=Paper=
{{Paper
|id=Vol-2608/paper68
|storemode=property
|title=Information-extreme machine learning on-board recognition system of ground objects with the adaptation of the input mathematical description
|pdfUrl=https://ceur-ws.org/Vol-2608/paper68.pdf
|volume=Vol-2608
|authors=Dovbysh Anatoliy,Naumenko Igor,Myronenko Mykyta,Savchenko Taras
|dblpUrl=https://dblp.org/rec/conf/cmis/AnatoliyIMT20
}}
==Information-extreme machine learning on-board recognition system of ground objects with the adaptation of the input mathematical description==
https://ceur-ws.org/Vol-2608/paper68.pdf
Information-Extreme Machine Learning On-Board
Recognition System of Ground Objects with the
Adaptation of the Input Mathematical Description
Anatoliy Dovbysh1[0000-0003-1829-3318], Igor Naumenko2[0000-0003-2845-9246],
Mykyta Myronenko1[0000-0001-5005-1672], Taras Savchenko1[0000-0002-9557-073X]
1,3,4
Sumy State University, Rymskogo-Korsakova st. 2, Sumy, 40007, Ukraine,
2
Scientific-research center of missiletroopsand artillery, Gerasim Kondratyev st, 165, Sumy,
400021, Ukraine,
1
a.dovbysh@cs.sumdu.edu.ua, 2790905@ukr.net, 3nikitam1996@ukr.net,
4
taras.savchenko01@gmail.com
Abstract. The method of machine learning of the on-board unmanned aerial
vehicle system for autonomous recognition of natural and infrastructural terres-
trial objects with the optimization of the frame size generated by the optical dig-
ital image of the region is considered. The problem of information synthesis of
the onboard recognition system is being solved in the framework of informa-
tion-extreme intellectual data analysis technology. As part of the functional ap-
proach to modeling the cognitive processes inherent in man in the formation
and making of classification decisions, the method of information-extreme ma-
chine learning onboard recognition system, which allows to adapt the input
mathematical description to the maximum full probability of correct recognition
of terrestrial features. In accordance with the proposed categorical model, an al-
gorithm of information-extreme machine learning was developed and pro-
grammatically implemented, during which the parameters of the sys-tem func-
tioning according to the modified Kullback information criterion are optimized.
Implementation of the proposed machine learning algorithm was carried out on
the example of recognition of natural and infrastructural land objects, among
which roads were considered as a zone of interest.
Keywords. extreme machine learning, onboard recognition system, digital im-
age of the region, information criterion, optimization.
1 Introduction
The main way to increase the functional efficiency of onboard systems of unmanned
aerial vehicles designed for autonomous recognition of ground objects is the applica-
tion of ideas and methods of machine learning [1,2]. Thus there is a need to overcome
a number of complications of a scientific and methodological nature, due to the fol-
lowing main reasons:
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
─ arbitrary initial conditions for the optical formation of digital images of terres-
trial objects;
─ significant intersection of the recognition classes that characterize terrestrial ob-
jects;
─ the multidimensionality of the feature dictionary and alphabet of recognition
classes;
─ strict requirements for the efficiency of machine learning and the operation of
onboard recognition system (ORS) directly in working mode.
Overcoming the above complications depends on both the functionality of the sim-
ulator, close to real conditions, and the method of machine learn-ing ORS. In the
works [3 – 5], the detection of terrestrial objects is carried out according to its dimen-
sions using descriptive methods or the determination of special (invariant) points by
spline methods of different order. The main disadvantage of such methods is poor
results with the same or approximate geometric parameters of the objects. It is clear
that in order to increase the functional efficiency of machine learning, the ORS needs
to increase the in-formativeness of the recognition feature dictionary by scanning the
entire digital image of the object. But it is important to choose the method of ma-
chine learning ORS, capable of analyzing large amounts of data at high power alpha-
bet a priori fuzzy recognition classes. The main disadvantage of apply-ing neural
structures is the dependence of their functional efficiency on the many dimensions of
data and the flexibility to retrain [6, 7]. Therefore, a promising area of informational
synthesis of ORS is the application of ma
chine learning methods built within the functional approach to modeling the cogni-
tive processes inherent in humans in the formation and decision mak-ing of classifica-
tion decisions. This area includes methods developed in the framework of the so-
called information-extreme intellectual technology (IEI technology) data analysis,
which is based on maximizing the information ca-pacity of the recognition system in
the process of machine learning [8, 9]. In the methods of information-extreme ma-
chine learning, practical invariance of the many dimensions of data is ensured by the
construction of decisive rules within the geometric approach. In addition, the decision
rules con-structed in the framework of the geometric approach are characterized by
high efficiency of making classification decisions, which is especially relevant for the
ORS. Extreme machine learning by analogy with human learning is considered as a
process of optimization of parameters that affect its func-tional efficiency. In this
case, the information criterion of optimization as a measure of diversity is considered
as a generalized criterion for the validity of partitioning of the feature space into rec-
ognition classes, since it is func-tional both from a remote measure of proximity and
from the exact charac-teristics of the classification decisions. But the functional effi-
ciency of infor-mation-extreme machine learning, as well as other methods, is signifi-
cantly influenced by the method of forming an input mathematical description of the
recognition system. The paper [10] considered the problem of informa-tion-extreme
machine learning of the onboard system for recognizing terres-trial objects at a given
frame size of the digital image of the observed region. The article proposes a method
of information-extreme machine learning of the ORS with the adaptation of the frame
sizes formed by the optical channel of digital image of the region to the maximum
likelihood of making the right classification decisions.
2 Formulation of the problem
Let's consider the scheme of algorithm of information-extreme machine learning with
optimization of the size of frames of digital image of the region according to the pro-
cedure (3): Consider the formalized formulation of the problem of information syn-
thesis capable to learn ORS with optimization of the size of frames of digital image of
the region. Let the alphabet of the { X mo | m 1, M } classes of recognition characterize
the frames of the image of natural and infrastructural objects. For each recognition
class, a three-dimensional training matrix || y m( j,)i || of the pixel brightness of the recep-
tor frame of frames is formed, in which a row { ym( j,i) | i 1, N } , where N is the number of
recognition features, is a structured vector of the recognition class features X mo , and
the column of matrix { y m( j,i) | j 1, n} s a random learning sample of the i -th values n. In
accordance with the concept of IEI technology, the input training matrix Y is trans-
formed into a working binary matrix X , which is changed by optimal coding of rec-
ognition features by the level of control tolerances in the process of machine learning.
Therefore, in the binary Hamming space is given a vector of parameters of operation
that affect the functional efficiency of machine learning ORS to recognize the vectors
of features of recognition class X mo :
g m xm , d m , , r , (1)
where xm is a vector averaged over the ensemble of realizations, the apex of
which defines the center of the hyperspherical container of recognition class X mo and
the size of which is determined by the number of recognition features; d m is the ra-
dius of the hyperspherical container of recognition class X mo , d m d{xm xc ) , where
d ( xm xc ) is the inter-center distance between vector xm and vector xc of the near-
est neighboring class X co ; is a parameter whose value is equal to half the symmet-
ric field of control tolerances for recognition features, H / 2 , where H is the
normalized tolerance field for recognition features; r is the side of a square frame of
a digital image of a region.
It is necessary to optimize the parameters of the vector (1) in the process of ma-
chine learning of the ORS, which provide the maximum value of the information
optimization criterion in the working (allowable) region of determining its function:
* 1 M
E max Em( k ) , (2)
M m1GE {k }
where Em(k ) is the value of the information criterion for optimization of vector pa-
rameters calculated at the k -th кроці step of machine learning (1); GE work area of
calculation of information criterion; {k} – set of learning steps.
When operating the ORS in exam mode, it is necessary to check the functional ef-
fectiveness of machine learning.
Thus, the problem of information synthesis capable of learning ORS is to optimize
the parameters of its machine learning by approaching the global maximum of infor-
mation criterion (2) to its maximum limit value.
3 Mathematical model of machine learning
Within the functional approach to the modeling of cognitive processes, a categorical
model of information-extreme machine learning is constructed in the form of an ori-
ented graph. The input mathematical description of the categorical model is presented
as a structure
I B G,T , , Z , K ,Y , X ; f1 , f 2
,
where G is the set of factors that influence the ORS; T is the set of moments in
which information is received; recognition features space; Z – the space of
states of the system, (alphabet of recognition classes); K – multiple frames of digital
image of the region; Y the input training matrix of the pixel brightness of the image
frame; X – working binary learning matrix; f1 is the operator of forming the input
training matrix Y ; f 2 is the operator of converting the matrix Y into a working binary
matrix X .
A categorical model of information-extreme machine learning of the ORS with the
optimization of the coordinates of the structured vector (1) is shown in Fig. 1.
Fig. 1. Categorical model of machine learning of the ORS
In Fig. 1 Cartesian product G T Z K sets the test universe, which is the
source of information. The thermal set E of the information criterion values is com-
mon to all contours of machine learning parameter optimization. Operator
~ ~
: E |M | builds at each step of learning partition |M| , which is displayed by op-
erator on the distribution of binary feature vectors. Next, operator : X I |S | ,
where I |S| is the set of S hypotheses, tests the main statistical hypothesis
1 : xm( j,i) X mo . The operator determines the set |Q | of the precision characteristics
of the classification solutions, where Q S 2 , and the operator calculates the set of
values E of the information optimization criterion, which is a functional of the preci-
sion characteristics. The loop of optimization of control tolerances for recognition
features is closed through a term set of D elements which is the value of the system
of control tolerances for recognition features. An optimization loop that includes a
term set of R values of the sides of a square image frame optimizes the area of the
frame. The operator r1 resizes the frame, and the operator r2 resizes the space of the
recognition features. The operator u governs the process of machine learning.
4 Information-extreme machine learning algorithm
According to the categorical model (Fig. 1), the information-extreme algorithm of
machine learning of the ORS with optimization of the frame size of the digital image
of the region will be presented in the form of an iterative procedure for finding the
global maximum of alphabet-averaged classes of recognition of the information crite-
rion in the working (allowable) area of determining its
(r )
r * arg max{max{ max E (3)
Gr G |GE {r}
(r )
where r * is the optimal side size of the square frame of the digital image; E
the information criterion for optimization of vector parameters calculated on the r -th
step of machine learning averaged by the alphabet of recognition classes (1); G is a
valid value range for parameter δ of the tolerance field.
The input to the machine learning algorithm is a training matrix in the form of a
three-dimensional array of feature vectors { ym( j,)i } and a system of fields of normalized
tolerances { H ,i } for recognition traits that specifies the range of values of the corre-
sponding control tolerances.
The main stages of information-extreme machine learning of the ORS are:
1. definition for a given alphabet of recognition classes { X mo } of base class X 1o ,
relative to which a system of control tolerances for recognition features is specified;
2. optimization by the information criterion (2) of the parameters of machine
learning of the ORS, which are included in the structure (1);
3. construction of decisive rules for optimal geometric parameters of containers
of recognition classes, which were restored in the process of machine learning in the
radial basis of the binary space of recognition features;
4. check the functional efficiency of machine learning ORS in exam mode.
The definition of base class X 1o is made according to the scheme:
1. the counter of base recognition classes is reset: b : 0 ;
2. the counter of base recognition classes is initialized: b : b 1;
3. the counter of the recognition classes is reset: m : 0 ;
4. m : m 1;
5. the counter of steps of changing the radii of containers of recognition classes is
reset: k : 0 ;
6. the averaged ym vector is defined for array { ym( j,i) } ;
7. if b b 1 and m m 1 , then ym : yb , that is, vector ym is taken as the
base and the point 8 is fulfilled, otherwise – the point 9;
8. are calculated for each i -th sign of vector yb lower AHK , i [b] and upper
ABK , i [b] control tolerances by the formulas
AÂK , i [b] yb ,i ,
9. where yb, i is the value of the i-th sign of the average vector of class yb rec-
ognition X mo ;
10. formed a three-dimensional array of binary learning matrix {xm( j,)i } , elements of
which are calculated by the rule
1, if AHK ,i [b] ymj ,i ABK ,i [b];
xm( j,i) (4)
0, if else.
11. for array {xm( j,i) } is determined by the average binary vector xm ;
12. if m M , then item 4, is fulfilled, otherwise – item 12;
13. for the set of vectors {xm } , a code distance matrix is constructed and pairs of
nearest neighbors for which hyperspherical containers of recognition classes are re-
stored in the process of machine learning;
14. m : m 1;
15. the counter of steps of change of radius of containers of recognition classes is
initialized: k : k 1;
16. the information criterion E m(k ) of optimization of machine learning parameters
is calculated according to the learning matrices of class X mo and its closest neighbor,
for example, in the form of a modified Kullback information measure:
1
Em( k ) {n [ K1(,km) K 2( k,m) , ]} log2
2n K1(,km) K 2(.km) 10 p
(5)
n (k ) (k )
K1, m K 2 , m 10
p
,
where K1(,km) is the number of events in which “their” recognition attribute vectors did
not belong to class X mo ; K 2(,km) is the number of events in which “alien” feature vec-
tors belonged to class X mo ; n is the number of feature vectors in the learning matrix
of each recognition class; 10 p is a sufficiently small number that is entered to avoid
division by zero (in practice, p is selected from the interval 1 p 3 .
17. if k d ( xm xc ) , then item 14 is fulfilled, otherwise – item 17;
18. in the work area GE is determined by the maximum value Em*(k ) information
criterion (5);
19. if b M , then item 2 is fulfilled, otherwise – item 19;
*
20. according to formula (2) the average maximum value E of criterion is calcu-
lated (5);
*
21. the recognition class for which the value of criterion E (5) is maximum is
taken as the base;
22. STOP.
After determining the base class, the ORS machine learning procedure (3) is start-
ed with the optimization of the control tolerance system for the features of recognition
and frame size. The main functions of the inner cycle of procedure (3) are:
─ mation criterion (5) at each step of machine learning with values of control tol-
erance field and frame size of region image set in corresponding external cycles;
─ search for the global maximum of the information criterion for optimization of
machine learning parameters in the working (valid) area of determining its function;
─ determination of the geometric parameters of recognition classes optimal in the
information understanding.
The input for the implementation of procedure (3) is the alphabet of recognition
classes { X mo } , in which class X 1o is the base, the corresponding three-dimensional
array of the training matrix { ym( j,)i } , parameter H , which determines the system of
normalized tolerances for recognition features and the maximum permissible size rmax
side square frames of digital image of the region .
Consider the scheme of the algorithm of information-extreme machine learning
with optimization of the frame size of the digital image of the region by the procedure
(3):
1. resetting the step counter of resizing frames in the region image: r : 0 ;
2. r : r 1 ;
3. reset the counter of recognition classes: m : 0 ;
4. m : m 1;
5. resetting the training frame resizing step counter: r : 0 ;
6. r : r 1 ;
7. resetting the step counter to change the tolerance field parameter: : 0;
8. : 1; ;
9. calculation of the lower and upper {AB,i } control tolerances for recognition
signs according to the rules
AH , i y1, i ; AB, i y1, i , (6)
10. where y1, i is the i -th sign of the averaged vector y1 of the base recognition
class X 1o ;
11. resetting the counter of the steps of changing the radius of the hyperspherical
container: k : 0 ;
12. k : k 1 ;
13. formed a three-dimensional array of binary learning matrix, the elements of
which are calculated by the rule (4);
14. the formation of an array of averaged vectors of signs {xm} whose elements are
determined by the rule
1 n ( j)
1, if x m ,i m ;
x m ,i n j 1
0, if else,
15. where m is the quantization level of the coordinates of binary vector xm ,
which by default is 0,5.
16. splitting the set of vectors {xm } into pairs of nearest “neighbors”
|m2| xm , xc , where x c is the averaged vector of the nearest neighbor class X co ;
17. the information criterion (2) is calculated;
18. if k N , then item 11 is executed, otherwise – item 17;
19. if H , then item 8 is executed, otherwise – item 18;
20. the maximum value of the criterion in the workspace of determining its func-
tion is determined, where the first and second reliability are greater than 0.5;
21. if m M 1 , then item 4, otherwise – item 20;
22. if r rmax , then item 6 is executed, otherwise – item 21;
*
23. determines the global maximum of average information criterion E in the
work area of determining its function;
24. determine the optimal values of parameter * , lower AH* ,i and upper AB* ,i con-
trol tolerances for all recognition features and size r* side square frames of the digital
image of the region;
25. STOP.
According to the optimal geometric parameters of the containers of recognition
classes obtained in the process of machine learning, productive decision rules were
constructed in the form
(X mo |M | )(x ( j ) |M | )[if ( m 0 ) & ( m max{ m )
{m}
(7)
then x ( j ) X mo else x ( j ) X mo ],
where x ( j ) is a recognizable vector; m is a function of belonging to vector x ( j ) of a
recognition class container X mo .
In expression (7), the membership function for a hyperspherical container of rec-
ognition class X mo is determined by the formula [3]
d ( xm* x ( j ) )
m 1 ,
d m*
where xm* , dm* – the optimal parameters of machine learning: averaged feature vector
and radius of hyperspherical container recognition class X mo respectively.
Thus, in the exam, it is determined by decisive rules (7) that the recognizable fea-
ture vector belongs to one of the classes in the given alphabet. At the same time, the
decisive rules, built within the geometric approach, are characterized by low computa-
tional complexity, which provides high efficiency of making classification decisions
in the operation of ORS in the operating mode.
5 Simulation results
An algorithm of information-extreme machine learning of ORS is implemented with
the purpose of optimizing the image of the region in understanding the information,
the receptor field of which is shown in Fig. 2 [11].
Fig. 2. Image of the region obtained by aerial photography
The input training matrix was formed by processing the image frames shown in
Figure 3 in the polar coordinate system according to [12]. As recognition classes, the
frames of the sections shown in Fig. 2 images of the region: class X1o – highway;
class X 2o – liquid forest; class X 3o – plowing field; class X 4o – sown field.
The selected frames are shown in Fig. 3.
а b c d
Fig. 3. Picture frames: а – class X1o ; b – class X 2o ; c – class X 3o ; d – class X 4o
In the previous stage of machine learning, the results of the implementation of the
above algorithm were identified as the base class of recognition X1o – highway.
Therefore, the system of control tolerances was determined relative to the averaged
vector of features of recognition class X1o .
In the process of machine learning ORS according to procedure (3), the value of
parameter r increased from one to 71 pixels of the receptor field of the video card.
Table 1 shows results of machine learning using side of the square frame optimi-
zation.
Table 1.– Results of machine learning
r 35 37 39 41 43 45 47 49 51 53 55
E 0,59 0,62 0,63 0,64 0,61 0,67 0,70 0,67 0,66 0,64 0,63
The analysis of Table 1 shows that, in the process of machine learning, the optimal
frame size of the image value is equal to r * 47 pixels with a maximum value of
*
E 0,70 information criterion.
Fig. 4 shows a graph of the averaged normalized information criterion (5) from
parameter of control tolerances system using optimal side of the square frame
Ē
1,0
0,8
0,6
0,4
0,2
0,0 δ
10 20 30 40 50 60 70
Fig. 4. Graph of information criterion dependence on parameter of control tolerances system
Fig. 4 shows a dark area on the graph of the working (admissible) area of deter-
mining the function of the information criterion of optimization, in which the first and
second reliability exceed respectively the errors of the first and second kind.
The analysis of Fig. 4 shows that, in the process of machine learning, the optimal
value of parameter of control tolerances system is equal to * 50 (scale of pixel’s
*
brightness) with a maximum value of E 0,70 information criterion. Fig. 5 shows
graphs of information criterion (5) dependence on the radii of containers of recogni-
tion classes the optimal values of which allow us to construct the decisive rules (7).
E1 E2
1,0 1,0
0,8 0,8
0,6 0,6
0,4 0,4
0,2 0,2
i
0,0 d 1 0,0 d2
5 10 15 20 25 30 5 10 15 20 25 30 35
а b
E3 E4
1,0 1,0
0,8 0,8
0,6 0,6
0,4 0,4
0,2 0,2
0,0 d 3 0,0 d4
1 2 3 4 5 6 1 2 3 4 5 6
c d
Fig. 5. Graphs of the criterion (5) on the radii of containers of recognition classes: а –
class X 1o ; b – class X 2o ; c – class X 3o ; d – class X 4o
The analysis of Fig. 5 shows that the optimum values of the radii of the containers
of the recognition classes are: for the class X 1o – d1* 26 (hereinafter in code units);
for class X 2o – d 2* 6 ; for class X 3o – d 3* 5 and class X 4o – d 4* 1 .
Fig. 6 shows a digitized image (Fig. 3), obtained by the results of the identification
of frames by the decisive rules (7) with the optimal frame size of the pixel image. The
numbers in the frames correspond to the numbers of the recognition classes.
Fig. 6. Results of the identification of frames
Visual analysis of Fig. 6 shows that highways that are of interest for vehicle rec-
ognition are identified with a sufficiently high accuracy when the frame size is opti-
mal.
6 Conclusion
1. Within the framework of functional approach to modeling of cognitive processes
of formation and decision-making of classification decisions, a catheter model is
proposed, which is considered as a generalized structural diagram of the algorithm of
information-extreme machine learning of the image recognition system
2. On the basis of the proposed categorical model, an algorithm of information-
extreme machine learning of the onboard recognition system was developed with
optimization according to the information criterion of the frame size of the digital
image of the region. The algorithm allows for a given flight altitude of an unmanned
aerial vehicle complex to determine quickly and with high accuracy the area of inter-
est in which the wanted land object may be located.
3. Since the decisive rules are not infallible by the learning matrix, to increase the
functional efficiency of ORS, it is necessary to increase the depth of machine learn-
ing by optimizing other parameters of operation, including the parameters of the for-
mation of the input mathematical description.
References
1. Muller, K.R, Mika S., Ratsch, G.: An introduction to kernelbased learning algorithms.
IEEE Transactions on Neural networks, vol.12(2), pp. 181-202 (2001).
2. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification: second ed. John Wiley & Sons,
New York (2001).
3. Jauregi Iztueta, E., Lazkano, E., Martinez-Otzeta, J.M., Sierra, B.: Visual Approaches for
Handle Recognition. Springer Tracts in Advanced Robotics, vol. 44, pp.313-322 (2008).
4. Huang, H., Lu, L., Yan, B., Chen, J.: A new scale invariant feature detector and modified
SURF descriptor. In: Proceedings Sixth International Conference on Natural Computation
(ICNC 2010), Yantai, Shandong, China, pp. 3734-3738 (2010).
5. Moskalenko, V., Moskalenko, A., Korobov, A., Boiko, O., Martynenko, S. Borovenskyi,
O.: Model and Training Methods of Autonomous Navigation System for Compact Drones.
In: Proceedings Second International Conference on Data Stream Mining & Processing
(DSMP), Lviv, IEEE, pp. 503-508 (2018). doi: 10.1109/DSMP.2018.8478521
6. Artale V., Collotta, M., Milazzo, C., et al.: Real-Time System based on a Neural Network
and PID Flight Control. Appl. Math. Inf. Sci., vol. 10(2)., pp. 395-402 (2016).
7. Jafari, M., Xu., H.: Intelligent Control for Unmanned Aerial Systems with System Uncer-
tainties and Disturbances Using Artificial Neural Network. Drones, vol. 3, pp. 24-36
(2018).
8. Subbotin, S.: The neuro-fuzzy network synthesis and simplification on precedents in prob-
lems of diagnosis and pattern recognition. Optical Memory and Neural Networks (Infor-
mation Optics), vol. 22(2), pp. 97-103 (2013). doi: 10.3103/s1060992x13020082
9. Dovbysh, A.S., Martynenko, S.S., Kovalenko, A.S., Budnyk, M.M.: Information-extreme
algorithm for recognizing current distribution maps in magnetocardiography. Journal of
Automation and Information Sciences, vol. 43(2), pp. 63-70 (2011). doi:
10.1615/JAutomatInfScien.v43.i2.60
10. Dovbysh, А.S., Moskalenko, V.V., Rizhova, A.S.: Information-Extreme Method for Clas-
sification of Observations with Categorical Attributes. Cibernetica and Systems Analysis,
vol. 52(2), pp. 45-52 (2016). doi: 10.1007/s10559-016-9818-1
11. The world's most detailed globe, https://www.google.com.ua/intl/en/earth/
12. Naumenko, I., Myronenko, M., Piatachenko, V.: Information-extreme learning of on-board
system for recognition of ground vehicle. CEUR Workshop Proceedings, p. 121–132
(2019).