWA) (Lampert al. 2014): This dataset includes 30,475 images of 50 animal subjects with seven views. For each image, six types of low-level features are extracted: RGB color histogram (CH), local self-similarity histograms (LSS), PyramidHOG (PHOG), SIFT, rgSIFT, SURF, and one deep feature (LLSVRC-pretraing ResNet101)..
NUS-WIDE-128 (NUS) Tang et al.) 2017): This dataset contains 43,800 single-label im- ages from 128 categories. For each image, six types of image features extracted: color histogram (CH), color correlogram (CORR), edge direction histogram (EDH), wavelet tex- ture (WT), block-wise color moments (CM), and bag of words based on SIFT descriptions (BoW), along with one text feature. The dataset is an extension of the NUS-WIDE dataset (Chua et al., 2009). In our experiments, we use subset consisting of 23,438 images from 10 categories, including animal, architecture, art, frr.flowrs, food, man, person, sky, toy, and water. Each image in this subset is related one label, and each category includes least 1,500 images.
Reuters (Amini al. 2009): This is multilingual multi-view dataset where each doc- ument is described by five different languages: English, French, German, Spanish, and Italian. To make the model efficiently work this data, reduce the dimensions of all views to 1,000 using PCA and add the Gaussian noise to all views or three views, resulting in two versions named Reuters5 and Reuters3, respectively.
CeeeCeleb: This a multi-view audio classification dataset constructed from the Vox- Celeb dataset (Nagrani et al., 2020). Specifically, extract each audio sample five view features extracted: two deep features (ecapa and resnet) and three traditional features (fbank, mfcc, and spec) and add the Gaussian noise to the ecapa and resnet mfcc to study the effect.
You' Tube-Facee (Wang et al. 2022): This dataset includes 3,425 videos of 1,595 different people downloaded from Tube. Similar to other datasets, we use subset consisting of 101,499 frames of 31 subjects, with the same five features extracted.
We additionally introduced seven standard datasets commonly used in TMVC methods to compare with the TEF method and further demonstrate its performance advantages. These datasets were not used in the main text primarily due to their smaller number of views and samples, as the TEF method can complete experiments quickly using evolutionary search within short time. To better highlight the advantages of TEF, we selected six more challenging datasets for demonstration, but we have also included the comparison results for these seven datasets in the appendix.
PIE: contains 680 instances, divided into categories, with three types of features
extracted: intensity, LBP, and Gabor.
Written:::n: It has 2000 handwritten digit instances, represented by six of features.
18

---

Published as a conference paper at ICLR 2025
Stratiffed sampling with
Stage I: Pscudo view
Original datavet
To train (81%)
geacration Alg
vallation
Stratified five- sampling
validbtee
(30%))
Train
Stage Trusted fasion
Alg
To (Bi
Text
Train
Test
Other compared methods
Compared methods
Figure 4: Details of the dataset partitioning for the training set, test set, and validation set in the experimental setup.
Scene15: It consists of 4485 indoor and outdoor scene images, with GIST, PHOG, and LBP features extracted.
101tech101: It contains 101 categories of images, where the top 10 categories were se- lected, and deep features were extracted using DECAF and VGG19,
CUB: It contains 11,788 bird instances, and image and text features were extracted from the top 10 categories.
Animal: It includes 50 categories with total of 10,158 images, where deep features were extracted using DECAF and VGG19.
consists of 31 categories with 30,000 images, described using five different perspectives.
A.4 IMPLEMENTATION DETAILS
In the experiments, to reduce the randomness introduced by data partitioning and network initializa- tion, we followed the strategy proposed in the literature (Shi et al. 2022). As shown in the Figure f we first performed 5-fold cross- pross-validation on the original dataset, dividing the data into training and testing sets in an 8:2 ratio. In the first phase of the evolutionary search pseudo-view generation framework, the training set was further split into training set and a validation set to prevent data leakage. In the second phase, continued to maintain consistent partitioning strategy with all comparison methods. The reported data represents the average performance and standard deviation from five data partitions. To ensure fairness in comparison, we conducted meticulous hyperparame- ter tuning for each method to optimize its performance. In multi-view fusion, unifying dimensions a key step; therefore, we standardized the dimensions of all methods 128.
Our computational environment was Ubuntu 16.04.4, 4, with 512 GB DDR4 RDIMM, 2x 40-core Intel Xeon CPU E5-2698 v4 @ 2.20 GHz, and NVIDIA Tesla P100 (16 GB GPU memory). TEF involves parameters across two stages: First Stage DNN Training: All DNN models were trained using the Adam algorithm. The learning rate was set 0.001, the exponential decay rate for the first moment estimate was 0.9, and for the second moment estimate was 0.999, Each network was trained for 100 epochs. To avoid overfitting, the training process was stopped if the neural network model performance did not improve after 10 epochs. Evolutionary Algorithm Parameters: To effectively utilize GPU resources, the population size was set as a multiple of the number of GPUs. Using 7 NVIDIA Tesla P100 GPUs, the population size was set to 28. Following (Shi et al. 2022 the number of generations was set to 20, with crossover and mutation probabilities set to 0.9 and 0.2, respectively. It is noteworthy that the same set of parameters
used for all six datasets. Our main goal was to obtain a fusion architecture to generate high-quality pseudo views in the first stage. The detailed hyperparameters used in the second stage of TEF for the six datasets shown in Table g
19

---

Published as a conference paper at ICLR 2025
Table 8: Detailed hyperparameters for TEF running on various datasets.
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
Learning rate
le-3
le-3
lc-4
lc-4
le-4
lc-4
Weight decay
le-5
le-5
le-5
le-3
lc-4
lc-5
Batch size
256
64
128
64
256
256
Optimizer
Adam
Adam
Adam
Adam
Adam
Adam
Maximum Epoch
500
500
500
500
500
500
Fusion dimension
128
128
128
128
128
128
Lr-patience
20
20
10
10
50
10
Lr-factor
0.3
0.3
0.3
0.3
0.3
0.3
Seed
1
1
Table 9: Comparison results on the impact of view enhancement position on TEF (mean + standard deviation), with the best performance highlighted in boldface.
Accuracy
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TEF
88.5910.225
72.73:1030
79.60:0..56
84.23+0.335
73.13=0.15
71.18:2.27
TEF2
91.60+:..20 73.71:0.48
79.9310.54
85.33
91.44=0.14
1..68
TEFS
93.16:11.21 75.06:10.66
81.1410..6
86.45:1..18
92.06=0.14
85.35:10.62
TEF
93.26:11.25
0.57
82.2611.23
86.4910.10
92.41=0.12
86.02.10441
A.5 ADDITIONAL RESULTS
In this section, we provide additional ablation studies and experimental results on the TEF frame- work to facilitate a comprehensive understanding of the TEF architecture. They include:
1. Impact analysis of fusion dimensions on TEF.
2. Impact analysis of the position where views are enhanced on TEF.
3. Impact analysis of layer where features are extracted to use view enhancement on TEF.
4. Impact analysis of different forms of encoding individual.
These experimental results help to better understand the key factors of the TEF architecture and its performance in different scenarios.
Impact analysis fusion dimensions on TEF. We conducted a discussion on the fusion dimen- sions the AWA dataset, examining the effects of different dimensions: 32, 64, 128, 256, and 512. Fig. shows the performance five metrics at these dimensions. It can be seen that as the fusion dimension increases, the performance of TEF improves significantly. For example, when the fusion dimension is 32, the accuracy 92.41 %, and increases to 93.51 % when the fusion dimen- sion reaches 256. This improvement is because higher dimensions bring more learnable parameters, thereby enhancing the model's 's learning capacity. As the dimensions increase, the model's 's learning capacity tends stabilize, with changes between 256 and 512 not being significant. Considering all factors, we chose 128 as the fusion dimension to balance performance and model size. It is worth noting that to ensure a fair comparison, the fusion dimension for all methods compared in this paper is set to 128.
Impact analysis the position where views are enhanced on TEF. This part aims investigate impact of enhancement position on TEF by comparing TEF with its three modified versions. Specif- ically, TEF denotes that the view enhancement removed from the TEF; TEF denotes that only decision output of the pseudo view network is used to pseudo view; TEF denotes the decision out- put of the pseudo view network is concatenated the fusion layer of the pseudo view network. From Table 9 it is clear that both the use of feature concatenation and the position where the features concatenated impact the performance of the TEF architecture. Compared with TEF TEF demon- strates significant performance advantage across all datasets, such as 9. 4.44 improvement on the
20

---

Published as a conference paper at ICLR 2025
Accuracy
Recall
Precision
Kappa
94.00%
XU.11
ALUS 93.35
93.00%
13.42
1244
92.13
92.00%
$1.06
01.00%
90.00 00.00%
85.00
89.005
88.005
64
256
3.12
64
128
256
32
236
5122
32
128
256
512
32
128
256
512
Figure The impact different fusion dimensions on the TEF architecture.
Accuracy
Recall
Precision
F1
Kappa
87.00%
A6.31
$4.33
05.55
14.3
00.31
$6.14
15.00
85.00%
65.00%
83.00%
82. 00%
81.00%
D000 0-3
1H2
1
8000
8-3
D-2
n-1
0900
1-3
D-2
161
none
D-1
B-2
B-1
0000
0-3
0-2
161
Figure 6: The impact of different feature layers TEF's ability to solve the imbalance in views.
YoutubeFace dataset. Compared to TEF3, TEF shows that the strategy of concatenating the deci- sion output of the pseudo view network into the original views generally superior concatenating them after view fusion but before entering the hierarchical stage. This indicates that concatenation the original view stage better preserves and utilizes multi-view information, thereby enhancing the performance of the TEF architecture.
Impact analysis of layer where features are extracted use view enhancement on TEF. We explored the effects of concatenating features at different layers to enhance the original views Reuters3 dataset. Specifically, we concatenated features from last four layers of fusion architecture to evaluate the final effeet of feature enhancement in TEF. Assuming the fusion archi- tecture has n layers, we extracted fcatures from the nth layer, (n - 1)th layer. (n 2)th layer, and (n 3)th layer, well as baseline without using any features. The experimental results shown in Fig. [ The closer to the last layer, the better the performance. For example, in terms of ac- curacy, concatenating features from the nth layer is 0.59% better than concatenating features from the (n 3)th layer. This is because the deepest layers of the fusion architecture often contain the complex and advanced representations of the model. These features tend to capture deeper patterns and more semantic information in the data. Using post-fusion multi-view representations enhance the original views helps improve the representational capacity of the views, preventing information loss during fusion. This approach contributes to achieving better results in multi-view fusion architecture and helps mitigate the multi-view imbalance problem to some extent.
Impact analysis of different forms of encoding individual. The individual can be encoded in different forms. Here, we further offer a binary tree form where the views are used as the leaf' nodes of the tree while the fusion operators used as the non-leaf nodes. Similar to its tuple form, the binary tree contains views, then must contain & fusion operators. From Fig. 7 be observed that the binary tree encoding strategy performs slightly better than the tuple form. However, for simplicity and generality of the architecture, we initially chose the tuple form. Of course, TEF naturally switch between both of them.
21

---

Published as a conference paper at ICLR 2025
Tree encoding strategy
Tree encoding strategy
90.00%
Tuple encoding strategy
95.00%
Tuple encoding strategy
91.02
80.00%
90.00%
17.028//25
75.20rs.12
14.4776.41
75.9973.17
24.7/76.65
56.34pe.00
72.057197
85.00%
54.9944.39
70.00%
80.00%
Accuracy
Recall
Precision
Kappa
Accuracy
Recall
Precision
F1
Kappa
(a) NUS dataset
(b) YoutubeFace dataset
Figure 7: A comparative analysis of different encoding methods across five evaluation metrics.
Table 10: Comparison on benchmark datasets used by other TMVC methods. "f" and we. indicate
that the results are reported the work (Xu et al.) 2024) and (Huang et al. 2025 respectively.
Method
PIE
HandWritten
Scene15
Caltech101
CUB
Animal
NUS
EDL (NeurIPS18) 18)
86,25=0.89'
96,90=0. 16'
52.76=0.54'
73.35=1..73
86,22-0.33"
14.30=1.776*
22.33-=0.64
DCCAE (ICML15)
1.09
95.45=00.351
7..62=1..21
89.56=00441
1.393=+1.36'
82.72+1..38
35.75=:0.48
CPM-Nets (ICML19)
88.53:11231
94.55=1.36
67.29:1.011
90.35:2.122 121
89.3220.38'
87.40=1.12"
35.37:1.05
DUA-Nets (AAAI21)
90.56:10.471
18.10:10.321
68.23:1.111
93.43:10.041
1..13:11667
78.65
39.38:1.34"
TMC (ICLR22)
9..85=0.23
98.51=0.133
67.71:10.30
92.80:10.00
90.57:2.96
10.43"
15.18:11.55
TMOA (AAA122)
92.33-40.361
99.25-+0.45
75.57-00.02
94.63-40.04
95.43-+0,20'
87.05+00.28
34.39+0.44"
RCML (AAAI24)
94.71=00.021
99.40-10.001
76. 16.119-0.12 12
95. 95.36=00.38 08
94,50=11.31
84.01
34.04-0..27'
RMVC (IF25)
91.18 01.24
98.51-0.04"
73.05
93.1840..47
87.67
04.68+0.332
TUNED (AAAI25)
96.83-0.01
99,20-0.23*
0.7990777'
97.38=0.45
99.00-0.33
89,52=00,13
37,46++0,25
TEF (Ours)
97.57=0.78
99.64:10133
78.00=0048
96.04=0.32
95.92=0.62
90.18=0.088
47.52=0.30
Table 11: Comparison benchmark confficting datasets used by other TMVC methods. s:n and weet indicate that the results are reported in the work (uu et al. 2024 and (Huang et al. respectively.
2025
Method
PIE
HandWritten
Scene15
Caltech 101
CUB
Animal
NUS
EDL (NeurIPS18)
21.76=0.67*
57.25-0.49*
14,28=0,24*
55.74=0.12*
53.75=0..2"
37.10=0,27
18.07=0.28
DCCAE (ICML15)
16.89=1.100
82.85-0.33
25.97
60.90:42.32
1..57=11228
34.02=0.11*
32.12
CPM-Nets (ICML19)
53.19=1.171
83.34=1.07'
19.63+1.12
66.5442.89
68.8220.171
64.8320.35
29.20=0.81
DUA-Nets (AAAI21)
56.45:1775
87.16:0.334
26.1813.10
75.19:2.344
1.75
62.4621.12*
31.82:1.433
TMC (ICLR22)
61.65:110031
92.76:10.15
42.27:11611
90.16:12.40'
13.37=2.16'
64.85:1.11
33.76::2.16*
TMOA (AAA122)
68.16-0..44
93.05-00.451
4.042+1.02
9063-+2.35
74.43++0.56'
64.20+0.15"
32.44+0.26
RCML (AAAI24)
84.00-10.141
94.40-1..051
56.97-4..22
92.36:+1.888
16.50=11.15
67.67-0..11
31.91
RMVC (IF25)
76.47=3.43*
94.75=0.75*
49.83=2.23'
80.56=0.71
72.78=0.42"
66.00=0.59
1..6
TUNED (AAAI2S)
86.02=0.19
96.75=0.55*
67.22-0.58
93.22-0041
76.67-1.38
90.90=0.118
34.09-0.14
TEF (Ours)
86.76:10.49
98.70=10.31
72.27=0.43
93.42=00.88
77.41-0477
76.10=0.12
43.84=0.31
A.6 COMPARISON ON BENCHMARK DATASETS USED BY OTHER TMVC METHODS
To fully demonstrate the advantages of our method and further verify its fairness, we also conducted evaluations on seven benchmark datasets commonly used by other TMVC methods (Wang et al.,
2015 Zhang al. 2019 Geng et al.) 202T Yue al., 2025a Huang et al. 2025). Using the same data partitioning strategy as RCML (Xu et al. (024)), we repeated the experiments ten times randomly and calculated the average results and standard deviations. The results shown in Table
indicate that our method exhibits significant advantages across all seven datasets.
Moreover, we show TEF's effectiveness in handling noisy or uncertain data by conducting rigorous tests on seven conflicting datasets, structured according to the method described by RCML (Xu ct al. 2024). TEF underwent ten iterations of testing on each dataset to ensure statistical robustness, with both mean values and standard deviations reported. In Table [I these results confirm TEF's effectiveness in managing datasets with inherent noise or uncertainty. As shown, TEF consistently delivers superior performance, even under challenging conditions involving noisy uncertain data. Notably, on the NUS dataset, TEF achieved a performance that was 11.75% higher than the second- best method, and the 1c dataset, it surpassed the next best by 5.05%.
22

---

Published as a conference paper at ICLR 2025
A.7 THE TEF FRAMEWORK ALGORITHM
The trusted multi-view classification enhancement through evolutionary view fusion (TEF) approach consists of stages: (1) Using neural architecture search to obtain the optimal pseudo-view gen- eration model, and extracting subsequent decision features for feature enhancement in the second stage, detailed in Alg. I (2) Fusion view-guided trusted fusion through evidence fusion, as referenced in Alg. The detailed evolutionary operations of Alg. 1 are described as follows:
Population Initialization: Randomly generate N chromosome vectors the initial population, where each chromosome p has different k-value.
Fitness evaluation: Decode chromosome p into a deep fusion neural network model, train it on multi-view dataset, and evaluate its fitness based on classification accuracy on the validation set.
Crossover operation: Perform crossover between chromosomes Pı and P2 generate new chromosome vectors pf and p2-
Mutation operation: Randomly select an individual p and, with certain probability, replace its view or fusion operator fg to achieve mutation.
Algorithm Evolutionary NAS method
1: Input:
2: N: population size;
3: T: maximal generation number;
4: D = =(X,Y): training dataset;
5: Đ = (X,Y): validation dataset;
6: a set of basic fusion operators:
7: Output: Optimal fusion architecture and decision output features.
8: Generate an initial population Po:
9: Evaluate the fitness of each chromosome vector in Po;
10: for 1 to T do
11: Generate offspring Qa using the crossover operator;
12: Conduct mutation on each chromosome Q
Evaluate the fitness of each chromosome in Q+;
14:
Select next generation population P.+1 from Q U P. using a selection operator;
end for
16:
Phest + Select the chromosome with the best fitness from Pr.
return The fusion network corresponding to Pbest and obtain the decision output features of this network.
A.8 LIMITATIONS AND FUTURE WORKS
Even though the proposed method achieves excellent performance, it still has some potential limi- tations. (1) Like other trustworthy fusion methods, we did not adjust the fusion order the trust- worthy fusion process. Specifically, when form opinions Mi, M2, ... Ma+1 from views and an additional (n + 1)th pseudo-view, their aggregation order is crucial as different orders can lead to different performance impacts. Therefore, future work, will conduct theoretical analysis of this phenomenon and propose solutions. (2) Additionally, not all opinions need to be aggregated. For example, some views may generate opinions that are entirely noise significantly degrade the fusion results. We need to exclude these invalid opinions to ensure the effectiveness of the fusion. In future work, we envision that an adaptive method for effectively selecting and aggregating these opinions to ensure the effectiveness of the entire framework and improve performance will be promising research direction. We consider these important future works.
23

---

Published as a conference paper at ICLR 2025
Algorithm Algorithm for trusted multi-view classification
1: Training
N
2: Input: Multi-view dataset: D = [x m== U X Un
==1
3: Initialize: Initialize the parameters the neural network.
4: while not converged do
5: for m = 1 to V do
6: Dir( xm) variational network output;
7: Subjective opinion M <- Dir(pT" xx");
8: end for
9:
Dir( x*) <- variational network output;
Subjective opinion M Di x*P);
11: Obtain joint opinion M with Eg. (II
Obtain Dir(
Q) with Eq. (13):
13: Obtain the overall loss by updating a and fa /==1 in Eq. 14
Maximize Eq.
(14) and update the networks with gradient descent;
15:
end while
16: Output: networks parameters.
17: Test
Calculate the joint belief and the uncertainty masses.
95.00%
95.00%
92.39
90.00%
90.22
TEF
90.00%
90.42
TEF
84.12
85.26
86.47
Precision (96)
85.75
82.12
80.00%
79.89
80.00%
75.00%
74.51
72.77
74.42
75.00%
75.17
70.00%
70.00%
65.0000
YeutubeFace ReutersS Reutersà AWA
NUS
YoutubeFace Reuters5 Reuters3 AWA
NUS
90.95
7EF
TEF
91.09
03.12
TEF
TEF:
90.00%
90.00%
96.34
85.00%
Kappa (%)
85.00%
$3./4
82.29
80.00%
79.88
80.00%
78.63
75.00%
73.05
74.65
70.35
70.00%
70.00%
05.00%
YoutubeFace Reuters5 Reuters3
AWA
NUS
YoutubeFace ReutersS Reuters3
AWA
NUS
Figure 8: Changes in TEF performance before and after addressing the view imbalance issue under different metrics (Recall, Precision, Fl, and Kappa).
24

---

Published as a conference paper at ICLR 2025
Table 12: Comparison results of the other four evaluation metries with SOTA algorithms (mean + std), with the best performance highlighted in boldface.
Recall
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TMC (ICLR22)
84.47: 71.70 79.60 83.62:40.91 040 01..:5555...1014.:1:0000 81.54:10.26 82.63:1.399
84.19:10229 04 64.06:1012 68.50:2.77
TMOA (AAAI22)
ETMC (TPAMI23)
2.1 0 85.85=0.22 81.51=0.26
RCML (AAA124)
84.34:0.88 0AA.:488777SSS000.22222001883122 74.53:0--66 80.59=0.18
EmbraceNet
7..3610.44 80.65+1.13
AWDR (PR19)
83.57=0.30
RMAR (INS22)
83.35++0.27
DC-NAS (AAA124)
73.7500.. 221. 00.1:00.0099.1411.. 84.69=0.46
TEF (Ours)
90.26:144744111.... 82.12 86.47666.01.50050
0.0. 89.1110.0 84.11
Precision
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TMC (ICLR22)
87.76:10.40 72.71 79.86 84.3:1049 73.26-1..33 82.53
TMOA (AAA122)
88.15++0.62 0253:66667777110001199----228280 04.40-4.2444440...1 84.38 87.59+
ETMC (TPAMI23)
87.68::0.63 72.3940.64 79.99 84.38......3344 87.28:0.15 83.40=2.33
RCML (AAA124)
35222412277552200022220011111222 442110446 84.34+0.88
EmbraceNet
83.71
AWDR (PR19)
89.94-0.32
RMAR (INS22)
92.19 90.64+0.08
DC-NAS (AAA124)
88.99::0.27 739 4AAAA00888...0077332222444544440 86.0770.21 91.73+1.11 87.14
TEF (Ours)
92.33 1.2.1.....5.710..01 0.32 86.65 93.011-0.19 0...6666...011.8311100011. 91.02-1.00
F1
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TMC (ICLR22)
01.35....7..44441 83.65::0.86 72.02+0.49 99.14:0.49842440222 82.02.1.33 84.85+0.25 84.60:10:49
65.22++0.09 71.92+22.06
TMOA (AAAI22)
ETMC (TPAMI23)
86.0311.20 10.97
RCML (AAA124)
2AB22118822000022223333005552222 75.87:0.55 82.30:0.15
84.82:11.05
BV SSV MR
82.49:0.225
18252214460021111019992022222233 86.55+00.27
84.444..77
85.03#0.29
EmbraceNet
81.61
AWDR 19)
87.72++0.21 11722220172222000077777722222220
86.51+0.12
RMAR(INS22)
86.69+10.17
DC-NAS (AAAI24)
88. 18:0077 01.188800227...62000222222888110 AAA.A011---777000020000000000010
85.81
TEF (Ours)
9.39 74.60 82.29 0.0.:07666..........00000000....
87.26
Kappa
Methods
AWA
NUS
Reuters5
Reuters3
VoxCeleb
YoutubeFace
TMC (ICLR22)
88.31 29.2266692224442 69.22+0.35 75.44=0.68 81.01:0:22 21 15.10 67.68+2.46
TMOA (AAAI22)
88.91#0.31 69. 19. 74.82-..50 0000::0005009941110 80.9740.33 84.55=0.42 82.60+0.29
ETMC (TPAMI23)
87.95+0.11 (599110..76661007777777011111113 81.44.0511 88.69=0.15 77.63+1.85
RCML (AAA124)
88.79++0.21 00000000000077755000000222221220 02.99-0344 80.85---444 79.97+0.22
EmbraceNet
78.9341.12
AWDR (PR19)
83.40+10118
DC-NAS 90440000880000005552200222222220
RMAR (INS22)
83.47:1021
83.7410.16
TEF (Ours)
84.39-0.49
25

---

Published as a conference paper at ICLR 2025
Table 13: The comparison results between TEF and five basic fusion operators well five ad- vanced fusion operators, with the best performance highlighted in bold. The table shows four met- rics:
Recall, Precision, Fl-score, and Kappa.
Basic fusion operators (Recall)
Methods Add
AWA
NUS
Reuters3
Reuters3
VoxCeleb
YoutubeFace
85.16:0.118
72.26-00.74
79.53
83.34
84.50
82.43+0.226
Mul
82.60=+0:45
0.738++0766
76.52=0.47
81.63++0.0
83.30=+1001 67.70++1.03
Cat
84.62+10.30
72.03+0.39
83.59#0.21 7928
84.94=0.200
83.40:0.47
Max
85.55:10.32
70.80+0.377
79.87=0.23
83.94:10.21
78.02:10.33
80.75=10.0
Avg
85.37:10.4
72.54:0.55
79.54=0.26
83.46=0.32
84.54:0.45
81.38:00.99
Advanced fusion operators (Recall)
MLB
84.45-H0.55
69.75+0066
79.95
83.57+0.34
84.27+00.8
84.72+0.25
MFB
85.11+0.77 70.53+0.44
79.04=0.23
83.11+0.19
81.87+0.41
81.89+0.42
TFN
75.62:10.58 1..33+1146
79.77=0.25
83.6710.27
51.94
80.33:10.61
LMF
85.47:0.62 70.92:0.86
79.90=0.17
83.6410.36
87.69
85.0711.22
PTP
84.13+00.49 71.27+00.66
7.14
84.01=00.18
85.94+0.32
84.78+0.24
TEF (Ours)
90.26
82.12 7.66
86.4710.10
89.21
84.11.1.84
Basic fusion operators (Precision)
Add
86.4410.25
72.46:10.54
83.6011..31 79,97=0.32
83.8510.39 07.9
Mul
83.76++0.57
64.09++0.40
7.22
82.44+0.43
1..09
84.31+1.34
Cat
86.17+0.43
71.94+0.21
80.03=0.33
83.81=0.17
87.73+0.17
84.36+1.00
Max
86.72++0.53
71.13+0..56
80.25=0.27
84.19:0.36
81.22+t0.51
83.13+1.111
Avg
86.8010..6
72.54:0.59
0.38
83.7810.28
87.34
84.5
Advanced fusion operators (Precision)
MLB
85.1110.47
71.09:0.776
80.64-0.26
84.3310.31
86.55+0.49
86.73.0.66
MFB
87.00:10:45
79.68 71.52:10.46
83.52+10.20
83.93
84.6440.25
TFN
77.92++0.79 63.13++1.20
80.42=0.44
84.00+0.48
58.89+00.6
03.5
LMF
86.78+0060
72.05+00.53
80229=0.20
84.08+0.31
89.15
87.02+0.46
PTP
85.63-10.33
71.99+1.44
80.50=0.06
84.2811.22
87.7440.34
86.24.10.5
TEF (Ours)
92.33+1.233
75.17
0.35
06.65
93.0110.19
91.022+1.02
Basic fusion operators (F1)
Add
85.56-H0.14
0.524
79.71=0.25
03.45
85.20-00449
82.92-0.224
Mul
82.91110.47
63.5240.62
77.13=0.39
81.93=0.68
67.92+1.07
83.5310.12
Cat 85.12:10.9
71.82+0.29
79.90=0.26
83.6810.18
85.4410.20
83.57+0.50
Max
85.96:10.36
70.90+10.44
80.02=0.20
84.04=0.26
78.35+0.40
81.8
Avg
85.85++0.99
72.46+0.55
7.26
83.59+0.28
84.93+0.400
82.70+0.22
Advanced fusion operators (F1)
MLB
84.5710..3
70.06:10.30
80119=0.14
1..22
85.37 0..6
MFB
85.6510.72
70.87+0.34
79.28=0.24
83.2810.18
82.33+0.31
83.1740.18
TFN
76.05-10.00
1..19
80.01-0.31
83.7910.33
52.3330.91
81.52+0.24
LMF
85.77+0.58
71.27+0.71
80.04=0.17
83.78+0.27
87.92+0.25
85.92+0.119
PTP
84.47-10.39
71.22+00.3
80.11=0.09
84.08
86.23+0.35
85.41+0.38
TEF (Ours)
9..96+1..00
74.65+00.66
82229=0.24
86.54+0.10
90.87+0.12
87.26
Basic fusion operators (Kappa)
Add
88.28
69.40-10.78
75.55
30.08-0.33
87.52
80.63-1..23
Mul
06.20++0.22
60.05+0.72
4..2
18.17+0.85
7..28+00.00
81.50+0.24
Cat 87.9410.18
68.8840.54
75.81=0.33
80.32+1.21
87.96+0..20
81.3810.56
Max 88.5611..33
67.7740.53
75.94=0.24
80.7410.33
81.55+00.41
79.5740.31
Avg
85.5710.33
69.62-0.557
75.55-0.36
80.22-10.4
87.26:10.33
80.36.10.27
Advanced fusion operators (Kappa)
MLB
87.40-1.22
66.8710.38
76.10-0.19
80.48 L0.34
87.10-00.67
80.69
MFB
8..60
67.72-40.45
7.25
79.83+0.22
85.21
81.044+0.21
TFN
00.5
58.86++1.26
7.36
+0.37
57.48+00.92
79.35-40.25
LMF
88.3910.44 17.1790.79
75.95-0.18
80.4311.34
89.91
84.0940.24
PTP 87,49-0.229 68.30-0.52
76.02-0.12
80.80-10.24
88.60
83.6810.31
TEF (Ours)
93.10:11.29
71.9710.64
78.63-0.28
83.7410.12
92.40.1..12
14.39
26


Reviews:
[{"review_id": "0FOzlSRX6R", "reviewer": "Reviewer_por9", "summary": "This paper illustrates two main issues in existing trustworthy fusion methods: the lack of feature interaction in late fusion and the insufficient attention given to multi-view imbalance, which leads to inadequate training and suboptimal performance. To address this, the authors innovatively propose an evolutionary computation adaptive method that introduces high-quality pseudo-views, significantly enhancing the performance of trustworthy fusion methods on complex multi-view datasets. Furthermore, the authors present an effective solution for view imbalance and conduct extensive experiments to validate its effectiveness.", "questions": "See in the weakness.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. The paper presents the motivation for the research in detail through illustrations, and the structure of the paper is logical and well-written.\n2. The paper demonstrates considerable innovation, as the authors first identify two key challenges in trustworthy multi-view fusion and provide effective solutions.\n3. The authors validate the effectiveness of their method through extensive experiments, with results showing significant advantages over existing trustworthy and non-trustworthy fusion methods across five evaluation metrics on six datasets.", "weaknesses": "1. I am interested in your concatenation operation. Why is the late-stage fusion information only concatenated with the pseudo-views and not with the original views? What effects would concatenation have?\n2. Why did you choose evolutionary computation for generating pseudo-views? Have you considered gradient neural architecture search or reinforcement learning?\n3. Can early fusion features not assist in training? Why was the final choice made to use late-stage features to address view imbalance?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "h8FXLZmZRp", "reviewer": "Reviewer_fWQm", "summary": "This research is significant in the field of trustworthy fusion and addresses two main challenges in current methods. First, many approaches overlook feature-level interactions, resulting in suboptimal performance. Second, high-quality pseudo-views exacerbate multi-view imbalance. The authors propose the TEF method, which utilizes evolutionary multi-view architecture search to generate high-quality pseudo-views, enabling adaptive selection of viewpoints and fusion operations. Experimental results demonstrate that this strategy significantly enhances TEF's performance on complex multi-view datasets, particularly in cases with three or more viewpoints. Evaluation results confirm the superiority of the proposed method compared to existing techniques.", "questions": "1. The paper indicates that introducing a single pseudo-view is effective; have there been any attempts to use multiple pseudo-views to further enhance the results?\n2. Is this method a general concept? Can other trustworthy fusion methods also adopt similar strategies to improve model performance?\n3.What do you believe is the fundamental reason behind achieving state-of-the-art results?\n4.Regarding the time-consuming issue caused by using the NAS algorithm, while the paper suggests some solutions, I would still like to know if the authors have plans for further research in the future to tackle more complex data or deeper network issues.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1. The authors first review previous work and identify its limitations.  \n2. They innovatively introduce neural architecture search to generate high-quality pseudo-view architectures, providing a detailed description that effectively addresses the issue of insufficient feature interaction. Although this technique is time-consuming, it offers an effective solution.  \n3. The use of concatenation operations to solve the imbalance between multi-views is actually quite interesting, appearing simple yet effective.  \n4. Extensive experiments also demonstrate the effectiveness of TEF.", "weaknesses": "See in the questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "EhuVC6baL9", "reviewer": "Reviewer_jfaY", "summary": "The paper presents TEF (Trusted multi-view classification via Evolutionary Fusion), aiming to address challenges in multi-view classification such as limited view interaction and learning imbalance. TEF utilizes evolutionary neural architecture search to create pseudo-views and applies a balanced fusion strategy. The method shows potential improvements over existing approaches in certain comparisons.", "questions": "1. Can you provide more justification or empirical evidence showing that learning imbalance within pseudo-view-guided multi-view classification significantly impacts model performance?\n\n2. The benchmarks used in the paper seem different from those used in prior TMVC studies. Were the TMVC methods evaluated under the same conditions as your proposed TEF? Clarifying this would address concerns about fairness in experimental comparisons.\n\n3. Can you show additional experiments or real-world examples demonstrating TEF's effectiveness in handling noisy or uncertain data?\n\n4. Actually, the method seems to rely on aligning pseudo-view generation with target domain performance using validation labels. However, when samples are noisy, there appears to be no specific strategy to mitigate this noise. How does your approach show advancements over existing methods, especially given that Evidential Deep Learning has known limitations in fusion frameworks that could risk performance degradation?", "limitations": "", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Combines evolutionary NAS with multi-view classification, offering a novel approach.\n2. The methodology is clearly explained with effective visuals.", "weaknesses": "1. The emphasis on learning imbalance within pseudo-view-guided multi-view classification may not be as critical as the authors suggest. As long as the overall contributions of different views are balanced, focusing on the specific imbalance of the pseudo-view might be unnecessary. More evidence or justification would be helpful to show that this imbalance significantly impacts performance.\n\n2. The experimental comparisons may not ensure fairness, as it seems that the benchmarks used in this study do not align with those originally used in previous TMVC methods (e.g. ECML [1]). This raises concerns about consistency and fairness. Clarifying whether all models were evaluated under similar conditions would improve the reliability of the results.\n\n3. The claimed robustness of TEF in handling noisy or uncertain real-world data is not well-demonstrated. More experiments simulating practical conditions are needed to validate this aspect.\n\n[1] Reliable conflictive multi-view learning. AAAI 2024", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "1WMVLV7wSm", "reviewer": "Reviewer_a8gx", "summary": "The paper addresses the issues present in pseudo-views generated by previous methods and proposes a solution. It introduces an evolutionary multi-view architecture search approach to generate high-quality fusion architectures to serve as pseudo-views, thus enabling adaptive selection of views and fusion operators.", "questions": "Could you please describe in detail the differences from other multi-modal NAS methods, such as the DC-NAS (Divide-and-Conquer Neural Architecture Search for Multi-Modal Classification) mentioned in the manuscript?\n\nAt the methodological level, what is the significance of concatenating pseudo-views with the original views? In principle, it seems that the pseudo-view already contains the information of the original view.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The overall writing of the paper is smooth and easy to understand.\n\nThe experimental results are extensive and solid.", "weaknesses": "I'm not sure if the proposed pseudo-view generation method is innovative compared to previous neural architecture search (NAS) methods. \n\nAdditionally, I'm uncertain whether the proposed method can be applied to large-scale end-to-end multimodal datasets. This is because the method might be inefficient, especially for high-dimensional and complex multimodal data, and the number of operators in the NAS process may be insufficient to cover all necessary functions. Increasing the number of operators might also lead to a significant increase in computational cost. I am open to increasing the score upon receiving a well-justified explanation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)