CC BY
11
UDC 004.272.26: 004.93
ADDITIONAL TRAINING OF NEURO-FUZZY DIAGNOSTIC MODELS
Oliinyk A. - PhD, Associate Professor, Associate Professor of the Department of Software Tools, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
Subbotin S. - Dr. Sc., Professor, Head of the Department of Software Tools, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
Leoshchenko S. - student of the Department of Software Tools, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
Ilyashenko M. - PhD, Associate Professor, Associate Professor of the Computer Systems and Networks Department, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
Myronova N. - PhD, Associate Professor of the Department of Software Tools, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
Mastinovsky Y. - PhD, Professor, Head of the Department of Applied Mathematics, Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine.
ABSTRACT
Context. The task of automation of diagnostic models synthesys in diagnostics and pattern recognition problems is solved. The object of the research are the methods of the neuro-fuzzy diagnostic models synthesys. The subject of the research are the methods of additional training of neuro-fuzzy networks.
Objective. The research objective is to create a method for additional training of neuro-fuzzy diagnostic models.
Method. The method of additional training of diagnostic neuro-fuzzy models is proposed. It allows to adapt existing models to the change in the functioning environment by modifying them taking into account the information obtained as a result of new observations. This method assumes the stages of extraction and grouping the correcting instances, diagnosing them with the help of the existing model leads to incorrect results, as well as the construction of a correcting block that summarizes the data of the correcting instances and its implementation into an already existing model. Using the proposed method of learning the diagnostic neural-fuzzy models allows not to perform the resource-intensive process of re-constructing the diagnostic model on the basis of a complete set of data, to use the already existing model as the computing unit of the new model. Models synthesized using the proposed method are highly interpretive, since each block generalizes information about its data set and uses neuro-fuzzy models as a basis.
Results. The software which implements the proposed method of additional training of neuro-fuzzy networks and allows to reconfigure the existing diagnostic models based on new information about the researched objects or processes based on the new data has been developed.
Conclusions. The conducted experiments have confirmed operability of the proposed method of additional training of neuro-fuzzy networks and allow to recommend it for processing of data sets for diagnosis and pattern recognition in practice. The prospects for further researches may include the development of the new methods for the additional training of deep learning neural networks for the big data processing.
KEYWORDS: data sample, diagnosis, additional training, neuro-fuzzy model, parameter, membership function.
ABBREVIATIONS
BPSad is a back propagation for additional training based on sample Sad ;
BPS is a back propagation for re-training based on sample S;
MATDNFM is a method for additional training of the diagnostic neuro-fuzzy models; NFN is a neuro-fuzzy network.
NOMENCLATURE
bmj is a parameter of the membership function;
\CS'| is a number of instances cs'q of the set CS'; cs'mq is a m -th coordinate of the q -th instance
cs'q e CS';
Cmj is a m -th coordinate of the center of the j-th cluster Cj ;
dmj is a parameter of the membership function;
emin is a minimum acceptable difference between the real and model values of the output parameter;
sj is a minimum acceptable change in the value of the criterion J;
M is a number of features in the sample of observations S;
^min is a parameter that determines the minimum acceptable membership degree of the instance snew to the set S' = < P', T' > of data on the basis of which the correcting block NB was synthesized;
Nr is a number of model NFN rules; P is a set of features (attributes) of observations in the given sample;
pqm is a value of the m-th feature (attribute) of the q-
th observation;
pm (snew) is a m-th coordinate of the evaluated instance snew S;
Q is a number of observations in the given sample of observations S;
Round(a) is a function that returns the result of rounding the number a to the nearest larger integer; S is a sample of observations (training sample);
Mastinovsky Y., 2018
tq is a value of output parameter of the q-th observation;
t'q is a measured value of the output parameter of the q-th instance s'q of sample S' = < P', T' > ;
tq (NFN) is a value of the output parameter of the q-th instance s'q of sample S' =< P', T' > , calculated by substituting the measured values of the input attributes p'qm
of the q-th instance in the model NFN; T is a set of output parameter values;
t
q mod
is a model value of the output parameter of the
q-th instance cs'q, calculated from the synthesized model
yNBj ;
Uj is a value of membership function of the q-th instance csq to the j-th cluster;
wmj is a customizable parameter of the function
yNBj .
INTRODUCTION
During operation of intelligent diagnostic systems, new information about diagnosed objects arises. In doing so, the information newly obtained from the measurements of the diagnosed objects can significantly contradict to the existing diagnostic models built on the results of previous observations. In such cases, it becomes necessary to re-synthesize diagnostic models using the data from previous and new measurements.
The object of study are the methods of the neuro-fuzzy diagnostic models synthesys.
However, when working with big data, the time for re-synthesis of such models can be significant, which in some cases is unacceptable. Therefore, during the operation of diagnostic systems, the task of adapting trained models by modifying them, taking into account the information obtained as a result of new observations, is relevant.
The subject of study are the methods of additional training of neuro-fuzzy networks.
The purpose of the work is to create a method for additional training of neuro-fuzzy diagnostic models.
1 PROBLEM STATEMENT
Suppose we have:
1) a sample of data S =< P, T > , containing Q instances, each of which is characterized by the values of the parameters pq1, pq2 , ..., pqM and the output parameter tq;
2) a neuro-fuzzy model NFN = NFN(struct, param) synthesized from a set of observations S =< P, T > with a definite structure struct (a set of computational ele-
ments connected in a certain way) and set of parameters
param = param(struct);
3) a data set S' =< P', T ' > obtained as a result of new QQ measurements of the object being examined (diagnosed).
Then it is necessary to synthesize the new model
NFNN = NFNN(structN, paramN) by modifying the
existing model NFN (struct, param) taking into account the new data S' =< P', T' > in such a way that an acceptable value of the specified quality criterion G of the neu-romodel NFNN: G(NFNN, S U S'min is provided. For example, a minimum of recognition error (in problems with a digital output T) or a minimum mean-square error (in the case where the output parameter T can take real values from a certain range T e [[„; tmax])can be used as the target criterion G for additional training neural-fuzzy models.
2 REVIEW OF THE LITERATURE
The additional training of diagnostic and recognition models built in the form of neural-fuzzy networks usually involves the modification of the existing network by including (adding) information about new observations to it. Such information is added to the constructed network in the form of new rules, represented by so-called singletons. This approach is simple enough to implement. However, in the case of a significant number of new observations, the application of this approach is little effective. The reason is that in this case the structural and parametric complexity of the network is significantly increased (each new observation, in fact, is added to the network in the form of a new rule), and its generalizing capabilities are also reduced.
Another approach involves a complete reorganization of the structure and parameters of the network with the appearance of new essential information about the objects under study. Consequently, the already synthesized model is re-trained on the basis of available S =< P, T > and
new S' =< P', T' > information. When processing big data, re-training the model is also undesirable, since this process takes a lot of time and requires a large amount of computational resources.
Therefore, it is advisable to develop a new method for adapting trained neural-fuzzy models to changing the functioning environment by modifying them, taking into account the information obtained as a result of new observations.
3 MATERIALS AND METHODS
In the developed method of training the neuro-fuzzy models, it is proposed to correct the existing model NFN (struct, param) by introducing additional structural computational elements that take into account the attributes of the new data set S' =< P' , T' > .
In the proposed method, the first step is to extract the correcting instances from the sample S' =< P',T' > . Corrective instances cs'q will be considered those observations of the sample S' =< P',T' > , diagnosing them using the existing model NFN(struct, param) leads to incorrect results. Consequently, the diagnosing model NFN used needs to be adjusted precisely with the help of instances csq .
Therefore, to construct a set of corrective instances CS', all sample S' =< P', T' > instances s'q are passed
through the model NFN, as a result of which the value of the output parameter t'q (NFN) of each q-th instance of
sample S = < P , T > is calculated. Then, the real tq and model tq (NFN) values of the output parameter are compared:
t -1
q q
q (nfn )
— smin . (1)
Condition (1) is used in solving estimation problems (for continuous values of the output parameter T). When solving recognition problems (with discrete values of the output parameter T) the following condition is used:
tq * tq (nfn ).
When the above conditions are met, the q-th instance sq of sample S =< P ,T > is counted as corrective and
entered into the set CS': CS' = CS' U s'q . Thus, as a result of the step of extracting the correcting instances, those instances of sample S' =< P',T' > that are similar to the instances of the original sample S =< P,T > are excluded from further consideration and, therefore, do not affect the quality of recognition or estimation by model NFN.
Later, instances cs'q of set CS' can be used as singletons in constructing a new block NB(structNB, paramNB), introduced along with the already existing model NFN (struct, param) in the new model NFNN = NFNN(structN, paramN).
However, when processing big data, the number of set's CS' instances can be significant, which will lead to a significant increase in the structural and parametric complexity of the new model NFNN . In addition, many instances of the set CS can be close to each other in the attribute space and, in fact, be similar. Therefore, including all instances cs'q e CS' as rules for a new model
block can also lead to a loss of its generalizing abilities.
Accordingly, before building a block NB, it is advisable to perform the step of grouping the correcting instances of the set CS with the selection of the most significant of them csInfq, concentrating around themselves a certain number of similar closely located specimens.
To do this, it is suggested to perform cluster analysis of the CS' set's instances in the attribute space P . The number of clusters Na in the developed method is determined in proportion to the number of rules NR in the existing model NFN, as well as the proportion of instances |CS'| of the set CS' in relation to the number of instances Q in the set S =< P,T > (2):
(
Nd = Round
H.
Q
Nr
(2)
After determining the number of clusters Na , the initial partitioning of instances cs'q e CS' over clusters is
performed. For this, a set of cluster centers C = {Q,C2,...,Cnc/ } is defined, where Cj = {dj,C2j,...,CMj} is the center of the j-th cluster, j = 1,2,...,Nci. The centers Cj can be selected randomly among instances csq of the set CS . It is also possible to create a set C = {Q, C2,...,Cnci } taking into account the spatial arrangement of the instances cs'q e CS'. For this,
an instance csa is first randomly selected from CS , which is considered the center of the first cluster C1 = {cs1a,cs2a,...,cs'Ma}. Then, as the center of the second cluster C2, the instance cs'b most remote from the instance cs'a is selected. The center of the third cluster C3 is selected in such a way that it is as far away from the centers of the first and second clusters. This procedure continues until Na is formed. With a large value Na , this approach will be associated with the need for complex calculations due to the search for instances characterized by the greatest distance to the current set of already defined cluster centers. Therefore, this approach is advisable to apply for small values of the number of clusters Nci or to combine it with an approach that involves the random formation of multiple cluster centers C = {d1,C2,...,CNCl}.
Then, the generation of elements uqj determining the
membership of the q-th instance csq to the j-th cluster
Cj is performed. In contrast to the method of fuzzy c-
means used as a basis, in the developed method, when creating the initial division of the instances, the generation of elements uqj will be performed not randomly, but
taking into account the location of the instances csq e CS in attribute space P . For this, the distances
. (
each cluster j = 1,2,...,Na are determined. As a metric for determining the distance D^sq, Cj), we can use the Euclidean metric (3):
Mastinovsky Y., 2018
^s'q,Cj) from the instance cs'q to the center Cj of
D{cs'q, Cj )= £ (Cs'mq - CmJ f
V m=1
(3)
The membership uqj of the q-th instance csq to the j-th cluster Cj is calculated by the formula (4):
f
uqJ =
Nci
I
JA=1
P('q, Cj ) D^Sq, CJA )
2 }
-1
mp-1
(4)
In the case where the instance
is the center of the
j-th cluster Cj (D^sq,Cj )= 0), then it is established:
uqj = ^ uqJA = 0VJA * j .
Further, according to the formula (5), the value of the
function J(R(i),u(i),C(i)) determining the quality of the
fuzzy partitioning R(i) in the i-th iteration of the cluster analysis is calculated:
I, ^ |CS ' |Nq / \
((i), u(i), C(i) )= X )pD2 (csq, Cj ). (5)
q=1 j=1
After that, the criteria (6) and (7) of the completion of the cluster analysis procedure are checked:
JoldR(i),u(i),C(i))- JR(i),u(i),C(i))<bj , (6)
i > maxIterClA. (7)
In this case, inequality (6) reflects a condition, the fulfillment of which characterizes too small a change in the
value of the target function J R(i),u(i), C(i)) , and accordingly, the inexpediency of further searching for the optimal partition R(i) . Condition (7) displays the situation when the current number of iterations reaches the maximum allowed value maxIterClA . If both conditions (6) and (7) are not fulfilled, the new values of the coordinates of the cluster centers are determined using formula (8):
Cs 1/ m
I Yp
q=1
cs,
mq
C =-
^mj
(8)
In case the modifiable model NFN(struct, param)
uses as a basis a neuro-fuzzy ANFIS network, then the structure of the correction block NB will also be based on the ANFIS network. The graphic representation of the correcting block NB is shown in Fig. 1.
In this case, the number N RNB of nodes of the second layer corresponding to fuzzy rules in the correcting block NB is proposed to be taken equal to the number of clusters (rules) allocated in the previous step: Nrnb = Nci. Given the nature of calculating parameter Na in the proposed method, the number of NB -block rules Nrnb will be proportional to the number of rules NR in the existing model NFN , as well as the proportion of instances |CS'| of the set CS' in relation to the number of instances Q in the set S = < P, T > . Therefore, the structural complexity of the correcting block N RNB will be proportional to the analogous value of the original model NFN and the proportion of new instances of the CS' set.
Neural elements of the first layer that determine the membership degree of the value of the input parameter
to the corresponding fuzzy term fi.
CS \ m '
I (Uqj )P q=1
Then, using the formulas (3)-(5), a new fuzzy partition R('+1) is searched (allocation of accessories uqj ).
This procedure is repeated until at least one of the conditions (6) or (7) is satisfied.
Consequently, as a result of the step of grouping the correcting instances, a plurality of cluster centers C = {Q,C2,...,CNd} and a plurality of cs'q instance attachments Uj are formed to the respective clusters.
After grouping the correcting instances, the stage of construction of the correcting block NB is performed.
mj
( j = 1,2,...,Nrnb ) are connected with the corresponding nodes of the second layer. Thus, in aggregate, the nodes of the first and second layers form antecedents of fuzzy rules NRj.
The information obtained at the previous stages of the developed method of additional training the neural-fuzzy models (a multiplicity of correcting instances CS', a multiplicity of cluster centers C = {QC2,...,Cnci} and a multiplicity of instance csq accessories uj to the corresponding clusters) will be used to determine the configurable parameters of membership functions
l4Lj (m = 1,2,...,M , j = 1,2,...,Nrnb ). As functions ^NBrnj that determine the membership degree of the value of the m -th input parameter pm to the j -th fuzzy term ftmj in the correcting block NB, we use the membership functions (9):
^NBmi (pm ) = exp
( - h )
\pm hmJ )
As
2d, h„
2
mj
(9)
a parameter bmj- (m = 1,2,...,M ,
j = 1,2,...,Nrnb ), that determines the shift of the center of the function relative to the center of coordinates of the characteristic axis pm , we will use the m -th coordinate of the j-th cluster center Cj from the set C = (Q, C2,..., Cnci } formed in the previous step.
Figure 1 - Graphical interpretation of the correcting block NB when modifying models NFN using as a basis a neural-
fuzzy ANFIS network
As a parameter dmj-, we will use the standard deviation of the correcting instances cs'q e CS' relative to j -th center of the cluster Cj along the m -th characteristic axis. It also takes into account the membership uqj of q-th correcting instance cs'q e CS' to j-th cluster Cj:
Having determined \iNjBmj
with account of the calcu-
lated estimates b„
dm
dmj =
1- v ( ' C )2
' I V uqj\smq Cmj j .
' lq=1
(10)
Using formulas (10) and (11) to define custom pa-
rameters bmj and dmj
membership functions \iNBmj
in
mj mj it is possible to calculate the values of the outputs of the second layer of the network ¡SB that determine the degree of fulfillment of the j-th
rule NRj, according to the formula:
M
¡NBj (snew ) = n VNBmj (pm (s new ^ (11)
m=1
The nodes of the third layer determine the relative degree of fulfillment of the j-th rule NRj :
the process of evaluating new instances snew € S using the correcting block NB , activate those fuzzy terms ftmj that together (m = 1,2,...,M ) correspond to certain clusters Cj (NRj fuzzy rules).
(3) ( M"NBj \sn
„) =
M"NBj (snew )
NR
V V-nBjB (snew) JB=1
of the fourth layer
(12)
m(4)
V-NBj
Neural elements (j = 1,2,...,Nrnb ) correspond to functions yNBj that
determine the value of the network output in the case of the operation of the corresponding rule NR- . Thus, each
j-th node of the network determines the contribution of the fuzzy rule NRj to the common output of the network
yNB. Functions yNBj, as a rule, are represented in the form of a linear regression, therefore, the values of the outputs of the nodes of the fourth layer ^NBj can be calculated from the formula (13):
MNBj (snew ) = M-NBj (snew )>NB/ (snew ) =
( M ^ (13)
= MNBj (snew ) X wmj (pm (snew ^ .
V m=0 /
It is assumed that P0 (snew) = 1, and w0- coefficient
corresponds to the value of the free linear regression term (13). The function yNBj- can be simplified as follows:
M
yNBj = X wmjPm . More complex nonlinear dependen-
m=0
cies can also be used as a basis of functions yNBj-.
Therefore, in order to synthesize a correcting block NB, it is necessary to restore the functions yNBj-, having
determined the values wmj- of the adjustable parameters
for this.
To determine the values of parameters wmj- in the developed method, it is proposed to use information not only about the values of the coordinates of the correcting
met. If this condition is met, then the instance
is add-
ed to the set Setj of instances related to the cluster Clj : Setj = Setj U cs'q. Further, using instances of the set Setj , the function yNBj is restored using the known parametric synthesis of models.
The second approach involves the use of all instances cs'q of the set CS' to construct all models yNBj . When
restoring the function y NBj that determines the output of
j-th node of the fourth layer of the correcting block NB, all instances cs'q e CS' are used, and also the membership
uqj of each of them to j-th cluster Clj (rule NRj) is taken into account.
In the process of restoring the function yNBj- as the
objective function E , we will use the function (14), which is a modified mean-square error function:
= 1 X ( Ej = jCSj X UqJq -
q mod
(14)
The model value tqmod of the output parameter of the q-th instance cs'q is calculated from the synthesized model yNBj :
^q mod
yNBj (cs'q)= Xwmj (Pm(c4)) . (15)
m=0
This function, in addition to the deviation between the actual tq and model value tq mod of the output parameter
instances cs'q e CS', but also information on their mem- of the instances cs'q, also uses information about the
bership degree uqj- to each of the clusters Clj (in fact, the fuzzy rule NRj ) determined by the centers C = {Q, C2,..., Cnci }.This will take into account the importance of the instances cs'q e CS' for restoring the functions yNBj corresponding to clusters Clj, and in determining the wmj parameters of the function yNBj ,
increase the contribution of those specimens that are characterized by high estimates of the membership degree of
membership uqj- of this instance to j-th cluster Clj as an estimate of the importance of the instance cs'q for restoring the function yNBj .
Substituting (15) into (14), reducing obtained ex-1
pression by a multiplier
lCS 'I
and taking into account
Uqj to the cluster Clj .
that pm[cs'q)= pqm, we obtain the objective function of the form (16):
|CS'| ( M
There are two approaches to determine the parameter
Ej = X uq
q=1
( M \
tq - X WmjP qm m=0
mj
>\(
The first approach involves building models yNBj on
the basis of corrective instances
with the maximum
M
( M
\2 ^
/ ((q ) - 2U qj q X wmjpqm + uqj I X WmjPq V m=0
m=0
(16)
estimates uq/- of membership to the corresponding clusters Clj . For each cluster Clj (NRj rule), the instances cs'q with the largest values of uqj are selected. So, it is considered that the instance cs'q belongs to the cluster Clj (cs'q e Clj) when the condition uqj = max{uqj-) i
is
|CS'|
= z
q=1 ^
To determine the values of adjustable parameters wmj-,
find their values at which optimum target criterion Ej ^ opt is reached. To do this, define the partial derivatives by the parameters wmj of the target criterion E j as functions of several variables: Ej = Ej (w0 j, w1 j, wMj-), then solve the system of equations (17):
dEJ
dw,
= 0, m = 0,1,2,...,M .
mj
Performing further transformations, obtain that the m-(17) th equation of system (17) can be written in the form (19):
Expression (17) is a system consisting of (M +1) linear equations of the form (18)
E ICS'lf r M W
dw,
= Z
2uqjtqpqm + 2uqjpqm
Z WmjPq
mjrqm \m=0 yy
|CS ' |CS '|
W0j Z(uq'pqmpq0 )+ W1 j ZkjPqmPq, )+
q=1 q =1
lCS'( ) C'( )
+ .... + wMj Z (uqj pqmpqM ) = Z (uq tqpqm ) q =1 q =1
or
Substituting the values m = 0,1,2,...,M in (19), we obtain a system of linear algebraic equations (20):
, _ _ _ _ _ , . . ,,=0 (18)
mj q=1
Z (uqjpqm ((0 jpq0 + W jpq1 + .... + WMjpqM))
q=1
lCS'( ) = Z(uqjtqpqm ] m = 0,1,2,...,M.
q=1
W0 j Z ((q0pq0 )+ W1 j Z (qjpq0pq1 )+ .... + WMj Z(p„ pM )=Z(»qtqpq0 );
q=1 q=1 q=1 q=1
CS'( ) lCS'( ) CS'( ) CS'( )
W0 j Zluq-pq1 pq0 )+ W1 j Z(qjpq1 ^q1 )+ .... + WMj Z(qjpq1 pqM )= Z(tqpq1);
q =1 q =1 q =1 q =1
(19)
CS t
CS t
(20)
CS t , CS ) , CS t , CS t ,
w0 j Z(qjpqMpq0 )+ W1 j Z(qjpqMpq1 )+ .... + WMj Z(qjpqMpqM )= ZlVqpqM ). q =1 q =1 q =1 q =1
Further, solving the system (20) by the known methods of linear algebra, the required values wmj are found.
As noted above, not only linear functions of the form
M
(yNBj = Iwmjpm ), but also more and more complex
m=0
nonlinear dependencies can be used as functions yNBj . In
such cases, the search for configurable parameters wmj of
yNBj function is performed by optimizing the target
functional (14) using known gradient (in the case of functions yNBj that are differentiable) or stochastic methods.
After determining the values of the adjustable parameters wmj of the functions yNBj , the values of the outputs
MwB/ of the neural elements of the fourth layer of the
correcting block NB can be calculated from formula (13). Then, the total output of the block NB (21) is calculated:
( )= Nrnb (4) ( )
yNB\snew) = Z ^NBj \snew). (21)
j=1
Then, the stage of combining the existing model NFN and the correcting block NB is performed. At this stage, the information about the data sets S = < P, T > and S'=< P',T' > , approximated by the model NFN and the correcting block NB, is generalized, respectively. The modified model NFNN by adding the correcting block NB to the existing model NFN(struct, param) is shown in Fig. 2.
Figure 2 - Graphical interpretation of the modified model NFNN
To evaluate the value of the output parameter t(snew ) of a new instance snew g S using the model NFNN modified (adapted to the new conditions) based on the new data S' =< P', T' > , it is proposed to use the formula (22):
tisnew) - yNFNÂsneW -
y^^ne^
Nr
U ^NBj >Mmin; j-1
Nr
(22)
yNFÂsnew), U - Mmin. j-1
As can be seen, if the new instance snew g S is characterized by a sufficiently large degree of belonging
nrnb
( U Vnbj > ^min) to the rules NRj of the correcting
j=i
block NB (accordingly, to clusters Clj synthesized on the basis of a new data set S' =< P', T' > ), the final value yNFNN is calculated using the correcting block NB. Otherwise, it is considered that the instance snew is more relevant to the source set S =< P, T > , and the value yNFNN is taken equal to the output value yNFN by the model NFN base.
It is important to note that the proposed approach to the construction of correcting blocks NB allows to synthesize and introduce into existing models new blocks with the appearance of new information S' =< P',T' > , the diagnosis of which leads to incorrect results of the model NFNN. Thus, the model shown in Fig. 2, can be consistently expanded by adding new blocks NB that generalize information about new observations of the investigated objects.
Consequently, the proposed method of additional training the neuro-fuzzy diagnostic models allows to adapt existing models to the change in the functioning environment by modifying them taking into account the information obtained as a result of new observations. The proposed method assumes the stages of extraction and grouping of correcting specimens, diagnosing with the help of the existing model leads to incorrect results, as well as the construction of a correcting block that summarizes the data of the correcting instances and its introduction into an already existing model. When determining the adjustable parameters of the correction block in the developed method, it is proposed to use information about the values of the coordinates of the correcting instances, as well as information on the degree of their membership to clusters in the feature space (and, accordingly, to the fuzzy rules presented in the correcting block). This allows one to take into account the importance of corrective instances for restoring the functions of the fourth layer of the correcting block and, when determining custom parameters, to increase the contribution of those specimens
that are characterized by high estimates of membership degree to a particular cluster.
Using the proposed method of additional training the neural-fuzzy diagnostic models allows not to perform the resource-intensive process of re-constructing the diagnostic model on the basis of a complete set of data, to use the already existing model as the computing unit of the new model. In addition, models synthesized using the proposed method are highly interpretive, since each block generalizes information about its data set and uses neuro-fuzzy models as a basis.
4 EXPERIMENTS
For testing the effectiveness of the developed method training of neuro-fuzzy models training, the problem of constructing diagnostic models for predicting the health status of patients with hypertension was solved [30].
Hypertension is a widespread disease that can threaten the life and health of the patient [30]. The nature of the course of hypertension is influenced by various factors (weather and climatic conditions, concomitant diseases, as well as the state of health in previous moments) [30]. In order to prevent significant pressure surges that can cause deterioration of the patient's condition, and possibly lead to death, it is necessary to predict the development of hypertension in the short term (for the next half of the day or day). This will allow timely implementation of preventive measures related to the intake of necessary medicines to prevent the expected negative consequences.
For prediction the health of a patient with hypertension, it is necessary to have a model that will be unique for each individual patient. Building such a model requires processing a large array of observations distributed over time.
Thus, since such a disease is of an individual nature [30] (the features of the disease are different for each patient as a result of which for each patient it is necessary to synthesize its own unique diagnostic model) and in connection with obtaining new information about the course of the disease over time, there is a need for periodic adjustment (additional training) of existing models for individual prediction of the patient's condition on the basis of constantly growing arrays of observations.
The initial sample of data on the state of health of a patient with hypertension was obtained in Zaporizhzhia (Ukraine). The sample S =< P, T > included observations from 2004 to 2014, where each sample was a set of data characterizing the patient's condition at a certain part of the day.
As objective clinical and laboratory features were used: p1 is observed blood pressure (systolic and diastolic, mmHg); p2 is a pulse (beats per minute (BPM)); data on medication ( p3 is an Amlo (0 is for patient that do not take medicines, 1 is for patient take medicines), p4 is an Egilok (0 is for patient that do not take medicines, 1 is for patient take medicines); p5 is a Berlipril (0 is for patient that do not take medicines, 1 is for patient
NFNN = NFNN(structN, paramN). It is worth noting that the following conditions were met when splitting the sample S =< P,T > : Str USad = S and Str flSad = 0 .
Let the variable ra represents a relationship (23) of the cardinality of the sets Sad and Str:
= |Sad|
\Sr
take medicines)). As subjective features used characteristics of health ( p6 is the presence of premature heart beat (0 is present, 1 is absent), p7 is the presence of headache (0 is present, 1 is absent), p8 is the presence of neck pain (0 is present, 1 is absent), p9 is the presence of pulsation (0 is present, 1 is absent), p10 is the presence of pain in the left side (0 is present, 1 is absent), p11 is presence of pain in the heart (0 is present, 1 is absent), p12 is lack of air (0 is present, 1 is absent), p13 is presence of stomachache (0 is present, 1 is absent), p14 is general weakness (0 is present, 1 is absent)). As meteorological characteristics used [30] (p15 is an air temperature (°C )), p16 is an atmospheric pressure (mmHg), p17 is type of cloud cover (0 is not cloudy, 1 is small cloudy, 2 is cloudy, 3 is overcast), p18 is the presence of thunderstorms (0 is present, 1 is absent), p19 is wind direction (0 is a windless, 1 is a northern wind, 2 is a northeasterly wind, 3 is a easterly wind, 4 is a southeasterly wind, 5 is a southern wind, 6 is a southwesterly wind, 7 is a westerly wind, 8 is a northwesterly wind), p20 is a wind speed (m/s), p21 is a solar phenomena data (Mg II index). As characteristics of time were used: date (year, month, day), identification of the day of week ( p22 ), time (hour) of observation ( p23 ), identification of the part of day (0 is a morning, 1 is an evening) (p24).
The observations obtained by the method of "Short-time transform" were used to form a sample to solve the problem of qualitative forecasting of the patient's condition for the next second half of the day according to the previous observations: as input features were used data for the previous (morning and evening) and the current day (morning), and as an output - the patient's condition in the evening in the current day (0 - normal, 1 - aggravation of symptoms, accompanied by an increase in blood pressure).
To carry out experiments on the researching of the developed method additional training of neuro-fuzzy diagnostic models the training sample S =< P, T > was divided into two parts, the first Str of which was used for training (synthesis) of the model NFN = NFN(struct, param) ,and the second Sad - for additional training of the already synthesized model NFN in order to obtain a new model
Table 1 - The results of experiments on the study of methods of neural-fuzzy networks training
(23)
The higher the value of the variable ra , the more new observations appeared after the previous construction (reconstruction) of the model NFN .
In the process of experimental studies will be applying different methods and approaches to the training of the constructed models at different values of the variable ra :
- additional training of the synthesized neuro-fuzzy model NFN using sample Sad by the Backpropagation method (BPSad) [1, 2]. In this case, the parameters of the existing model NFN , pre-synthesized by sampling Str , were used as the initial parameters of the new model NFNN ;
- re-training of the neuro-fuzzy model using the data of the combined sets Str U Sad = S (BPS);
- using the developed method for additional training for finishing the diagnostic neuro-fuzzy models (MATDNFM). Herewith, the finish of the model was performed on a sample Sad , base model NFN was synthesized based on a sample Str .
As criteria for comparison the methods additional training of the neuro-fuzzy models shall be using:
- training time tad is an amount of time that was spent on building the model NFNN (without taking into account the time that was used to synthesize the base model NFN );
- error Es of the model NFNN on the sample data S =< P,T > ;
- error Estr of the model on the sample data ;
- error Esad of the model on the sample data ;
- model error Et on test data (observation data not reflected in the sample S =< P,T > ).
5 RESULTS
The results of the experiments are given in table 1.
ra, % tad Es EStr ESad Et
BPSad BPS MATDN FM BPSad BPS MATDN FM BPSad BPS MATDN FM BPSad BPS MATDN FM BPSad BPS MATDN FM
1 0.8139 82.632 0.6918 0.0936 0.0296 0.0296 0.0945 0.0299 0.0299 0 0 0 0.1756 0.0572 0.0555
10 7.4727 82.632 6.7255 0.0591 0.0296 0.0296 0.0649 0.0270 0.0324 0 0.0556 0 0.1109 0.0572 0.0555
20 13.7 82.632 11.645 0.0542 0.0296 0.0296 0.0592 0.0237 0.0237 0.0294 0.0588 0.0588 0.0637 0.0572 0.0555
50 27.4 82.632 20.824 0.0443 0.0296 0.0345 0.0519 0.0296 0.0296 0.0294 0.0294 0.0441 0.0521 0.0572 0.0647
100 41.1 82.632 25.893 0.0345 0.0296 0.0345 0.0294 0.0294 0.0294 0.0396 0.0297 0.0396 0.0406 0.0572 0.0647
6 DISCUSSION
Table 1 shows that the additional training time tad , that was spent on the construction of the model NFNN using the method of BPS is constant (tad = 82.632 sec.) and does not depend on the value of the variable ra , because before training the neuro-fuzzy network with this approach is performed by using the entire data sample S =< P, T > and does not depend on its division into the
sample Str, which was used to train the basic model NFN, and the sample Sad for the additional training of the already synthesized model NFN (building a new model NFNN . It should be noted that for small amounts of data (a low number of instances of the training sample S =< P, T >), the synthesis time of the model is acceptable. However, the use of this approach in the processing of BPS large data sets for the restructuring of the already synthesized models is undesirable, and in some cases impossible, because the process of learning (re-training) will require significant time and hardware resources of the computer.
The additional training time tad in the case using the method BPSad depends on the value of the variable ra (changes from 0.8139 sec. with ra = 1% to 41.1 sec. with ra = 100%) due to the fact that a reduced sample Sad is used as the sample for which the neuro-fuzzy model is being trained. Similar results shows the proposed method MATDNFM. However, the additional training time a few below (changes from 0.6918 c. with ra = 1% to 25.893 c. with ra = 100% ) compared to additional training time with using BPSad. This is conditioned by the fact that the proposed method is pre-grouping of new instances, thereby significantly reducing the number of new rules that are introduced in the neuro-fuzzy diagnostic model, and this, in turn, reduces the number of configurable parameters and, accordingly, the time of model learning.
The error Es on the sample S =< P,T > for the BPS method is constant ( Es = 0.0296) and such, which does not depend on the value of the variable ra , because the additional training (re-synthesis of the model) is performed throughout the data sample S = Str U Sad . The error Es for the BPSad method is slightly worse in comparison with the BPS (especially at low values of ra : ES = 0.0936 with ra = 1%, ES = 0.0345 with ra = 100%), because a reduced sample Sad is used for additional training , which is only a certain part of the sample S = < P,T > . As can be seen from the table, the
error Es for the BPSad method decreases with increasing value of ra . This is conditioned by the increase in the sample Sad share relative to S =< P, T > the increase ra . It is worth noting that in solving practical problems the number of new data (value of ra ) is usually significantly lower than the amount of initial information (sample S =< P,T > ). This confirms the expediency of using
© Oliinyk A., Subbotin S., Leoshchenko S., Ilyashenko M., Myronova N., Mastinovsky Y., 2018 DOI 10.15588/1607-3274-2018-3-12
the proposed method, in which the error Es on the sample S =< P, T > is almost unchanged (does not significantly depend) when the value of the variable ra change and is commensurate with the magnitude of the error Es using the BPS approach. This is due to the use of formulas (22) to calculate the values of the output parameter T, which takes into account both the preliminary compilation of data samples Str in the form of the underlying model NFN (output parameter value t(s) is calculated according to the basic model NFN in the case that the instance s has nrnb
low degree of belonging U H-NBj - Mmin to the rules of
j=1
the new structural element of the model in the form of the correction unit) and a new data sample Sad , summarized in a correcting block NB (the value of the output parameter t(s) is calculated by correcting block NB in the case, if the s instance is characterized by a high degree of belong-nrnb
ing U M-NBj > M-min to the rules of the new structural
j=1
element).
The error Estr value on the sample Str for the BPS method (ranges from 0.0237 to 0.0299) is similar to the error value Es . The error Estr calculated on the basis of the sample Str using the model built using BPSad method is high enough for small values of the variable ra (EStr = 0.0945 with ra = 1%, EStr = 0.0649 with ra = 10%, EStr = 0.0592 with ra = 20%). This is an unacceptable result, which is justified by the using of sample Sad instances when building a new model NFNN. Error Estr when using the method MATDNFM is quite low, including at small values of the index ra (Estr = 0.0299 with ra = 1%, EStr = 0.0324 with ra = 10%, EStr = 0.0294 with ra = 100%). Such values EStr confirm that the proposed method is appropriate to use at low values of ra , that is, in cases where the volume of new information Sad about the objects or processes is significantly lower than the amount of available information Str that was used to build the basic model of NFN.
The table shows that the value of the error Esad calculated on the basis of the sample Sad at small values of the variable ra (1% and 10%) is zero for all methods (except for the value Esad = 0.0556 for the BPS method with ra = 10%), what indicates their ability to implement new data into the existing model. However, comparing the values of the values Esad , Estr and Es , we can conclude that the method BPSad, in contrast to the proposed method MATDNFM, loses its ability to approximate the model (the value Es increases to an unacceptable value at low levels of value of ra ). The BPS method
is similar to the proposed method and provides synthesis (training) of neuro-fuzzy models with acceptable approximating properties ( Es = 0.0296), but the time before additional training (re-synthesis) of the model using the BPS method is high enough (tad = 82.632 sec.) and commensurate with the training time of the basic model that, unlike the proposed method MATDNFM (tad = 0.6918 sec. with ra = 1% and tad = 25.893 sec. with ra = 100%, what is significantly less than when using the method BPS), significantly limits its use in practice, especially when processing big data.
Low values of the error Et of model NFNN on test data (with the exception of the method BPSad at low values of the variable ra), calculated for the test sample data (data about observations, which are not reflected in the sample S =< P, T >) confirm the ability to the generalization data by neuro-fuzzy diagnosis models which passed the additional training process .
Thus, the proposed method of MATDNFM is advisable to use at low values of ra , that is, in cases where the volume of new information Sad about the objects or processes is significantly lower than the amount of available information Str that was used to build the basic model of NFN.
Given that the number of new data (variable ra) is usually significantly lower than the amount of initial information when solving practical problems, the use of the proposed method is appropriate, since the model NFNN error Es on the sample S =< P,T > does not change almost when the values of the variable ra change, and the additional training time is much less than when using the BPS method.
CONCLUSIONS
The urgent problem of automation of the process of assessing the informativeness of features in solving problems of diagnosing and pattern recognition has been solved.
The scientific novelty of obtained results is that the method has been developed for additional training of diagnostic neuro-fuzzy models, which allows to adapt existing models to the change in the functioning environment by modifying them taking into account the information obtained as a result of new observations. The proposed method assumes the stages of extraction and grouping of correcting specimens, diagnosing with the help of the existing model leads to incorrect results, as well as the construction of a correcting block that summarizes the data of the correcting instances and its introduction into an already existing model. When determining the adjustable parameters of the correction block in the developed method, it is proposed to use information about the values of the coordinates of the correcting instances, as well as information on the degree of their belonging to clusters in the feature space (and, accordingly, to the fuzzy rules presented in the correcting block). This allows one to take
into account the importance of corrective copies for restoring the functions of the fourth layer of the correcting block and, when determining custom parameters, to increase the contribution of those specimens that are characterized by high estimates of the degree of belonging to a particular cluster. Using the proposed method of learning the diagnostic neural-fuzzy models allows not to perform the resource-intensive process of re-constructing the diagnostic model on the basis of a complete set of data, to use the already existing model as the computing unit of the new model. In addition, models synthesized using the proposed method are highly interpretive, since each block generalizes information about its data set and uses neuro-fuzzy models as a basis.
The practical significance of obtained results is that the practical tasks of diagnosing and recognizing images are solved. The results of the experiments showed that the proposed method makes it possible to carry out additional training of diagnostic neuro-fuzzy models on the basis of new information and can be used in practice for solving practical problems of diagnosing and pattern recognition.
Prospects for further research are to develop the new methods for the additional training of deep learning neural networks for the big data processing
ACKNOWLEDGEMENTS
The work is supported by the state budget scientific research project of software tools department of Zapo-rizhzhya National Technical University "Methods and means of decision-making for data processing in intellectual recognition systems" (state registration number 0117U003920).
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Received 25.06.2018.
Accepted 02.08.2018.
ДОНАВЧАННЯ Д1АГНОСТИЧНИХ НЕЙРО-НЕЧ1ТКИХ МОДЕЛЕЙ
Олшник А. О. - канд. техн. наук, доцент, доцент кафедри програмних засобiв Запорiзького национального техтчного ушверситету, Зап^жжя, Укра!на.
Субботш С. О. - д-р. техн. наук, професор, зав^вач кафедри програмних засобш Зап^зького национального техшчного ушверситету, Зат^жжя, Украша.
Леощенко С. Д. - студент кафедри програмних засобгв Зага^зького нацюнального техничного унгверситету, Зат^ж-жя, Украша.
Ильяшенко М. Б. - канд. техн.наук, доцент, доцент кафедри комп'ютерних систем та мереж Зап^зького нащонального техничного ушверситету, Зап^жжя, Украша.
Миронова Н. О. - канд. техн. наук, доцент кафедри програмних засобiв Зап^зького национального техшчного уншер-ситету, Запорiжжя, Украша.
Мастиновський - канд. фiз.-мат. наук, професор, зав^вач кафедри прикладно! математики Зап^зького национального техшчного ушверситету, Запорiжжя, Украша.
АНОТАЦ1Я
Актуальнiсть. Виршено задачу автоматизаци синтезу даагностичних моделей при д1агностуванш та розтзнаванш об-раз1в. Об'ект дослщження - методи синтезу нейро-нечгтких д1агностичних моделей. Предмет дослщження - методи донав-чання нейро-нечтжих мереж.. Мета роботи - створення методу донавчання нейро-нечтжих д1агностичних моделей.
Метод. Запропоновано метод донавчання д1агностичних нейро-нечтжих моделей, який дозволяе адаптувати до змши се-редовища функцюнування гснуюч модел1 шляхом 1х модифжаци з урахуванням шформаци, отримано! в результат нових спостережень. Даний метод передбачае виконання еташв видобування та угрупування коригувальних екземпляргв, д1агнос-тування за якими за допомогою гснуючо! модел1 призводить до некоректних результата, а також побудову коригувального блоку, який узагальнюе дат коригувальних екземпляргв, [ впровадження його у вже гснуючу модель. Використання запро-понованого методу донавчання д1агностичних нейро-нечггких моделей дозволяе не виконувати ресурсномюткий процес повторно! побудови д1агностично! модел1 на основ1 повного набору даних, використовувати вже наявну модель в якост обчислювального блоку ново! модели Модел1, синтезоваш за допомогою запропонованого методу, характеризуются висо-кою штерпретовшстю, оскiльки кожен блок узагальнюе шформацта про св1й наб1р даних [ в якосп базису використовуе нейро-нечпш моделг
Результати. Розроблено програмне забезпечення, яке реал1зуе запропонований метод донавчання нейро-нечггких мереж [ дозволяе виконувати перебудову юнуючих д1агностичних моделей на основ! ново! шформаци про дослщжуваш об'екти або процеси.
Висновки. Проведет експерименти тдтвердили працездаттсть запропонованого метод донавчання нейро-нечгжих мереж [ дозволяють рекомендувати його для використання на практищ при обробщ масивгв даних для д1агностування та розт-знавання образгв. Перспективи подальших дослвджень можуть полягати в розробщ нових методгв донавчання глибоких нейромереж для оброблення великих даних.
КЛЮЧОВ1 СЛОВА: виб1рка даних, д1агностування, донавчання, нейро-нечгтка модель, параметр, функция належност!
УДК 004.272.26: 004.93
ДООБУЧЕНИЕ ДИАГНОСТИЧЕСКИХ НЕЙРО-НЕЧЕТКИХ МОДЕЛЕЙ
Олейник А. А. - канд. техн. наук, доцент, доцент кафедры программных средств Запорожского национального технического университета, Запорожье, Украина.
Субботин С. А. - д-р техн. наук, профессор, заведующий кафедрой программных средств Запорожского национального технического университета, Запорожье, Украина.
Леощенко С. Д. - студент кафедры программных средств Запорожского национального технического университета, Запорожье, Украина.
Ильяшенко М. Б. - канд. техн. наук, доцент, доцент кафедры компьютерных систем и сетей Запорожского национального технического университета, Запорожье, Украина.
Миронова Н. А. - канд. техн. наук, доцент кафедры программных средств Запорожского национального технического университета, Запорожье, Украина.
Мастиновский Ю. В. - канд. физ.-мат. наук, профессор, заведующий кафедрой прикладной математики Запорожского национального технического университета, Запорожье, Украина.
АННОТАЦИЯ
Актуальность. Решена задача автоматизации синтеза диагностических моделей при диагностировании и распознавании образов. Объект исследования - методы синтеза нейро-нечетких диагностических моделей. Предмет исследования - методы дообучения нейро-нечетких сетей. Цель работы - создание метода дообучения нейро-нечетких диагностических моделей.
Метод. Предложен метод дообучения диагностических нейро-нечетких моделей, который позволяет адаптировать к изменению среды функционирования существующие модели путем их модификации с учетом информации, полученной в результате новых наблюдений. Данный метод предусматривает выполнение этапов извлечения и группировки корректирующих экземпляров, диагностирование по которым с помощью существующей модели приводит к некорректным результатам, а также построение корректирующего блока, который обобщает данные корректирующих экземпляров, и его внедрение в уже существующую модель. Использование предложенного метода дообучения диагностических нейро-нечетких моделей позволяет не выполнять ресурсоемкий процесс повторного построения диагностической модели на основе полного набора данных, использовать уже имеющуюся модель в качестве вычислительного блока новой модели. Модели, синтезированные с помощью предложенного метода, характеризуются высокой интерпретабельностью, поскольку каждый блок обобщает информацию о своем наборе данных и в качестве базиса использует нейро-нечеткие модели.
Результаты. Разработано программное обеспечение, реализующее предложенный метод дообучения нейро-нечетких сетей и позволяющее выполнять перенастройку существующих диагностических моделей на основе новой информации об исследуемых объектах или процессах.
Выводы. Проведенные эксперименты подтвердили работоспособность предложенного метода дообучения нейро-нечетких сетей и позволяют рекомендовать его для использования на практике при обработке массивов данных для диагностирования и распознавания образов. Перспективы дальнейших исследований могут заключаться в разработке новых методов дообучения глубоких нейросетей для обработки больших данных.
КЛЮЧЕВЫЕ СЛОВА: выборка данных, диагностирование, дообучение, нейро-нечеткая модель, параметр, функция принадлежности.
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