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ШС004.021:004.023
PROSPECTS OF APPLICATION OF THE AUTOMATED SYSTEM OF RECOGNITION AND AUTHENTICATION OF COMPUTER USERS DESCRIBED ON THE BASIS OF MODEL DISCRETE
ZAYATS V.M._______________________________________
In the article, on the basis of model discrete, systems approach to construction of the automated system of recognition of computer users is described. The discrete model recurrently connected the delays of time at entered information from the keyboard of computer in the real regime of time. Expedience of the developed approach is illustrated during realization of automated authentication of computer users on the basis of determined and probabilistic methods and directions perspective of application of the created system are marked.
I. Problem
For created modern real devices, research of the unknown physical phenomena or processes, for construction of the systems of recognition and authentication, that has the desired descriptions of informative signal or descriptions, what are subject to the study expediently to conduct the computer analysis and designing, creating adequate mathematics model of object that is developed or studied. Such approach requires considerably less technical facilities comparative with the physical experiment, especially on the previous stage of development in default of reliably apriority information.
Lately in a nonlinear dynamics wide application the discrete models of the systems [5-9] for which discrete is in nature of object of researches, instead of are investigation results of discrete the continuous system. Expedience of the use of models discrete on the nature is explained by such their features:
- by simplicity of mathematical description on comparison with continuous models;
- by a presence substantially wider spectrum of the dynamic modes, is comparative with the known models;
- by endless measurable, that allows to design every new accordion of process by her introduction to the vector of state variables, while for continuous systems for the decision of this task is necessary to promote the dimension of the system;
- by absence of necessity to determinate of step of discrete, estimations of local and global errors of numeral methods, regions of stability and synchronization;
- the best adapted to apply computer experiment on comparison with continuous models.
The models, discrete in their nature is applicable as to construction of devices, that have the desired regimes and to recognition and authentication of such regimes in
the systems with a complicated dynamics and conduct, what allows promoting efficiency of their work.
At such rising of task is actually the problem of development of reliable approaches to establishment of priority primary signs, what are formed in the process of recognition in the real mode of time.
II. Purpose
The purpose of the given article is description of the automated system of recognition and reliable authentication of objects and phenomena of complicated nature for providing of reliable process of recognition and authentication of the explore systems. The perspective directions of development of recognition systems of the complicated nature on the basis of discrete models and directions of their expedient application are also given in this work.
III. Basic Part
A. Analysis of basic results
For the systems creation of objects recognition and their reliable authentication are need in systems approach, essence of which consists in forming of primary signs about the object of recognition, to establishment of their priority and choice or development and realization reliable criteria's of recognition and reliable authentication of objects and processes
The first researches in industry of recognition in our country were conducted A. A. Harkevich [14] - one of founders of information theory and signals. Considerable payment in development of recognition theory did V.M. Gloushkov, V.S. Mihalevich, O.G. Ivahnenco, Y.I. Gouravlov, Y. Z. Tsipkin, V.I. Vasilev. Among foreign scientists it is necessary to remember to the robot F. Rosenblatt, which in 1957 offered a machine, which studied to recognize appearances and was named perseptron (in translation from English of "to percept” -to perceive - сприймати). This was the simplest model of activity of human brain. Considerable contribution to subsequent development of theory of pattern recognition did I. Gardner, R. Douda, G. Sebastian, Dg. That, C. Fou, P. Hart, S. Vatanabe et al .
The first works in pattern recognition were devoted to the theory and practice of construction of reading submachine (then appearance a sign, image, letter or number). The theory of statistical decisions was a mathematical apparatus for the decision of tasks of recognition from the moment of their origin [15].
On today the results of theory of statistical decisions become a base for construction of recognition algorithms, which to provide attributing of object to his class on the basis of experimental ofa posteriori data, that characterize an object and an apriority data, that describe the classes of objects. Later a mathematical apparatus broadened due to the use of methods of boolean algebra and some sections of the applied mathematics, information theory, mathematical programming and systems analysis [1617].
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Without regard, that such methods and algorithms of recognition all in a greater degree become the inalienable part of the such applied systems as of medical and technical diagnostics, authentication of complicated dynamic processes and phenomena, ecological monitoring and social informatics, meteorological prognostication and geological secret service, facilities of supervision and systems of introduction and destroying of information in computer [9], graphic and linguistic, intellectual systems of acceptance of decisions, in literature - both domestic, and in foreign - systems approach to the tasks of recognition so far did not become dominant.
Today the problem of recognition equates with construction of optimum algorithms of recognition and research of terms which allow realizing such algorithm to a great extent. Theoretical researches are oriented on the decision though and tasks important, but partial the applied character. To such tasks in the first turn it is needed to deliver the tasks of reliable recognition, essence of which is taken to the division of space of signs, by the language of which objects or processes of recognition are described, on regions, that answer the classes of these objects, that is to the choice of the best granits (rules ) of division of classes. But the decision of these tasks is possible only then, when the classes of objects and signs by the language of which recognizable objects and their classes are described, are known apriority. However the developer of the system of recognition, as a rule, does not own this information. Even in simplest case of recognition of letters of alphabet, finger-prints, words of language, extremes and special points of functions (where no question about classes is), their informing signs and apparatus for their determination are not known - it is the article of untraditional researches.
There is a question about the reasons of such attention to the tasks of description of classes by the language of signs and construction of optimum algorithms of recognition.
First reason in that these tasks, is comparative, are easily given to the formal and analytical decision, that and determines their attractiveness for researchers. The second reason consists that considerable part of researchers limits the activity to only theoretical researches. Third problem in considered traditionally, that the systems of recognition are autonomous. It is justified in some partial tasks, although in general case such formulation of question is not legitimate. And in the systems of technical and medical diagnostics, in the automated systems of management, recognition of mechanisms defects and machines, determination of patient diagnosis, recognition of the complicated regimes, classification of production situations is not for itself. Their recognition is needed for the receipt of information initial for the subsystem of management with the purpose of acceptance of leading decisions, adequate to the results of recognition of unknown objects, phenomena, situations, states.
It is possible to assert that reliable recognition of concrete situations is not the sufficient condition of achievement
potentially of possible efficiency of the system of management. But this is a necessary condition. It is heavy to represent that a doctor, who put a wrong diagnosis will find the correct method of medical treatment or no exposure of the unsteady hesitating regimes will provide reliable work of technical device.
At development of any systems of recognition is need systems approach essence of which consists in that, that in the conditions of inevitable limitations financial and technical the system of recognition provided realization potentially of possible efficiency to the management system. Procedure of measuring of primary signs about the process of recognition, establishment of priority of these signs and their influence on integral descriptions of the explored process or object must precede to the choice or creation of recognition criteria. From the mathematical point of view description of such system is to provide the minimum error of recognition and reliable authentication of recognition object after certain signs and decisionmaking criteria
B. Method of identification of computer users on base of primary discrete informative signs
Essence of method consists in that, to provide procedure of authentification of concrete user during his works with the keyboard of computer. Some common reasons in relation to creation of such system are given in work [17].
Obviously, for organization of recognition process is necessary to enter the text (standard) for each of objects of recognition in memory of computer . In default of standard an object is not recognized or it is suggested to create a new class of objects by the task to the standard of handwriting (it is possible to use for providing of the sanctioned access to the resources of computer). Parallel at creation of standard after the hand motor signs of object the informative model of object by determination of functions of distributing of time delays at introduction of information to the computer is formed. In quality of primary signs about an object о different sentinel delays are used during work of object with the keyboard of computer. To set priority of each of primary signs that is possible by an experimental way and it is offered in work [19]. During authentication of object again we will realize procedure of choice or development of criteria of decisionmaking and on the basis of these criteria [15] and we make decision about attributing of object to the certain class. In the case of ambiguous solution it is possible to apply the functions of distance (determined approach) and simply choose a class (with the least middle square rejection of signs). We will mark that different informative signs can have a different priority which also it is possible to set experimentally. With the purpose of increase of efficiency of the system expediently to chop off the not determined chaotic motions of hand of person by previous filtration of information, that is entered by an user in the real-time regimes, creating the same the continuous sequences (sets) of characters.
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In work [11-13] is formulated and analyzed a plenty of descriptions. We will bring only most informative over its and accessible for the rapid forming. Consequently, for construction of the system of recognition of person after its hand motor reactions the following descriptions were select:
1) relative deviation of pause before button - distributing of relative rejections of pause before given button the mean value of pause before all buttons in the given continuous sequence of set
DevB = ——— ■ 100%. (1)
^cp
where t. - duration of pause before by button; t -middle duration of pause before the buttons in the sequence of the collected text.
2) relative deviation of button delay - distributing of relative deviation duration of pressed given button to middle duration of pressed button in the given continuous sequence
DevP = li <cp •!()()% (2)
^cp
The example of the given distributing is represented on figure 1. On abscising axis relative rejections are postponed in percents, and on ay-axis - relative frequency of hits in the proper interval of rejections.
between classes Q and within the limits of every group of descriptions is calculated after the formula of standard deviation:
Dist(A-) = I— (mp - mf )2 (4)
v n i=i w
where nij - mean value of selection of i-i description of the given group of class Cl. Dist(k) - distance between classes after the group of descriptions 1.
Fig. 1. Distribution 84 of time deviations delays of the pushed button T
Distances are measured between the mean values, as the middle can be appraised already after relatively small numbers of experiments (10-20), that are important for reduction of volume of text that is w ritten by the objects of recognition
3) relative deviation of pause after button - similar to previous description:
DevA = '' 'cp • 100%. (з)
^cp
4) the relation of pause value before button to duration of delay of this button;
5) the relation of pause value before button to the size of pause after button;
6) the relation of pause value after button to duration of delay of this button;
7) distributing of frequencies of the buttons use of register change.
In work [11] 18 of characteristics are considered, but most information is higher resulted.
Descriptions 1 -6 are formed for each of the buttons, that was involved in the set. But simplifiers balancing of importance of descriptions at construction of the system the given decision to collate first six descriptions in groups, as it considerably diminish their amount (and within the limits of group it is possible to unbridle them as equivalent). On grouping of descriptions directly influences the selected method of their comparison.
In the first variant of construction of the recognition system is realizated of procedure authentication were used the functions of distance. As weight of descriptions of every group couldbedifterent, distances were calculated separately on each of groups of descriptions. Distance
Groups of descriptions 1-6 are not equivalent in quality of decisions, which are adopted on their basis. Before connection of results for the decision-making on recognition, it is necessary to balance the scales of groups between itself. Balance of descriptions was carried out inversely proportional to probabilities to make an error of the second family (when two objects of different classes are identified as if they belong to one class) on each of groups of descriptions in particular: l/p^ l/p2: 1/ p3: l/p4: l/'p5: l/p6 : l/p7. The relation of groups gravity was experimentally got 1-7 as 4:12:8:6:5:2:6 accordingly. The draw back of the system on the basis of functions of distance is that she on principle can not define probability of rightness or incorrectness of decision on recognition. Every strange user will be like that or other authorized user of the system.
The developed second variant of construction of the system of recognition is based on the use of method of confidence intervals. For verification of hypothesis about steam's of objects belonging to one class we should check the hypotheses about equality of mean values of distributing [17] of all descriptions of every group.
For this purpose we use such formulas for calculating the values of mean a and selective standard s :
1 "
а = -.^х,- (5)
n ~zI
S = ((•>
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For the computation of confidence intervals the law of distributing of mean value is taken into account:
f(xcp)
/— П / 4
", 2(XcP~X0) ^_e 20
<7>/2л
(7)
For the selections of small volume estimation of mean value is specified by means of distributing Student [18],
q — m
after which a size is distributed и =----. Density of his
distributing is set by a formula:
Sep
П+1
Г(—) -
S(u,n) =---і--(1+—) 2
r,n, / n
Г (— iv im
(8)
Let'spresume an error ofthe first family Pa atcomparison of steam of the proper distributing and there will be N such pairs. Consequently, we can presume that integral description of group of class and object coincides with probability >1 -Pa, if the amount of unconfirmed hypotheses Na does not exceed a number of Pa- N , in other case we consider that an object does not belong to the class.
Such results (yes/no) we will get for each of six groups of descriptions. These groups are not equivalent on quality of decisions that are adopted on their basis as well as in the case of the system on the basis of function of distance. Each of them has its own probability of error of the second family.
On the basis of practical experiments on recognition the errors of the second family were explored with every group of descriptions. The system checked separate hypotheses up with the level of value a = 0.05.
This way we got probabilities of errors of the second family 35%, 13%, 20%, 27%, 32%, 78%. These probabilities of errors were got for comparison not large numbers of experiments on authentication (105 experiments). For the large group of people the probability of errors can some differ from adduced.
During the testing of the developed system on the explored objects was made only one error on 22 conducted recognitions (the two offered classes were looking like an object, one among which was correct).
Close estimation of error to confuse the object of one class with the object of other does not exceed 35% at presence of 112 classes incorporated in the system.
The system recognizes the authorized user after he typed 5-8 sentences consists of 60 symbols each, after introducing 300-500 symbols.
If user has sufficient qualification (speed of typing 200 symbols per minute) the system can recognize him even if he types an arbitrary text in place of task.
There are cases in which recognized user was t> ping English text. This is common for highly skilled user (speed of typing more than 300 symbols for a minute),
when probability of chaotic motions of hand from the set sentinel mode is improbable.
C. Approach to description of the authentification system of computer user on the basis of discrete model
Approach to construction of discrete models of hesitating processes with a difficult structure offered in works [6-
8] is possible to apply to description of the hesitating system of any nature on condition that its states are characterized by discrete features. For the arbitrary number of variables N we have N - measurable vector of state variables with matrix of transitional states with determinant which equal of unit. The simplest way to do this is when N -2 lines of matrix have units on the main diagonal, and all the other elements are equal to zero. Despite this last two lines of this matrix are the combination of harmonic functions of initial phase of cp:
(\ 0 0 ... 0 0 0 л
0 1 0 ... 0 0 0
0 0 1 ... 0 0 0
0 0 0 ... 1 0 0
0 0 0 ... 0 cos q> sing)
,0 0 0 ... 0 - singi cos q>
Then the mean square value of N - measurable vector of state variables, which can be calculated with the task of concrete set of functions f will answer amplitude of vibrations. The analysis of discrete model in work [20] with introduction to the matrix of transition of the states
(9) N - measured vector of the states confirms that the period here again can be appraised on the basis of formula
(10) .
Efficiency of such approach to description of computer system of user authentification for his hand movements which are determined by different sentinel intervals (time of pressing the key, duration of pause before pressure of the key, duration of pause after pressing the key) as absolute so attributed to their mean value, or one sentinel interval to other is confirmed by the results of computer design.
On the basis of offered approach there is a computer system of user authentification of computer from movements of his hand this system is realized in an environment the DELPHI. In the real mode of time while a user is typing some text the functions of distributing different sentinel delays which are approximated by the normal law of distributing are forming. On the basis of comparison of streaming values of the mathematical hopes and dispersions for each of the formed distributing with the a priori set standards that or the other user w ould be identified. Efficiency of such system does not exceed 65 % during registration of all sentinel features.
For the increase of efficiency of the developed system it is offered to describe her as a system of the discrete equations of sixth order according to the formed values
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of discrete features (sentinel delays). The choice of base functions for description of such system of recognition is problematic, because there are to be the probabilistic functions of distributing, which in accordance with hands actions of user are to foresee appearance of that or other letter on the keyboard of computer and forecast the size of sentinel delay at its pressure or size of pause before and after pressure. But regardless of type of these base functions in the case of description of process as a discrete model, when for features to choose the relation of deviation of time of holding to the pause before the key and relations of deviation of pause to time of pressing the key, the maximal informational content is confirmed by the results of computer design. The estimation of period of reiteration of the following of letters on a keyboard can be calculated by a formula:
If to go out from the real middle time of pressing the button 0.3s, taking into account pauses before and after by pressing the button the period of typing letters will not exceed Is, that answers the initial phase ф of vibrations 2 71 .
Consequently, at introduction to the algorithm of recognition block of forming continuous sequence of letters, when in the real mode of time any chaotic motions (casual carelessness, mechanical delay, pressure of a few keys, forced pause and others like that) are absent, efficiency of such system of user identification grows considerably. How showed the results of statistical tests at presence of 200 users in a data-base the error of recognition did not exceed 5%.
D. Prospects of development and application of discrete models of the oscillating systems to the analysis of dynamics of complicated objects
The results of the conducted analysis of the computer system of user identification of computer confirm expedience of the use of discrete models to the decision of wide class of the applied problems, related to recognition of the difficult dynamic modes that take place in the objects of hesitating nature. Always, when from a priori reasoning it is possible to define the elements of transition matrix of the states for two variables, the hesitating system of any order can be given in a discrete kind [7] by using for the record of matrix of the states of presentation (9). Application of this approach to description of the system of computer user identification advanced authenticity of recognition in 1,4 times. The successful choice for the functions of change of amplitudes of sentinel delays allows not only effectively realize procedure of recognition, but also analyze the psycho physiological state of computer user r and foresee appearance of that or other word in screen of monitor. Thus, this system can be effectively applied to the decision of tasks of medical diagnostics at creation of the biometrical measuring systems.
Application of the described approach to construction of the system of recognition of handwritten letters seems expedient, its algorithm and architecture are described in works [21,22,23,24] on the basis of structural approach.
Obviously, it is necessary to go out not from the structure of writing letter, but to build the system of recognition taking into consideration direction of hand motion (motion from top to bottom and from bottom to top, motion from the left to the right and in reverse direction) and time spent on writing the letter. After estimating the mathematical hope of time spent on writing of every letter, what is special for every user it is possible to realize procedure of recognition. From the mathematical point of view, taking into account direction of hand motion, this will be the discrete system of a 12 order. Accordingly to (10) it is possible to assert that at forming of continuous sequences of letters the time spent on their writing is to be multiple to the integer.
This interval-sentinel approach to forming primary informative features about an object or research process oriented to the use of discrete models with success can be applied to construction of the systems of information defense, medical diagnostics, systems biometrical, decision of transport tasks, working of data flows and creation of intellectual knowledge bases.
IV. Conclusion
In this work the method of forming primary features at construction of the computer system of recognition of computer users is described, an algorithm and method of realization of such system, features of its functioning are noted. The offered ways increase of recognition exactness and providing of authenticity of authentication of computer users by establishing priority of primary discrete features and use of discrete models, what links duration of pauses with duration of buttons delay during input of information from the keyboard of computer in real regime of time. In the article are described basic directions of development of the automated systems of objects recognition and processes built on the basis of discrete models, are marked and the fields of their expedient application.
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Поступила в редколлегию 27.01.2009
Рецензент: д-р техн. наук, проф. Кривуля Г.Ф.
Zayats Vasyl Mykhaylovych, head of the Information-Computer Technologies and Systems Department, Chornovil State Institute of Modem Technologies and Managements. Scientific interests: mathematical design of dynamics of the oscillation systems and recognition of objects of complicated nature.Адрес: Украина, Львов, ул. Генерала Чупринки, 130, к. 405, тел. 258-91-11, e-mail: zvmOl'a'rambler.ru.
УДК 519.1
ЛОКАЛИЗАЦИЯ ЗНАЧЕНИЯ ЛИНЕЙНОЙ ФУНКЦИИ, ЗАДАННОЙ НА ПЕРЕСТАНОВКАХ
ДОНЕЦ Г.А.. КОЛЕЧКИНА Л.Н.______________
Рассматривается задача комбинаторной оптимизации на комбинаторной конфигурации перестановок, анализируются методы решения таких задач. Предлагается метод локализации значения целевой линейной функции на основании применения теории графов.
Введение
Задачи комбинаторной оптимизации возникают при исследовании многих теоретических и прикладных проблем [1-4]. Например, в связи с развитием современных средств связи, Интернета, различных информационных технологий возрос интерес к задачам получения надежных кодов, позволяющих корректиро-в ать искажения информации при ее получении с носителей, пересылке и т.п. При исследовании проблем теории кодирования нередко возникают задачи, математические модели которых формулируются в терминах комбинаторной оптимизации. Среди них задачи построения помехозащищенных кодов, нахождения оценок их объема, представляющие большой теоретический и практический интерес. Таким образом, расширение применений комбинаторных задач приводит к их усложнению, в частности, к появлению новых или рассмотрению недостаточно изученных комбинаторных моделей [5,6], которые имеют большую размерность, специальную структуру, неточную информацию о значениях. Решение этих задач связано со значительными трудностями и требует разработки и
обоснования новых или модификации известных методов. В этом смысле очень полезным будет применения теории графов.
С помощью теории графов хорошо описываются многие типы комбинаторных задач. При этом графические представления являются не просто иллюстрациями, но и позволяют получать новые подходы к решению, а также результаты.
Данная работа продолжает исследования [7-11 ] и дает возможность решить более сложную постановку задачи локализации значений линейной функции на перестановках.
В частности, в работе [ 10] рассмотрен методупорядо-чения значений целевой функции на множестве перестановок, который дает возможность построить гамильтонов путь в перестановочном многограннике, в работе [11] рассматривается задача на графах с учетом повторений элементов перестановки.
В настоящей работе локализуется значение линейной функции на перестановках. Следует отметить, что алгоритм, представленный а данной статье, можно использовать для решения задач на различных комбинаторных конфигурациях при наличии дополнительных ограничений.
1. Постановка комбинаторной задачи оптимизации
В общем виде экстремальные комбинаторные задачи можно сформулировать так: имеется ц -множество элементов, на нем задается конечное множество комбинаторных конфигураций А = [ 71 j } = {(at -а 2 аг)}.
Под комбинаторными конфигурациями щ = а |. а 2 аг
можно понимать перестановки, сочетания, комбина-
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