=Paper=
{{Paper
|id=Vol-3702/paper16
|storemode=property
|title=The Modified Algorithm Tree Method in the Geological Data Classification Problem
|pdfUrl=https://ceur-ws.org/Vol-3702/paper16.pdf
|volume=Vol-3702
|authors=Igor Povkhan,Oksana Mulesa,Olena Melnyk,Vasyl Morokhovych
|dblpUrl=https://dblp.org/rec/conf/cmis/PovkhanMMM24
}}
==The Modified Algorithm Tree Method in the Geological Data Classification Problem==
https://ceur-ws.org/Vol-3702/paper16.pdf
The modified algorithm tree method in the geological
data classification problem
Igor Povkhan 1 , Oksana Mulesa 1 , Olena Melnyk 1 , Vasyl Morokhovych 1
1 Uzhhorod National University, Zankoveckoy str., 89B, Uzhhorod, 88000, Ukraine
Abstract
This study presents the development of an advanced algorithmic tree synthesis method predicated on
a set configuration of initial data for the task of geological data recognition. The devised classification
tree algorithm of the second type demonstrates precise classification of the complete training dataset,
adhering to the established classification schema. It boasts high interpretability, a straightforward
structure, and incorporates autonomous algorithms for classification and scheme recognition as
vertices within a graphical framework. The refined construction methodology for the tree algorithm
facilitates handling substantial volumes of discrete data across diverse categories, ensuring remarkable
accuracy of the classification schema. Moreover, it judiciously utilises hardware resources during the
creation of the definitive classification schema and supports the development of models with specified
accuracy levels. The paper advocates a novel synthesis approach for recognition algorithms, drawing on
a repository of extant algorithms and theoretical recognition methods. Employing the proposed second
type tree algorithm, a suite of models has been constructed that adeptly classifies extensive arrays of
geological data. The constructed models of classification trees have verified the absence of errors in both
training and testing datasets, substantiating the efficacy of the second type tree method algorithm.
Keywords
Algorithmic tree, classifier, pattern recognition, feature, initial sample. 1
1. Introduction
Classification and image recognition represent critical problem domains within the sphere of
artificial intelligence, notable for their extensive diversity, varying degrees of structural
complexity, and significant applicability across numerous sectors of human economic and social
endeavours. In disciplines such as geology, where the challenges of classification are tackled
through sophisticated information systems, the importance and intensity of research in this area
are well-documented [1-10]. These classification challenges demand the development and
decomposition of mathematical models tailored to the specific systems under study. Presently,
the field of artificial intelligence lacks a universally applicable approach capable of addressing the
full spectrum of these complex problems. However, several broadly applicable theories and
methodologies have emerged, with neural networks being particularly prominent due to their
versatility in addressing a wide array of classification challenges [11-14]. In practical scenarios,
specifically configured artificial neural networks often outperform traditional algorithms and
established decision tree models, such as gradient boosting methods, especially in tasks involving
unstructured data, discrete image sets, or textual content. Conversely, when dealing with
structured datasets comprising large volumes of massive discrete data, which exhibit diverse
feature spaces, decision tree-based methods and algorithms exhibit distinct advantages [15].
Generally, classification tree methodologies facilitate effective data processing across various
magnitudes, presenting the input information in its inherent form. Numerous contemporary
strategies and concepts are focused on developing recognition systems (RS) and classifications
using logical/algorithmic classification tree models (LCT/ACT structures). The growing interest
in tree-like graph-schematic representations of classifiers is driven by their numerous
CMIS-2024: Seventh International Workshop on Computer Modeling and Intelligent Systems, May 3, 2024,
Zaporizhzhia, Ukraine
igor.povkhan@uzhnu.edu.ua (I. Povkhan); oksana.mulesa@uzhnu.edu.ua (O. Mulesa);
olena.melnyk@uzhnu.edu.ua (O. Melnyk); morv77@ukr.net (V. Morokhovych)
0000-0002-1681-3466 (I. Povkhan); 0000-0002-6117-5846 (O. Mulesa); 0000-0001-7340-8451 (O. Melnyk);
0000-0002-4939-6566 (V. Morokhovych)
Β© 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
advantageous properties [16]. One promising area of application for the classification tree model,
specifically within the realm of algorithmic trees, is in the classification of geological informations
[22].
2. Formal problem statement
Let be π»1 , π»1 , β¦ , π»π the system of classes (images) defined on the set πΊ consisting of objects π₯π , (π =
1, β¦ , π). The nature of the division of the set πΊ into the corresponding classes is specified using the
following training sample (TS):
((π₯1 , ππ
(π₯1 )), (π₯2 , ππ
(π₯2 )), β¦ , (π₯π , ππ
(π₯π ))). (1)
Let us note that here π₯β β πΊ, ππ
(π₯) β {0,1, β¦ , π β 1}, (β = 1,2, β¦ , π), π β the number of TS
classes, π β the total number of TS objects, and ππ
(π₯) is some finitely significant function that
determines the division of the set πΊ into corresponding images. The ratio ππ
(π₯β ) = π,
(π = 0,1, β¦ , π β 1) means that π₯β β π»π . We note that each TS of the form (1) can be according
(with the help of some algorithm or representation method) to a wholly defined LCT, which
matches ππ
(π₯β ) the objects of TS (1) with the value of the function π₯β , (β = 1, β¦ , π), which
specifies the partition π
on the set πΊ. Therefore, the task will be to build a structure of the
classification tree (LCT/ACT), the structure of which would be optimal f R ( x j ) β opt with the
initial data of TS.
3. Literature review
The current study delves into the theory of fixed-type decision trees, focusing on algorithm
trees and the classification of discrete objects [14, 23, 25]. Notably, research [20] underscores
that the classification rules and decision schemes, derived from any branching feature selection
method or algorithm, manifest a tree-like logical structure. A typical decision tree classifier
comprises an organized sequence of nodes, features, and attributes structured into layers or
levels, each established during a specific phase of the classification tree synthesis [15].
A significant challenge identified in [18] is the effective construction of recognition tree
structures, which can take the form of tree-like structures or algorithm graphs (ACT structures).
Consequently, decision tree methodologies facilitate the creation of innovative classifiers based
on a modular principle, utilizing well-known recognition algorithms [19-21]. The study [14]
explores fundamental issues related to the generation of decision tree structures, particularly
when features are low-informative, including their sets and combinations. Within the sphere of
intelligent data analysis, the invariant capacity of LCT/ACT structures to execute one-
dimensional branching allows for the analysis of the influence, importance, and quality of
individual variables. This capability is essential for managing different types of variables as
predicate sets. The persistent challenge with decision tree methods and structures is evaluating
the quality and efficiency of the branches (generalized features) that serve as autonomous
classification algorithms [15].Logical decision tree classification methods are prevalently
employed in intelligent data analysis, aiming to synthesize operational models that predict the
value of a target variable based on an initial set of data formatted as a structured training sample
[19]. From an applied perspective, numerous methods and algorithms grounded in the decision
tree concept are utilized for classification tasks; however, C4.5/C5.0 and CART have emerged as
particularly popular. The C4.5/C5.0 methods employ a theoretical-informational criterion for
node or vertex selection, whereas the CART algorithm relies on the Gini index, which assesses the
relative distances between class distributions within the metric of the training sample [20, 21].
The set of methods and algorithms for branching feature selection (ACT structures) is based on
optimally approximating the initial training set using a ranked series of classification algorithms
[22]. A key issue within LCT/ACT methods, as discussed in [23], involves choosing an effective
branching criterionβthat is, selecting nodes, attributes, and features of discrete objects for LCT
schemes and algorithms for ACT. These foundational issues are thoroughly examined in another
paper [24], which addresses the qualitative evaluation and informativeness of individual discrete
features, their sets, and fixed combinations, ultimately supporting the efficient implementation
of a branching mechanism within the logical/algorithmic tree structure. Concerns regarding the
convergence of the classification tree construction process, including the selection of stopping
criteria for the synthesis of logical and algorithmic trees, remain significant [25]. The concept of
classification trees accommodates the use of not only individual attributes and object features
but also their combinations and sets as features, attributes, and nodes of the recognition tree
structure. By adopting independent individual recognition algorithms (evaluated using training
data) instead of object attributes as branches, a novel ACT structure is realized [21-24]. This
research specifically targets the exploration of fixed-type ACT structures within the practical
domain.
4. The general second type trees method algorithm
Let the initial TS of the general form (1) be given as a sequence of training pairs of known
classification (power π) and some system (set) of independent and autonomous recognition
(classification) algorithms for the initial TS πΌ1 (π₯), πΌ2 (π₯), β¦ , πΌπ (π₯). Next, it is necessary to enter
the following sets, which represent the breakdown of the data of TS by the corresponding
classification algorithms ππ :
πΊπ1 ,β¦,ππ = {π₯ β πΊ/πΌπ (π₯) = 1}, (π = 1, β¦ , π). (2)
Note that to simplify explanations, each autonomous classification algorithm πΌπ (π₯) generates
output values only within the binary set {0,1}, particularly πΌπ (π₯) = 1 in the case of successful
object classification π₯ and πΌπ (π₯) = 0 in the opposite case.
Note that the system of sets πΊπ1 ,β¦,ππ will represent a complete step-by-step division of the set
πΊ (with an increase in the size of π the involved classification algorithms), which is implemented
by independent algorithms πΌ1 , πΌ2 , β¦ , πΌπ . Note that depending on the initial selection of a set of
classification algorithms, πΌ1 , πΌ2 , β¦ , πΌπ some of the sets πΊπ1 ,β¦,ππ may be empty (in case one or
more algorithms are not suitable for approximating the current TS) [21].
At the next stage, we denote by the value ππ1 ,β¦,ππ the number of occurrences of those training
pairs (π₯π , ππ
(π₯π )), (1 β€ π β€ π) which satisfy the basic condition of belonging, in the initial TS π₯π β
πΊπ1 ,β¦,ππ .
π
Accordingly, by the value ππ1 ,β¦,ππ , (π = 0,1, β¦ , π β 1) we denote the number of occurrences in
the TS of those pairs (π₯π , ππ
(π₯π )) (π = 1,2, β¦ , π), which satisfy the conditions π₯π β πΊπ1 ,β¦,ππ and
ππ
(π₯π ) = π.
So, taking into account the above, what was said and by analogy with the methods of selection
of sets of elementary features, the following values can be introduced, which should be
considered as a certain criterion of branching in the structure of the ACT:
π
ππ1 ,β¦,ππ π ππ ,β¦,π π
πΏπ1 ,β¦,ππ = π
, ππ1 ,β¦,ππ = π 1 π
, ππ1 ,β¦,ππ = max ππ1 ,β¦,ππ . (3)
π1 ,β¦,ππ π
Note that if the object π₯π β πΊπ1 ,β¦,ππ is for all π = 1, β¦ , π, then it is clear that πΏπ1 ,β¦,ππ = 0 and
π
ππ1 ,β¦,ππ = 0 for π = 0,1, β¦ , π β 1.
Particularly the quantity πΏπ1 ,β¦,ππ characterizes the frequency of occurrences of members of the
sequence π₯1 , π₯2 , β¦ , π₯π (discrete objects) in the set πΊπ1 ,β¦,ππ , and accordingly, the quantity
π
ππ1 ,β¦,ππ characterizes the frequency of belonging to some object π₯ of the image (class) π»π ,
provided that π₯ β πΊπ1 ,β¦,ππ . It should be noted that the given condition is equivalent to the
condition that in the sequence of algorithms π1 , β¦ , ππ there is such an algorithm ππ¦ that ππ¦ (π₯) =
1. Then the value πΏπ1 ,β¦,ππ characterizes the information efficiency of recognizing the belonging of
some object π₯ to one of the classes π»0 , π»1 , β¦ , π»πβ1 provided that π₯ β πΊπ1 ,β¦,ππ .
At the next stage, a fundamental question arises again regarding the object's belonging to
π₯ classes π»0 , π»1 , β¦ , π»πβ1 (the question of forming a classification rule). It is clear that the object
should be assigned π₯ to the class π»π for which a simple relation is fulfilled:
π
ππ1 ,β¦,ππ = ππ1 ,β¦,ππ . (4)
Note that here {0 β€ π β€ π β 1}, and relation (4) represents a certain classification rule, and it
is clear that the greater the value of the value of ππ1 ,β¦,ππ , the higher the effectiveness of the rule.
Since the only information that represents the partitioning of images π»0 , π»1 , β¦ , π»πβ1 is the
initial TS, then the class π»π is understood as the set of all training pairs (π₯π , ππ
(π₯π ))of TS that
satisfy the ratio ππ
(π₯π ) = π, that is, the condition of belonging.
It is clear that an algorithmic tree is not the only possible construction (structure)
classification algorithm that can be organized in the form of a tree-like recognition model (several
types of such structures can be proposed). Next, we will propose one scheme for organizing a set
of classification and recognition algorithms (πΌ1 , πΌ2 , β¦ , πΌπ ) in the form of an ACT model, which
we will call an algorithmic classification tree of the second type.
Let us note that a set of autonomous classification and recognition algorithms
(πΌ1 , πΌ2 , β¦ , πΌπ )can act as a set of primary features (attributes) for an arbitrary discrete object of
π₯π some initial TS of the general form (1). Moreover, with regard to a fixed discrete object π₯π of
the initial TS, information about the appearance of the generalized feature (GF), which is built by
the current classification algorithm, and information about the general possibility of recognizing
this discrete object (presence of failure, incorrect classification, impossibility) will be necessary
for this ACT scheme GF to describe this object, etc.).
Therefore, let each training pair (π₯π , ππ
(π₯π )) of the TS correspond to its training pair of the
following form:
(π₯π (π(πΌ1 ), π(πΌ2 ), β¦ , π(πΌπ )), ππ
(π₯π )), π(πΌπ ) β {0,1} where. (5)
Moreover π(πΌπ ) = 1, if this discrete object is approximated by some GF ππ , which is built by
the πΌπ set classification algorithm (πΌ1 , πΌ2 , β¦ , πΌπ ) at the corresponding stage of ACT generation.
Similarly π(πΌπ ) = 0, if for a given discrete object the algorithm πΌπ did not build a suitable GF
(which would ensure its approximation, classification), this situation also includes failures and
classification errors (errors of the first and second kind).
By the algorithmic tree of the second type, we will understand some tree-like construction, the
general view of which is presented in (Fig. 1), at the vertices of which there are appropriate labels
(classification and recognition algorithms, πΌπ as well as sets of GFs that they generate at a specific
step of the ACT construction procedure). Note that the logical tree of this construction belongs to
the class of regular logical trees of full complexity (this logical tree will be equivalent to a logical
function of four arguments, the arguments of which take values from the set {0,1}).
The following basic ACT scheme for synthesizing a tree of algorithms of the second type based
on a branched selection of generalized features allows us to build ACT structures of arbitrary
complexity and efficiency (Fig. 1).
Stage of initial selection and evaluation of independent classification algorithms. At the
initial stage, it is necessary to select and evaluate the basic set (fixed set) of classification and
recognition algorithms (πΌ1 , πΌ2 , β¦ , πΌπ ) from the initial algorithm library. Note that this procedure
is performed based on the selected (fixed) performance criterion, followed by ranking β
interactive or randomly. The performance criterion may vary depending on the type of act
structure that is being built and cannot be changed during the classification tree synthesis
process. The set of autonomous algorithms (πΌ1 , πΌ2 , β¦ , πΌπ ), as well as their total number in the
set, are selected depending on the applied aspects of the problem and can be selected even on the
basis of a complete search of the algorithm library (of course, with significant losses of hardware
resources and processor time). At the initial stage of synthesis of the second type of ACT model,
by selecting (ranking) a set of classification algorithms and their total number, the final structural
complexity of the algorithm tree can be controlled.
Stage of synthesis of the algorithm tree structure and generalized features. At the next
stage, the central task is to build a complete regular classification tree (fixed LCT structure),
where the corresponding tiers of the structure contain the selected classification algorithms
(πΌ1 , πΌ2 , β¦ , πΌπ ), fixed at the first stage of constructing classifier sets.
A special feature of the algorithm tree of the second type is that in the constructed
classification tree structure (LCT structure), each vertex has two transitions to the next level,
denoted by a value from the binary set {0,1}. This is why the structure of the algorithm tree is
represented using a regular LCT construct. Based on this, all attributes (labels) of the same type
(classification algorithms and generated generalized features) are located at each of the levels of
this structure. In such a regular classification tree structure, nodes are independent algorithms
(classifiers) (πΌ1 , πΌ2 , β¦ , πΌπ ). Generalized feature sets (GFs) of ππ are also generated during the
synthesis step of the algorithms tree structure. Therefore, we can conclude that the algorithm
tree generates a tree of generalized features.
The idea of the second stage of synthesis of the algorithm tree structure (ACT type II model)
is the procedure for synthesizing a set of generalized features ππ (vertices of the generalized
features tree) based on pre-selected sets of independent classification and recognition algorithms
πΌπ . Note that the total number of GFs ππ generated by the corresponding classification algorithm
depends on the initial parameters of the ACT model and synthesis parameters, the specifics of the
application problem, and the resource constraints of the classification tree synthesis system.
Figure 1: The general block - diagram of the second type tree method
At the end of the second stage, after the formation of a set of synthesized generalized features
ππ for a given application problem is completed, they are located in the corresponding nodes, tiers
of the tree of algorithms of the second type (the structure of the tree of generalized features is
constructed).
Stage of checking the constructed structure of ACT. At the final stage of synthesizing the
second type of algorithm tree, you need to check the constructed ACT model. For each element
(object) of the test sample, the corresponding values of π(πΌπ ) are calculated. This value is
calculated based on a set of previously constructed generalized features - for each node of the
corresponding tree level. The constructed generalized features define the corresponding route
(bounded classifier) in the structure of the tree of algorithms of the second type. For such a GFs
structure, each of the nodes in the algorithm tree, in the event of a possible approximation of an
object of unknown classification, increases the corresponding counter of the class belonging to it
and leaves it unchanged in the event of a classification error or failure. This procedure allows you
to make a final assessment of the effectiveness of the constructed tree of algorithms of the second
type.
5. Experiments and results
The experimental validation of the proposed second type algorithm tree construction scheme
underscores its capability to tune the complexity and accuracy of the resulting classification tree
model. The model comprises various autonomous classification algorithms which, during the
modeling process, evolve into a hierarchical structure of generalized features. The selection of an
optimal model from the array of constructed Algorithmic Classification Trees (ACTs) for a specific
task hinges on evaluating multiple parameters and the effectiveness of the model, which is
typically assessed through techniques such as cross-validation against the training set (TS) data.
An essential stage in this process involves identifying the most critical parameters of the model,
such as the feature space size, the number of vertices, transitions, and algorithms. This step is
crucial for estimating the ACT's error relative to the input data set, facilitating comparison, and
aiding in the selection of a specific ACT model from the pre-defined ensemble.
Quality criteria of the constructed algorithm trees are paramount and depend on several
factors including model error, the robustness of the initial TS data set, the size of the testing
sample, and the dimensional characteristics of the problem (e.g., the number of model
parameters). At the optimization stage of the constructed ACT model, priority is given to
minimizing errors across the training and test datasets for each class defined by the initial
conditions of the current applied problem.
A significant ongoing challenge is reducing the complexity and structural pruning of the ACT
model. This reduction pertains to the overall count of functions (classifiers) and algorithms
within the ACT framework, the total number of vertices (generalized features), and the number
of transitions within the structure, as well as optimizing total memory usage and processing time
of the information system. Consequently, the defining measure of the quality and efficiency of a
constructed model, whether ACT or Logical Classification Trees (LCT), is determined by an overall
integral quality indicator:
πΈππ΄ππ
πΉππ΄ππ β
πππππ = π β
π ππ΄ππ . (6)
π΄ππ β
βπ ππ
Note that in formula (6), the set of parameters ππ represents the most important
characteristics of the constructed classification tree that is evaluated:
1) πΈππ΄ππ β the total number of errors of the ACT model on the data arrays of the initial test and
training samples;
2) ππ΄ππ β the total capacity (volume) of data arrays of training and test samples;
3) πΉππ΄ππ β the number of vertices of the obtained ACT model with the resulting values
ππ
(recognition functions, i.e. leaves of the classification tree);
4) ππ΄ππ β represents the total number of all types of vertices in the structure of the ACT model;
5) πππ§ β the total number of generalized features used in the classification tree model;
6) ππ΄ππ β the total number of transitions between vertices in the structure of the constructed
classification tree model;
7) ππ΄ππ β the total number of different autonomous classification algorithms ππ used in the
classification tree model.
Note that this integral indicator of the quality of the ACT model will take values from zero to
one. The smaller it is, the worse the quality of the constructed classification tree will be, and the
larger the indicator, the better the resulting model will be.
The Orion software complex was developed at the Uzhhorod National University based on
classification tree methods to generate autonomous recognition systems. The algorithmic library
of the system includes 18 recognition algorithms, among which tree schemes of algorithms of
three types are implemented.
The primary task on which the effectiveness of algorithm tree methods was tested was the
task of recognizing geological data β the task of separating oil-bearing and water-bearing strata.
The initial parameters of this applied problem of geological data classification are presented in
(Table 1).
Information about objects of two classes is presented in the TS. At the examination stage, the
constructed classification system should effectively recognize objects of unknown classification
relative to these two classes. Before starting work, the training sample was automatically checked
for correctness - finding and removing errors of the first kind. The system implements a
retraining and error correction scheme in the classification tree (REC algorithm).
The training sample of the presented problem consisted of 1342 objects, of which 761 were
oil-bearing objects. The effectiveness of the constructed ACT model was evaluated on a test
sample of 267 objects. The data from training and test samples were obtained based on geological
exploration in the territory of the Transcarpathian region in the period from 2001 to 2019. A
fragment of the main results of the above experiments, constructed models of LCT/ACT of various
types, are presented in (Table 2).
Table 1
Initial parameters of the classification problem
Description of The The The Relation of objects of
classes π»π tasks dimension power total different classes IS βπ»π /π
of the of data number
feature array of of
spaceπ the classes
primary by data
IS βπ splitting
IS βπ
Oil-bearing (12/10) 1342 2 761 / 1342
layers ( π»1 )
Aquifers ( π»2 ) (12/10) 1342 2 581 / 1342
(Table 3) presents information on the classification models' generation time, the total number
of vertices, and elementary and generalized features on the basic hardware configuration
Intel i7-12700H. All constructed schemes of classification trees (structures of LCT/ACT) provided
the necessary level of accuracy given by the task condition, speed, and consumption of the
system's working memory.
Table 2
Comparison table of built ACT/LCT models for classification of geological data
Classific Method of Integral feature The overall The
ation synthesis of of model indicator of number of
tree classification tree quality πππππ the structural errors and
model structure complexity of failures to
No the classify the
classification LCT/ACT
tree model model on
πππππ the data
set πΈππ΄ππ
No. 1 The method of
full LCT based on 0.004786 121 7
the selection of
elementary traits
(extensive
selection of
features)
No. 2 The LCT method
with a one-time 0.002271 144 12
assessment of the
importance of
features
No. 3 Limited method
of construction of 0.003193 97 16
LCT
No. 4 Algorithmic tree
method (type I) 0.005287 52 10
No. 5 Algorithmic tree
method (type II) 0.003033 64 8
No. 6 A limited method
of building ACT 0.002654 55 14
No. 7 Algorithm tree
based on 0.007221 31 6
hyperspheres
No. 8 A tree of
algorithms based 0.004418 54 19
on
hyperparallelepip
eds
No. 9 A tree of 0.006476 30 8
algorithms based
on hyperellipses
No. 10 Algorithm tree 0.006251 37 11
based on
hypercubes
Table 3
General structural parameters of the constructed models of LCT/ACT
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9 No. 10
Total time of
classification
tree 34 21 18 65 82 55 47 56 50 98
synthesis (s.) (s.) (s.) (s.) (s.) (s.) (s.) (s.) (s.) (s.)
ππ΄ππ
The number
of tiers of 12 10 9 26 30 23 21 24 22 34
the LCT/ACT
structure
π
π΄ππ
The total
number of
attributes /
vertices of 102 91 86 234 244 212 198 223 207 219
the LCT/ACT
structure
ππ΄ππ
The total
number of
elementary
/
generalized
features in 56 72 40 17 41 30 18 47 21 35
the (el.) (el.) (el.) (g.) (g.) (g.) (g.) (g.) (g.) (g.)
structure of
the
classification
tree
πππ /πππ§
Therefore, the algorithmic tree classification method proposed in the paper (second-type ACT
methods) was compared with the complete LCT method and the limited method of selection of
elementary features and showed a generally acceptable result.
6. Conclusion
The developed models of classification trees (ACT/LCT structures) have successfully met the
requirements for quality and speed in geological data classification schemes while maintaining a
compact structure (parameter πππππ ). The sets of independent classification algorithms selected
for generating GF groups also demonstrated their effectiveness within the scope of this applied
problem. Notably, the models of ACT employing basic geometric classifiers were found to be the
most effective upon critical evaluation. Furthermore, the composite ACT structures resulted in a
relatively low number of classification errors in both the training and testing datasets. The full
model of the second type ACT, based on geometric classifiers, showed promising results
(πππππ = 0,003033), largely due to the inclusion of a universal algorithm of hyperspheres in the
scheme. In contrast, the structure of the first type ACT exhibited superior quality
(πππππ = 0,005287) compared to second type algorithm trees. This superiority is attributed to the
more complex construction of the model (πππππ =52), which, consequently, required longer
generation times. However, it is essential to consider the limitations of the selected geometric
classifiers, which may not always provide effective approximation of the TS data. A notable
drawback of the ACT models presented, identified during this task, is the relatively high time
consumption during the synthesis stage of the classification tree models, especially when
compared to the LCT structures. The time difference in constructing the first type of ACT models,
which includes a step-by-step assessment of feature informativeness, was nearly 34% greater
than that of LCT.
The scientific novelty lies in the fact that for the first time a modified method for constructing
algorithm trees based on evaluating and ranking a set of autonomous recognition algorithms for
generating a classification tree structure (ACT model) has been proposed.
The practical implications of these findings are significant. The proposed method for
constructing ACT models (of the second type) enables the creation of economical and efficient
classification models with specified accuracy. This method has been integrated into the algorithm
library of the "ORION" system, addressing various applied classification challenges and
demonstrating a high degree of versatility across a range of applications. The efficacy of the
classification tree models and the associated software have been confirmed through practical
applications. Looking ahead, future research could focus on the further development of ACT
methods, including the introduction of new types and schemes of classification trees.
Additionally, optimizing the software implementations of the proposed ACT method and its
practical validation on a variety of precise classification and recognition tasks could provide
valuable insights and enhancements to the field.
Acknowledgements
The presented work was carried out within the framework of projects: Expanding
Opportunities of High Technologies for Higher Education Institutions (Skills2Scale) - HEI
Initiative; Innovative teaching methods to support partnership relations - "InovEduc" - grant
project No. CBC01008 of the Norwegian State Fund with the solidarity budget of the Slovak
Republic within the framework of the SK08 cross-border cooperation program; Research work
"Modeling and prediction of emergency situations in the Carpathian region and the countries of
Central Eastern Europe", state registration number of the work - 0106V00285, work category -
fundamental research, 01 Fundamental research on the most important problems of natural,
social and humanitarian sciences.
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