Choosing allowability boundaries for describing objects in subject areas

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 13, No. 1, March 2024, pp. 329∼336
ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i1.pp329-336 ❒ 329
Choosing allowability boundaries for describing objects in
subject areas
Musulmon Lolaev1
, Shavkat Madrakhimov2
, Kodirbek Makharov2,3
, Doniyor Saidov2
1Center for Resilient and Evolving Intelligence, Kyungpook National University, Daegu, South Korea
2Department of Algorithms and programming technologies, National University of Uzbekistan named after Mirzo Ulugbek,
Tashkent, Uzbekistan
3Department of Applied Informatics, Kimyo International University in Tashkent, Tashkent, Uzbekistan
Article Info
Article history:
Received Jun 1, 2022
Revised Mar 31, 2023
Accepted Apr 12, 2023
Keywords:
Data cleaning
Dirty data
Invalid objects
Machine learning
Outliers
Preprocessing
Valid intervals
ABSTRACT
Anomaly detection is one of the most promising problems for study and can be
used as independent units and preprocessing tools before solving any fundamen-
tal data mining problems. This article proposes a method for detecting specific
errors with the involvement of experts from subject areas to fill knowledge. The
proposed method about outliers hypothesizes that they locate closer to logical
boundaries of intervals derived from pair features, and the interval ranges vary in
different domains. We construct intervals leveraging pair feature values. While
forming knowledge in a specific field, a domain specialist checks the logical al-
lowability of objects based on the range of the intervals. If the objects are logical
outliers, the specialist ignores or corrects them. We offer the general algorithm
for the formation of the database based on the proposed method in the form of a
pseudo-code, and we provide comparison results with existing methods.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Kodirbek Makharov
Department of Algorithms and programming technologies, National University of Uzbekistan named after
Mirzo Ulugbek
Niyazova Street, Tashkent, Uzbekistan
Email: maxarov.qodirbek@gmail.com
1. INTRODUCTION
The problem of data preprocessing to detect and remove invalid data values to improve the efficiency
of algorithms for solving problems becomes an urgent task due to the growth in the volume of processed
data. In the works of [1], various approaches have been proposed for data cleaning based on metric functional
dependencies and minimizing statistical distortions measured with the Earth Mover’s Distance [2]. It should be
noted that searching for logically incompatible data values in describing objects of subject areas for various sets
of 2 or more features is a difficult task for implementation in practice. The problem lies in the need for more
methods for checking the allowability of feature value relationships on such sets. Hypothetically, the answer
to the question of the allowability of relationships can be obtained from competent experts in the subject areas.
The process requires: i) development of special methods for analyzing and visualizing data to detect outliers;
ii) constructing and filling of knowledge bases to control the belonging of data values to intervals with allowable
boundaries.
The logical incompatibility of values for a pair of quantitative attributes within the framework of the
subject area is considered a solution to the problem of finding the boundaries of the allowability of relations for
this pair. Acceptance limits define intervals to control the correctness of the data used. Among the universal
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330 ❒ ISSN: 2252-8938
restrictions on the use of intervals can be attributed invariance to the scale of measurements of features. The
following example will show the incompatibility of the concepts of the allowability of values for each feature
and a pair of features. A whale is the age of 5 and weighs 45,000 kilograms, two values are acceptable for their
ranges separately, but when analyzed by pairs of these feature values, they are unacceptable or doubtful.
Building a regression relationship between features is one of the ways to describe the relationship
between them. An example of using such a dependency is filling in missing values in data. The imperfection of
this method can be judged by the decrease in the generalizing ability of recognition algorithms on samples, in
which the missing values in data are randomly generated. Jouravlev proved the need for introducing additional
restrictions on the concept of “allowable object” [3]. The introduced restrictions expand the possibilities for
controlling the correctness of the data used. The proposed method for checking the correctness of data does
not in any way override the existing ones. It is recommended to use it in cases where the “classical methods”
could not detect errors. The use of this method in practice is preceded by the creation of a knowledge base,
with the help of which the user is able to analyze the reasons for the incorrectness of the data. The relevance of
research on this issue is increasing in connection with the use of cloud storage technologies for the processing
of big data.
The efficiency of using the boundaries of permissible values when forming a training data set can be
checked through the indicators of the generalizing ability of the algorithms. For comparison “clean” samples
can be used, and samples with additional falsifier objects, in the description of which there are violations of
the allowability boundaries. For example, in classification problems, noise objects are unallowable relative
to their class and negatively affect the accuracy of the solution algorithm. This factor can be used to test the
stability of algorithms, in particular, in [4], the “data + noise” technique is proposed, the use of which, on the
one hand, contributes to a “smoother” convergence of the procedure for interactive search for logical patterns.
On the other hand, “noisy” objects perform an essential function of falsifiers, the “collision” contributing to an
increase in the robustness of the solutions obtained.
Detecting anomalies of objects that differ from the main part of the data in the subject areas during
data mining [5], there are several approaches to detecting outliers depending on the type of task: parsing,
data transformation, methods of enforcing integrity constraints, duplicate detection methods, and others [6].
Almost fully similar works were overviewed by [7] in 2018. According to that paper, there are some categories
of outlier methods: global vs. local; labeling vs. scoring; supervised vs. unsupervised; parametric vs. non-
parametric methods. While, over the years there are many types of outlier detection techniques have been
proposed for various purposes [7], [8]: statistical - checking the input value in the interval, which is formed
from the standard deviation based on the Chebyshev inequality [9]; deviation-based; density-based techniques
based on a distance between objects; cluster-based such as “density-based spatial clustering of applications with
noise” [10], [11]; association templates of rules - validate the input against some template, the representation
of which is considered correct.
2. RELATED WORKS
One of the fastest ways to detect abnormal objects is the Isolation Forest method [12]. Most current
methods for detecting anomalous objects first create a normal object model, and then it is required to check all
objects of the sample for abnormal. The process creates significant computational complexity. The classical
method of Isolation Forest is thoroughly analyzed and augmented by bringing an innovative approach [13].
This approach is a k-Means-based Isolation Forest that allows building a search tree based on many branches
in contrast to the only two considered in the original method. A set of methods enhancing the Isolation Forest
based on Fuzzy C-Means was proposed [14]. The main goal of the study is to analyze the possibilities of using
the grouping method using Fuzzy C-Means at the stage of building a search tree [15]. In particular, it is utilized
the information on the degree of membership of a given object to the group of similar objects positioned close
to a given tree node. The memberships are determined based on distance from the so-called middle of the
cluster, i.e., the average value of the feature [16].
The idea behind the algorithm density-based spatial clustering of applications with noise (DBSCAN)
is that there is a higher density of objects inside each cluster than the density outside the cluster [10]. The
selection of noise objects is made on the assumption that the density in these regions is lower than in any of
the clusters. Moreover, for each point of the cluster, its neighborhood of a given radius ϵ (eps) must contain at
least a certain number of points, which is set by the threshold value MinPts. A new concept of moveability and
Int J Artif Intell, Vol. 13, No. 1, March 2024: 329–336

Int J Artif Intell ISSN: 2252-8938 ❒ 331
constructed new, comprehensive, hybrid feature-based density measurement method was defined that considers
temporal and spatial properties [17]. After, proposed the improved DBSCAN algorithm using the new density
measurement method. Another density-based clustering algorithm has been presented based on DBSCAN, and
computational geometry [18]. It represents three significant modifications or extensions to DBSCAN: selection
of parameter ϵ (eps) using the radii of empty or Voronoi circles; selection of parameter MinPts for the same
epsilon; redistribution of noise points to suitable clusters using the concept of centroid hinged clustering.
The main drawbacks of most existing approaches to anomaly detection are summarized [19], [20].
These approaches are not optimized for detecting anomalies, a consequence, these approaches are often not
efficient enough, which leads to too many false alarms (when normal instances are identified as anomalies) or
too many anomalies; many existing methods are limited to low-dimensional data and small data size due to
their legacy algorithms. Based on this overview in the previous paragraphs, we compare our method with these
methods regarding our statement of the task, and the main contributions of the paper in continuity [20] are:
− We construct a latent feature by a simple-linear combination of two features in order to conduct logical
analysis based on two features;
− We propose an expert-based model which leverages the latent feature to solve the problem of logical incon-
sistencies;
− We suggest how to utilize this model providing a general example, and we also compare the results with
results of existing methods, even though many of them are suitable for another task. For example, the
DBSCAN is a clustering algorithm, however, it can separate the noisy clusters too [21].
3. METHOD
A method for detecting logically invalid values by pairs of quantitative features in the description of
sample objects in the studied subject area is proposed and is focused on detecting errors in the input data [3].
Dividing the feature values by medians or means of the current features provides a scale-invariant property for
the method. Since the median is a random variable, its values for a real sample of data can be considered and
interpreted according to the law of large numbers [22]. As the sample size grows, the mathematical expectation
of the median tends to a stable value, i.e., is an unbiased estimate.
Let’s denote object E0 = {S1, . . . , Sm} is given, described by a set of features X = (x1, . . . , xn)
with different types, and I, J a set of indices of features, respectively, quantitative and nominal features. For
each pair of features (xi, xj) ⊂ X(n), i ̸= j, i, j ∈ I, we calculate the latent feature for feature pairs in (1):
R(i, j) =

aki
Pi
−
akj
Pj

k∈{1,...,m}
, (1)
where Sk = (ak1, . . . , akn), Sk ∈ E0, Pi, Pj - are the values of the medians of the features xi, xj on the set
E0, and the boundaries of the intervals z1, z2 calculated (2)
z1 = min
E0
R(i, j), z2 = max
E0
R(i, j). (2)
Checking the allowability of nominal features is determined through the membership of their grada-
tions in a finite set of values. The use of dimensionless quantities for calculating the boundaries of feature
ratios according to (2) and data visualization allows an expert to interactively determine the correctness of ob-
ject descriptions and enter information into the knowledge base of the subject area. To inform the user about
the interval [z1; z2] recommended to split it into a given number (for example, 10 or 100) parts. The choice
of the number of chunks depends on the size of the original dataset or the recommendations for conducting
exploratory data analysis. The suspicion of an anomalous object is determined when its values belong to the
extreme (right or left) parts of the interval [z1; z2]. The method is implemented in 3 stages:
− Forming the intervals {[z1; z2]} set
Π =
[
i,j∈I,i̸=j

Su, Sv
aui
Pi
auj
Pj
= z1 and
avi
Pi
avj
Pj
= z2

; (3)
− ∀Su ∈ Π and aui
Pi
auj
Pj
∈ {[z1, z2]} making an expert decision on its allowability (inallowability);
Choosing allowability boundaries for describing objects in subject areas (Musulmon Lolaev)

332 ❒ ISSN: 2252-8938
− Removing invalid objects from E0 and forming a set of intervals Z =
S
i,j∈I,i̸=j[z1; z2] according to (2)
and (3).
Pseudocode for this algorithm is given as a following:
while True do
generate the set of objects that are on the boundaries of the intervals
for all object in set do
make an expert decision on its allowability or inallowability
if object’s inallowability is true then
remove this object from dataset E0
end if
end for
if any object is deleted then
forming a set of intervals from E0
else
break while
end if
end while
DBSCAN algorithm scans whole dataset only one time and needs to calculate the distance of any
pair of objects in the dataset. Time complexity of original DBSCAN algorithm is high - O(n2
). Using efficient
indexing structures complexity can be reduced to O(n log n) [23]. iForest has time complexities of O(tψ log ψ)
in the training stage and O(nt log ψ) in the evaluating stage, where t - the number of trees, ψ - the number of
samples, n - testing data size [12]. Proposed method has time complexity of O(n · m(m−1)
2 ) in the evaluating
stage, where m - number of features, n - testing data size. The training stage complexity is independent of
specialist decisions. In one iteration of the training stage, it will be equal to O(m(m−1)
2 ).
4. RESULTS AND DISCUSSION
We conduct our experiments on a dataset titled “Kalahari Kung San people” to explore Kalahari Kung
San people collected by Nancy Howell, and publicly available [24], [25]. It contains 545 people’s information,
and each person is described by four features: height, weight, age, and sex, but we only consume numerical
features. Before exploring, we omit logically incorrect and missing rows, therefore the modified version of
datasets may also contain some anomaly objects too, but we assume it does not have any logically incorrect
instances during our simulations. Table 1 depicts the results of calculating the values of the boundaries of the
intervals for each pair and objects that were on the boundaries of the interval for pairs of features.
Table 1. The boundaries of a latent feature formed from pair features
# Pair-feature names Interval ranges The boundary objects
left right
1 (Height, Weight) [-0.58, 0.46] 5 (163.83, 62.99) 359 (109.22, 11.71)
2 (Height, Age) [-1.90, 0.72] 164 (140.97, 85.60) 359 (109.22, 2.00)
3 (Weight, Age) [-1.79, 0.99] 222 (35.81, 82.00) 182 (61.80, 22.00)
Table 2 represents examples of issuing the results of checking for the presence of invalid objects with
an indication of the error status: “Critical error” - the value of the attribute according to (1) lies outside the
interval; “Possibly a mistake” - the values of the feature according to (1) lie in the “dangerous” proximity to
the boundaries of the interval, determined by the entry into [z1; z1 + h] or [z2 − h; z2], where h – is the step of
dividing the interval into a given number of parts. In this experiment, h = 1% for testing purposes. Moreover,
we omit one object in each iteration and test the skipped object to be an anomaly during this experiment.
Because forgetting the one-test object, the intervals vary in each row in Table 2.
Figure 1 illustrates an example of objects that are close to the critical ranges regarding their location.
The two lines indicate the upper and lower borders of the interval based on pair feature values, and we calculate
them using 3h, h = (z2 −z1)/100, where 3h - the gap between two lines and the ranges. The objects outside of
the two lines are considered outliers. To compare methods for finding anomalous objects, we artificially create
20 anomalous objects to the original data [24]. We experiment with two forms of data: we use all data in the

first form, we fit the method using original data, and we use the trained model to identify anomalous objects in
the second form. Table 3 illustrates the test results. Since the proposed method works with a pair of features,
in the testing process, if an object is anomalous regarding any pair of features, then the object is considered
anomalous. Experimenting with separated data on the DBSCAN method is not supported using Scikit-learn
library. The proposed and Isolation Forest methods get 100% in accuracy. We leverage precision and F1 score
to compare the results to make the comparison more precise.
Table 2. Examples of defining objects with potentially invalid values
Objects no. Feature’s name Feature’s value Interval Value of features by pairs Error status
6 Height 163.83 -0.41, 0.44 -0.47 Critical error
Weight 62.99
20 Height 105.41 -0.47, 0.44 0.36 Possibly a mistake
Weight 13.95
57 Height 165.74 -0.47, 0.44 -0.35 Possibly a mistake
Weight 58.60
90 Height 136.53 -2.23, 0.66 -2.01 Possibly a mistake
Age 79.00
114 Height 124.46 -0.47, 0.44 0.38 Possibly a mistake
Weight 18.26
165 Weight 40.94 -2.15, 0.73 -2.15 Critical error
Age 85.60
Figure 1. Visual representation of the process of identifying invalid objects
Table 3. The comparison results of identifying anomalous objects by methods
Test number
Isolation Forest DBSCAN Proposed
F1 score Precision F1 score Precision F1 score Precision
Test 1 0.70 0.70 0.92 0.90 0.85 1.00
Test 2 0.80 0.80 0.90 0.86 0.91 1.00
Test 3 0.75 0.75 0.90 0.86 0.88 1.00
Test 4 0.70 0.70 0.90 0.86 0.91 1.00
Test 5 0.70 0.70 0.92 0.92 0.72 0.62
Test 6 0.65 0.65 0.90 0.90 0.88 1.00
Test 7 0.60 0.60 0.90 0.90 0.91 1.00
Test 8 0.70 0.70 0.88 0.82 0.68 0.59
Test 9 0.75 0.75 0.88 0.82 0.91 1.00
Test 10 0.70 0.70 0.85 0.81 0.68 0.59
Expected 0.70 0.70 0.89 0.86 0.83 0.88
According to Table 3, the DBSCAN’s results overperform the proposed method in most tests concern-
ing F1 scores, but the proposed method overperforms in many test cases concerning precision scores. Actually,
our task is to find anomaly objects in the dataset, and therefore by the definition of the precision score (also
called true positive value), we can conclude that the proposed method can find anomaly objects more than
DBSCAN. Moreover, we provide another example, like this experiment, in contrast to the previous one. We

334 ❒ ISSN: 2252-8938
only use two features to find anomaly objects in DBSCAN and the proposed methods. The results of this ex-
periment ended up with the same average of accuracies 0.9390, 1.00, and 0.8864 of scores F1, precision, and
recall, respectively, in each test, but we removed one feature “age” and some rows from anomaly datasets to be
correct with our setup. During this experiment, we made a trade-off with the values of h individually for each
test in order to get high performance in the proposed method. That is the reason why the results are the same.
In contrast, we did not make a like trade-off technique for the previous experiment due to our main reason
being to illustrate a simple method.
4.1. Discussion
The construction of logical intervals for a pair of features in problems related to the solution of practi-
cal problems is considered separately for each subject area. According to the example in the Introduction, it is
impossible to be a person with a 1-meter height of 250-kilogram weight. However, in other subject areas, for
example, animals, a 1-meter tall animal can weigh 250 kilograms, even more. For this reason, we added the
phrase “subject area” to the title. Also, we included the term “describing objects” in the title because the same
objects can be used to build different boundaries, for example, when objects are grouped.
The proposed model allows the construction intervals for a pair of features with the help of experts.
This allows determining an allowable range of values by pair of features. Therefore, the proposed method
can be used in the process of filling the knowledge bases of subject areas. The method is nonparametric and
has linear computational complexity, which makes it possible to apply it to problems with big data. The main
limitation of the proposed work is the need for an expert to build knowledge, and this is a common problem
that is considered a limitation of artificial intelligence too in other types of machine learning, such as labeling
data in the classification task.
In contrast, other approaches mainly focused on finding anomaly objects in data. For example,
DBSCAN is a clustering algorithm based on density level estimation with many modifications. One of the
most significant drawbacks is using distance which may cause the problem of the curse of dimensionality.
However, this limitation doesn’t affect the results in this paper because we used only three features.
During experiments, we have done several trade-offs on parameters of both DBSCAN and proposed
methods to get acceptable accuracies. However, we only cared a little about the Isolation forest method because
the nature of this algorithm requires more objects and features in datasets to get high outcomes, and this method
may not match our setups. In practice, the field of experts is required to build the ranges which identify
anomaly objects using the proposed model, so if the ranges on latent features are built properly, the results of
the proposed method can be more accurate than the results. For the reason that the accuracies of the proposed
method in experiments did not overperform in all cases. Moreover, we leveraged DBSCAN method in scikit-
learn library [26] in our experiments with parameters ϵ = 0.1 and min samples = 5.
5. CONCLUSION AND FUTURE WORK
A method of searching for logically incompatible quantitative data in describing objects of subject
areas for various sets of two features has been proposed. Using the values of the medians of the analyzed
features gives the method the property of invariance to the scale of measurements of features, which expands
the range of application of the method. The general use of the method has been illustrated to form a knowledge
base about the incompatibility of values based on intervals of paired features from the data of the subject
area. The quantitative features space has been considered in this work. Future research will be aimed to adapt
the method for different types of feature space, reduce the specialist’s decision-making role, and correct the
detected logical errors.
ACKNOWLEDGEMENTS
This work is supported by BK21 Four Project, AI-Driven Convergence Software Education Research
Program 4199990214394 2, and also supported by the National Research Foundation of Korea 2020R1A2C101
2196.
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BIOGRAPHIES OF AUTHORS
Musulmon Lolaev holds a master of science degree from National University of Uzbek-
istan in 2019 with dissertation “Analytical description of the own features space of objects for mod-
eling decision-making processes” and he finished bachelor degree in “Applied math and informatics”
in 2017. He has published about 15 scientific papers in international and national journals and con-
ferences. He is currently a Computer Science Ph.D. student at Center for Resilient and Evolving
Intelligence of Kyungpook National University, Daegu, South Korea, and his research interests in-
clude artificial intelligence, data mining, computer vision, pattern recognition, numerical modeling
and software engineering. He can be contacted at email: musulmon.lolayev.94@gmail.com or musul-
mon@knu.ac.kr.

336 ❒ ISSN: 2252-8938
Shavkat Madrakhimov received the D.Sc. degree in computer science from the Tashkent
University of Information Technologies, Tashkent, Uzbekistan, with the dissertation “Detection sys-
tems of hidden regularity on the basis of the methods of calculation of generalized estimates”. He is
a Professor of the faculty Applied mathematics and intellectual technologies, National University of
Uzbekistan, Tashkent, Uzbekistan, since 1989. In addition, he is Head of the department “Artificial
intelligence”. His research interests are in data mining, knowledge discovery, pattern recognition, and
software engineering. He has published more than 70 scientific papers in journals and conferences.
He can be contacted at email: sh.madrahimov@nuu.uz.
Kodirbek Makharov holds a master of science degree from National University of Uzbek-
istan in 2013 with dissertation “Determining the regularities by the dominance intervals of the fea-
tures of objects” and he finished bachelor’s degree in “Informatics and information technologies” in
2011. He has published about 25 scientific papers in international and national journals and confer-
ences. He is currently a computer science teacher and researcher, and his research interests include
artificial intelligence, data mining, pattern recognition, and software engineering. He can be con-
tacted at email: maxarov.qodirbek@gmail.com.
Doniyor Saidov holds a Ph.D. degree in computer science field from the National Univer-
sity of Uzbekistan (NUUz), Uzbekistan in 2017. He also received his B.Sc. (Computer science) and
M.Sc. (Computational mathematics) from NUUz in 2008 and 2011, respectively. He is currently an
associated professor at the Department of Algorithms and Programming Technologies in NUUz. His
research includes machine learning, data mining, graph theory, and data structures. He has published
over 10 papers in international journals and conferences. From February 2018 to July 2018, he was
a post Ph.D. research fellow in Keele University, United Kingdom. He can be contacted at email:
doniyorsaidov86@gmail.com.

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