Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics
A distinctive feature of this work is grouping naive Bayesian classifiers in the scheme of "one against all" and using the extended features space. Metric and categorial variables are present in the original sample. The scheme of "one vs. all" with the use of other methods of cla...
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| Date: | 2014 |
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Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України
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| Cite this: | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics / N. Kondrashova, V. Pavlov // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2014. — Вип. 6. — С. 11-23. — Бібліогр.: 22 назв. — англ. |
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| citation_txt | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics / N. Kondrashova, V. Pavlov // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2014. — Вип. 6. — С. 11-23. — Бібліогр.: 22 назв. — англ. |
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| description | A distinctive feature of this work is grouping naive Bayesian classifiers in the scheme of "one against all" and using the extended features space. Metric and categorial variables are present in the original sample. The scheme of "one vs. all" with the use of other methods of classification gives an improvement in the accuracy of the differential diagnosis on exam sample compared to a single Bayesian classifier, but not in the case of the Naive Bayesian classifiers. The obtained results allow us to compare methods accuracies with such as GMDH and canonical discriminant analysis in solution of classification problem.
Відмінною особливістю даної роботи є ансамблювання наївних Байєсівських класифікаторів в схемі «один проти всіх» і використанні розширеного простору ознак. У первинній вибірці присутні метричні і категорійні змінні. Схема «один проти всіх» із застосуванням інших методів класифікації дає поліпшення на екзамені точності диференціальної діагностики порівняно з єдиним класифікатором, але не у випадку наївних Байєсівських класифікаторів. Отримані результати точності дозволяють порівняти їх з результатами інших методів розв'язання задачі класифікації: таких як МГУА і канонічний дискримінантний аналіз.
Отличительной особенностью данной работы является ансамблирование наивных Байесовских классификаторов в схеме «один против всех» и использовании расширенного пространства признаков. В исходной выборке присутствуют метрические и категориальные переменные. Схема «один против всех» с применением других методов классификации дает улучшение на экзамене точности дифференциальной диагностики по сравнению с единым классификатором, но не в случае наивных Байесовских классификаторов. Полученные результаты точности позволяют сравнить их с результатами других методов решения задачи классификации: таких как МГУА и канонический дискриминантный анализ.
|
| first_indexed | 2025-12-07T15:21:02Z |
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N.Kondrashova, V.Pavlov
УДК 681.513.8
NAIVE BAYESIAN CLASSIFIERS FOR PURPOSES OF MEDICAL
DIFFERENTIAL DIAGNOSTICS
Nina Kondrashova1, Vladimir Pavlov2
1 International Research and Training Center for Information Technologies and Systems
of the National Academy of Sciences and Ministry of Education and Science of Ukraine,
2 National Technical University "KPI"
NKondrashova@ukr.net, vpavlo@bk.ru
Відмінною особливістю даної роботи є ансамблювання наївних Байєсівських
класифікаторів в схемі «один проти всіх» і використанні розширеного простору ознак. У
первинній вибірці присутні метричні і категорійні змінні. Схема «один проти всіх» із
застосуванням інших методів класифікації дає поліпшення на екзамені точності
диференціальної діагностики порівняно з єдиним класифікатором, але не у випадку наївних
Байєсівських класифікаторів. Отримані результати точності дозволяють порівняти їх з
результатами інших методів розв'язання задачі класифікації: таких як МГУА і канонічний
дискримінантний аналіз.
Ключові слова: метод групового урахування аргументів (МГУА), наївний Байєсівський
класифікатор, "один проти всіх", медична диференційна діагностика.
A distinctive feature of this work is grouping naive Bayesian classifiers in the scheme of "one
against all" and using the extended features space. Metric and categorial variables are present in the
original sample. The scheme of "one vs. all" with the use of other methods of classification gives an
improvement in the accuracy of the differential diagnosis on exam sample compared to a single
Bayesian classifier, but not in the case of the Naive Bayesian classifiers. The obtained results allow
us to compare methods accuracies with such as GMDH and canonical discriminant analysis in
solution of classification problem.
Keywords: Group Method of Data Handling (GMDH), Naive Bayes classifier, "one vs. all",
medical differential diagnosis.
Отличительной особенностью данной работы является ансамблирование наивных
Байесовских классификаторов в схеме «один против всех» и использовании расширенного
пространства признаков. В исходной выборке присутствуют метрические и категориальные
переменные. Схема «один против всех» с применением других методов классификации дает
улучшение на экзамене точности дифференциальной диагностики по сравнению с единым
классификатором, но не в случае наивных Байесовских классификаторов. Полученные
результаты точности позволяют сравнить их с результатами других методов решения задачи
классификации: таких как МГУА и канонический дискриминантный анализ.
Ключевые слова: метод группового учета аргументов (МГУА), наивный Байесовский
классификатор, "один против всех", медицинская дифференциальная диагностика.
Introduction
In order to quickly analyze and make decisions about prescribing drugs a com-
puter programs are created to improve the quality of disease diagnosis. Specialists
develop programs for processing of information, which helps the doctor to make a
diagnosis, taking into account the individual characteristics of the patient and accu-
mulated knowledge in the subject area. Automated technology of medical assistance
should work in a shortage of time and resources for conducting expensive examina-
Індуктивне моделювання складних систем, № 6, 2014
11
mailto:NKondrashova@RAMBLER.
Naive bayesian classifiers for purposes of medical differential diagnostics
tions of each patient. Solution to the problem of computer diagnosis of blood diseases
makes avoid lengthy and costly researches to establish the diagnosis and expedite the
process of treatment and recovery of the patient.
The purpose of diagnosis is to understand what the diagnoses have the patients
(to which classes they should be attributed) based on their observed clinical signs.
Building classifiers are the main part of the diagnostic system. There are many ap-
proaches, methods and algorithms for this purpose.
The most well-known classification methods are a support vector machine
(SVM) [1], clustering [2, 3], factor analysis [4], discriminant analysis [5], classifica-
tion trees, statistical methods and neural networks. The book [6] in Russian includes
three issues [3-5]. The SVM method is sensitive to noise and normalizing the data.
Solving linear programming problem underlies SVM, and in the case when the
classes are linearly inseparable there is no common approach to the automatic selec-
tion of nucleus [7]. In addition, it is slow learning [8]. In a cluster analysis union of
similar objects in a group can be carried out by various methods. It is known at least
eleven methods of cluster analysis, the most famous of which is k-means [9]. Factor
analysis and the method of k-means work only with continuous data; k-means also
requires pre-specifying the number of classes. Iteration according to the principle of
k-means is extremely sensitive to poor initial partition, and it becomes even more
complicated when the initial approximation is chosen randomly [10].
Features of the original data in our task are:
1) The mixed nature of the input and output variables: some of them are categorial
and some metric;
2) The complexity of the introduction of a common metric for the dispersive crite-
rion.
Using statistical methods make the following data requirements:
1. Objects should not be correlated with each other.
2. The distribution of the objects should be close to normal.
3. Objects should satisfy the requirement of stability, which is understood as the
lack of influence on their values of random factors.
4. The sample should be homogeneous.
In the paper in view of above remarks for solving the problem of classification
we have tried to use the ideas contained in the well-known classification methods of a
statistical approach [11]. In contrast to [12] described a common Bayesian classifier
into four classes in this paper is used ensemble classifiers constructed on the principle
of "one against all." In the construction naive (or raw) Bayesian classifiers an ex-
panded space of features is used, viz the except a categorial is present the metrical
variables in the original sample. First, classifiers "are trained" on a sample of U
( U =70) of patients with known diagnoses, characterized by individual dataset. Then
the diagnostic system for the patient from exam sample С ( C =10) defines the diag-
nosis based on him observable clinical symptoms ( CU ∩ =∅).
As the initial data about the disease mild form of coagulopathy and thrombocy-
topathy were used information about hemorrhagic signs inherent to patients (women
aged 19-49 years). Hemorrhagic symptoms such as vaginal bleeding, nosebleeds, etc.
Індуктивне моделювання складних систем, випуск 6, 2014
12
N.Kondrashova, V.Pavlov
are connected with blood incoagulability. Ten categorial (of attributive) variables,
called symptoms, and one metrical (quantitative) variable, viz the age are taken into
account.
The set of studied diagnoses is presented by von Willebrand disease, disaggrega-
tion thrombocytopathy, coagulopathy and combined pathology of the hemostasis sys-
tem. Each of the four diagnoses was established for initial sample patients in a clini-
cal laboratory using modern and expensive reagents and using the latest advances in
medical technology.
The idea of constructing a naive Bayesian classifier common for all four classes,
which was built according to the formula of Bayes-Laplace, on the basis of which the
most likely diagnosis was chosen, has already been considered in [11]. Precision was
30% at verification on the examination sample. We take into account that many sta-
tistical classification, clustering and recognition methods work on Bayesian decision
rules. Bayes method has a number of possibilities and advantages [13]. The loss func-
tion of Bayesian strategy is minimal when changing the model parameters [14]. It
should be noted that the method of expert estimates which widely used in medicine
works on the "coarse" estimates of probability (frequencies). Two expert methods are
offered and tested in [15, 16] to solve the problem of medical differential diagnosis.
In this paper, the following possibilities were considered:
1) Approach "one against all" unrealized in [12] for building an ensemble of
classifiers, which helped improve the accuracy of classification in [17]; and
2) Biased estimates of the probability (frequency) by "Laplace smoothing" for
taking into account the values of signs, which were not observed on the training set,
but may appear on the examination sample. Laplace smoothing (not to be confused
with Laplasian smoothing) is a technique used to smooth categorial data. It is histori-
cally known as the sunrise problem [18].
1. Problem statement
We start of the probabilistic nature of the observed sample. Practically the each
patient received their disease independent of the others and that only the presence of
common features can characterize this or that disease in the patients’ specific group
with the same disease.
We calculated the diagnosis probability according to the Bayes-Laplace formula
of the form [19]
( )
,
)|()(
),...,,()(
)|()(
)|()(
)(
),(
)|(
1
21
1 ∑∑ ==
=== k
j jsj
jsj
k
j jsj
jsj
s
js
sj DpDp
DpDp
DpDp
DpDp
p
Dp
Dp
X
xxx
X
X
X
X
X
where features values of the individual patient, for which are estimated the
diagnosis probabilities, belong to the area of integer values , ; a sign of
age (х
ix
XΩ Xx Ω∈i
1) takes the values from the range: , and most of signs are: }49,...,20,19{
1
=Ωx
Індуктивне моделювання складних систем, № 6, 2014
13
Naive bayesian classifiers for purposes of medical differential diagnostics
mi
i
,2},1,0,1{
1\ =−+∈Ω ∈ xXx ; "dictionary" of clinical signs values: U
i ixX Ω=Ω ;
where | | is the total number values of all the clinical signs in the "dictionary".
Value of feature “+1” indicates its presence in the disease, “-1” is the absence of it;
“0” means that there were no conditions for its appearance (for example, in some
patients never removed the tooth and therefore not been possible to fix the bleeding
while teeth removing);
XΩ
)|( sjDp X is the conditional probability that a patient with a set of clinical
signs = belongs to class (diagnosis) DsX ],...,,[ 21 sxxx j, kj ,1= , that's this, we need
to calculate, where k is total number of diagnoses, equal to four, m is the total number
of clinical signs, equal to eleven, DjD Ω∈ , kD =Ω ;
)( jDp is unconditional probability the patient of class Dj in the whole sample;
( )js Dp ),...,,( 21 xxx is conditional probability of a patient having a specific set
of symptoms ],...,,[ 2211 sjsjj xxx === xxx among all patients of class Dj ;
)( sp X is unconditional probability of a patient with a set of features sX =
],...,,[ 21 sxxx in the whole sample.
We need the most likely diagnosis, i.e. it is necessary to calculate the probabili-
ties for all classes and to choose the class that has the highest probability. Used for
this purpose a Bayesian classifier based on a posteriori estimation to determine the
most likely class
)(
)|()(
maxarg
,1
*
s
jsj
kj p
DpDp
D
X
X
=
=
Denominator (the probability a specific patient) is a constant and can not affect
the ranking of the classes, so we can ignore it
)|()(maxarg
,1
*
jsjkj
DpDpD X
=
= (1)
As the volume of data is not sufficient ( U =70, т=11), to take into account the
interdependence of signs is not possible (not possible to calculate the conditional
probabilities of all combinations of features when other combinations of signs present
and specified diagnosis, i.e. ),,...,,...,( 1 jsqv Dp xxxx ).
Naive Bayesian classifier operates with a set of clinical features that condition-
ally do not depend on each other. Based on this assumption, conditional probability
the patient to have a set of symptoms can be approximated by the product of the con-
ditional probabilities of all clinical signs available at the patient
Індуктивне моделювання складних систем, випуск 6, 2014
14
N.Kondrashova, V.Pavlov
∏
Ω∈∀
==⋅⋅=≈
Xx
xxxX
i
jijsjsjjjs DpDxpDxpDp )|()|(...)|()|( 11 , kj ,1= . (2)
The most likely diagnosis is calculated using posteriori probabilities when
substituted (2) into (1) by the formula naive Bayesian classifier as:
])|()([maxarg
,1
* ∏
Ω∈∀=
=
Xx
x
i
jijkj
DpDpD . (3)
If a patient is necessary to consider a sufficiently large number of clinical symp-
toms, will have to multiply the large number of very small numbers. In order to avoid
arithmetic overflow below are commonly used property the product of the loga-
rithms. Since the logarithm is a monotonic function, its application to both parts of
expressions of the form (2) will only change their numerical values, and not the pa-
rameters at which it has the maximum (3). In the case when the logarithm of the
number near zero, it is negative, but in absolute value significantly greater than the
initial number. It makes the logarithmic probability values more suitable for analysis.
Therefore, we rewrite our formula using logarithms. The base of the logarithm in this
case does not matter. We will use the natural logarithm.
)]|(ln)([lnmaxarg
1,1
*
ji
i
jkj
DpDpD x
X
∑
Ω
==
+= . (4)
The assessment of probabilities )( jDp and are)|( ji Dp x implemented on the
learning sample. Probability of class can be estimated as
U
D
j n
n
Dp j=)( , where is
the total number of patients in learning sample of 70; is the number of patients diag-
nosed. Estimating the probability of a unique value of the clinical feature in the class
is held on the multinomial Bayesian model
Un
:
∑ Ω∈
=
X
x
l lj
ij
ji w
w
Dp )|( , (5)
where are the number times that a unique value of i-th clinical sign found in
patients class ;
ijw
jD XΩ is the set of all unique values of clinical signs ("dictionary").
Other words, the numerator of the formula (5) shows how many times, some
unique value of clinical sign found in a particular class of patients (including repeti-
tions), and the denominator is the total number (with replays) of unique values of
clinical signs in all patients given class.
If we meet the recognition stage (on examination sample) clinical sign, the value
of which did not meet during learning (e.g., a certain value of patient's age х1), then
this value is , and hence probability will be zero. This will lead to 01 =jw )|( 1 jDp x
Індуктивне моделювання складних систем, № 6, 2014
15
Naive bayesian classifiers for purposes of medical differential diagnostics
what the patient with this clinical feature could not be recognized because it will have
zero probability by to all classes
A typical solution to the problem of unknown values of clinical signs is additive
smoothing (Laplace smoothing) [20].
∑∑ Ω∈Ω∈ +Ω
+
=
+
+
=
XX X
x
l ll l j
ij
j
ij
ji w
w
w
w
Dp
α
α
α
α
)(
)|( , (6)
where α > 0 is the smoothing parameter (α=0 corresponds to no smoothing).
Using the Laplace's rule of succession, some authors have argued that α should
be 1 (in which case the term add-one smoothing [21, 22] is also used), though in
practice a smaller value is typically chosen. We believe if α =1, then an essence (6)
lies in the fact that we met the value of clinical signs at one time more and should add
1 to its frequency. Thus, the value of one of the clinical signs that we have not met
during training model, gets, though small, but not zero probability. Naturally, this ap-
proach shifts the assessment of probabilities in the direction of less probable results.
The greater number of values shall take signs and the greater the number of features,
the less displacements of probability. Substituting the estimates (6) into (4), we ob-
tain the final formula that will be Bayesian classification:
]
1
ln[lnmaxargmaxarg
1,1
* ∑
∑
Ω
= Ω∈
Ω∈= +Ω
+
+==
X
XXi j
ij
U
D
Djkj w
w
n
n
DD j
Dj l l
.
2. Classification problem solution
To implement the Bayesian classifier, we need a learning sample, in which are
put correspondences between the patients and the classes to which they belong. Then
we need to collect the following statistics from the sample that will be used on the
stage of classification and recognition:
- The relative frequencies of the classes in the sample, i.e. how often patients of
a particular class appeared;
- The total number of clinical signs in patients of each class;
- The relative frequencies of the clinical signs within each class;
- Number of unique clinical signs in the sample.
The totality of this information, we will call the original data for constructing a
classifier. Then, at step classification is necessary for each class calculate the value of
the following expression
∑∈ +Ω
+
+= Qi
j
ij
U
D
j L
w
n
n
q j
X
1
lnln . (7)
and select the class with the maximum value . In this formula, all terms except
the already mentioned plurality of values of clinical symptoms Q of the patient by
jD
jq
Індуктивне моделювання складних систем, випуск 6, 2014
16
N.Kondrashova, V.Pavlov
which they are classified (including repeats for counting ) and the total number of
values L
ijw
j clinical features of patients class in learning sample. jD
Now, in order to say how likely a patient with a set of features is diag-
nosed , need for the values of logarithms of the probability to return to the values
of the probabilities themselves. For this is necessary to do the inverse operation rais-
ing to the power and normalize the probability to get one in the sum form:
],...,,[ 21 sxxx
jD
∑ Ω∈
=
D
j
j
j
q
q
sj
e
eDp )|( X , (8)
where
jq is assessment of the logarithm of class appearance. jD
To find , for each of the four classifiers is necessary to calculate the
probability of hitting the patient to the class , and the probability of a patient
misses to class (i.e. the probability of hitting the one of the other three classes).
Thus, a classification scheme "one against all" is implemented.
)|( sjDp X
jD
jD
D1 is von Willebrand disease (VWD), D2 is coagulopathy (СP), D3 is disaggre-
gation thrombocytopathy (DT); D4 is the combined pathology of the hemostasis sys-
tem (СPHS).
Observations distribution in the classes and the samples is following.
Disease VWD: there are 20 patients in learning sample U and 4 patients in ex-
amination sample С;
Disease СP: there are 15 patients in learning sample U and 2 patients in exami-
nation sample С.
Disease DT: there are 27 patients in learning sample U and 4 patients in exami-
nation sample С.
Disease СPHS: there are 8 patients in learning sample U and 0 patients in ex-
amination sample С.
Patient age encoded, so the presence in the initial sample patient the age х1 with
value, for example, equal to 29, as х1(29). Hemorrhagic signs are encoded in the
Latin alphabet from х2 to х11 and its values in parentheses. For example, х2(-1) denote
"in the absence of the patient's juvenile uterine bleeding", х2(0) "in the absence of the
conditions for the appearance of clinical sign", х2(+1) means "in the presence of this
sign". Values clinical signs are encoded. All designations used for clinical signs are
shown in Table 1.
Table 1
Designations for clinical signs
Clinical sign Designation
Patient age х1(19) – х1(49)
Juvenile uterine bleeding х2(-1), х2(+1)
Індуктивне моделювання складних систем, № 6, 2014
17
Naive bayesian classifiers for purposes of medical differential diagnostics
Continuation of Table 1
Nosebleeds х3(-1), х3(+1)
Bleeding gums х4(-1), х4(+1)
Bleeding after teeth extraction х5(-1), х5(0), х5(+1)
Intra-and postoperative bleeding х6(-1), х6(0), х6(+1)
Post-traumatic hematoma х7(-1), х7(+1)
Bleeding from superficial wounds х8(-1), х8(+1)
Prolonged not wound healing х9(-1), х9(+1)
After injection hematoma х10(-1), х10(+1)
Postpartum bleeding х11(-1), х11(0), х11(+1)
Each patient has a unique set of clinical signs, so for each patient in the formula
(7) the naive Bayesian classifier has its own set of frequencies . The same are in-
dicators , L
ijw
jDn j, involved in the formula (7) in the limits of a given class, and XΩ ,
are common to all classes. Un
3. Results of classifiers synthesis
In tables 2, 3, 4 are statistics needed to compute the naïve Bayesian classifiers
according to formula (7).
Table 2
The frequency of bleeding symptoms
wijFeature VWD CP DT CPHS
х2(-1) 0 2 4 1
х2(+1) 20 13 23 7
х3(-1) 2 5 3 4
х3(+1) 18 10 24 4
х4(-1) 6 6 12 4
х4(+1) 14 9 15 4
х5(-1) 1 3 3 1
х5(0) 8 1 9 3
х5(+1) 11 11 15 4
х6(-1) 0 2 2 0
х6(0) 15 6 18 3
х6(+1) 5 7 7 5
х7(-1) 10 5 10 3
х7(+1) 10 10 17 5
Індуктивне моделювання складних систем, випуск 6, 2014
18
N.Kondrashova, V.Pavlov
wijFeature VWD CP DT CPHS
х8(-1) 10 7 12 2
х8(+1) 10 8 15 6
х9(-1) 10 10 18 5
х9(+1) 10 5 9 3
х10(-1) 19 13 26 7
х10(+1) 1 2 1 1
х11(-1) 4 5 11 1
х11(0) 10 8 9 5
х11(+1) 6 2 7 2
Table 3
Frequencies patients’ age
WijAge VWD CP DT CPHS
х1(19) 2 2 2 0
х1(20) 1 4 0 1
х1(21) 1 0 3 1
х1(22) 0 0 2 1
х1(23) 0 2 1 1
х1(24) 2 0 0 0
х1(25) 1 0 1 1
х1(26) 0 0 0 0
х1(27) 1 0 1 1
х1(28) 1 1 2 0
х1(29) 1 0 1 0
х1(30) 0 0 2 0
х1(31) 1 0 0 0
х1(32) 0 1 0 0
х1(33) 0 0 3 0
х1(34) 2 0 0 0
х1(35) 0 1 0 0
х1(36) 2 0 0 0
х1(37) 0 0 1 0
х1(38) 1 1 1 0
х1(39) 0 0 2 1
х1(40) 0 0 0 0
х1(41) 0 0 1 0
х1(42) 1 0 0 0
х1(43) 0 1 0 0
х1(44) 0 0 1 0
х1(45) 1 0 0 0
Індуктивне моделювання складних систем, № 6, 2014
19
Naive bayesian classifiers for purposes of medical differential diagnostics
WijAge VWD CP DT CPHS
х1(46) 1 0 0 0
х1(47) 1 1 0 0
х1(48) 0 0 0 0
х1(49) 0 1 3 1
The probability of falling into the -th class ("his" class) and the hitting into
any of the other three classes (i.e., the probability of the miss to -th class) is nec-
essary to calculate using these data, for each patient. Then the probability that a pa-
tient belongs -th class receives by formula (8). All these steps should be repeated
for all four classes, and the comparing obtained probability, choose a maximum of
them. The diagnosis (class) with the maximum probability will be diagnosed with a
particular patient.
jD
jD
jD
The tables 3 and 4 shows that "dictionary" symptoms XΩ =54- X¬Ω =51,
where 54 is the sum of all the unique signs of the first column in this group of pa-
tients. The set is a set of attribute values that can appear in a patient in the ex-
amination sample. These are patients with age 26, 40 and 48, and the value of attrib-
utes will be х
X¬Ω
1(26), х1(40) and х1(48) respectively (the cells are denoted).
Data for "their" class will look follows:
VWD CP DT CPHS Total, Un
frequency classes,
jDn 20 15 27 8 70
the total features number, Lj 220 165 297 88
Data for not "their" class will have the form:
\DΩ VWD \DΩ CP \DΩ DT \DΩ CPHS Un
frequency classes,
jDn 50 55 43 62 70
the total features number, Lj 550 605 473 682
Accuracy was defined as the proportion of correctly classified objects to all ob-
jects in the class in each of the samples. For example, on the examination sample was
Індуктивне моделювання складних систем, випуск 6, 2014
20
N.Kondrashova, V.Pavlov
correctly recognized two of the four patients with a diagnosis of VWD, one of the
four with a diagnosis of DT and neither of the two with a diagnosis of CP.
Table 4
Statistics for models calculation of (7) is:
VWD CP DT CPHS
nDj 20 15 27 8
nU 70 70 70 70
|ΩX| 51 51 51 51
"Their"
class
Lj 220 165 297 88
nDj 50 55 43 62
nU 70 70 70 70
|ΩX| 51 51 51 51
Another
classes
Lj 550 605 473 682
Table 5 shows the characteristics of the naive Bayes classifiers.
Table 5
Characteristics of the obtained classifiers
Accuracy, % VWD CP DT CPHS
Whole sample U+С 83,33 52,94 77,42 37,5
Learning U 90 60 85,19 37,5
Examination C 50 0 25 -
On average, the accuracy of the exam is: three from ten, i.e. 30% objects were
correctly recognized. It is obvious that such a low accuracy is due to non-compliance
with the demands to data for the application of statistical methods in this problem.
4. Conclusions
Solution of the diagnostic problem accomplished using a naive Bayesian classi-
fier. This type of classification was chosen in view of the fact that it is the basis of
many methods of statistical classification and can operate on a "one against all." This
approach in conjunction with other methods gives improved accuracy of the differen-
tial diagnosis as compared with a single classifier for all classes. However, in the case
with a naive Bayesian classifier, it does not allow to increase its precision at verifica-
tion of the new (examination) data. The results obtained in the classification of the
total sample (62.8%), teaching (68.17%) and examination (30%) allow us to compare
these results with ones other approaches for solving the problem of classification:
such as the method of expert estimates, GMDH and canonical discriminant analysis.
Індуктивне моделювання складних систем, № 6, 2014
21
Naive bayesian classifiers for purposes of medical differential diagnostics
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| id | nasplib_isofts_kiev_ua-123456789-83989 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | XXXX-0044 |
| language | English |
| last_indexed | 2025-12-07T15:21:02Z |
| publishDate | 2014 |
| publisher | Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
| record_format | dspace |
| spelling | Kondrashova, N. Pavlov, V. 2015-07-02T06:51:06Z 2015-07-02T06:51:06Z 2014 Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics / N. Kondrashova, V. Pavlov // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2014. — Вип. 6. — С. 11-23. — Бібліогр.: 22 назв. — англ. XXXX-0044 https://nasplib.isofts.kiev.ua/handle/123456789/83989 681.513.8 A distinctive feature of this work is grouping naive Bayesian classifiers in the scheme of "one against all" and using the extended features space. Metric and categorial variables are present in the original sample. The scheme of "one vs. all" with the use of other methods of classification gives an improvement in the accuracy of the differential diagnosis on exam sample compared to a single Bayesian classifier, but not in the case of the Naive Bayesian classifiers. The obtained results allow us to compare methods accuracies with such as GMDH and canonical discriminant analysis in solution of classification problem. Відмінною особливістю даної роботи є ансамблювання наївних Байєсівських класифікаторів в схемі «один проти всіх» і використанні розширеного простору ознак. У первинній вибірці присутні метричні і категорійні змінні. Схема «один проти всіх» із застосуванням інших методів класифікації дає поліпшення на екзамені точності диференціальної діагностики порівняно з єдиним класифікатором, але не у випадку наївних Байєсівських класифікаторів. Отримані результати точності дозволяють порівняти їх з результатами інших методів розв'язання задачі класифікації: таких як МГУА і канонічний дискримінантний аналіз. Отличительной особенностью данной работы является ансамблирование наивных Байесовских классификаторов в схеме «один против всех» и использовании расширенного пространства признаков. В исходной выборке присутствуют метрические и категориальные переменные. Схема «один против всех» с применением других методов классификации дает улучшение на экзамене точности дифференциальной диагностики по сравнению с единым классификатором, но не в случае наивных Байесовских классификаторов. Полученные результаты точности позволяют сравнить их с результатами других методов решения задачи классификации: таких как МГУА и канонический дискриминантный анализ. en Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України Індуктивне моделювання складних систем Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics Article published earlier |
| spellingShingle | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics Kondrashova, N. Pavlov, V. |
| title | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics |
| title_full | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics |
| title_fullStr | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics |
| title_full_unstemmed | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics |
| title_short | Naive Bayesian Classifiers for Purposes of Medical Differential Diagnostics |
| title_sort | naive bayesian classifiers for purposes of medical differential diagnostics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/83989 |
| work_keys_str_mv | AT kondrashovan naivebayesianclassifiersforpurposesofmedicaldifferentialdiagnostics AT pavlovv naivebayesianclassifiersforpurposesofmedicaldifferentialdiagnostics |