The method of machine learning of the on-board unmanned aerial vehicle system for autonomous recognition of natural and infrastructural terrestrial objects with the optimization of the frame size generated by the optical digital image of the region is considered. The problem of information synthesis of the onboard recognition system is being solved in the framework of information-extreme intellectual data analysis technology. As part of the functional approach to modeling the cognitive processes inherent in man in the formation and making of classification decisions, the method of information-extreme machine 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 algorithm of information-extreme machine learning was developed and programmatically implemented, during which the parameters of the sys-tem functioning 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.
The main way to increase the functional efficiency of onboard systems of unmanned aerial vehicles designed for autonomous recognition of ground objects is the application 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 following main reasons:
─ arbitrary initial conditions for the optical formation of digital images of terrestrial objects;
─ significant intersection of the recognition classes that characterize terrestrial objects;
─ 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 simulator, 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 dimensions 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 machine learning ORS, capable of analyzing large amounts of data at high power alphabet 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 cognitive processes inherent in humans in the formation and decision mak-ing of classification decisions. This area includes methods developed in the framework of the socalled 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 machine 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 recognition 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 efficiency of infor-mation-extreme machine learning, as well as other methods, is significantly 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
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
procedure (
It is necessary to optimize the parameters of the vector (
max E m(k ) ,
M m1GE {k}
(
When operating the ORS in exam mode, it is necessary to check the functional effectiveness 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
information criterion (
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 oriented graph. The input mathematical description of the categorical model is presented as a structure
I B G,T ,, Z, K,Y , X ; f1, f2 , 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 ; f2 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 (
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 common to all contours of machine learning parameter optimization. Operator : E ~|M| builds at each step of learning partition ~|M| , which is displayed by operator 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 precision 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 criterion in the working (allowable) area of determining its r * arg max{max{ max E
Gr G |GE {r}
(r)
(
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 corresponding 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 X1o ,
relative to which a system of control tolerances for recognition features is specified;
2. optimization by the information criterion (
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 X1o 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 recognition X mo ;
10. formed a three-dimensional array of binary learning matrix {xm(j,i) } , elements of
which are calculated by the rule
xm(j,i) 1, if AHK,i[b] ymj ,i ABK,i[b];
0, if else.
(
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:
E (k ) 1
m n
2n K1(,km) K2(.km) 10 p
{n [K1(,km) K2(,km), ]}log2 K1(,km) K2(k,m) 10 p ,
(
After determining the base class, the ORS machine learning procedure (
The input for the implementation of procedure (
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
(
AH,i y1, i ; AB,i y1, i ,
(
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 (
14. the formation of an array of averaged vectors of signs {xm} whose elements are determined by the rule 1, if xm,i 0, if 1 n xm(j,i) m ; n j1 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 xc is the averaged vector of the nearest neighbor class Xco ;
17. the information criterion (
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}
then x( j) X mo else x( j) X mo ],
(
In expression (
Thus, in the exam, it is determined by decisive rules (
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].
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 X3o – plowing field; class X 4o – sown field.
The selected frames are shown in Fig. 3.
а b c d
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 (
Table 1 shows results of machine learning using side of the square frame optimization. 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 (
Fig. 4 shows a dark area on the graph of the working (admissible) area of determining 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 (
The analysis of Fig. 5 shows that the optimum values of the radii of the containers of the recognition classes are: for the class X1o – d1* 26 (hereinafter in code units); for class X 2o – d2* 6 ; for class X 3o – d3* 5 and class X 4o – d4* 1 .
Fig. 6 shows a digitized image (Fig. 3), obtained by the results of the identification
of frames by the decisive rules (
Visual analysis of Fig. 6 shows that highways that are of interest for vehicle recognition are identified with a sufficiently high accuracy when the frame size is optimal. 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 informationextreme 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 interest 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 learning by optimizing other parameters of operation, including the parameters of the formation of the input mathematical description.