Semi-Supervised Fuzzy DBN-Based Broad Learning System for

Forecasting ICU Admissions in Post-Transplant COVID-19 Patients

Xiao Zhang and

Angela Nebot

Soft Computing Research Group at the Intelligent Data Science and Artiﬁcial Intelligence Research Center,

Universitat Polit

ecnica de Catalunya, Barcelona, Spain

Keywords:

Fuzzy System, Broad Learning System, ICU, Covid-19, Manifold Regularization, Organ Transplant.

Abstract:

This paper introduces a novel semi-supervised neuro-fuzzy system to predict ICU admissions among post-

COVID organ transplant recipients. Addressing the challenges of small sample sizes and lacking labels in

organ transplantation, our study takes on these issues by proposing a DBN-Based Dual Manifold Regularized

Fuzzy Broad Learning System (D-DMR-FBLS). This system utilizes the streamlined and ﬂat architecture

of the Broad Learning System (BLS), integrating Deep Belief Networks (DBN) and Takagi-Sugeno-Kang

(TSK) systems to enhance representation learning capacities during the Unsupervised Training Phase (UTP).

The system combines the strong feature learning capabilities of DBN with the powerful fuzzy rule extraction

capacity of the TSK system, enhancing the model’s predictive performance and generalization capability.

Moreover, we propose two types of graph-based manifold regularization, sample-based and feature-based,

within this novel D-DMR-FBLS framework. Our method enhances its predictive ability by exploiting both the

similarity among unlabeled and labeled patient samples, as well as the correlations between features within

the fuzzy feature space. Employed to predict ICU admission risks in post-transplant COVID-19 patients, the

method has demonstrated superior performance over existing methods, particularly in scenarios with limited

samples and labels, thereby providing more accurate decision support for medical professionals in optimizing

resource allocation for transplant patients.

1 INTRODUCTION

Since its emergence in late 2019, COVID-19 has led

to over 700 million infections and caused more than

6 million deaths globally, constituting a major public

health crisis (Worldometer, 2024). Organ transplant

recipients, particularly vulnerable due to their com-

promised immune systems and reliance on immuno-

suppressants, have faced increased mortality risks

during this period (Mamode et al., 2021). The pan-

demic has intensiﬁed the demand for critical medical

resources such as ventilators and ICU beds, highlight-

ing the urgent need for better medical oversight and

protection for these at-risk patients. Current research

on optimizing medical resource allocation for trans-

plant recipients using machine learning (ML) is in-

sufﬁcient. Utilizing ML to predict the medical needs

of these patients can identify those at highest risk

more effectively, thereby optimizing resource alloca-

tion, reducing the load on healthcare systems, and

potentially decreasing mortality rates in this group.

Moreover, precise predictive models can assist in clin-

ical decision-making and play a vital role in manag-

ing resource distribution during peak demand periods,

ensuring that critical support is directed towards those

most in need.

Current research in organ transplantation increas-

ingly utilizes machine learning (ML) to predict post-

transplant survival rates, with Random Forest (RF),

XGBoost and deep learning (DL) gaining popular-

ity for their accuracy and ease of implementation,

as noted in recent studies (Liu et al., 2020; Mark

et al., 2023). However, the efﬁcacy of advanced

DL models, does not consistently outperform en-

semble learning models in this domain, often show-

ing limited performance improvements despite in-

creased complexity, particularly with data granular-

ity challenges (Zhang et al., 2022; Ershoff et al.,

2020). In contrast, Fuzzy Neural Networks (FNN) are

recognized for their ability to manage non-linearity

and high-dimensional data effectively, crucial for

handling the inherent uncertainty and ambiguity in

complex medical datasets (Shihabudheen and Pillai,

2018).

Zhang, X. and Nebot, À.

Semi-Supervised Fuzzy DBN-Based Broad Learning System for Forecasting ICU Admissions in Post-Transplant COVID-19 Patients.

DOI: 10.5220/0012856300003758

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2024), pages 415-422

ISBN: 978-989-758-708-5; ISSN: 2184-2841

415

The Fuzzy Broad Learning System (FBLS) rep-

resents an innovative integration of fuzzy logic into

the Broad Learning System (BLS), creating a frame-

work particularly adept at handling ambiguous or im-

precise data (Feng and Chen, 2018; Feng and Chen,

2021; Feng et al., 2020; Liu et al., 2021; Gong et al.,

2021; Zhang et al., 2020). FBLS leverages the advan-

tage of fuzzy logic to enhance its capability to pro-

cess uncertain information, thereby increasing its ef-

ﬁciency in environments characterized by data ambi-

guity. A distinctive feature of FBLS is its streamlined,

ﬂat network architecture derived from BLS. This ar-

chitecture facilitates rapid feature learning and expe-

dites information processing, setting it apart from hi-

erarchical deep learning models. Such a conﬁgura-

tion makes FBLS particularly well-suited for manag-

ing high-dimensional and nonlinear data sets.

The transplantation ﬁeld faces the challenge of a

scarcity of labeled samples, stemming from privacy

concerns and the frequent loss of follow-up among

recipients. This limitation complicates the collec-

tion of adequate labeled data essential for traditional

supervised learning models. Addressing the chal-

lenges of small sample sizes and lacking labels in

the organ transplantation domain, this paper presents

a novel neuro-fuzzy system named the DBN-based

Dual-Manifold Regularized Fuzzy Broad Learning

System (D-DMR-FBLS). In the unsupervised train-

ing phase, DBN (Deep Belief Networks) and TSK

(Takagi-Sugeno-Kang) fuzzy systems are integrated

for representation learning. This system leverages

the strengths of DBN in deep feature extraction and

representational learning, along with the ﬂexibility

of TSK fuzzy systems in handling uncertainty and

fuzzy information. Furthermore, this system also in-

corporates two types of graph-based manifold regu-

larization strategies: feature manifold regularization

and sample manifold regularization. Sample mani-

fold regularization exploits the geometric distribution

of samples to enhance the model’s capability to cap-

ture and utilize the intrinsic associations and similar-

ities among samples. Feature manifold regularization

improves the model’s ability to learn complex patterns

within the fuzzy feature space, thereby effectively uti-

lizing the intrinsic correlations among features. As a

semi-supervised learning approach, this method not

only enhances the feature representation from a lim-

ited number of labeled samples but also leverages

the similarities among samples, including those un-

labeled samples, and the correlations within the fuzzy

feature space, thereby further improving the model’s

predictive performance. Our proposed method has

been applied to predict ICU utilization in recipients

infected with COVID-19 post-transplantation, and the

experimental results demonstrated its effectiveness

compared to other algorithms.

2 THE PROPOSED

METHODOLOGY

The architecture of the proposed D-DMR-FBLS sys-

tem is depicted in Figure 1. The training process is

methodically divided into two distinct phases. The

initial phase, known as the Unsupervised Training

Phase (UTP), focuses on feature representations from

the input data through DBN and TSK fuzzy systems.

The aim is to augment the feature representation ca-

pabilities of the FBLS. During this phase, the DBN

and TSK fuzzy systems extract latent feature rela-

tionships and structure information within the input

data. Following this, the second phase utilizes the

feature representations derived from the ﬁrst phase as

inputs to the subsystems of the FBLS. Here, a series

of nonlinear transformations are applied to compute

the outputs of the enhancement nodes. An innovation

in this phase is the introduction of a graph-based dual

manifold regularization strategy, designed to not only

unearth intrinsic relationships and correlations within

the fuzzy feature space but also to bolster the system’s

ability in learning from unlabeled samples. Termed

the Supervised Training Phase (STP), this stage in-

volves training the system’s parameters under super-

vision to determine the output layer’s weights.

2.1 Neural Representation Based on

Deep Belief Networks

During the UTP phase, we integrated a neural rep-

resentation based on DBN to enhance the represen-

tation learning capability of FBLS. A DBN consists

of multiple layers of stacked Restricted Boltzmann

Machines (RBM). The input layer nodes correspond

to the dimensionality of the input space, with d fea-

tures in the dataset. The hidden layers form the

complete DBN neural representation. Assuming the

DBN has l hidden layers, the topmost layer nodes are

= [h

,...,h

], and the layer below has nodes

l−1

. This hierarchical structure abstracts high-level

features, progressively reducing or eliminating noise

in the data.

The DBN pre-training starts with the ﬁrst RBM,

where the visible layer contains d nodes represented

by v

= x, and the ﬁrst hidden layer nodes are h

,...,h

]. Unlike conventional DBNs requir-

ing supervised ﬁne-tuning, our model utilizes only

the unsupervised pre-training stage to acquire neu-

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416

Figure 1: The structure of the proposed D-DMR-FBLS.

ral representations for each hidden layer. The Con-

trastive Divergence (CD) algorithm determines the

weight matrix W

, visible layer biases b

, and hidden

layer biases c

between the layers of each RBM.

For computational convenience, h

k j

and v

are set

to 1 if their probabilities exceed a random threshold,

otherwise set to 0. The sigmoid function is deﬁned as

Eq. (1).

sigm(x) =

1 + e

−x

(1)

The update formulas for weights w

, biases b

and c

during the t-th iteration are deﬁned as Eq. (2):

(t)

(t−1)

+ ε





(t−1)

| v

(t−1)



(t−1)



− P



r(t−1)

| v

r(t−1)



r(t−1)





(t)

(t−1)

+ ε



(t−1)

− v

r(t−1)



(t)

(t−1)

+ ε



(t−1)

| v

(t−1)



− P



r(t−1)

| v

r(t−1)



(2)

After pre-training each RBM, the ﬁrst hidden

layer output h

becomes the visible layer input for the

next RBM, repeating this process sequentially for all

RBMs. Once training is complete, the DBN parame-

ters (W

, b

, and c

) are ﬁxed. Given an input vector

x = [x

,...,x

], the nodes in the k-th hidden layer

= [h

,...,h

] are calculated by Eq.( 3).

k j

= sigm

∑

i=1

ki j

+ c

k j

(3)

In the top hidden layer, the feature representation

,...,h

] is integrated with the TSK fuzzy sys-

tem output to form a neural fuzzy system. This sys-

tem leverages the DBN’s data representation capabil-

ities to capture complex features while enhancing the

model’s understanding and capability to address com-

plex data structures.

2.2 Fuzzy Representation Based on

TSK Fuzzy System

FBLS comprises n fuzzy subsystems and p en-

hancement node groups. It accepts input data

denoted as X = (x

,...,x

)

within R

N×M

where each sample feature is represented as x

,...,x

),s = 1,2,...,M. Each fuzzy subsys-

tem contains a set of fuzzy rules designed to extract

features from the input data. For the i-th fuzzy sub-

system with k

fuzzy rules, a series of ﬁrst-order TSK

fuzzy system rules are deﬁned based on the input fea-

tures, which can be expressed as:

= f

,...,x

) =

∑

t=1

(4)

where k = 1,2,...,k

is the fuzzy rule of the i-th fuzzy

subsystem, α

is a coefﬁcient uniformly distributed

on the interval [0,1]. In this study, for the i-th fuzzy

subsystem, the training data is segmented into k

clus-

ters, represented by c

, utilizing the FCM method.

Semi-Supervised Fuzzy DBN-Based Broad Learning System for Forecasting ICU Admissions in Post-Transplant COVID-19 Patients

417

The FCM clustering method is used to minimize the

objective function:

(U,C) =

∑

s=1

∑

k=1

∥

− c

∥

(5)

In Eq. (5), m represents a fuzziﬁcation coefﬁcient,

U = (u

)

N×k

is a membership matrix, u

indicates

the degree of membership of x

in cluster k, and c

the centroid of cluster k in M-dimensional space. The

optimization of the objective function J

(U,C) can be

solved by iteratively updating the membership u

and

the centroid c

, following these formulas:

∑

t=1



∥

− c

∥

− c

∥



m−1

−1

(6)

∑

s=1

· x

∑

s=1

(7)

Distinct from the k-means method, in the fuzzy

C-means approach, the weighted ﬁring strength in the

i-th fuzzy subsystem is set as w

= u

. This elim-

inates the need for deﬁning additional membership

functions for the fuzzy rules. The intermediate out-

put vector of the i-th fuzzy subsystem Z

is given by:



,...,w



(8)

2.3 DBN-Based Fuzzy Broad Learning

System

Integrating the top hidden layer feature vectors of

DBN with the output vectors of the TSK fuzzy sys-

tem, we consider the feature representation vector of

DBN, [h

,...,h

], as well as the system output

vector of the TSK Fuzzy System, Z

. Given the

dimensionality of the DBN’s top hidden layer fea-

ture vector as n

, and the output of each TSK Fuzzy

subsystem based on k

fuzzy rules, we construct a

combined feature representation vector, Z

, shown as

Eq. (9).

= [h

,...,h

,...,Z

] (9)

where Z

∈ R

N×

(

∑

i=1

)

. Here, Z

,...,Z

represent the output vectors from each subsystem of

the TSK Fuzzy System, and h

,...,h

represent

the feature representation vector from the top hidden

layer of the DBN.

Utilizing Z

, this method employs nonlinear trans-

formations in the enhancement layer (comprising p

groups of enhancement nodes) to obtain the output

of the enhancement layer, H

. This is deﬁned as

Eq. (10).

= (H

,...,H

) ∈ R

N×

(

+...+E

)

(10)

Herein, H

( j = 1, 2, . . . , p) is computed as:

= ϕ

+ β

) ∈ R

N×E

(11)

Here, E

denotes the number of neurons in the j-th

group of enhancement nodes. W

and β

are respec-

tively the weights and biases for the intermediate out-

put Z

from the fuzzy subsystems to the enhancement

layer, which are randomly distributed within the range

of [0,1]. ϕ(·) represents a type of nonlinear transfor-

mation.

Y = [Z

| H

]





= AW

(12)

Here, W

is the weight matrix for the combined

feature representation matrix Z

to the output layer.

is the mapping matrix for the enhancement layer.

W is the weight matrix connecting all fuzzy subsys-

tems and enhancement node layers to the output layer,

calculated based on the system’s output. According

to (Cao et al., 2017), W can be derived as:

W =



λI + AA



−1

Y (13)

2.4 Dual Manifold Regularization

Framework

In this study, DMR-FBLS incorporates dual mani-

fold regularization mechanisms: sample-based and

feature-based manifold learning. Sample-based man-

ifold learning preserves the distributional character-

istics of samples in the original space, ensuring that

proximity in the original sample space is maintained

in the lower-dimensional projected space. Feature-

based manifold regularization hypothesizes that sim-

ilar feature dimensions in the fuzzy feature space

should have similar corresponding weights, ﬁltering

out noise and redundant features, thereby improving

learning efﬁciency and generalization capability. This

dual strategy effectively utilizes the internal struc-

ture of samples and the relations between fuzzy fea-

tures, enhancing learning performance, especially in

datasets with substantial unlabeled data.

2.4.1 Sample Manifold Regularization

If two samples are proximate in the input space, their

outputs should be proximate in the target space. We

use a Gaussian kernel function to measure the dis-

tance between samples:

s(x

) = exp

−



− x



2σ

(14)

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418

Here, σ

controls the kernel spread, affecting dis-

tance measurement. The similarity matrix S is con-

structed, treating samples as nodes and their similari-

ties as edges, forming an adjacency graph. The regu-

larization term is deﬁned as:

(w) =

∑

i, j=1

i j



− y



= tr



(AW )



(15)

Here, L

= H

− S is the Laplacian matrix. This

regularization strategy boosts the model’s generaliza-

tion performance by maintaining sample positions in

the target space and capturing latent structural infor-

mation in unlabeled data.

2.4.2 Feature Manifold Regularization

The FBLS framework may result in a high-

dimensional feature matrix with redundant features.

Inspired by sample-based manifold regularization, we

introduce feature-based manifold learning to reduce

redundant feature inﬂuence. We hypothesize that cor-

related feature dimensions in the fuzzy feature space

will have similar weight coefﬁcients. The Gaussian

kernel function quantiﬁes the correlation between fea-

ture dimensions:





= exp

−

∥

− A

∥

2σ

(16)

The manifold regularization term is deﬁned as:

(W ) =

N×

(

C+E

+...+E

)

∑

q,t=1



−W



= tr





(17)

Here, L

= H

− F is the Laplacian matrix. This

approach effectively captures structural information

in the fuzzy feature space.

2.5 Semi-Supervised DMR-FBLS

The objective function of the original FBLS fuzzy

system is redeﬁned as:

min

D∥y − AW ∥

+ α∥W ∥

+ βtr



(AW )



+ λtr





(18)

By differentiating and setting the derivative to

zero, we obtain:

QAW + αW +βA

AW + λL

W = A

Qy (19)

W can be directly derived from the (19) as:

W =



QA + αI + βA

A + λL



−1

Qy (20)

In semi-supervised learning, our framework inte-

grates both labeled and unlabeled data. The labeled

dataset is encapsulated as

{

}

{

}

i=1

, where

l denotes the count of labeled instances. Conversely,

the unlabeled dataset is denoted as X





j=1

with u symbolizing the number of unlabeled samples.

In (20), α, β, λ are coefﬁcients corresponding to the

regularization term, the sample manifold regulariza-

tion, and the feature manifold regularization, respec-

tively. The weight matrix Q, a diagonal matrix, plays

a role in ﬁltering and weighting the samples. In this

study, for the diagonal matrix Q, the diagonal ele-

ments corresponding to the ﬁrst l rows and columns,

which represent the labeled data, are set to 1. The re-

maining diagonal elements are set to 0. The Laplace

matrices L

and L

are computed based on similar-

ity measures derived from both labeled and unlabeled

data. This design efﬁciently exploits the structural in-

formation and feature relationships inherent in the un-

labeled data.

3 EXPERIMENTAL SETUP

In this section, we will provide a detailed description

of the dataset utilized in this experiment, as well as

the classiﬁers and evaluation metrics employed.

3.1 Dataset

The IDOTCOVID database represents a comprehen-

sive global resource, encompassing data from approx-

imately 1200 patients across 78 transplant centers

in 11 different countries, collected between March

2020 and March 2021. This database incorporates a

wide array of variables, including demographic and

transplant-related information, as well as epidemio-

logical, clinical manifestations, and treatment man-

agement of solid organ transplant (SOT) patients dur-

ing the COVID-19 pandemic. The descriptive statis-

tics for the IDOTCOVID database are shown in Ta-

ble. 1.

3.2 Classiﬁers and Evaluation Metrics

To evaluate the DMR-FBLS model’s performance

and compare it with other mainstream algorithms,

we selected eight distinct ML models. These mod-

els, including XGBoost, RF, and AdaBoost, repre-

sent various ML categories and have been validated

in their domains, particularly in organ transplanta-

tion research for their accuracy and robustness (Zhang

Semi-Supervised Fuzzy DBN-Based Broad Learning System for Forecasting ICU Admissions in Post-Transplant COVID-19 Patients

419

Table 1: Descriptive Statistics for IDOTCOVID database.

Data Statistics results

Recipients 1267

Average Age 56.17

Gender Female (448), Male (819)

Average Age at SOT 47.39

Total Attribute 206

SOT Type Kidney: 64.88%, Liver: 33.46%

Patient Country Spain (908), Mexico (211), Argetina (147), Italy (69), etc.

Demographic Attributes Age, Gender, Country, DOB, Age at SOT, etc.

Clinical Attributes Type of SOT, Diagnosis, Symptoms, Manifestations, etc.

Treatment Attributes Kaletra, Remdesivir, CsA-Red, etc.

Admission Attributes Blood Pressure, Vasoactive drugs, X-ray, etc.

Categories of Attributes

Various (incl. Demographics, Clinical,

Treatment, Admission)

et al., 2022; Liu et al., 2020). Decision Trees (DT)

are known for their interpretability and efﬁciency with

categorical data, essential in clinical decision-making.

BLS and Multi-Layer Perceptron (MLP) represent

neural networks with strong function mapping capa-

bilities. FBLS and TSK are fuzzy systems that handle

uncertainty well, showing good performance in mul-

tiple studies (Peng and ChunHao, 2022; Xue et al.,

2018). This diverse selection ensures a thorough as-

sessment of D-DMR-FBLS across different scenarios.

We split each dataset into 70% training and 30% test-

ing sets, optimized hyperparameters using ﬁve-fold

cross-validation on the training set, and executed each

algorithm 50 times. Performance was evaluated using

four key metrics: accuracy, AUC, F1-score, and G-

mean.

4 EXPERIMENTAL RESULT AND

DISCUSSION

4.1 Comparative Results and Analysis

The results in Table 2 compare the performance

of various models predicting ICU admission among

COVID-19 infected organ transplant recipients. The

D-DMR-FBLS model excelled across all metrics,

achieving an accuracy of 0.899, AUC of 0.853, G-

mean of 0.727, and F1-score of 0.666, outperforming

other models. This conﬁrms D-DMR-FBLS’s supe-

rior accuracy and balanced classiﬁcation efﬁciency.

The mainstream ML algorithms like XGBoost,

RF, and Adaboost performed well in AUC but poorly

in G-mean and F1-score, crucial for handling class

imbalance. The FBLS model outperformed the BLS

model across all metrics, showing its capability in

processing complex data. Integrating the TSK fuzzy

subsystem into BLS improved its recognition of mi-

nority class samples.

Figure 2 shows the performance of four BLS-

based algorithms across four metrics. Ablation ex-

periments highlight D-DMR-FBLS’s superior perfor-

mance, especially in G-mean and F1-score. The

Table 2: The performance comparison for different models

on ICU admission prediction.

Method Accuracy AUC G-mean F1-score

D-DMR-FBLS 0.899 0.853 0.727 0.666

FBLS 0.890 0.833 0.706 0.618

BLS 0.867 0.815 0.678 0.579

TSK 0.875 0.823 0.702 0.611

XGBoost 0.862 0.837 0.629 0.518

RF 0.861 0.842 0.516 0.400

MLP 0.856 0.824 0.687 0.506

Adaboost 0.868 0.839 0.569 0.475

DT 0.846 0.790 0.601 0.468

Figure 2: Comparative results of ablation experiments

across various metrics for D-DMR-FBLS, DMR-FBLS,

FBLS, and BLS.

Table 3: Results of the Wilcoxon signed-rank test, with D-

DMR-FBLS serving as the control algorithm. If the p-value

for a particular method is less than 0.05, it indicates a sig-

niﬁcant performance difference between that method and

D-DMR-FBLS.

Accuracy AUC F-score G-mean

FBLS 0.0409 0.0000 0.0000 0.0012

DMR-FBLS 0.8333 0.0106 0.0037 0.0991

BLS 0.0000 0.0000 0.0000 0.0001

TSK 0.0002 0.0000 0.0000 0.0040

XGBoost 0.0000 0.0048 0.0000 0.0000

RF 0.0000 0.0056 0.0026 0.0000

MLP 0.0000 0.0000 0.0000 0.0001

Adaboost 0.0000 0.0027 0.0012 0.0000

DT 0.0000 0.0000 0.0000 0.0000

FBLS model showed performance improvements

over BLS. Adding graph manifold regularization

(feature-based and sample-based) to DMR-FBLS fur-

ther enhanced performance by uncovering the cor-

relation within feature space and hidden data struc-

ture. Incorporating DBN into DMR-FBLS to form

D-DMR-FBLS improved all metrics. DBN deepens

the model’s representation learning, capturing hidden

data characteristics and boosting classiﬁcation perfor-

mance when combined with the TSK fuzzy system.

Table 3 uses the Wilcoxon signed-rank test to

compare D-DMR-FBLS against other algorithms.

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420

(a) Accuracy comparison. (b) G-Mean Comparison.

Figure 3: Performance of accuracy with unlabeled training samples and varying quantities of labeled training samples.

Except for DMR-FBLS, which showed no signiﬁcant

difference in accuracy and G-mean (p-values > 0.05),

most other algorithms had p-values < 0.05, indicating

signiﬁcant differences and rejecting the null hypoth-

esis. This demonstrates D-DMR-FBLS’s substantial

performance advantage.

4.2 Comparative Experiment on Using

Unlabeled and Limited Labeled

Samples

To evaluate our proposed algorithm with limited la-

beled and unlabeled samples, we compared it with

other fuzzy systems. From the original ICU admis-

sion dataset, we extracted 567 samples and concealed

their labels to create an unlabeled dataset. We then

stratiﬁed samples according to label categories and

selected 200, 300, 400, 500, 600, and 700 labeled

samples to test the model’s performance with varying

labeled data. This approach assesses the applicabil-

ity and performance of the proposed algorithms in a

weakly-supervised learning context.

In this experiment, we evaluated and compared

the performance of three fuzzy systems—D-DMR-

FBLS, FBLS, and TSK—using unlabeled samples

and a varying number of labeled samples. Through

this experiment, we aim to evaluate the performance

of different fuzzy systems in scenarios with small

sample sizes and lacking labeled samples. As can be

seen from Figure. 3a and Figure. 3b, at fewer labeled

sample sizes (200 and 300 samples), the result reveals

that the accuracy of the D-DMR-FBLS model consid-

erably surpasses that of FBLS and TSK fuzzy mod-

els, indicating D-DMR-FBLS’s effective learning ca-

pability and strong generalization ability with limited

label. As the number of labeled samples increases

to a relatively higher range (from 500 to 700 sam-

ples), the improvement in accuracy and G-mean val-

ues for all three models starts to stabilize. Within this

sample size bracket, the DMR-FBLS model main-

tain the highest accuracy, yet the performance gap

between the TSK and FBLS models begins to nar-

row. In general, the trend suggests that when faced

with a small number of labeled samples and the pres-

ence of unlabeled samples, the D-DMR-FBLS model

demonstrates a signiﬁcant advantage over the other

two fuzzy systems. However, while the performance

of all models improves with an increase in the num-

ber of labeled samples, the rate of improvement de-

celerates, indicating that additional labeled informa-

tion has a limited impact on enhancing model per-

formance beyond a certain sample volume thresh-

old. Overall, from the experimental results, we can

conclude that the D-DMR-FBLS model demonstrates

strong learning capabilities and robust generalization

abilities compared to the other fuzzy systems under

the scenario with a small number of labeled and unla-

beled samples.

5 CONCLUSION

This study introduces a novel semi-supervised Dual-

Manifold Regularized Fuzzy Broad Learning System

(D-DMR-FBLS), aimed at enhancing the predictive

performance for ICU admissions among post-COVID

organ transplant recipients. Our method enhances

the representation learning capability through the use

of DBN and TSK fuzzy systems in the UTP phase,

thereby enriching the model’s capacity to process and

learn from complex data structures. Besides, our ap-

proach integrates feature manifold regularization and

sample manifold regularization with FBLS, improv-

Semi-Supervised Fuzzy DBN-Based Broad Learning System for Forecasting ICU Admissions in Post-Transplant COVID-19 Patients

421

ing the model’s generalization capability. Accord-

ing to experimental results, the D-DMR-FBLS out-

performed other models in terms of accuracy, AUC,

F1-score and G-mean. Besides, its performance sur-

passes the FBLS and TSK fuzzy systems, especially

in scenarios with limited labeled samples. This new

neuro-fuzzy system shows promise for use in contexts

with limited medical resources, assisting the decision-

making for the allocation of medical care to organ

transplant recipients. Future research could further

explore the application of D-DMR-FBLS across other

medical datasets, validating its effectiveness in varied

medical contexts.

ACKNOWLEDGEMENTS

This paper is part of project

PID2022-143299OB-I00, ﬁnanced by

MCIN/AEI/10.13030/501100011033/FEDER,UE.

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