=Paper=
{{Paper
|id=Vol-3403/paper17
|storemode=property
|title=Dendritic Artificial Immune Network Model for Computing
|pdfUrl=https://ceur-ws.org/Vol-3403/paper17.pdf
|volume=Vol-3403
|authors=Mykola Korablyov,Oleksandr Fomichov,Matvii Ushakov,Mykyta Khudolei
|dblpUrl=https://dblp.org/rec/conf/colins/KorablyovFUK23
}}
==Dendritic Artificial Immune Network Model for Computing==
https://ceur-ws.org/Vol-3403/paper17.pdf
Dendritic Artificial Immune Network Model for Computing
Mykola Korablyov 1, Oleksandr Fomichov 1, Matvii Ushakov 1 and Mykyta Khudolei 2
1
Kharkiv National University of Radio Electronics, Kharkiv 61166, Ukraine
2
Taras Shevchenko National University, Kyiv, 01033, Ukraine
Abstract
Today, a large number of methods and models of intelligent information processing have been
developed, among which artificial immune systems (AIS) can be distinguished, which are used
to solve various practical problems. At the same time, existing models of AIS have a number
of disadvantages, the main of which are low productivity and relatively low accuracy.
Therefore, the work sets out the task of building such an AIS model that would provide better
calculation characteristics both in terms of speed and accuracy. A new model of an AIS in the
form of a dendritic artificial immune network (DaiNET) is proposed, which is built using graph
theory and allows increased speed, ensures acceptable accuracy of results, and reduces the
complexity of the antibody network formation process. The formation of the dendritic structure
of the immune network is considered an example of solving the object clustering problem,
which is one of the main areas of the practical application of AIS. It is proposed to form a k-
connected graph of antibodies, in which the affinity of antibodies is used as a measure that
determines the strength of the connection between antibodies in the immune network. The
determination belonging to the clusters of antibodies of the immune network is based on the
values of their avidity for each of the clusters, which are based on the affinity between immune
objects. The general scheme of the data clustering algorithm based on the DaiNET immune
model is considered, which is represented by the sequential execution of the stages of
preparation, formation of a K-connected immune network, and network interaction. The
peculiarities of the work of immune operators of the DaiNET model are considered. The results
of a comparative analysis of the proposed DaiNET immune model with existing immune
models and other clustering methods on different data sets are presented, which showed that it
outperforms other immune models both in terms of speed and accuracy of object grouping.
Keywords 1
Dendritic Artificial Immune Network, Antibodies, Model, Clustering, Affinity, Avidity,
Graph, Level of Stimulation
1. Introduction
The theory of artificial immune systems (AIS) is one of the directions in the organization of artificial
intelligence systems [1-3]. To date, there are several common AIS models that are used to solve various
practical problems [4, 5]: a) negative/positive selection model, b) clonal selection model, c) artificial
immune network (AIN) model. These models differ from each other in the ways of editing the antibody
population, ways of organizing immune operators, and in the possibilities of interaction between
immune objects.
Among the listed immune models, the most promising for practical application is the AIN model,
since it involves the organization of interaction not only between populations of antibodies and antigens
but also the interaction between antibodies within one population [2]. This makes it possible to use this
COLINS-2023: 7th International Conference on Computational Linguistics and Intelligent Systems, April 20–21, 2023, Kharkiv, Ukraine
EMAIL: mykola.korablyov@nure.ua (M. Korablyov); oleksandr.fomichov@nurel.ua (O. Fomichov); matvii.ushakov@nure.ua (M.Ushakov);
hudoley1999nik@gmail.com (M. Khudolei)
ORCID: 0000-0002-8931-4350 (M. Korablyov); 0000-0001-9273-9862 (O. Fomichov); 0000-0003-0230-1555 (M. Ushakov), 0009-0006-
8979-4346 (M. Khudolei)
©️ 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
model not only for solving practical problems with supervised learning but also for solving problems
with self-learning [3, 6]. In addition, due to the possibility of interaction between antibodies, the AIN
model is easier to modify than the other listed models and allows the formation of hybrid models that
operate on the basis of various biological and non-biological approaches for organizing calculations.
It should be noted that the existing AIN models, such as Artificial Immune Networks (aiNET) and
Resource Limited Artificial Immune Networks (RLAIN) [2, 3] have a number of disadvantages, which
increases the relevance of the task of modifying them for solving practical problems. The main
disadvantages of the aiNet model are low performance and relatively low accuracy, which manifests
itself, for example, in solving problems of classification, clustering, and pattern recognition. The
RLAIN model also has a number of disadvantages associated with high implementation complexity,
high depending on the method for determining the level of antibody stimulation, and narrow
specialization expressed in solving problems of data classification with supervised learning.
In accordance with this, the task is to build a tree-type immune network model using graph theory,
which will solve the problem of increasing the speed of the aiNet model, provide acceptable accuracy
of the results, and also reduce the complexity of the process of forming a network of antibodies and
recognition areas, which is typical for the RLAIN model.
2. Formation of the dendritic structure of the immune network
We will consider the formation of the dendritic structure of the immune network using the example
of solving the object clustering problem, which is one of the main areas of the practical application of
AIS [2, 3]. It is proposed to form a connected graph of antibodies. The concept of affinity is used as a
measure that determines the strength of the connection or similarity between AIN antibodies [1]:
aff 1 d ij 1
, (1)
where d ij is the Euclidean or Manhattan distance between the features of the i th and j th immune
objects. According to this, before the formation of a dendritic network of antibodies, affinities are
calculated between all initial antibodies within a certain feature space. The process of forming the
dendritic structure of the immune network is multi-stage. In the first stage, the antibody network is
formed as a graph [7], where each vertex is connected to all other vertices of this graph (see Figure 1).
Figure 1: The first stage of the formation of a dendritic immune network
The process of forming a network of antibodies is a process of optimizing a fully connected graph
of objects, the vertices of which are antibodies, and the edges are the affinities between them.
Optimization means reducing the number of connections between antibodies in order to reduce the
number of computational operations between pairs of antibodies. At the same time, the value of the
Natural Affinity Threshold (NAT), which is the average affinity between all antibodies in the
population, is used as a criterion that regulates the number of affinity connections between antibodies:
aff abi , ab j
n n 1
NAT AB
i 1 j 1 (2)
nn 1
,
where n is the number of antibodies in the population; aff abi , ab j is the affinity value between the
i th and j th antibodies according to (1).
Accordingly, connections between antibodies are removed if their affinities do not exceed the NAT
value. Thus, due to the use of NAT in immune training and self-regulation of the network, the number
of edges in the fully connected graph of antibodies is significantly reduced, which allows the speed of
the operation of the immune network. In addition, to reduce the number of calculations in the dendritic
immune network of antibodies, objects characterized by a high level of stimulation are selected. Levels
of antibody stimulation are determined based on the closest antibody affinities of the dendritic immune
network. Selected objects, characterized by a high level of stimulation, participate in solving the task
of classification, clustering, skeletonization, and pattern recognition. Other antibodies are not amenable
to cloning, mutation, and suppression, which leads to a reduction in the number of computational
operations and increases the speed of the immune model.
Thus, the reduction of the number of connections between antibodies occurs due to the removal of
connections characterized by minimum values of affinities. According to the expression used to define
affinity (1), the range of affinity values is measured within (0.0; 1.0]. At the same time, the smaller the
affinity value, the weaker the connection between objects, that is, the smaller the similarity between an
increase in the affinity value means a stronger bond between a pair of immune objects.
When reducing the number of connections between antibodies of a dendritic immune network, it is
assumed to use some input parameter K that limits the number of connections between antibodies of
the network. That is, each antibody can create no more than connections with other antibodies in the
network, other connections created by this antibody are removed. This idea is borrowed from the
method of classification of k Nearest Neighbors (kNN) [8, 9]. Accordingly, during the formation of a
dendritic network of antibodies, each antibody can form no more than K connections characterized by
maximum affinities. Figure 2 shows a dendritic K -connected network of antibodies with parameter
K = 3.
Figure 2: Dendritic K -connected network of antibodies ( K = 3)
It should be noted that the parameter can vary in the range from 2 to many connections. At the same
time, an increase in the number of active connections that remain during the construction of a dendritic
immune network leads to a significant decrease in the speed of the immune clustering algorithm.
However, a decrease in the number of connections between antibodies of the dendritic immune network
leads to a decrease in the accuracy of clustering and the appearance of a significant number of immune
object grouping errors.
However, as a result of the formation of a dendritic network, some immune objects located in
clusters of antibodies may have a large number of connections exceeding the value of K . This happens
because such an antibody independently forms K bonds and accepts additional bonds from other
antibodies that are in close proximity according to its affinity. Thus, thanks to the reduction of the
number of connections between antibodies in the network, a dendritic structure of the antibody network
is formed from the initial graph with complete connections between objects, in which cluster centers
are subsequently selected.
At the second stage, after the formation of a K -linked network of antibodies, the level of stimulation
of each antibody is calculated based on its affinity with other immune objects forming the network [10]:
si aff abi , ab j ,
1 K
(3)
K j 1
where si is the value of the stimulation level of the i th antibody to the antibodies associated with it;
K is a parameter that determines the number of antibody connections in the network.
Candidates for cluster centers are determined based on the value of the antibody si stimulation
level. At this stage of the formation of the dendritic immune network, a set of antibodies is formed,
which are characterized by high levels of stimulation and the number of connections exceeding the
value of the parameter K . The set of antibodies obtained in this way forms a set of candidate objects
for cluster centers (see Figure 3). It should be noted that the number of such selected candidate cells for
cluster centers may exceed the number of clusters determined at the beginning of the clustering process.
Figure 3: Determination of antibodies with a high level of stimulation
In Figure 3, which shows the result of selecting candidate antibodies for cluster centers, objects with
a minimum level of stimulation that cannot be selected as cluster centers are marked in light gray, and
antibodies that are characterized by a large number of strong affinity bonds and with a high level of
stimulation, are displayed as white peaks with a dark gray outline. Thus, in the process of choosing
potential centers of clusters, antibodies located on the periphery of the AIN do not participate, which
leads to an increase in the speed of the object clustering algorithm.
Cluster centers are selected using a parameter that regulates the number of clusters that should be
selected as a result of clustering [11, 12]. The value of the threshold affinity of NAT (2), which is
determined at the first stage of the formation of the dendritic immune network, also takes part in this
process. During the selection of cluster centers, the antibody is characterized by the maximum number
of connections with other antibodies in the network, and the maximum level of stimulation is chosen
for the centers from all candidate antibodies. Such an antibody is chosen as the center of the first cluster.
The centers of other clusters are determined relative to the selected center of the first cluster.
According to this, in order for a candidate object for cluster centers to be selected as the center of a new
cluster, the value of its affinities with other antibodies - the centers of clusters that were determined
earlier should not exceed the value of the threshold affinity of the NAT network [13]. If the affinity
between the candidate antibody for the cluster centers exceeds the NAT threshold with at least one of
the selected cluster centers, this antibody is excluded from the set of candidate objects for the cluster
centers. Thanks to this, only a small number of the farthest antibodies, which are characterized by a
weak affinity between them, are selected from the entire set of potential cluster centers.
Fig. 4 presents the result of the selection of cluster centers for a dendritic immune network with K
connections. At the same time, all affinity connections between antibodies in the network are marked
in light gray color, candidate objects for cluster centers are marked with white vertices with a dark gray
outline, and objects selected as the centers of formed clusters are marked in green. It should be noted
that in this case the formation of two clusters is expected in the clustering process.
Figure 4: The result of the selection of cluster centers
In the fourth stage, after the distribution of the centers of the clusters, the process of determining the
belonging of the antibodies of the immune network to them takes place. First, the immune objects that
are characterized by a strong affinity connection with antibodies are clustered, which are the centers of
the clusters, that is, the objects that have direct connections with the clusters in the tree-shaped immune
network with K connections.
It should be noted that at this stage, the processes of immune modification of the network, which are
accompanied by cloning, mutation, and editing of the population of grouped antibodies, are not
performed. This is due to the high computational complexity and significant time costs that inevitably
arise when conducting these immune processes. Therefore, to increase the speed of clustering, all
antibodies that have a strong affinity to one of the selected cluster centers are joined to the same cluster
with which they are associated. Thus, after the clustering of antibodies that are close to the centers of
the clusters, groups consisting of a limited set of immune objects are formed. Clusters of this type are
called clusters with centers of strong condensation.
Further, in order to carry out clustering of other antibodies that are not characterized by a strong
affinity connection with any of the centers of the formed clusters, their affinities to each of the clusters
and its antibodies that form the center of strong condensation are determined. The definition of avidity
is based on the affinity between immune objects [14]. The avidity of an antibody with other antibodies
belonging to the same cluster is defined as the sum of affinities between them:
m
avi aff abi , ab j , (4)
j 1
where avi is the value of the avidity of the i th antibody with other antibodies of the cluster; m – the
number of antibodies in the cluster; aff abi , ab j - affinity value between antibodies of the same cluster
according to (1). The avidity determined in this way reflects the level of strength of the immune
connection between the objects of the cluster and this antibody.
The concept of avidity antibodies and antigens, or between antibodies in an immune network, is
often used in aiNet models that are used to solve classification, clustering, and data analysis problems
[14]. Figure 5 shows the result of the grouping of immune objects that have a direct strong affinity
relationship with antibodies selected as the centers of the formed clusters in the dendritic immune
network. Cluster center antibodies are marked in green, antibodies associated with two different cluster
centers are marked in blue and yellow, and the rest of the antibodies are shown in light gray.
Figure 5: Clustering of objects associated with cluster centers
After determining the avidities between the antibodies that form the center of strong cluster
condensation, these values are averaged. The average avidity obtained in this way determines the cluster
and will be used in the clustering of other objects of the dendritic immune network that do not have a
direct strong immune connection with the center of any cluster.
In the fifth stage, clustering of other objects occurs, triggering immune processes in a dendritic
immune network of antibodies thanks to the operators of cloning, mutation and the use of suppression
of clones and the network of antibodies that do not belong to any cluster. At the same time, for each
clone, after its mutation, affinities with target objects are determined, which are clustered antibodies
and which form clusters with a center of strong condensation.
During selection, for each cloned antibody, one object is selected from the entire set of its clones,
characterized by maximum avidity antibodies forming the center of a cluster of strong condensation.
This clone replaces the antibody from which it was created during the operation of the population
suppression operator of antibodies with undefined cluster membership. It should be noted that the
immune process of cloning, mutation, suppression of clones, and suppression of antibodies of the
dendritic immune network will be completed in the event that there is no antibody left in the network
that has an avidity to one of the cluster centers, which will be lower than the avidity in the clusters with
centers of strong condensation.
Thus, the process of clustering of objects that do not participate in the formation of centers of strong
condensation and cannot be selected as the center of a new cluster occurs through the process of immune
self-regulation of the antibody network and is determined by using the avidities of antibody generations.
At the same time, such antibodies are created thanks to the use of immune operators, which determine
the formation of a generation of antibodies on iterations of the process of immune self-regulation of the
antibody dendritic network.
In Figure 6 shows the clustering result of the artificial immune dendritic network of antibodies
distributed between two defined clusters.
Figure 6: The result of antibody network clustering
Thus, the use of the graph theory model to create a dendritic model of the DaiNET immune network
allows solving the problem of low performance of the aiNET immune model, as well as reducing the
complexity of the process of forming the antibody network and recognition regions, which is
characteristic of the RLAIN immune model.
3. General scheme of the data clustering algorithm based on the DaiNET
immune model
The process of clustering a set of input objects based on the DaiNET immune model can be
represented as a sequence of the following stages:
1. Setting the clustering parameters and obtaining the initial set of objects.
2. Determination of the scales of characteristics of the studied objects.
3. Formation of a K-linked dendritic immune network.
4. Selection of cluster centers.
5. Determination of cluster identities.
6. Immune self-regulation of the network.
7. Conclusion about the clustering of objects.
Since the most common model of AIN operation is the aiNET model, it is the basis for building
immune models using AIS principles. Despite their versatility and the possibility of self-regulation and
learning, most immune methods cannot be used without additional modifications when solving the tasks
of classification and clustering of objects. To increase the speed of immune learning in the proposed
DaiNET immune model, the main immune operators were modified: primary selection operator,
mutation operator, clone suppression, and antibody suppression operators.
To improve the quality of clustering and increase the speed of the object grouping process, it is
advisable to carry out additional work with a set of objects from which the initial population of
antibodies is formed. In the course of preparatory work, it is necessary to determine the scales of
features of objects. This happens if these scales are not defined before the start of the clustering process.
When examining the scales of the initial data, the ranges of possible values for all features that
characterize the set of objects for clustering are determined [15, 16]. Accordingly, for each group of
features, when determining the data scales, the maximum and minimum possible values that can be
taken by this or that feature during the mutation of the immune object are determined. This must be
done so that during the mutation, the characteristics of the clones do not take on values that go beyond
the permissible range of values, because this can lead to a significant decrease in the speed of clustering.
To increase the speed of data clustering, operators of data scaling and the formation of a K-connected
dendritic network of antibodies, an operator for determining the initial centers of clusters, as well as an
operator for determining affinities, which is used at the final stage of object grouping during antibody
clustering, have been added to the operation of the DaiNET immune model that do not form centers of
strong cluster condensation. It should be noted that the scaling operator is not necessary and data
clustering can occur without its use. However, the use of this operator leads to an increase in the speed
of network self-regulation and, as a result, leads to an increase in the speed of clustering.
Accordingly, at the level of immune operators, the DaiNet immune model is represented by the
sequential execution of the corresponding stages given by the expression (5):
Scaling AB
PRP
DaiNet AB, K , c P resentatio n AB
NATCalculation AB
DKnetCreat ion AB, K
DKN
CalcStimul ation AB
CentersSel ection AB, c, NAT
DendricClu stering ( AB )
(5)
Cloning AB , CL
NET
Mutation CL
P resentatio n CL , AB , AB
CLSupressi on CL , AB , AB ,
NetSupress ion CL , AB
AvCalculation AB .
ClusterSel ection AB
In this expression, DaiNet (AB, K, C) is a notation for the method of clustering input AB objects
using a dendritic K-linked immune antibody network, and the criterion C used to indicate the number
of clusters formed.
The stage of preparation for clustering is denoted by the abbreviation PRP and contains several
operators: operator Scaling(AB) – is used for scaling objects; operator Presentation(AB) – used to
determine the affinities between antibodies of the formed immune network; operator
NATCalculation (AB) – used to determine the threshold affinity of NAT in the population of antibodies.
The stage of work aimed at forming a K-connected immune network has the conventional
designation DKN and contains the following operators: operator DKnetCreation (AB, K) – is used to
form a K-connected tree network of antibodies; operator CalcStimulation (AB) – used to determine the
level of antibody stimulation; operator CentersSelection (AB, c, NAT) – used to select cluster centers;
operator DendricClustering (AB') – used to form clusters of strong condensation.
The stage of network interaction has the designation NET and contains the following operators:
cloning operator Cloning (AB'', CL) - used to spread the population of antibodies not related to any of
the formed clusters; mutation operator Mutation (CL) – is used to change the characteristics of clones;
target object presentation operator Presentation (CL, AB', AB'') – used to determine the affinities
between clones and objects that form clusters of strong condensation; clone suppression operator
CLSupression (CL, AB', AB'') – used to edit the clone population; antibody network suppression
operator NetSupression (CL, AB') – used to reduce the number of objects in the immune network; the
operator for determining the avidity antibodies and clusters of strong condensation AvCalculation (AB'')
– used to distribute non-clustered objects between the clusters being formed; operator
ClusterSelection (AB'') – used to determine whether antibodies belong to clusters.
The proposed organization of calculations based on the DaiNET immune model in the example of
solving the object clustering problem, according to the formal representation at the level of immune
operators (5), consists of the following main steps.
Step 1. Preparatory stage:
Conducting scaling for the population of immune objects.
Presenting antibodies to each other.
Determination of the NAT affinity threshold for the population of antibodies.
Step 2. Construction of a dendritic K-connected immune network:
Selection of K-connections with maximum affinities in the network.
Determination of antibody stimulation levels.
Selection of cluster centers based on stimulation levels and NAT.
Formation of clusters of strong thickening.
Step 3. Self-regulation and clustering of antibodies, the cycle of execution of operators:
Cloning of antibodies that did not determine belonging to the cluster.
Mutation of formed clones.
Presentation of clusters of strong concentration of clone population.
Suppression of clones.
Suppression of cloned antibodies.
Determination of avidities for antibodies with an undefined cluster.
Determining whether antibodies belong to clusters based on avidities.
As a result of the operation of the DaiNET model, clustering of the initial population of antibodies
occurs. At the same time, these objects belong to one of the selected clusters in the process of immune
interaction of the dendritic K-linked network of antibodies. Carrying out the stage of determining
avidities allows the clustering of antibodies clusters of strong condensation.
4. Peculiarities of work of immune operators in the DaiNET model
Features of the work of immune operators on the DaiNet model, given in (5), play a major role in
increasing the speed and accuracy of calculations. In the DaiNet model, both the immune operators and
some principles of the aiNET model have been transformed. Therefore, let's consider in more detail the
immune operators used in the DaiNET model.
The antibody presentation operator Presentation (AB) is used at the initial stage of the clustering
algorithm. At the same time, an initial population of antibodies is formed from a set of initial objects,
and affinities between all antibodies are determined. The use of affinity allows forming an immune
network of antibodies for further clustering.
The NATCalculation (AB) operator is used to calculate the value of the NAT threshold affinity, which
is used at various stages of the formation of the K-linked dendritic immune network and to determine
the initial cluster centers, on the basis of which the strongly thickened clusters will be formed.
The operator DKnetCreation (AB, K) allows you to form a network of antibodies with a limited
number of connections between objects. At the same time, affinity is the main indicator of the strength
of the connection between antibodies. To speed up the network, the number of connections between
antibodies is reduced using the external parameter K. As a result of the operation of this operator, a K-
linked network of antibodies is formed for the further determination of the initial centers of clusters, as
well as the formation of strongly thickened clusters.
The operator CalcStimulation (AB) is used to determine the level of antibody stimulation of the
immune network. The use of stimulation levels makes it possible to distinguish from the initial
population of antibodies, immune objects that are characterized by a large number of strong affinity
connections with the antibodies of the network. Thus, the antibodies of the immune network stimulate
these immune objects and cluster around them. From these groups of antibodies, clusters of strong
condensation are subsequently formed.
The operator CentersSelection (AB, c, NAT) is used to form clusters of strong condensation. At the
same time, the search for the initial centers of clusters takes place, after which clusters with a center are
formed. Then, all antibodies that are associated with this center form clusters with a center of strong
condensation. At the same time, the centers of clusters can only be immune objects characterized by
the maximum number of connections exceeding the number of K. These antibodies are sorted by the
value of the stimulation level in ascending order. The center of the first cluster is the antibody that has
the maximum level of stimulation and the number of connections with other antibodies in the network
exceeding the K value.
Other cluster centers are determined iteratively. After determining the first cluster center, the center
of the second cluster in its group should be characterized by a high level of stimulation, and also have
an affinity with the center of the first cluster, less than the NAT value that was previously determined.
In the next iteration, from the remaining antibodies, with a high level of stimulation, an antibody is
selected that has affinities with previously selected cluster centers lower than the NAT value. If no
antibody has a large number of connections, but meets the NAT value requirements, it can be selected
as the center of a new cluster.
The operator DendricClu stering ( AB) forms clusters of strong condensation from initial clusters with
a selected center. This stage of DaiNet work is carried out exclusively thanks to the affine connections
of the dendritic network without starting the network self-regulation mechanism, that is, without using
operators of cloning, mutation and editing of the population of clones and antibodies of the network.
The formation of clusters with centers of strong condensation takes place by joining to clusters of
antibodies connected to their center by strong affinity bonds.
The cloning operator Cloning AB, CL creates a population of clones that are identical to the cloned
antibodies. It should be noted that an increase in the number of clones leads to a decrease in the speed
of immune training due to the fact that each formed clone undergoes mutation and is presented to target
objects, which increases the time of immune training. Thus, as a result of the operation of the cloning
operator, the number of generated clones for each antibody should not be too large or too small, because
this will negatively affect the time of immune training. Therefore, DaiNet uses proportional cloning
with increased affinity, which allows to form the population of clones in the best way. Accordingly, the
number of clones during cloning is determined as follows:
Nc i M C m max aff abi , ag j , (6)
where Nci is the number of clones of the i-th antibody; M – total number of antibodies; C m – affinity
amplification factor; max aff abi , ag j – maximum affinity with one of the target objects. It should be
noted that the affinity gain coefficient C m is an integer value that is used in the DaiNet model as an
input argument and takes values in the range [1;10].
The clone mutation operator Mutation (CL) is used to make changes to the characteristics of clones.
In the DaiNet model, the inversely proportional mutation is used with the limitation of the lower
threshold for determining the mutation coefficient. At the same time, the lower limit of the range of
possible values used to determine this coefficient is limited. The mutation coefficient is determined
according to the following expression:
1
rand 1 aff ab, AB; 1 aff ab, AB , (7)
2
where aff ab, AB – affinity between the parent antibody and a set of target objects or antigens. Thanks
to this, the maximum change in the characteristics of clones depending on the change in affinity is
achieved, while minimizing the probability of loss of specificity of antigens or other target objects.
The operator P resentatio n CL, AB, AB is used at the stage of self-regulation of the dendritic
immune network and is used to represent antibodies that did not determine belonging to one or another
cluster or to antibodies that form centers of strong condensation of clusters. On the set of unclassified
antibodies, there are other antibodies that form clusters of strong condensation, previously isolated. This
leads to a significant increase in performance and an increase in the speed of object clustering.
The clone suppression operator CLSupressi on CL, AB, AB edits the population of clones after
mutation. The affinities of clones with their target objects are used, which are chosen as antibodies that
form the centers of clusters of strong condensation. Editing of a set of clones is carried out by comparing
their stimulation levels, and as a result of the operation of the clone suppression operator, one object
with the best stimulation level remains in the population. Thanks to this, the speed of immune learning
increases without losing classification accuracy.
After the immune network is formed and clones selected as a result of suppression are added to it, it
is edited using the network suppression operator NetSupress ion CL, AB . At the same time, the criteria
regulating the process of network suppression are the levels of stimulation of cloned antibodies. If the
level of stimulation of an antibody by one or another center of a cluster of strong condensation is lower
than the corresponding level of a clone formed from this antibody, this antibody is removed and
replaced by a clone. Otherwise, the clone is removed, and the antibody remains in the population and
is again exposed to the action of the cloning operator. Thus, only antibodies with maximum levels of
stimulation to the centers of cluster condensation remain in the network.
After the operation of the network suppression operator is completed, the affinities between
antibodies and the selected centers of clusters of strong condensation are determined based on the
operator AvCalculation AB , whose work is completed by determining the affinities with all antibodies
that form clusters of strong condensation. The self-regulation cycle of the DaiNET model is completed
by the operation of the operator ClusterSel ection AB , during which each antibody determines whether
it belongs to one or another cluster based on the value of avidities with antibodies that form the centers
of strong condensation of clusters and avidities determined within the clusters. The conclusion that the
antibody belongs to one or another cluster is made if the avidity between this antibody and the cluster
is not less than the avidity between the antibodies of the center of strong condensation of the cluster.
The main condition for the completion of training is the achievement of full specificity of antibodies
to the formed clusters. Large populations of antibodies are required to achieve this state. At the same
time, it is mathematically impossible to determine the number of populations necessary to achieve full
specificity, so the DaiNet model uses a static stopping criterion that determines the maximum number
of antibody populations that are formed in the process of immune learning and network self-regulation.
5. Experimental results of object clustering based on the DaiNET model
For a comparative analysis of the proposed DaiNET immune model with existing immune models
and other common data clustering methods, three sets of objects with a limited number of features were
formed. These sets differ in the number of objects and the number of clusters that should be obtained
as a result of clustering. The characteristics of the data sets are given in Table 1.
Table 1
Sets of objects for clustering
Number
Identifier
Objects Clusters
Set 1 100 3
Set 2 500 5
Set 3 2500 10
The given sets of objects are used in two ways: 1) as initial data sets for clustering algorithms; 2) as
control samples to check the quality of classification. This happens because the specified data sets are
already classified, but can be used without specifying the initial belonging of this or that object to some
class or cluster.
A comparison of the proposed approach with other immune and non-immune methods of data
grouping is given in the table. 2. When analyzing the performance of the proposed DaiNet model,
reference clustering methods MST (Minimum Spanning Tree) and C-means [8, 9], as well as immune
models Clonalg and aiNet [2] were used. When comparing algorithms, two main metrics were used: T
is the time spent by the clustering algorithm on grouping the initial set of objects; A is the accuracy of
clustering, which is determined as a result of comparing the clusters formed during the operation of the
clustering algorithm and the belonging of a set of objects to the input classes.
Table 2
Results of object clustering
Algorithm Set 1 Set 2 Set 3
T 38% 36% 39%
MST
A 88% 85% 82%
T 72% 74% 72%
C-means
A 100 % 100 % 100 %
T 100 % 100 % 100 %
Clonalg
A 80% 83% 81%
T 98% 95% 93%
aiNet
A 52% 50% 50%
T 48% 46% 47%
DaiNet
A 95% 93% 96%
According to the clustering results given in Table 2, we note that the C-means algorithm is
characterized by the maximum accuracy of the grouping of objects A, and the Clonalg algorithm by the
worst speed T. Therefore, these algorithms were chosen as the absolute maximum values (100%). On
the other hand, the MST method is characterized by the best performance, that is, when using this
method, clustering takes the least time, approximately 4 times less than clustering using the Clonalg
method. But at the same time, the MST method is significantly inferior to other methods in terms of the
accuracy of the grouping of the studied set of objects.
It should be noted that the use of the proposed DaiNet model for data clustering is characterized by
high grouping accuracy. According to this characteristic, it is inferior only to the C-means method by a
few percent. However, the DaiNet model outperforms the C-means method in terms of performance by
almost 10% and is inferior only to the MST method in terms of this indicator. hen comparing the
DaiNET model with other immune models that are usually used to solve data classification and
clustering problems, it should be noted that the DaiNet model outperforms other immune models both
in terms of speed and accuracy of object grouping. This makes the proposed model the most adapted to
the organization of calculations for solving practical problems based on the use of the immune approach.
6. Conclusions
The theory of AIS is currently one of the areas of intelligent information processing, which is used
to solve various practical problems. Among the existing immune models, the most promising for
practical use is the artificial immune network model, which involves the organization of interaction not
only between populations of antibodies and antigens, but also the interaction between antibodies within
the same population. The existing models of artificial immune networks aiNET and RLAIN have a
number of disadvantages, the main of which are low speed and relatively low accuracy. To increase the
speed, ensure acceptable accuracy of the results, and reduce the complexity of the antibody network
formation process, a new IIS model has been proposed in the form of a DaiNET dendritic artificial
immune network, which is built using graph theory.
The formation of the dendritic structure of the immune network is considered in the example of
solving the object clustering problem. It is proposed to form a K -connected graph of antibodies, in
which the strength of the connection between the antibodies of the immune network is determined by
the affinity of the antibodies. A NAT threshold affinity value is used to regulate the number of affinity
connections between immune network antibodies. To reduce the number of calculations in the antibody
tree network, objects characterized by a high level of stimulation, which is determined on the basis of
the closest affinities of the antibodies forming the network, are selected. Based on the value of the level
of stimulation of antibodies, the centers of clusters are determined, and the determination belonging to
clusters of other antibodies of the immune network is based on the values of their affinities to each of
the clusters. The general scheme of the data clustering algorithm based on the DaiNET immune model
and the peculiarities of its immune operators are considered. The DaiNET model is represented at the
level of immune operators by the sequential execution stages of preparation, formation of a K-linked
immune network, and network interaction of antibodies. The practical significance of the obtained
results lies in the development of software modules for the implementation of the proposed DaiNET
model, which can be used to solve a wide range of practical problems. Experimental studies of the
proposed DaiNET immune model for solving the problem of clustering on various data sets were carried
out and its comparison with existing immune models and other clustering methods was carried out,
which showed that the DaiNET model is superior to other immune models both in terms of speed and
accuracy of the grouping of objects.
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