Access to this full-text is provided by Springer Nature.
Content available from BMC Medical Genomics
This content is subject to copyright. Terms and conditions apply.
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
https://doi.org/10.1186/s12920-025-02109-4
RESEARCH Open Access
© The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if
you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or
parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To
view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
BMC Medical Genomics
Disease candidate genes prediction using
positive labeled andunlabeled instances
Sepideh Molaei1 and Saeed Jalili1*
Abstract
Identifying disease genes and understanding their performance is critical in producing drugs for genetic diseases.
Nowadays, laboratory approaches are not only used for disease gene identification but also using computational
approaches like machine learning are becoming considerable for this purpose. In machine learning methods,
researchers can only use two data types (disease genes and unknown genes) to predict disease candidate genes.
Notably, there is no source for the negative data set. The proposed method is a two-step process: The first step
is the extraction of reliable negative genes from a set of unlabeled genes by one-class learning and a filter based
on distance indicators from known disease genes; this step is performed separately for each disease. The second step
is the learning of a binary model using causing genes of each disease as a positive learning set and the reliable nega-
tive genes extracted from that disease. Each gene in the unlabeled gene’s production and ranking step is assigned
a normalized score using two filters and a learned model. Consequently, disease genes are predicted and ranked. The
proposed method evaluation of various six diseases and Cancer class indicates better results than other studies.
Keywords Disease gene prediction, Positive-unlabeled learning, Gene expression profile, Score relevance, Support
vector machine
Introduction
Genes are the factors of inherited and genetic disorders
that can path through into future generations. Also,
they can be hidden and may be revealed in the future.
Hence, genetic disease treatment or prevention has been
challenging for physicians and health researchers from
the past to now. ereby, predicting disease genes and
understanding their mechanisms is the first critical step
in pharmacology and medicine for treatment and preven-
tion. Today, new studies have significantly enhanced for
finding the disease’s molecular basis to prevent, diagnose,
and treat genetic diseases.
e utilization of machine learning methods to solve
various problems has shown promising performance
compared to traditional and experimental methods. In
particular, machine learning techniques in medicine have
attracted significant attention. Experimental and labo-
ratory-based methods for solving medical problems are
often cost-intensive and time-consuming, which has led
to a growing interest in computational methods, includ-
ing machine learning. Furthermore, while some genes are
classified as non-disease genes, they may be identified
as disease-related in different contexts. is complexity
has made it difficult to definitively classify non-disease
genes, as knowledge in this area remains limited. How-
ever, recent studies have shown that some human genes
play a role in diseases and can be valuable for predicting
disease-related genes using machine learning methods.
In predicting and ranking disease genes using machine
learning, the disease-known genes are considered a posi-
tive data set, and unknown genes are considered unla-
beled genes. Prediction and labeling the genes causing
a disease (based on ranking) among the unknown genes
using that disease’s known genes is the purpose of this
*Correspondence:
Saeed Jalili
sjalili@modares.ac.ir
1 Computer Engineering Department, Tarbiat Modares University, Tehran,
Iran
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 2 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
issue. Due to the data nature, one of the most proper
solving methods of this issue (which consists of the data’s
nature) is the Positive Unlabeled Learning (PU-Learning)
approach [1]. e PU-Learning method is semi-super-
vised; this method is used for binary classes with positive
labeled and unlabeled samples. is type of learning has
no negative labeled samples, and it distinguishes it from
other learning types. e available data in this type of
learning is as two following types: (i) data set including
positive labeled samples; (ii) data set without label that
potentially can be the cause of the disease (positive) or
non-disease (negative). e studies regarding solving this
issue with the PU-Learning approach are classified into
two general approaches: 1) Identifying negative samples
approach; 2) not identifying negative samples approach.
e negative genes (non-disease) are initially selected
among the unlabeled genes in the identifying negative
samples approach. Next, binary models are learned sep-
arately for each disease using data set containing genes
causing that disease (with positive label) and non-disease
genes (with negative genes). Selecting reliable negative
genes is the main challenge in this strategy. e more
reliable they are the learning will be accurate in the next
step. In the not identifying negative samples approach,
learning of one class is only carried out using positive
samples. is method will be useful if the number of pos-
itive samples is ample and sufficient.
Moreover, the efficiency of this method is very low if
the number of positive samples is insufficient [2] or the
entire unlabeled genes consider negative samples. Con-
sequently, the problem will be changed to an unbalanced
binary classification, and then binary models will be
learned. Since the dataset of unlabeled genes is included
potential negative and positive samples, utilization of this
method have high error. Recently, the use of this method
has been reduced [3].
e extraction of reliable negative genes in the pro-
posed method is as follows: negative genes extraction is
carried out separately for each disease in the one-class
learning step. en, the most distant negative genes from
known disease genes are selected. Indeed, designing reli-
able negative gene extraction in such a way will enhance
the trust in extracted negative genes. Disease genes will
be selected separately for each disease in the binary
model learning step based on the proposed method’s
designed scoring system. e score-relevance indicator
is used for this purpose. e score of each disease gene
is normalized using a scoring system. en, it is decided
whether or not to select any disease gene as positive edu-
cational data based on the score of each gene. Eventually,
a binary disease model is learned using the Support Vec-
tor Machine (SVM) algorithm. e other two filters are
used in the unlabeled genes’ prediction and ranking step
after determining the sample’s label using the learned
binary model. ese two filters are based on: 1) each
gene’s distance from the support vector; 2) the closeness
of the gene to disease genes. A normalized score is laid
out for each gene using the designed scoring system in
the proposed method and the distance of every unla-
beled gene from the disease binary model’s support vec-
tors. Next, another score is laid out for each gene using
a designed scoring system and score relevance related to
every unlabeled gene. Eventually, a single score for each
gene is obtained by formulating scores. en, the deci-
sion is made for the unlabeled gene (in other words,
whether the gene is a candidate for the disease or not).
Besides, the rank of the gene is determined if it is a candi-
date for the disease. e outcomes of evaluating the pro-
posed method compared to the best previous available
proposed method are as follows:
e recall measure of Adrenal, Colon, Lung, Prostate,
and Heart Failure diseases and Cancer disease class are
increased by 0.53%, 5.32%, 1.29%, 3.33%, 4.04%, and
3.11%, respectively. Moreover, the increase of precision
measure is 2.64%, 2.14%, 1.75%, 3.14%, 3.13%, and 2.38%,
respectively. e increase of AUC measure for Neurolog-
ical disease is 8.82% compared to other studies.
Basic concepts
Gene expression prole (GEP)
Gene expression data provides valuable information
regarding cellular situations, biological networks, and
understanding of genes’ performance. Indeed, the genetic
codes have been stored in DNA strands. Furthermore,
they will interpret by gene expression. Determining how
genes are expressed in non-disease and diseased cells is
one of the purposes of gene expression interpretation.
Scientists utilize DNA microarray (biochips) to measure
gene expression amount. A set of gene expression samples
is the result of determining the gene expression amount’s
experiment. Every row in the gene expression matrix indi-
cates the related gene expression profile. Time series of
gene expression profiles (which state the gene expression
level in determining periods) are used in this study.
Similarity‑based communication principle
Similarity-based communication principle is used in
most disease candidate gene prediction problem-solv-
ing methods. e mentioned principle declares that the
greater the physical and performance similarity of genes,
the greater the probability of their role in developing the
same diseases. e closeness amount to the disease genes
can be used as a rank.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 3 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
Score relevance
e scores for each gene based on Score-Relevance can
be considered a score for the effectiveness of that gene
in the specific disease formation. Indeed, the mentioned
scores are based on the simultaneous presence of two ele-
ments in the Medline1 document. is score is based on
a formula (the base of this formula is the Boleyn model)
and is calculated for finding coincident documents and
their conformity amount. Overall, the mentioned for-
mula has used the concepts of Term Frequency-Inverse
Document Frequency (TF-IDF), Vector Space, Coordina-
tion factor, and field length normalization [4].
Comparing the number of documents in which two
elements are present next to each other and the number
of documents in which elements independently appear
with the expected amount is carried out based on the
hypergeometric distribution. e greater the simulta-
neous presence of elements (compared to the expected
amount) will reduce the random occurrence of this hap-
pen. Consequently, the scores will enhance [5]. Unfor-
tunately, these scores are not significant absolutely and
only are sequentially significant in the related genes list of
each disease and have particular importance. Moreover,
the absolute amounts of scores may vary from one ver-
sion to another version.
Research history
e previous studies regarding disease candidate gene
prediction are introduced in two groups.
Identifying negative samples approach
Yousef and Moghadam [6] used proteins’ amino acid
sequences for predicting and ranking the diseases’ genes.
ey construct four various characteristic vectors using
amino acid sequences. Moreover, they use cosine dis-
tance for extracting reliable negative genes. Eventually,
the characteristics of a model are learned separately for
each vector. e results of every category are integrated,
and the final result will be announced.
VasighiZaker and Jalili [7] presented the C-PUGP method.
In this method, the clustering of positive samples is con-
sidered initially. Next, a one-class model with an OCSVM
learning algorithm is carried out for every cluster. Labeling
of unlabeled samples is performed using learned models.
en, the unlabeled gene, which gives a negative label based
on the entire one-class models, is considered a reliable nega-
tive sample. Finally, the SVM binary model is learned using
the obtained negative samples and initial positive samples.
Many initial studies considered the entire unlabeled genes
as negative samples and learned a binary model. Since the
dataset of unlabeled genes is included negative and posi-
tive samples, utilization of this method have high error.
Smalter etal. [8] predicted disease candidate genes using
the protein–protein interaction dataset and SVM binary
model. Radivojac etal. [9] used three various datasets and
learned an SVM binary model for every dataset. ey iden-
tify disease candidate genes using these three disease binary
models’ results. e used datasets were protein sequences,
protein performance information, and the PPI network.
Not identifying negative samples approach
Learning is carried out only with positive samples in this
method. e efficiency of this method is very low if the
number of positive samples is insufficient [2]. Yousef and
Moghadam [10] identified disease genes using the SVDD
one-class model (only by using the sequences of disease
genes). is method generates the characteristic vector
by converting protein consequences to numerical vectors
using their physicochemical properties translation. en,
they reduced the characteristics sizes to find the criti-
cal characteristics using Principal Component Analysis
(PCA). e disease genes (positive samples) are learned
using SVDD one-class model in the next step. e unla-
beled samples will predict using the learned model. e
entire disease genes are initially considered a positive set
in the method of VasighiZaker and Jalili [11]. is set will
normalize by the Min–Max method. en, the number of
the characteristic will reduce using the PCA method. Next,
the learning is performed by OCSVM one-class model.
e unlabeled genes are labeled after finding the optimal
parameters. Nikdel and Jalili [12] studied the clustering of
disease genes based on a constructed matrix by measuring
semantic similarity among the disease types; this is carried
out based on the gene ontology. Next, the Hidden Markov
Model (HMM) is learned for each cluster; a threshold is
calculated for each cluster separately. e unlabeled genes
are given to the entire learned hidden Markov models of
that disease. e label of that gene will identify given the
probability obtained from each hidden Markov model and
calculated threshold for each cluster. In other words, if at
least one of the hidden Markov models (among the entire
learned hidden Markov models of that disease) considers
an unlabeled gene as a disease candidate, the positive label
is attributed to that gene. After normalizing gene expres-
sion data, Vasighizaker etal. [13] used a one-class support
vector machine model with a linear kernel for predicting
disease genes in Acute Myeloid Leukemia (AML) cancer.
The proposed method
e scoring-based method using the SVM binary model
is introduced to solve the prediction and ranking prob-
lem of disease candidate genes; this method scores
1 It is one of the most famous free databases worldwide and includes biblio-
graphic research information for the entire medical and biology fields.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 4 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
effective factors in predicting and ranking disease candi-
date genes. e main aim of this method is disease can-
didate genes prediction and ranking from an unlabeled
gene set. e higher priority belongs to the gene more
likely to belong to the disease candidate genes group.
Unlabeled genes are human genome that does not belong
to disease genes. Notably, determining gene expression is
performed in various laboratories. erefore, a gene may
have more than one gene profile. Consequently, the entire
calculation is carried out separately for a gene’s profile.
e S-PUL2 proposed method has four following steps:
1) data normalization; 2) reliable negative genes extrac-
tion; 3) disease binary model learning; 4) disease candi-
date genes prediction and ranking (see Fig.1). e gene
expression data is normalized in the first step. In the sec-
ond step, reliable negative genes are extracted from unla-
beled samples separately for every disease. e binary
model is learned separately for every disease with posi-
tive samples (disease genes) in the third step. In the fourth
step, reliable negative genes are eliminated from unlabeled
genes (U). en, the remaining unlabeled gene set (Rui) is
given to the disease binary model for label prediction.
e term "S-PUL" stands for Scored-Positive Unla-
beled Learning. It is a combination of two used methods:
Positive Unlabeled Learning (PUL) and a Scoring system.
e scoring aspect refers to the integration of a scoring
system within the Support Vector Machine (SVM) algo-
rithm. is hybrid approach leverages the strengths of
both techniques to enhance the learning process.
Data normalization step
Each gene’s time expression range is different, and their
difference is high. e entire data is normalized sepa-
rately for two datasets (disease and unlabeled genes). e
normalization is carried out based on Eq.1. e highest
and lowest amounts of every gene’s time expression are
indicated by Xmax and Xmin in Eq.1, respectively.
Reliable negative genes selection step
Learning disease binary model, in addition to disease
genes set (as positive samples), requires reliable nega-
tive genes set (as negative samples). It is evident that the
accuracy of predicting unlabeled genes by the disease
binary model (as disease genes) increases with enhancing
the trust degree in the identified negative genes (among
unlabeled genes). Figure2 illustrates the reliable negative
gene extraction process related to each disease class.
In the first action (i.e., Action 1 Algorithm), the Robust
Gaussian, KNN, Parzen window, and SVDD one-class
classification algorithms are used for learning the positive
samples model separately for each disease class. Moreo-
ver, other disease classes’ genes (after eliminating common
genes) are used as test data. After learning a disease model,
other diseases genes are expected to appear in the negative
data role. Hence, the evaluation indicator to select the best
learning algorithm is the percentage of considered accurate
negative samples. Eventually, the learned one-class algo-
rithm that has the highest percentage of accurate negative
samples is selected as the best one-class model of i-th dis-
ease. In the Action2, unlabeled genes are given to the best
one-class model as input, and unlabeled genes are labeled.
e outcome of this step is a set of negative genes. Finally,
Reliable negative genes are selected from the set of nega-
tive genes in the third step (i.e., Filter1 algorihtm.). e
shortest Euclidean distance of every negative gene is cal-
culated from its correspondent disease genes. If a disease
gene expression profile (Ne) from the NDi set is shown by
Ne ={d1,d2,d3,...,dm}
and the negative gene expression
profile (Ngi) is shown by
Ngi={n1,n2,n3,...,nm}
, the
Euclidean distance is calculated using Eq.2. us, the mini-
mum distance of every negative gene from its correspond-
ent disease genes is calculated based on Eq.3. Eventually,
the farthest genes from disease genes are selected as reliable
negative genes for every disease i (RNDi).
(1)
X
normalized =
(X
max
−X)
(Xmax −Xmin)
Fig. 1 S-PUL proposed method process
2 Scored-Positive Unlabeled Learning.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 5 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
Action1 Algorithm (Learning one-class model of i-th Diseases)
Learning step ofthedisease binary model
e prediction and ranking problem of disease candidate
genes are solved based on binary model learning. Figure3
indicates the learning process of the disease binary model.
Selecting the positive training data from the disease genes
set of every disease is another challenge of this study.
(2)
Dis
Eu(Ne,Ngi)=
m
k=1
(dk−nk)2
(3)
Ne
k=min
∀Ne∈NDi
Dis_Eu Ne,Ng i
It is worth noting that the role of genes in the arising of
disease has different degrees. e reliability of learning
results will enhance using genes (as training data) that have
higher correspondent S-R3 values in the learning process.
e selection of disease genes is performed using S-R for a
positive training set in this study. e value of S-R related
to every disease gene (separately for each disease) is avail-
able in [4].
Positive genes selection (Filter 2)
Positive genes of each disease are selected in four steps.
is process is described step by step in the following
and presented formally by "Filter 2 algorithm".
In the first step, disease class genes are categorized based
on their S-R values (separately for each disease). e gene
Fig. 2 The reliable negative genes extraction process
3 Score Relevance (explained in "Score relevance" section).
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 6 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
will belong to a higher category by enhancing its S-R value,
thus obtaining a higher score. e categories with equal
intervals of ten units will create for categorizing genes
based on their S-R value. erefore, the first category is
related to the genes whose range is [0,10). In other words,
the first category has the lowest value. Accordingly, each
gene will belong to a category (the length of these catego-
ries is 10). One of the challenges of this study is determin-
ing the value of these categories’ range. e distribution
of disease genes number based on the S-R values is not
uniform. Each category’s range should be determined so
that it does not lead to the over-elimination of genes. e
length of 10 for categories is a logical number for the entire
disease. e mentioned length has been obtained by trial
and error in this study. Moreover, this number can be cal-
culated more accurately in future studies.
In the second step, every category gets a portion of 100
points according to its obtained score. In other words,
the highest percentage will obtain by the highest cat-
egory. e category score related to the i-th category is
shown by
NGri
; this reaches the base of 100. e
NGri
can be calculated by Eq.4.
e category score of the entire genes belonging to the
disease is saved in Gr set. In Eq.4, Max(|Gr|) is the high-
est category score of a gene belong to a disease class; S-Ri
indicates the S-R value related to the i-th gene of Gr set.
In the third step, the final score of the i-th gene F_
Scorei is calculated by Eq.5.
e mean scores range
(
−
IL)
is calculated based on the
Eq.6 (separately to every disease). Moreover, some genes
are selected as positive training data (their final score
is over the mean of the scores range). In Eq.6, the final
score of the entire genes is in the {F_Score} set.
(4)
NGr
i=(
SRi
10
+1)×
200
Max {|Gr|}(Max {|Gr |}+1
)
(5)
F_Scorei=NGri×S−Ri
(6)
IL
=
Max{F_Score}+Min{F_Score}
2
Filter2 Algorithm (Positive genes selection)
Fig. 3 Learning process of disease binary model
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 7 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
Positive genes selection (Filter3)
Filter 3 is an optimization step in the proposed method
designed to eliminate low-significance genes and
reduce noise in the data. Specifically, this filter removes
genes that received a negative label from the SVM
binary model during the learning phase, and have S-R
values in the lowest scoring range ([0, 10)).
e primary goal of this filter is to focus the learning
process on genes that are more likely associated with
the disease, while excluding genes that have the least
impact on disease formation. By doing so, the learning
process is refined, and it is expected that the prediction
accuracy for disease candidate genes will improve.
Binary model learning
In Action3 of Fig.3, the binary learning using binary
learning algorithms is performed using selected posi-
tive training genes (PDi) from i-th disease genes and
reliable negative genes (RNDi) from unlabeled genes.
Eventually, the algorithm that obtains the highest recall
evaluation value for all diseases is selected.
Disease candidate genes prediction andranking step
e remaining unlabeled gene sets (i.e., the unlabeled
genes set that the extracted negative genes are elimi-
nated in that set in Reliable negative genes selection
step) are given to the disease binary model as test data
after learning and selecting the best binary learning
algorithm (SVM) with having the best learning param-
eters. A scoring algorithm is also used in the disease
candidate prediction and ranking step, as illustrated in
Fig.4. ere are two critical factors in the scoring algo-
rithm: 1) e distance of every unlabeled gene from the
disease gene; 2) e distance of every unlabeled gene
from the support-vector of the i disease model. genes
give a score based on each mentioned factor. e final
score of the gene will obtain by multiplying these two
scores. Eventually, the prediction and ranking are car-
ried out according to the final score.
Action4‑ Identifying thevaluable genes
e unlabeled genes given to the i disease (i.e.; the
extracted reliable negative genes of i-th disease elimi-
nated from the unlabeled genes set; RUi indicates
this set) are labeled and stored in the DS1 set using
the i-th disease learning model. Suppose that the
expression profile of disease gen (Ne) from the NDi
set is
Ne ={d1,d2,...,dm}
, and the expression pro-
file of an unlabeled gene (Ru) from the RUi set is
Ru ={u1,u2,...,um}
. e closet i disease gene (Ne) to
each Ru studied expression profile from the RUi dataset
is identified using Eqs.2 and 3(in terms of Euclidean dis-
tance). Moreover, it is stored in the DS2 set. Negatively
labeled genes are eliminated from the DS1 dataset to pre-
serve valuable genes (separately to each profile). eir
correspondent S-R values are settled in the DS2 dataset
of the first category (the least valuable category). e
remaining genes are stored in the VRUi dataset. ese
remaining genes are negatively labeled genes with high
S-R and positive labeled genes that are valuable genes.
Action5‑ The prediction andranking ofdisease candidate
genes
e
F_Score
value of the nearest disease gene is attrib-
uted to Ru studied gene profile from the VRUi dataset.
It is worth noting that the nearest disease gene to each
studied gene profile is identified in the "Reliable negative
genes selection step" section and maintained in the DS2
dataset. In this method, the given label to each Ru studied
gene is maintained from the VRUi dataset. Each gene has
many gene profiles. us, the final score of a gene is the
algebraic summation of scores of that gene’s profiles. e
output of this step is the DS3 dataset, which contains the
entire valuable genes input from the VRUi to this step,
along with the second score of each gene (
DP_Scorei
). It
is worth noting that the reliability of the sample belong-
ing to the i disease class increases with enhancing the
distance of the tested sample from the support vectors of
the i disease model. In contrast, the reliability of the sam-
ple belonging to the i disease class reduces by reducing
Fig. 4 The prediction and ranking process of disease candidate genes
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 8 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
the distance of the tested sample from the support vec-
tors of the i disease model. Consequently, the gene score
will increase by distancing the studied gene (VRUi) from
the support vectors of i disease in the calculation of the
second score of each gene (
DS_Scorei
). e calculation of
the third score is carried out in three steps.
In the first step, the value of
Grsv
parameter for i-th
gene from positive and negative labeled genes are consid-
ered
⌊DSi⌋+1
value and
⌊DSi⌋
value, respectively.
Grsv
is
the category’s score, including the ith gene, and DSi is the
distance of the i-th gene from the Support Vector.
In the second step, the Eq.7is used to calculate the
value of
NGrsvi
; it is the category’s score of the i-th gene
(
Grsvi
). e mentioned score has reached the base of 100.
e category’s score of all genes belonging to the disease
is in the
{Grsv }
set.
In the third step, the final correspondent score with the
i-th gene
DS_Scorei
is calculated by Eq.8.
e second and third scores are simultaneously used
for predicting and ranking disease candidate genes. Each
gene may have several profiles in the unlabeled genes
dataset. us, each gene obtains a score based on its pro-
file number. e final score for that gene is obtained from
the algebraic summation of gene profiles.
e final score of the studied gene (
Final_Scorei
) is
calculated based on the Eq.9with the algebraic summa-
tion of gene profiles’ scores (
DP_Scorei
and
DS_Scorei
for each profile of that gene). e prediction of disease
candidate genes is carried out based on the score of
each gene.
e number of gene profiles is indicated by m in Eq.9.
Finally, genes whose
Final_Score
values are negative
will eliminate; other genes are predicted as disease candi-
date genes. e obtained final score of each disease can-
didate gene is used for ranking.
Results
e efficiency of the S-PUL method is evaluated in six ver-
sions, namely S-PUL_Vn in this section. e number of
S-PUL versions and used filters in that version are reported
in Table1. It is worth noting that the version of S-PUL_V5
is the proposed S-PUL method, which uses all filters.
(7)
NGr
svi =Grsvi ×
200
Max
{|Grsv |}(
Max
{|Grsv |}+
1
)
(8)
DS_Scorei=NGr svi ×|DS i|
(9)
Final
_Scorei=
m
i=1
(DS_Scorei×|DP _Scorei|
)
e efficiency of the S-PUL method results (separately
for each version) is compared with the previous studies.
Finally, this method’s efficiency is evaluated separately in
2016 and 2020 using the newly identified disease genes.
e MATLAB Software (2019 version) is used for learn-
ing binary classification and calculation. Moreover, the
dd-tools library is used for learning one-class models.
e entire evaluation is carried out on a computer with
an Intel Core TM i5 processor and main memory of
32GB in Windows 10 pro.
Dataset
e used genes in the learning and testing phases are
extracted from the dataset of Yang etal. (2014) [14] (the
second row of Table2). e dataset for the Cancer dis-
ease class has 210 genes, these 210 genes are common
among the three diseases: colon, prostate, and lung (the
number of disease genes is provided in Table8), and the
dataset of unlabeled genes has 12,001 genes. GeneCards
[4] (the third and fourth rows of Table2) are used for the
dataset of disease genes from 2015 to 2020. e charac-
teristics of disease genes are represented in Table2 sepa-
rately for each disease and period. Notably, each disease
gene may be the cause of several diseases.
Evaluation measures
e accuracy, recall F1, and AUC measures (area under
the ROC curve, which is the changes of TPR to FPR) are
used to evaluate the S-PUL method). e mentioned
measures are defined in Table3. In these equations: the
TP parameter is the number of positive samples that are
categorized correctly; the TN parameter is the number of
negative samples that are categorized correctly; the FP is
the number of negative samples that are categorized as
positive incorrectly (in other words, the number of spuri-
ous positive samples); the FN is the number of positive
samples that are categorized as negative incorrectly (in
other words, the number of spurious negative samples);
the TPR is the correct positive rate; FPR is the spurious
positive rate. is study has considered disease genes as
positive samples and extracted negative samples from
Table 1 The used filters in the versions of the S-PUL proposed
method
S‑PUL_
Version Filter 1 Filter 2 Filter 3 Second
Score Third Score
S‑PUL_V0 ✓
S‑PUL_V1 ✓ ✓
S‑PUL_V2 ✓✓✓
S‑PUL_V3 ✓✓✓✓
S‑PUL_V4 ✓ ✓ ✓ ✓
S‑PUL_V5 ✓✓✓✓ ✓
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 9 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
unlabeled genes. All evaluations are performed with
K-fold C.V and k = 10.
The evaluation ofextracted reliable negative genes
e extraction of reliable negative genes is carried out in
two steps (extraction of negative genes using a one-class
learning algorithm and selecting reliable negative genes
using distance measure). e quality of reliable negative
genes extraction is evaluated at each step.
Selecting theone‑class learning algorithm
Negative genes are initially extracted separately for each
disease to select the one-class learning algorithm and
each one-class classification learning algorithm of SVDD,
Robust Gaussian, KNN, and Parzen Window (the first
and second steps in Reliable negative genes selection
step). Each algorithm’s parameters and a brief introduc-
tion are provided below, with references for detailed
explanations.
Support Vector Data Description (SVDD) is a machine
learning algorithm used for anomaly detection and clas-
sification. It constructs a sphere in the feature space that
encompasses the training data. e parameter used in
this algorithm is the width parameter in the RBF kernel
[15].
Robust Gaussian is an algorithm that models data dis-
tribution as a Gaussian distribution and employs robust
statistics to handle outliers. e parameter for this algo-
rithm is the error tolerance on the mean and covariance
matrix [16].
K-Nearest Neighbors (KNN) is an instance-based algo-
rithm that classifies data based on the distances to the
k-nearest neighbors. e parameter for this algorithm is
the number of neighbors [17].
Parzen Window is a non-parametric method for esti-
mating the probability density function of a dataset using
kernel functions. e parameter for this algorithm is the
width parameter [18].
en, each one-class learning algorithm’s efficiency is
examined through two evaluation methods.
e first evaluation method: e percentage of cor-
rect negative samples (%TN) is considered the evalua-
tion method in the first method. e selected parameters
of each one-class learning algorithm are presented in
Table 4. e error value on the target class (Fracrej)
parameter considers 0.1 for all one-class learning algo-
rithms. e efficiency results of each one-class learning
algorithm are reported in Table5.
The rst evaluation method
e percentage of correct negative samples (%TN) is
considered the evaluation method in the first method.
e selected parameters of each one-class learning algo-
rithm are presented in Table 4. e error value on the
target class (Fracrej) parameter considers 0.1 for all one-
class learning algorithms. e efficiency results of each
one-class learning algorithm are reported in Table5.
Table 2 Characteristics of genes expression profile datasets
The name of the disease class Cancer Endocrine Cardiovascular Neurological
The name of the disease Colon Lung Prostate Adrenal Heart Failure Neurological Row number
Sequence length of gene expression profiles 18 18 5 37 9 42 1
Biologists [14]
Number of disease genes by 2014 342 245 325 81 107 219 2
Biologists [4]
Number of new disease genes from 2015 to 2016 240 - 191 9 - - 3
Biologists [4]
Number of new disease genes from 2017 to 2020 56 27 67 29 58 16 4
Total known disease genes 638 272 583 119 165 235 5
Table 3 The relations of evaluation measures
A. Precision measure – this measure indicates the percentage of positive
predictions that are performed correctly. Moreover, this measure is calculated
from Eq.18in Table3
B. Recall measure – this measure indicates the percentage of positive samples
that are categorized correctly. Moreover, this measure is calculated from
Eq.19in Table3
C. F1 measure – it is a compatible mean between precision and recall. Moreover,
this measure is calculated from Eq.20in Table3. Additionally, R symbol refers to
recall and P symbol refers to precision
D. Trust in Negative Genes ( TNG) measure – this measure is used for trust
value in extracted negative genes measurement in unlabeled genes. Indeed, it
compares the extracted negative genes and disease-known genes from 2014
to 2020. The trust value in negative genes is calculated from Eq.21in Table3.
In Eq.21, A is the number of extracted negative genes, the B parameter is the
number of available common genes in the disease genes list from 2014 to 2020
and extracted negative genes
Equation
number Equation Equation
number Equation
18
Precision
=
TP
TP+FP
∗
100
19
Recall
=
TP
TP+FN
∗
100
20
F
1=
2∗P∗R
P+R
21
TNG
=
A−B
A
∗
100
22
TPR
=
TP
TP+FN
23
FPR
=
FP
FP+TN
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 10 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
e highest efficiency of the one-class learning algo-
rithm is related to SVDD. SVDD labeled the most percent-
age of negative samples for the entire types of diseases.
The second evaluation method
In this evaluation method, the efficiency of the S-PUL_
V5 learning method is learned using considered positive
disease genes separately for each extracted reliable nega-
tive genes set for each one-class learning algorithm (Reli-
able negative genes selection step). e results of this
evaluation are illustrated in Fig. (5a to f) for each disease
separately. It is worth noting that the number of selected
reliable negative genes for each disease is equal to the
number of disease genes; this prevents the unbalanced
problem of positive and negative data).
According to Fig. 5, the highest efficiency is related
to the S-PUL_V5 method if reliable negative genes are
extracted using the SVDD method (compared to the
other three one-class learning algorithms).
Measuring thetrust degree intheextracted negative genes
According to Eq.21, the trust degree in negative genes
is extracted by the SVDD algorithm for each disease
separately (see Table6); it demonstrates that the reliability
of extracted negative genes by the SVDD algorithm is high.
Evaluation ofthebinary classication algorithms
performance andselection ofthedisease genes
Table 7 reports the parametrization for learning algo-
rithm and disease separately. Moreover, Table8 presents
used disease genes information in the binary models
learning for each disease individually.
e efficiency evaluation of five binary classification
algorithm results is illustrated in Fig. 6 in the filtered/
unfiltered status of disease genes.
Figure6 indicates the evaluation results. e recall meas-
ure increased using S-PUL-V1 compared to the efficiency
evaluation of S-PUL_V0 classification algorithms. e
precision and, subsequently, the F1 measures increase if it
does not affect the recall measure. Hence, the filtering dis-
ease genes method in the S-PUL method will be used. Fur-
thermore, the efficiency of the SVM binary model learning
algorithm is more than other algorithms (see Fig. 6).
Hence, the SVM binary classification method in the S-PUL
method will be used. Table9 indicates the value of the used
parameter in the SVM learning algorithm. If the kernel is a
Table 4 The selected parameters for each one-class learning algorithm separately for each disease
1 Width parameter
2 Error tolerance on mean and cov. Matrix
3 Number of neighbors
4 Width parameter in the RBF kernel
The name of the
disease ↓
Algorithm
→
SVDD KNN Robust Gaussian ParzenWindow
Parameter
→
ɤ4kernel 3K2Tol 1h
Adrenal 0.14 RBF 2 e-3 1
Colon 0.14 RBF 1 0.015 1.2
Lung 0.3 RBF 2 e-3 1
Prostate 0.2 RBF 1 e-3 1
Heart Failure 0.14 RBF 2 e-3 0.9
Neurological 0.14 RBF 2 0.005 1
Table 5 The results of one-class learning algorithms efficiency evaluation in the extraction of reliable negative genes based on the
percentage of correct negative samples measure (%TN)
The name of the disease
↓
Algorithm
→
SVDD KNN Robust Gaussian Parzen Window
Adrenal 89.5% 73% 74.8% 52.7%
Colon 82.1% 75.8% 12.6% 35.1%
Lung 84% 80% 19.4% 64%
Prostate 82.6% 69.3% 71% 72%
Heart Failure 78.4% 75.7% 37% 42.8%
Neurological 71% 42.62% 49.5% 68.7%
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 11 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
quadratic function,
γ
parameter is set to the one divided by
the number of features (1/ number of features).
The evaluation ofdisease candidate genes prediction
andranking
e efficiency of disease candidate genes prediction and
ranking is examined in this section for implementing fil-
ter 3, using the second and third scores separately.
The evaluation ofselecting valuable genes eciency (lter 3)
is section assesses the elimination of genes given a
negative label by the SVM binary learning algorithm, and
their S-R is in the first category ([0,10) range). e statis-
tics of eliminated genes based on their related S-R range
are presented in Table10 for each disease.
Figure7 illustrates the evaluation results of the S-PUL_
V2 version (by implementing filter 3) compared to the
S-PUL_V1 version (without implementing filter 3) to
evaluate the filter 3 implementation value.
According to Fig.7, by implementing filter 3, the recall
measure of S-PUL_V2 increases in all diseases. Contrary,
without implementing filter 3, the recall measure reduces
in all diseases. e highest and lowest increase in recall
measures in S-PUL_V2 is related to Lung disease (7.40%)
and Colon disease (0.67%), respectively. erefore, filter 3
will be used in the S-PUL method.
The eciency evaluation ofutilizing thesecond genes
oftheVRU set
Every gene has several gene expression profiles. us, in
the S-PUL_V1, the gene will be considered a disease can-
didate gene if at least one of its gene expression profiles
Fig. 5 The results of one-class learning algorithm efficiency evaluation in the extraction of reliable negative genes based on the efficiency
of the S-PUL_V5 method
Table 6 The trust degree in extracted negative genes (TNG)
using the SVDD method
1 Parameter A represents the number of extracted negative genes
2 Parameter B represents the number of common samples between the two sets
of disease genes from the years 2014 to 2020 and the set of extracted negative
genes
The name of the disease Parameter B2Parameter A1TNG
Adrenal 0 77 100%
Colon 2 323 99.38%
Lung 12 191 93.71%
Prostate 16 268 94.02%
Heart Failure 2 101 98.01%
Neurological 7 151 95.36%
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 12 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
Table 7 The values of parameters for learning algorithm and disease separately
The name of the
disease ↓
Algorithm →Logistic Regression KNN Decision Tree Discriminative
Parameter →Distribution Size K ɵType δ
Adrenal Binomial 1 1 0.25 Quadratic 0
Colon Binomial 1 1 0.25 Linear 0.11
Lung Binomial 1 2 0.32 Quadratic 0
Prostate Binomial 1 1 0.25 Linear 0.14
Heart Failure Binomial 1 2 0.24 Quadratic 0
Neurological Binomial 1 2 0.30 Quadratic 0
Table 8 Disease genes information for each disease
The name of the disease Number of disease genes
before ltering S‑R range S‑R rating range S‑R score
threshold Number of disease
genes after
ltering
Adrenal 81 [0.08 , 108.21] [0.12 , 1803.5] 901.68 77
Colon 342 [0.14 , 225.43] [0.05 , 1878.583] 939.26 323
Lung 245 [0.1 , 216.63] [0.03 , 1883.739] 941.84 191
Prostate 325 [0.1 , 251.1] [0.02 , 1860] 929.98 268
Heart Failure 107 [0.12 , 109.44] [0.18 , 1824] 911.90 101
Neurological 219 [0.07 , 42.06] [0.46 , 1402] 700.76 151
Fig. 6 The results of efficiency evaluation of binary classification algorithms for disease genes filtering (S-PUL_V1) and non-filtering (S-PUL-V0)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 13 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
obtains a positive label. Consequently, the number of
spurious positive samples is very high. erefore, the
method for reducing the number of spurious positive
samples is presented in "Action5- e prediction and
ranking of disease candidate genes" section.
Figure 8 illustrates the results of S-PUL_V3 version
efficiency in disease candidate genes ranking using the
second score (“Action5- e prediction and ranking of
disease candidate genes” section). According to these
figures, the precision measure value enhances in the V3
version while recall is maintained. Moreover, Table 11
reports statistical information of the second score imple-
mentation in “Action5- e prediction and ranking of
disease candidate genes” section for each disease and
unlabeled gene number (which is introduced as a disease
gene in this step).
The eciency evaluation ofusing thethird score ofVRU set
genes
Another measure (the third score) is used in “Action5-
e prediction and ranking of disease candidate genes"
sectionto reduce the number of spurious positive sam-
ples; this measure is calculated from the distance of the
unlabeled gene for the support vector.
Table 9 Setting parameters of the SVM learning algorithm with
polynomial kernel for each disease separately
The name of the disease Parameter C Parameter
γ
Colon 15.33 0.14
Lung 16.43 0.14
Prostate 9.20 0.2
Adrenal 8.75 0.14
Heart Failure 13.61 0.14
Neurological 11.52 0.14
Table 10 Statistics of eliminated genes (genes having negative
labels and being in the first S-R category)
The name of the disease S‑R range Number of
deletion
genes
Adrenal [0.08 , 10) 68
Colon [0.06 , 10) 51
Lung [0.1 , 10) 21
Prostate [0.1 , 10) 37
Heart Failure [0.12 , 10) 48
Neurological [0.07 , 10) 28
Fig. 7 The results of the S-PUL_V2 version evaluation (by implementing filter 3) compared to the S-PUL_V1 version (without implementing filter 3)
for each disease
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 14 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
Figure 8 demonstrates the results of the S-PUL_V4
efficiency evaluation in disease candidate genes rank-
ing using the third score. According to the figures, the
entire evaluation measures increased in the V4 version.
e highest and lowest increase value of recall measures
is in Adrenal disease (2.52%) and Lung disease (0.19%),
respectively. Further, the highest and lowest increase
value of the precision measure is in the Adrenal disease
(17%) and Colon disease (4.02%), respectively. Based
on the results, using the third score in the V4 version
(compared to the V2 version) dramatically increases the
precision measure with maintaining the recall measure.
Additionally, Table 12 reports the statistical informa-
tion of the third score implementation in “Action5- e
prediction and ranking of disease candidate genes" sec-
tionfor each disease and unlabeled gene number (intro-
duced as the disease gene in this step).
The evaluation oftheS‑PUL method eciency
Figure 8 illustrates the results of the efficiency evalua-
tion of the S-PUL method (introduced in Table1 with the
S-PUL_V5 version) in disease candidate genes ranking
using 1 and 2 filters in the learning step and using filter
Fig. 8 The evaluation and comparing results of S-PUL of the V2 version (with implementing filter 3), V3 version (using the second score), V4 version
(using the third score), and V5 version (using both second and third scores) in the prediction and ranking of disease genes
Table 11 Statistical information of the second score implementation in "Action5- The prediction and ranking of disease candidate
genes" section for each disease
The name of the disease S‑R range Score range Number of candidate
disease genes The second score
range of disease
genes
Adrenal [2.98 , 108.21] [4.51 , 1803.5] 46 [4.52 , 116.15]
Colon [2.53 , 204.15] [3.83 , 6495.6] 332 [1.11 , 2244.57]
Lung [9.57 , 164.87] [3.78 , 1107.8] 28 [6.47 , 2285.45]
Prostate [10.09 , 102.672] [6.20 , 347.4] 274 [36.09 , 4246.79]
Heart Failure [4.45 , 72.04] [6.74 , 873.21] 66 [13.52 , 1600.88]
Neurological [1.79 , 29.05] [11.93 , 581] 20 [30 , 1452.5]
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 15 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
3 and both second and third scores compared to V2, V3,
and V4 versions. According to the figures, all of the evalu-
ation measures are enhanced in the V5 version compared
to V2, V3, and V4 versions. e precision measure in
Adrenal, Colon, Lung, Prostate, Heart Failure and Neu-
rological diseases is enhanced by 12.48%, 13.78%, 17.68%,
22.31%, and 5.38%, respectively; besides, the recall meas-
ure for these diseases is increased by 2.52%, 1.47%, 7.6%,
1.84%, 6.11%, and 6.94%, respectively.
Comparing theeciency oftheS‑PUL proposed method
withother methods
e efficiency of the S-PUL proposed method is com-
pared with previous methods in this section.
Table13 reports the efficiency results of the proposed
method compared to the [12] study. e recall measure is
increased in Colon and Prostate diseases for all versions
of the S-PUL method and Lung disease in the V5 ver-
sion of the S-PUL method. e reason for comparing the
results of S_PUL only with Reference [12] in Table13 is
due to the fact that these particular diseases were exclu-
sively studied in that reference. However, from Tables14,
15, 16 and 17, the diseases are common among various
studies, allowing for comparisons across multiple refer-
ences. e values of precision and recall are enhanced
in the V5 version of the S-PUL method of each illness.
e recall measure’s highest and lowest increase values
are in Colon disease (5.32%) and Lung disease (1.29%),
respectively. e precision measure’s highest and lowest
increase values are in Prostate disease (3.14%) and Lung
disease (1.75%).
According to Table14, the precision and recall meas-
ures values for Cardiovascular disease class, including
Heart Failure disease in the V5 version of the S-PUL
method, are increased by 4.04% and 3.13%, respectively,
compared to the [12] study. Recall measure in both V3
and V4 versions of the S-PUL method is increased by
0.59% and 2.32%, respectively, compared to the [12]
study. e highest value of the recall measure is reported
in the ProDige [19] study among the previous methods.
e mentioned measure is increased by 0.25% and 1.97%
in the V3 and V5 versions of the S-PUL method, respec-
tively. e F1 measure in all S-PUL versions is increased
compared to previous studies, except for the [12] and
EPU [14] studies.
According to Table15, the recall value for Endocrine
disease class (including Adrenal disease) increased by
0.53% in all V3, V4, and V5 versions of the S-PUL method
than the [12] study (which had the best efficiency). Nota-
bly, this study’s recall value for the Endocrine disease
class reached 100%. In addition to the recall measure, the
precision measure is increased by 2.46% in the V5 version
of the S-PUL method. e F1 measure is increased n V3,
V4, and V5 versions of the S-PUL method compared to
the previous studies, except for the [12] study.
Table 12 The statistical information of the third score implementation in "Action5- The prediction and ranking of disease candidate
genes" section for each disease
The name of the disease Distance interval from
Support Vector Score range Number of candidate
disease genes The third score
range of disease
genes
Adrenal [−3.28 , 1.12] [−131.2 , 74.66] 45 [0.16 , 14.32]
Colon [−6.21 , 14.78] [−155.25 , 184.75] 338 [1.71 , 295]
Lung [−9.25 , 3.78] [−168.18 , 151.2] 28 [0.05 , 153.7]
Prostate [−8.4 , 12.6] [−168 , 180] 280 [0.43 , 302.5]
Heart Failure [−7.1 , 3.03] [−157.7 , 121.2] 44 [1.9 , 123.5]
Neurological [−6.93 , 5.66] [−173 , 161.71] 18 [0.03 , 301.71]
Table 13 Comparing the performance of the S-PUL method (for
four versions separately) with the [12] study
The name of
the disease Method Precision Recall F1
Colon Nikdel et al. [12] 93% 94% 93%
S-PUL_V1 82.66% 97.84% 89.61%
S-PUL_V3 88.55% 99.32% 93.69%
S-PUL_V4 86.68% 98.98% 92.42%
S-PUL_V5 95.14% 99.32% 97.19%
Lung Nikdel et al. [12] 91.1% 95% 93.3%
S-PUL_V1 79.06% 88.69% 83.6%
S-PUL_V3 89.28% 92.59% 90.9%
S-PUL_V4 85.71% 88.88% 87.27%
S-PUL_V5 92.85% 96.29% 94.54%
Prostate Nikdel et al. [12] 92% 95% 93%
S-PUL_V1 77.46% 96.98% 86.13%
S-PUL_V3 93.06% 98.83% 95.86%
S-PUL_V4 89.64% 97.28% 93.3%
S-PUL_V5 95.14% 98.83% 96.95%
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 16 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
e efficiency results of the proposed method are
reported in Table16 compared to the efficiency of the
previous methods for predicting the Cancer disease class
candidate genes, including Colon, Prostate, and Lung dis-
eases for V3, V4, and V5 versions of the S-PUL method.
Based on the evaluation results, the efficiency of all three
versions of the S-PUL method is enhanced compared to
the [12] study (which had the best efficiency). e best
results relate to the V5 version of the S-PUL method
compared to the [12] study; its precision, recall, and F1
measures are improved by 2.38%, 3.11%, and 4.75%.
e AUC value in the V5 version of the S-PUL method
for Neurological disease class (including Neurologi-
cal disease) is increased by 8.82%, compared to the SFM
method [6] (the best previous method), according to
Table17. e recall measure in all versions of the S-PUL
method is more than in previous methods. e best pre-
cision, recall, and F1 measures’ values are related to EPU
[14] by 78.2%, 80.4%, and 78.6%. ese measures’ values
reached 84.21%, 100%, and 91.42% in the V5 version of
the S-PUL method.
Comparing theeciency oftheS‑PUL proposed method
withbiologists’ eciency
It is worth noting that the biological researchers identi-
fied other unlabeled genes as disease genes (six diseases
introduced in Table2) from 2015 to 2020 through labora-
tory methods. en, they are introduced in the [4] data-
set. e predicted disease genes by the S-PUL method
and [12] study with the disease genes set (introduced
for the 2015–2016 period and 2017–2020 period by bio-
logical researchers) are compared in Tables 18 and 19,
respectively, to determine the efficiency. Notably, 2015 to
2016 and 2017 to 2020 sets are reported in the third and
fourth rows of Table2, respectively.
According to Table18, the efficiency of the V5 version
of the S-PUL method compared to the [12] study is as
follows:
e prediction in Adrenal disease is the same; in Colon
disease has ten more disease genes; in Prostate disease
has 11 more disease genes. On the other hand, the V5
version of the S-PUL method has predicted two disease
Table 14 Comparing the performance of the S-PUL method
with previous methods in the prediction of unlabeled genes of
Cardiovascular disease class (including Heart Failure disease)
Method Precision Recall F1
PUDI [20] 83.6% 75.3% 79.2%
ProDiGe [19] 57.3% 87.7% 69.3%
Smalter et al. [8] 76.4% 58.8% 66.5%
Xu et al. [21] 75.4% 62% 68%
EPU [14] 88.1% 87.7% 87.9%
Nikdel et al. [12] 94.79% 99.47% 97.07%
S-PUL_V1 67.05% 97.47% 79.45%
S-PUL_V3 82.60% 100% 90.47%
S-PUL_V4 84.44% 100% 91.56%
S-PUL_V5 97.43% 100% 98.7%
Table 15 Comparing the efficiency of the S-PUL method with
previous methods in the prediction of unlabeled genes of
Endocrine disease class (including Adrenal disease)
Method Precision Recall F1
PUDI [20] 82% 80.3% 80.4%
ProDiGe [19] 54.3% 96.3% 69.3%
Smalter et al. [8] 75.4% 67.6% 70.6%
Xu et al. [21] 72.1% 60% 65.4%
EPU [14] 85.2% 81% 84.1%
Nikdel et al. [12] 91.87% 94.23% 93.03%
S-PUL_V3 84.84% 96.55% 90.32%
S-PUL_V4 85.93% 94.82% 90.16%
S-PUL_V5 95% 98.27% 96.61%
Table 16 Comparing the efficiency of the S-PUL method with
the previous methods in the prediction of Cancer class unlabeled
genes, including Colon, Prostate, and Lung diseases
Method Precision Recall F1
PUDI [20] 76.3% 80% 78%
ProDiGe [15] 71.1% 79.8% 75.3%
Smalter et al. [8] 73.8% 79% 76.3%
Xu et al. [21] 71% 79.7% 75.1%
EPU [14] 81.2% 84.5% 82.6%
SFM [6] 76.9% 79.8% 78.3%
Nikdel et al. [11] 96.73% 95.83% 94.28%
S-PUL_V3 98.94% 98.94% 98.94%
S-PUL_V4 98.76% 98.94% 98.85%
S-PUL_V5 99.11% 98.94% 99.03%
Table 17 Comparing the efficiency of the S-PUL method with
previous methods in the prediction of the unlabeled genes of
Neurological disease class (including Neurological disease)
Method Precision Recall F1AUC
PUDI [20] 70.3% 80.1% 74.9% 85.4%
ProDiGe [19] 63.1% 74% 68.1% 64.6%
Smalter et al. [8] 60.6% 65.6% 63.1% 73.9%
SFM [6] - - - 88.2%
Xu et al. [21] 59.7% 66.7% 63% -
EPU [14] 78.2% 80.4% 78.6% -
S-PUL_V1 78.82% 93.05% 85.35% -
S-PUL_V3 80% 100% 88.88% -
S-PUL_V4 83.33% 93.75% 88.23% -
S-PUL_V5 84.21% 100% 91.42% 97.02%
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 17 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
genes and only one disease gene lesser than biologists [4]
in Prostate and Colon diseases, respectively.
According to Table19, compared to biologists, the V4
and V5 versions of the S-PUL method are predicted all
genes in Adrenal and Neurological diseases. Moreover,
the V5 version of the S-PUL method only predicted one
disease gene lesser than biologists in Colon, Per, Lung, and
Heart Failure diseases. Hence, according to the learned
models, the V5 version efficiency of the S-PUL method in
predicting disease genes is very proper based on the 2014
dataset (introduced in the second row of Table2).
Conclusion
In two steps, the reliable negative genes are extracted in
this study to reduce available noise in extracted nega-
tive genes from unlabeled genes. ese two steps are
(i) one-class learning and (ii) filtering based on the dis-
tance measure. e proposed method initially filters
positive educational genes in the disease binary model
learning step. en, the SVM binary model is learned
using selected positive samples and extracted reliable
negative samples for each disease separately. In the
prediction step, the binary model is learned to predict
unlabeled samples’ labels (labeling) and rank them.
Moreover, two filters of (i) nearness of gene to disease
genes and (ii) distance of each gene from the support
vector are used.
Using influential factors to predict and rank disease
candidate genes and properly use them in the S-PUL
method leads to the strong performance of this method
compared with previous methods. In this line, the men-
tioned claim is proved by 99.51% average correspond-
ence of predicted disease genes with introduced disease
genes from 2015 to 2016 and 98.54% from 2017 to 2020.
Moreover, 96.74% lack of average of considered nega-
tive genes in evaluating disease genes during the men-
tioned periods proves this claim.
e following propositions are presented for future
studies in this regard based on the performed imple-
mentation and advantages and disadvantages of the
presented method:
Table 18 Comparing the S-PUL method efficiency and the [12] study with biologists in the prediction of disease genes from 2015 to
2016
The name of the
disease ↓
Method→Biologists [4] Nikdel etal. [12] SPUL_V3 SPUL_V4 SPUL_V5
Adrenal Number of genes 9 9 8 8 9
Recall 100% 88.88% 88.88% 100%
Colon Number of genes 240 229 233 238 239
Recall 95.41% 97.08% 99.16% 99.58%
Prostate Number of genes 191 178 182 188 189
Recall 93.61% 95.28% 98.42% 98.95%
Table 19 Comparing the S-PUL method efficiency with biologists in predicting disease genes from 2017 to 2020
The name of the disease
↓
Method→Biologists [4] SPUL_V3 SPUL_V4 SPUL_V5
Adrenal Number of genes 29 28 29 29
Recall 96.55% 100% 100%
Colon Number of genes 56 54 55 55
Recall 96.42% 98.21% 98.21%
Prostate Number of genes 67 62 66 66
Recall 92.53% 98.50% 98.50%
Lung Number of genes 27 23 25 26
Recall 85.18% 92.59% 96.29%
Heart Failure Number of genes 58 50 56 57
Recall 86.20% 96.55% 98.27%
Neurological Number of genes 16 13 16 16
Recall 81.25% 100% 100%
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 18 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
A) e delimitation of distances and scoring to genes
are carried out discretely and integrity units in the
S-PUL method. More or less of the genes located at
borders (even fractional) can lead to changes in cate-
gory and score in such a way that eliminates or main-
tain the gene. is method should be improved.
B) Two steps are used in this study to find reliable nega-
tive genes. It is proposed to use other information
sources (such as the PPI network) to increase trust in
extracted negative genes.
C) Two filtering methods based on statistical measures
are used in this study to reduce errors in identify-
ing and ranking disease candidate genes. Meanwhile,
other genetic factors that are effective in the forma-
tion of a disease can consider and introduce in the
final score.
D) A deep learning approach in PU learning is proposed
to improve the results of identifying and predicting
disease candidate genes.
Abbreviations
AML Acute Myeloid Leukemia
AUC Area Under the Curve
DNA Deoxyribonucleic Acid
DP_Score Disease Prediction Score
DS1 Dataset 1
DS2 Dataset 2
DS3 Dataset 3
DS_Score Disease Score
F1 F1 Score (Harmonic Mean of Precision and Recall)
F_Score Final Score
FN False Negative
FP False Positive
FPR False Positive Rate
Fracrej Fraction Rejected
GEP Gene Expression Profile
HMM Hidden Markov Model
IL Interval Length
KNN K-Nearest Neighbors
NGr Normalized Gene Relevance
OCSVM One-Class Support Vector Machine
PCA Principal Component Analysis
PPI Protein–Protein Interaction
Precision Proportion of correctly predicted positive cases
PU-Learning Positive-Unlabeled Learning
RBF Radial Basis Function
Recall Percentage of correctly predicted disease genes
Recall (TPR) True Positive Rate
RUi Remaining Unlabeled Gene Set
S-PUL Scored-Positive Unlabeled Learning
S-R Score Relevance
SVM Support Vector Machine
SVDD Support Vector Data Description
TF-IDF Term Frequency-Inverse Document Frequency
TNG Trust in Negative Genes
TN True Negative
TP True Positive
TPR True Positive Rate
VRUi Valuable Remaining Unlabeled Gene Set
Acknowledgements
Yang, Peng, et al. "Ensemble positive unlabeled learning for disease gene identifi-
cation." PloS one 9.5 (2014): e97079. https:// www. genec ards. org/ ,29/ 04/ 2020.
Authors’ contributions
S.M. wrote the main manuscript text. S.J. supervised the study and edited and
improved the manuscript. The proposed method was presented and evalu-
ated by S.M., and reviewed and enhanced by S.J.
Funding
The authors have no funding to declare that are relevant to the content of this
article.
Data availability
No datasets were generated or analysed during the current study.
Declarations
Ethics approval and consent to participate
Not applicable. The gene expression data used in this study were obtained
from the publicly available GeneCards database.
Consent for publication
Not applicable. This study does not involve any individual data requiring
consent for publication.
Competing interests
The authors declare no competing interests.
Received: 23 October 2024 Accepted: 18 February 2025
References
1. Fusilier DH, et al. Detecting positive and negative deceptive opinions
using PU-learning. Inform Process Manage. 2015;51(4):433–43.
2. Shao YH, et al. Laplacian unit-hyperplane learning from positive and
unlabeled examples. Inform Sci. 2015;314:152–68.
3. Zhang Z, et al. Biased p-norm support vector machine for PU learning.
Neurocomputing. 2014;136:256–61.
4. Genecards, the human gene database, Weizman Institute of Science.
https:// www. genec ards. org. Accessed 24 Apr 2020.
5. Scoring theor y. https:// www. elast ic. co. Accessed 11 May 2020.
6. Yousef A, Charkari NM. SFM: a novel sequence-based fusion method for
disease genes identification and prioritization. J Theor Biol. 2015;383:12–9.
7. Vasighizaker A, Jalili S. C-PUGP: A cluster-based positive unlabeled learn-
ing method for disease gene prediction and prioritization. Comput Biol
Chem. 2018;76:23–31.
8. Smalter A, Lei SF, Chen XW. Human disease-gene classification with
integrative sequence-based and topological features of protein-protein
interaction networks. 2007 IEEE International Conference on Bioinformat-
ics and Biomedicine (BIBM 2007).
9. Radivojac P, et al. An integrated approach to inferring gene–disease
associations in humans. Proteins: Structure, Function, and Bioinformatics.
2008;72(3):1030–7.
10. Yousef A, Charkari NM. A novel method based on physicochemical prop-
erties of amino acids and one class classification algorithm for disease
gene identification. J Biomed Inform. 2015;56:300–6.
11. Vasighi Zaker A, Saeed J. Candidate disease gene prediction using one-
class classification. Soft Computing J. 2016;4(1):74–83.
12. Nikdelfaz O, Jalili S. Disease genes prediction by HMM based PU-learning
using gene expression profiles. J Biomed Inform. 2018;81:102–11.
13. Vasighizaker A, Sharma A, Dehzangi A. A novel one-class classifica-
tion approach to accurately predict disease-gene association in acute
myeloid leukemia cancer. PLoS ONE. 2019;14(12):e0226115.
14. Yang P, et al. Ensemble positive unlabeled learning for disease gene
identification. PloS one. 2014;9(5):e97079.
15. Tax DMJ, Duin RPW. Support vector data description. Mach Learn.
2004;54(1):45–66.
16. Huber PJ. Robust Statistics. New York: John Wiley & Sons; 1981.
17. Cover T, Hart P. Nearest neighbor pattern classification. IEEE Trans Inf
Theory. 1967;13(1):21–7.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 19 of 19
Molaeiand Jalili BMC Medical Genomics (2025) 18:73
18. Parzen E. On Estimation of a Probability Density Function and Mode. Ann
Math Stat. 1962;33(3):1065–76.
19. Mordelet F, Vert J-P. ProDiGe: Prioritization Of Disease Genes with
multitask machine learning from positive and unlabeled examples. BMC
Bioinformatics. 2011;12(1):1–15.
20. Yang P, et al. Positive-unlabeled learning for disease gene identification.
Bioinformatics. 2012;28(20):2640–7.
21. Xu J, Li Y. Discovering disease-genes by topological features in human
protein–protein interaction network. Bioinformatics. 2006;22(22):2800–5.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in pub-
lished maps and institutional affiliations.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
1.
2.
3.
4.
5.
6.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
apply.
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
not:
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
control;
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
writing;
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
content.
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
onlineservice@springernature.com
