Volume 04 Issue 03-2024
149
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
04
ISSUE
03
Pages:
149-155
SJIF
I
MPACT
FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
A
BSTRACT
In the primary processing of information, in particular in character recognition, an important issue is the
selection and classification of an informative feature or a set of features classifying objects. Despite the fact
that a number of methods and algorithms have been proposed to solve these problems, there are many
problems in this direction that are waiting to be solved. This is due to the fact that many of the proposed
approaches strongly depend on the nature of the object of study, the number of its features, the type of
perceived values of features, the size of the study sample, etc., and impose certain requirements on the
above. In addition, each method or algorithm will strongly depend on whether the criterion of informative
selection of features and the defining rule determining the quality of the choice made are correctly chosen.
This article presents a description of the algorithm developed taking into account the above approaches to
the selection of information complexes of signs, as well as recommendations on the application of this
algorithm in practical matters of the medical field, i.e. in ischemic heart disease obtained as an object of
study (5 classes, 507 objects, 89 signs, including X_1 class “strenuous angina”, X_2 class “Acute myocardi
al
infarction”, class X_3 “Arrhythmic form”, class X_4 “Postinfarction cardiosclerosis”, for class X_5 “Persistent
Journal
Website:
http://sciencebring.co
m/index.php/ijasr
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Research Article
AN ALGORITHM FOR SELECTING AN INFORMATIVE
SYMBOLIC COMPLEX BASED ON CLASSIFICATION ERROR
COEFFICIENTS AND PROBABILISTIC INDICATORS IN THE
REPRESENTATION OF SYMBOLS
Submission Date:
March 20,
2024,
Accepted Date:
March 25, 2024,
Published Date:
March 30, 2024
Crossref doi:
https://doi.org/10.37547/ijasr-04-03-27
Juraev Gulomjon Primovich
Associate Professor of the Department of Methods of Exact and Natural Sciences, National Center for
Teacher Training in New Methods of the Kashkadarya Region, Uzbekistan
Saparov Saidkul Khojamurodovich
Doctoral student, Tashkent University of Information Technologies named after Muhammad al-Khwarizmi,
Uzbekistan
Volume 04 Issue 03-2024
150
International Journal of Advance Scientific Research
(ISSN
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2750-1396)
VOLUME
04
ISSUE
03
Pages:
149-155
SJIF
I
MPACT
FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
form of atrial fibrillation”) formulated training was applied to the selection and positive results were
achieved.
K
EYWORDS
Primary data processing, training sample, classification, selection of an informative symbolic complex,
classification error.
I
NTRODUCTION
The experience conducted during the pandemic
in the world has shown the need to accelerate the
work on digitalization of medicine while
eliminating problems in the field of medicine. In
particular, in the field of medicine, special
attention is also paid to the development and
development of data mining methods that
correspond to human decisions.
Important scientific projects carried out by
scientific societies and research institutes
engaged in medical research around the world
are genomics and the Human Genome project,
vaccines and vaccination, medical robots, blood
detection and analysis technologies, medical
digital technologies, geonomics (bioanalysis),
medical rehabilitation technologies, the latest
scientific research in the field of medicine and the
results count. These researches, aimed at the
scientific development of medical science, serve
as the basis for the intellectual analysis of medical
information in solving classification issues,
choosing a set of informative signs, forming
symptom complexes and diagnosing diseases
based on them. Usually, the size of the medical
information that the disease evaluator collects
and stores is tens or hundreds of characters.
Based on this information, the decision-making
process by industry professionals becomes an
extremely complex process.
Therefore, issues related to the transition from a
large size to a smaller one, which is more
important in the primary processing of medical
information, that is, with the selection and
evaluation of information sign complexes, the
formation of symptom complexes in the context
of information sign complexes and the
development of modern recognition systems that
help industry specialists in solving issues such as
diagnosis on based on them. In particular, the
decision on the transition from a large size to a
smaller significant size during primary data
processing, that is, on the set of informative
symbolic complexes, was of interest to scientists
around the world, and in this regard, a number of
studies are underway [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15].
This article also develops an algorithm for
selecting an informative set of symbols based on
classification error coefficients and probabilistic
indicators in the representation of symbols.
T
HE MAIN PART
The standard was chosen for the preparation of
𝑥
𝑝1
, 𝑥
𝑝2
, … , 𝑥
𝑝𝑚
𝑝
∈ 𝑋
𝑝
,
𝑝 = 1, 𝑟;
̅̅̅̅̅
cognitively, the
Volume 04 Issue 03-2024
151
International Journal of Advance Scientific Research
(ISSN
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2750-1396)
VOLUME
04
ISSUE
03
Pages:
149-155
SJIF
I
MPACT
FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
question of choosing a set of characters is the
symbol value with a space in the part
𝜆 =
(𝜆
1
, 𝜆
2
, … , 𝜆
𝑁
), 𝜆
𝑗
∈ {0,1}, 𝑗 = 1, 𝑁;
̅̅̅̅̅̅
is included in
the vector.
Here, the main problem of the
𝜆
vector is to
ensure the transition from an N-dimensional
character space to an
ℓ
-dimensional character
space small enough for the
𝑁
number.
Here
𝜆
means that the signs corresponding to the
components of the vector that are equivalent
together mean that the selected part has a set of
characters in space, and signs equal to zero mean
that the corresponding characters do not
participate in the extracted information character
set.
Definition 1.
The studied vector space
𝜆
is called
ℓ
-dimensional if, for an arbitrary vector
𝜆
under
consideration, the sum of its components is equal
to
∑ 𝜆
𝑗
𝑁
𝑗=1
= ℓ
Similarly, in an
ℓ
-dimensional vector space, let
the set in which the vectors
𝜆
are located be
denoted by
Λ
ℓ
.
By definition, the mathematical expression
of this set will be:
Λ
ℓ
= { 𝜆: ∑ 𝜆
𝑗
𝑁
𝑗=1
= ℓ , 𝜆
𝑗
∈ {0,1}, 𝑗 = 1, 𝑁;
̅̅̅̅̅̅ }
here, set of
Λ
ℓ
number of vectors
𝜆
is equal to
𝐶
𝑁
ℓ
=
𝑁!
ℓ!(𝑁−ℓ)!
.
if
ℓ = 1, 𝑁
̅̅̅̅̅
, in this set
2
𝑁
− 1
is
𝜆
vectors:
∑ 𝐶
𝑁
ℓ
=
𝑁
ℓ=1
2
𝑁
− 1.
Definition 2.
Λ
ℓ
vectors
𝜆
which are
elements of the set
ℓ
are called informative
vectors. The number of non-zero components of
these vectors is
ℓ
. Suppose that the objects of the
training sample based on the reference table
𝜃(𝑁)
have a classification error, and the number of
incorrectly recognized objects is
ϰ(𝑁)
.
Learning here on the other hand, the total number
of objects in the sample is
𝑀
, then the
classification error in
𝑁
-dimensional space is
calculated using the formula
𝜃(𝑁) =
𝜘(𝑁)
𝑀
.
Let the mechanism of operation of the
proposed algorithm be defined as follows. First,
the probability vector for selecting symbols of the
objects
of
the
training
sample
𝑝
𝜈
=
(𝑝
𝜈
1
, 𝑝
𝜈
2
, … , 𝑝
𝜈
𝑁
)
is introduced.
Here
𝑝
𝜈
means that the
𝜈
in the index of the
probability vector is the probability vector.
Usually, this index will be associated with the
choice of a probability vector. The first choice of
𝜈 = 1
bo‘lib,
𝑝
1
𝑗
=
1
𝑁
; 𝑗 = 1, 𝑁
̅̅̅̅̅;
Similarly,
𝑝
𝜈
= (𝑝
𝜈
1
, 𝑝
𝜈
2
, … , 𝑝
𝜈
𝑁
)
probability
vector
ℓ
is informative
𝜆 ∈ Λ
ℓ
in vector space we
want
𝑝
𝜈
|
𝜆
= (𝜆
1
𝑝
𝜈
1
,
𝜆
2
𝑝
𝜈
2
, … , 𝜆
𝑁
𝑝
𝜈
𝑁
)
the form is
characterized.
Based on the initial given probability,
Λ
ℓ
from the set
𝑝
𝜈
=
(𝑝
𝜈
1
, 𝑝
𝜈
2
, … , 𝑝
𝜈
𝑁
)
, to the
probability vector
𝜆
, the vector is randomly
selected, and this is denoted as
𝜆
𝜈1
, 𝜆
𝜈2
, … , 𝜆
𝜈𝑘
. .
In the context of all the features of this
training sample, the classification process is
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International Journal of Advance Scientific Research
(ISSN
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VOLUME
04
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03
Pages:
149-155
SJIF
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FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
carried out on the basis of sequential calculation
of the following Formulas (1), (2) and (3:
1.
Initially, each object belonging to the
𝑋
𝑝
class
is compared with objects in its class, as well
as with objects in other classes
𝑥
𝑝𝑖
the
proximity function between the object and
objects
𝑥
𝑝𝑞
of the
𝑋
𝑝
class
𝜌
𝑗
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
)
is
calculated as:
𝜌
𝑗
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
)
= {
1, if |𝑥
𝑝𝑖
𝑗
− 𝑥
𝑝𝑞
𝑗
| = 0
0, otherwise
(1)
Here
𝑗 = 1, 𝑁;
̅̅̅̅̅̅ 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑖, 𝑞 = 1, 𝑚
𝑝
̅̅̅̅̅̅̅; 𝑖 ≠ 𝑞;
.
2. Comparative evaluation for each class,
that is, each object of this class
𝑋
𝑝
is
Г
𝑝
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
)
for
𝑥
𝑝𝑖
Г
𝑝
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
) =
1
𝑚
𝑝
∑ ∑ 𝜌
𝑗
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
), 𝑖 = 1, 𝑚
𝑝
; 𝑖
𝑁
𝑗=1
𝑚
𝑝
𝑞=1
≠ 𝑞 ; (2)
3.
Based on the results obtained in a
comparative assessment, the maximization
problem is solved using the formula
Г
𝑝
∗
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
) = max
𝑝=1,𝑟;
̅̅̅̅̅
Г
𝑝
(𝑥
𝑝𝑖,
𝑥
𝑝𝑞
), 𝑖, 𝑞 = 1, 𝑚
𝑝
; 𝑖
≠ 𝑞; (3)
And in result
𝑥
𝑝𝑖
∈ 𝑋
𝑝
.
It determines the levels of individual
significance of all features in the reference sample
of training. This is a reference training without
selection
𝑝
𝜈
=
(𝑝
𝜈
1
, 𝑝
𝜈
2
, … , 𝑝
𝜈
𝑁
)
using
the
probability vector, the column containing one
character is excluded from the training sample
and the classification error coefficient is
calculated on the segment of the remaining
characters
𝜃(𝑁 −
1)
. These processes include
the following two important cases.
The first case:
the difference in
classification errors if
𝜃(𝑁) =
𝜃(𝑁 − 1)
, in this
case, this character is completely removed from
the training sample, and the number of characters
is reduced by one character.
The second case:
otherwise
,
𝜃(𝑁) ≠
𝜃(𝑁 − 1)
, in this case, this symbol will be left in
the training sample, and the process will start
againIn the second case, the number of signs of
educational selection does not change.
Description of the proposed algorithm
1-step.
Initial classification error is
𝜃(𝑁)
;
2-step.
the value
ℓ
is entered ,
ℓ << 𝑁
;
3-step. In
𝜈 = 1
is
𝑝
𝜈
= (𝑝
𝜈
1
, 𝑝
𝜈
2
, … , 𝑝
𝜈
𝑁
)
for
𝑝
𝜈
𝑗
=
1
𝑁
; 𝑗 = 1, 𝑁;
̅̅̅̅̅̅
initial values are assigned;
4-step.
One character is randomly selected
from
𝑁
characters and subtracted from the array.
Than, In the cross section of
𝑁 − 1
characters, the
classification process is performed. In a result for
𝑁 − 1
characters, the error coefficient is equal to
𝜃(𝑁 − 1)
;
5-step.
If
𝜃(𝑁) = 𝜃(𝑁 − 1)
, here, in this
case, this symbol is completely removed from the
training sample, otherwise this symbol remains in
the training sample, and the process begins with
step 4. This process is reversible as long as
𝑁 −
ℎ = ℓ
.
If
𝑁 − ℎ = ℓ
, in this case is formed number
of the signs
ℓ
and a signal solution with multiple
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VOLUME
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Pages:
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)
(2024:
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)
OCLC
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characters is formulated and proceeds to step 6.
Similarly, if equality is not satisfied, the process
continues until all characters are processed one
by one. However, after all the symbols are
considered, we proceed to the next step;
6-step.
Suppose that
𝑁 − ℎ = ℓ
, then given
the
following
𝑝
𝑗
=
1
2𝑁−ℎ
, 𝑗 =
1, ℎ;
̅̅̅̅̅̅ 𝑝
𝑗
=
2
2𝑁−ℎ
, 𝑗 = ℎ + 1, 𝑁;
̅̅̅̅̅̅̅̅̅̅̅̅
with probability 4
–
process,
in the reverse step, only those symbols that were
selected earlier, which should be chosen
randomly, and those that remained in the system
differ from each other in probabilities.
Then go to
step 5.
With the help of a software package created based
on this algorithm, informative symbolic medicine
complexes for coronary heart disease were
selected (see Table 1).
1-table
information symbolic complexes selected in
103 variants when
𝓵 = 𝟗
𝓵 = 𝟗
𝓵 = 𝟗
𝓵 = 𝟗
𝓵 = 𝟗
𝑥
3
, 𝑥
5
, 𝑥
10
, 𝑥
11
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
52
, 𝑥
53
, 𝑥
56
, 𝑥
62
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
10
, 𝑥
11
, 𝑥
40
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
80
𝑥
3
, 𝑥
11
, 𝑥
40
, 𝑥
41
, 𝑥
48
, 𝑥
52
, 𝑥
53
, 𝑥
59
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
64
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
63
, 𝑥
72
, 𝑥
80
𝑥
10
, 𝑥
11
, 𝑥
40
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
59
, 𝑥
63
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
40
, 𝑥
49
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
10
, 𝑥
11
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
68
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
14
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
11
, 𝑥
40
, 𝑥
52
, 𝑥
53
, 𝑥
59
, 𝑥
62
, 𝑥
71
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
, 𝑥
85
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
34
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
41
, 𝑥
48
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
25
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
64
, 𝑥
80
, 𝑥
89
𝑥
10
, 𝑥
11
, 𝑥
40
, 𝑥
52
, 𝑥
53
, 𝑥
59
, 𝑥
62
, 𝑥
63
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
81
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
32
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
25
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
89
𝑥
3
, 𝑥
5
, 𝑥
10
, 𝑥
11
, 𝑥
41
, 𝑥
52
, 𝑥
53
, 𝑥
63
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
24
, 𝑥
52
, 𝑥
53
, 𝑥
62
, 𝑥
63
, 𝑥
80
𝑥
3
, 𝑥
5
, 𝑥
11
, 𝑥
41
, 𝑥
42
, 𝑥
52
, 𝑥
53
, 𝑥
80
, 𝑥
89
𝑥
10
, 𝑥
11
, 𝑥
40
, 𝑥
52
, 𝑥
53
, 𝑥
59
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Volume 04 Issue 03-2024
154
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
04
ISSUE
03
Pages:
149-155
SJIF
I
MPACT
FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
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C
ONCLUSION
As a criterion of informativeness in solving the
problem of choosing a set of informative features,
which is one of the main tasks of primary data
processing, the classification error coefficient and
the probability vector of the features of the
sample objects were obtained, aimed at reducing
the classification error. In addition, the
probability vector used when selecting symbols
prevents the inappropriate exclusion of
significant object symbols from the selection.
With the help of a software package developed on
the basis of the proposed algorithm, it was
possible to select and diagnose (classify) based on
a set of informative signs that are part of coronary
heart disease, which can serve as a basis for the
diagnosis of the disease, that is, the class is
considered as class
𝑋
1
-
“Strenuous angina”, class
𝑋
2
“Acute myocardial infarction”, class
𝑋
3
“Arrhythmic form”, class
𝑋
4
“Postinfarction
cardiosclerosis”, class
𝑋
5
“Persistent form of atrial
fibrillation, in particular, based on clinical signs in
patients.
R
EFERENCES
1.
Bykova V.V., Kataeva A.V. Methods and means
of analyzing the informative value of signs in
the processing of medical data//Software
products and systems /Software & Systems №
2 (114), 2016.-c. 172-178.
2.
Fazylov Sh.Kh., Nishanov A.Kh., Mamatov N.S.
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155
International Journal of Advance Scientific Research
(ISSN
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2750-1396)
VOLUME
04
ISSUE
03
Pages:
149-155
SJIF
I
MPACT
FACTOR
(2022:
5.636
)
(2023:
6.741
)
(2024:
7.874
)
OCLC
–
1368736135
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