=Paper=
{{Paper
|id=Vol-3171/paper115
|storemode=property
|title=Eye Tracking in the Study of Cognitive Processes
|pdfUrl=https://ceur-ws.org/Vol-3171/paper115.pdf
|volume=Vol-3171
|authors=Vitaliy Pavlenko,Tetiana Shamanina
|dblpUrl=https://dblp.org/rec/conf/colins/PavlenkoS22
}}
==Eye Tracking in the Study of Cognitive Processes==
https://ceur-ws.org/Vol-3171/paper115.pdf
Eye Tracking in the Study of Cognitive Processes
Vitaliy Pavlenko 1, Tetiana Shamanina 1
1
Odessa Polytechnic National University, Shevchenko av. 1, Odessa, 65044, Ukraine
Abstract
Developed computing and software tools for building a nonlinear dynamic model of the
human oculomotor system (OMS) based on input-output experiments using test visual stimuli
and innovative Eye-tracking technology. The Volterra model is used for identification in the
form of multidimensional transition functions of the 1st, 2nd and 3rd orders, taking into
account the inertial and nonlinear properties of the OMS. Eye-tracking software developed
by Matlab is being tested on real OMS experimental data.
Keywords 1
Eye-tracking technology, oculo-motor system, cognitive processes, psycho-physiological
states, Volterra model, identification
1. Introduction
The study of human eye movements and the trajectory of their movement reveals the structure of
the relationship of the individual with the environment, man with the world. Knowledge of eye
movement is of great theoretical and applied importance, expanding the possibilities of studying the
specifics of many professions in order to increase the efficiency of the subject of labor [1-4].
The process of acquiring knowledge is a central part of the learning process. Management of this
process involves the availability of effective objective indicators to assess the intellectual abilities of
the individual. Proposed in the project methods of psychological identification of the individual on the
basis of experimental data using innovative Eye-tracking technology and computational means of
their processing allow to monitor and diagnose the state of cognitive processes during students'
learning activities [5-9].
The aim is to develop software tools for building a non-parametric dynamic model of human OMS
taking into account its inertial and nonlinear properties based on experimental input-output data using
test visual stimulus and innovative eye tracking technology; introduction of the received information
models in diagnostic practice of states of cognitive processes.
The identification process is based on the use of test visual stimuli that are displayed on the
computer monitor screen at different distances from the starting position (Fig. 1).
Laptop, visual stimulus, eye tracker Respondent Responses of the OMS – eye-
tracker output signals
Figure 1:Diagram of the eye tracking process
COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland
EMAIL: pavlenko_vitalij@ukr.net (V. Pavlenko); tatanatv8@gmail.com (T.Shamanina)
ORCID: 0000-0002-5655-4171 (V. Pavlenko); 0000-0002-3857-1867 (T.Shamanina)
2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
The developed software enables support of the following tasks:
1. The relationship study of mental states and cognitive processes in educational activities [10-
14].
2. The interaction of mental states and cognitive processes during the educational activities of
students, an objective assessment of their cognitive development level, assessment of the
effectiveness of training to improve mental processes and for psychological correction of
personality [2].
3. Extension of the individual's creative life due to the early diagnosis of degenerative processes
of cognitive functions of the brain. Identification of a gifted personality (building a psychological
model of the personality) and evaluation of its abilities. Professional selection (the identification
and education of leaders) [9].
4. The assimilation of scientific knowledge and their respective skills serves as the main goal
and the main result of educational activities. The process of mastering knowledge is the central
part of the learning process. Managing this process implies the existence of effective objective
indicators for assessing an individual’s intellectual abilities [7].
The methods of psychological identification of an individual proposed in the project, based on
obtaining experimental data using eye tracking technology and computing means of processing them,
allow monitoring and diagnostics of the state of cognitive processes during the educational activities
of students.
2. Volterra Model and the Method of the Identification OMS
The basis for creating a mathematical (information) model of the object under study is the results
of measurements of its input and output variables, and the solution of the identification problem is
associated with obtaining experimental data and processing them taking into account measurement
noise.
To describe objects of unknown structure, it is advisable to use the most universal nonlinear
nonparametric dynamic models - Volterra models [15-17]. The nonlinear and dynamic properties of
the object under study are unambiguously described by a sequence of multidimensional weight
functions – Volterra kernels, invariant with respect to the type of input signal.
The input-output ratio for nonlinear dynamic systems (NDS) with an unknown structure (such as a
"black box") with one input and one output can be represented by a discrete Volterra polynomial of
degree N = 3 in the form [18]:
N 3 m m m
y[m] yˆ n [m] w1[k1 ]x[m k1 ] w2[k1, k2 ]x[m k1]x[m k2 ]
n 1 k1 0 k1 0 k 2 0
m m m
(1)
w3[k1, k2 , k3 ]x[m k1]x[m k2 ]x[m k3 ],
k1 0 k 2 0 k 3 0
where yˆ n [m] is the n-th partial component of the NDS model response; w1[k1], w2[k1,k2], w3[k1,k2,k3]
– discrete weight functions of the first, second and third orders; x[k], y[k] – input (stimulus) and
output (response) functions of the system being modeled, respectively; k is the time variable.
The block diagram of the Volterra model has the form (Fig. 2).
Figure 2: Block diagram of the Volterra model
The task of identification is to select test effects x[m] and develop an algorithm that allows the
measured reactions y[m] to identify partial components yn[m], (n=1, 2, 3) and determine on their basis
Volterra kernels w1[k1], w2[k1,k2], w3[k1,k2,k3] [18].
3. Eye movement tracking to identify OMS
The information technology of construction of non-parametric dynamic model of human OMS
taking into account its inertial and nonlinear properties on the basis of data of experimental researches
"input-output" is developed. The OMS Volterra model is used in the form of multidimensional
transient functions (MTF) [19, 20].
Methods and tools for the identification of OMS have been developed using technology tracking.
The obtained MTF are used to construct the space of diagnostic signs and to carry out the optimal
classification of neurophysiological states of personality for research in neuroinformatics and
computational neurology. Experimental studies of individuals' OMS were performed using the Tobii
TX300 eye tracker (frame rate 300 Hz) and the corresponding software in the Laboratory of Motion
Analysis and Ergonomics of Interfaces of the Lublin University of Technology (Lublin, Poland) [18].
Taking into account the specifics of the studied OMS, test step signals are used for identification.
If the test signal x[m]=θ[m], where θ[m] is a unit function (Heaviside function), then the partial
components of the response y1[m], y2[m], y3[m] will be equal to the transient function of the first order
h1[m] and diagonal sections of the transient functions of the second and third orders h2[m, m],
h3[ m, m, m] respectively [18]:
m
y1[m] h1[m] w1[m k1 ],
k1 0
m m
y2 [m] h2 [m, m] w2 [m k1, m k2 ], (2)
k1 0 k 2 0
m m m
y3[m] h2 [m, m, m] w3[m k1, m k2 , m k3 ].
k1 0 k 2 0 k 3 0
Determination of subdiagonal intersections of transient functions is based on the NDS test using L
test step signals with given amplitudes ai, i=1,2,…,L (L>=N, N is the degree of the Volterra
polynomial). In this case the responses of the NDS are denoted by y1[m], y2[m], …, yL[m]. Reviews of
the Volterra model will be view
~
y i [m] ai yˆ1[m] ai2 yˆ 2[m] ai3 yˆ 3[m], i 1, L (3)
where yˆ [m] hˆ [m], yˆ [m] hˆ [m, m], yˆ [m] hˆ [m, m, m] – obtained estimates of the partial components
1 1 2 2 3 3
of the model – MTF.
To determine the transient functions h1[m], h2 [m, m], h3[m, m, m] is used the method of least
squares (LSM), which provides the minimum standard error of the deviation of the model responses
from the responses of the OMS to the same stimulus:
2
L N
J N y j [m] a nj yˆ n [m] min (4)
j 1 n 1
The minimization of criterion (4) is reduced to solving a system of normal Gaussian equations,
which in vector-matrix form can be written as
A Aŷ A y , (5)
where
a1 a12 a1N y1[m] yˆ1[m]
2 N y [ m] ˆ
A 2
a a2 a2
, y 2 , ŷ y2 [m] .
yˆ N [m]
2 N
a L a L a L y L [m]
The system of Gaussian normal equations (5) produces good results on the approximation of
functions if the number of measurements L is large enough (much greater than the degree of the
approximating polynomial N) or the measurement errors are small. Otherwise, the determinant of the
system turns out to be close to zero and the system becomes ill-conditioned. In this case, large errors
in the parameters estimation of the approximating polynomial are possible.
Tikhonov's method of regularization [21], which is based on a variational method for constructing
a regularizing operator, is used to obtain a solution of linear algebraic equations system (5) that is
stable against measurement errors. This method is reduced to finding an approximate solution vector
ŷ that minimizes certain smoothing functional. The only vector satisfying the condition of the
smoothing functional minimum can be determined from the solution of linear algebraic equations
system:
(Α Α αI)ŷ α Α y , (6)
where Α is the transposed matrix; I is the identity matrix; is the Tikhonov regularization
parameter.
When implementing this algorithm, the regularization parameter is chosen sufficiently small
from the analysis of the available information about the error of the initial data and the calculation
error. In the work, the appropriate value of the regularization parameter α is determined by selection,
i.e. repeated calculations ŷ , for different values of . The quasi-optimal value of the parameter
0 is selected from the condition
|| ŷ α i1 ŷ α i || min , (7)
where i 1 i , 0 1, i 0,1,2,.. . It should be noted that different ways of determining the
regularization parameter can give different results and, as a consequence, different regularized
solutions.
4. Computing of transient functions OMS
Information technology of the constructing a nonparametric dynamic model of the human OMS
taking into account its inertial and nonlinear properties based on the data of experimental studies
input-output was developed. As a basic OMS model – the Volterra model is used in the form of
multidimensional transient functions.
Methods and tools for the identification of OMS have been developed using the help of eye
tracking technology, and building a features space and optimal classification human states using
machine learning [22]. In the Laboratory of Motion Analysis and Interface Ergonomics at the Lublin
University of Technology (Lublin, Poland), joint studies of the human OMS were performed to obtain
diagnostic information for solving urgent problems in the neuro informatics and the computational
neuroscience. Experimental research was carried out using eye tracking technology with the use of the
video based Tobii TX300 (300 Hz sampling rate) eye tracker and appropriate software [18].
The following instrumental algorithmic and software tools are developed to achieve the goal of the
research:
1. Formation of test signals in the form of bright dots on the computer monitor screen at
different distances from the initial position horizontally, vertically and diagonally.
2. Preprocessing (bringing the OMS responses to a common start and rationing to one) and
analyzing the data obtained from the eye tracker.
3. Constructing an identification model of OMS in the form of multidimensional transient
functions (integral transformations of Volterra kernels).
4. Visualization of data and processing results of experimental research.
4.1. Experimental research of the OMS
When conducting experimental studies, such actions are carried out:
1. The test subject is placed in front of the computer so that his eyes are at the center of the
monitor at a distance of 40-50 cm from him.
2. The subject’s head is fixed in order to prevent its movements during the study and to ensure
the same experimental conditions.
3. On the subject’s readiness, the Signal Manager of the test visual stimulus program is
launched.
4. A red circle appears in the center (or from its edge) – of the screen in the starting position.
5. After a short pause (2-3 sec.), the circle in the starting position disappears and a circle of a
different color appears at the point with the specified coordinates – a visual stimulus (test signal),
which is displayed in this position for a specified duration (1-2 sec.) – the action makes the eye
move in the direction of the visual stimulus.
6. Then this stimulus circle disappears and a red circle appears in the starting position – this
makes the eye move in the opposite direction to the starting position, after these actions the
experiment ends.
7. Using the eye tracker, the coordinates of the pupil of the eye are determined during its
movement (reaction to the visual stimulus) in the period between the starting positions and the
coordinate values are stored in the xls-file.
In the studies of each respondent, three experiments were successively implemented for three
amplitudes of test signals in the horizontal direction. The distance between the starting position and
the test incentives is equal to: 0.33 lx, 0.66 lx, 1.0 lx, where lx is the length of the monitor screen.
Coordinates of the starting position (x = 0, y = 0.5 ly), ly – mean the width of the monitor screen.
5. Research results
The experiments were organized in order to classify subjects by the state of fatigue. The data for
constructing the model – the OMS responses to the same test signals, were obtained using the Tobii
Pro TX300 eye tracker at different times of the day: "In the Morning" (before work) and "In the
Evening" (after work).
In Fig. 3 and Fig. 4 presents graphs of experimental data at different amplitudes of the test signals
"Morning" and "Evening", received from the eye tracker.
Figure 3: OMS responses at different amplitudes Figure 4: OMS responses at different amplitudes
of test signals "In the Morning " of test signals "In the Evening "
The average values of the OMS responses obtained from the eye tracker at various amplitudes of
the test signals "In the Morning" and "In the Evening" are shown in Fig. 5.
Graphs of transition functions for the states of the respondent "In the Morning" and "In the
Evening" at N = 1 are presented in Fig. 6, at N = 2 - in Fig. 7.
According to averaged data of OMS responses on visual stimuli with a different distance from the
start position on the basis of formula (5) the functions of the OMS were defined when approximation
models of degrees N = 3 were used. Graphs of the transient functions estimates for the "In the
Morning" and "In the Evening" states of the subject based on model (1) are shown in Fig. 8.
Figure 5: averaged OMS responses at various Figure 6: the transient functions estimates of
amplitudes of test signals "In the Morning" and the 1st order (N = 1) for states of the test
"In the Evening" subject "In the Morning" and "In the Evening"
Figure 7: the transient functions estimates of the Figure 8: the transient functions estimates of the
1st and 2nd orders (N =2) for states of the test 1st, 2nd, and 3rd orders (N = 3) for states of the
subject "In the Morning" and "In the Evening" test subject "In the Morning" and "In the
Evening"
Received responses with the help of calculations on models at N = 1, N = 2 and N = 3 from various
amplitudes of test signals "In the Morning". Graphs these are presented in comparison with similar
responses OMS in figures 9-11. Graphs of responses of the model OMS at N = 3 at various
amplitudes of the test signals "In the Morning" and “In the Evening” are illustrated in Fig. 12.
Figure 9: the responses of the OMS and the Figure 10: the responses of the OMS and the
model at N = 1 at various amplitudes of the test model at N = 2 at various amplitudes of the test
signals "In the Morning" signals "In the Morning"
Figure 11: the responses of the OMS and the Figure 12: the responses of the model at N = 3 at
model at N = 3 at various amplitudes of the test various amplitudes of the test signals "In the
signals "In the Morning" Morning" and "In the Evening"
5.1. Deviation of the transient functions
The variability (deviation) of the MTF of different orders n of the approximation model of OMS
for the states of the respondent "In the Morning" and "In the Evening" is quantified using the indicator
of εnN – normalized standard deviation (8). The indicators deviation of the MTF of different orders n
of the OMS approximation model for respondent states "In the Morning" and "In the Evening" are
given in Table 1 and are represented by diagram in Fig. 13.
1/ 2
M
yˆ ne [m] yˆ nm [m] 2
ε nN m 0 M , n 1, N . (8)
nm ( ˆ
y [ m ]) 2
m 0
Figure 13: the diagram of deviations indicators εnN
Table 1
The deviation indicators of multidimensional transient functions
N ε1N ε2N ε3N
1 0.019 – –
2 0.051 0.232 –
3 0.04 0.199 0.322
As can be seen from Fig. 13, the obtained transient function of the 1st order for the "In the
Morning" and "In the Evening" are virtually independent of the status of the subject. However, the
diagonal cross section of the transient functions of the second and third order change significantly in
magnitude and, therefore, can be effectively used as the primary data source when building models of
classifiers of psychophysiological conditions of the person using machine learning.
5.2. Building a classifier of the fatigue
To assess the psycho-physiological state of a person based on the OMS model, studies were
carried out:
1. Getting a feature space for building a human state classifier using machine learning.
2. Building classifiers using deterministic and statistical learning methods for pattern
recognition based on the data obtained using eye tracking technology.
The discriminant function d(x) is sequentially calculated on the basis of training datasets for object
classes A ("In the Morning"), B ("In the Evening").
Gaussian classifier is built for separate the two classes (dichotomy case) a discriminant function of
the form is used:
1 1 |S |
d (x) x (S 21 S11 ) x (S11m1 S 21m 2 )x (m1 S11m1 m2 S 21m 2 ln 2 ) λ max (9)
2 2 | S1 |
where x=(x1,x2,…,xn)' – features vector, n – features space dimensionality, mi – mathematical
expectation vector for a features of class i, i=1, 2; Si=M[(x-mi)(x-mi)'] – covariance matrix for class i
(M[] – mathematical expectation operation). Si1 – matrix inverse to Si, |Si| – matrix determinant Si,
max – classification threshold providing the highest criterion probability of correct recognition
training sample objects.
The informativeness of various features was investigated, such as integral of the transient
functions (Table 2), the argument and value at maximum derivative of the transient functions (Table
3), the argument and value at minimum derivative of the transient functions (Table 4), the argument
and value at the maximum transient response (Table 5). The analysis of the quality of various features
combination is carried out on the basis of the criterion probability of correct recognition (PCR, P).
The quality of the combination of the selected features from the considered set of features is assessed
based on the classification results on the studied data sample.
Table 2
Investigated heuristic features – integral of the transient functions
# Features Formal definition
M
1 x1 x1 h1 (m)
m 0
M
2 x2 x 2 h2 (m, m)
m0
M
3 x3 x 3 h3 (m, m, m)
m0
Table 3
Investigated heuristic features – the argument and value at maximum derivative of the transient
functions
# Features Formal definition
1 x4 x 4 max h1' (m)
m [ 0, M ]
2 x5 x5 arg max h1' (m)
m [ 0, M ]
3 x6 x6 max h2' (m, m)
m [ 0, M ]
4 x7 x7 arg max h2' (m, m)
m [ 0, M ]
5 x8 x8 max h (m, m, m)
3
'
m [ 0, M ]
6 x9 x9 arg max h3' (m, m, m)
m [ 0, M ]
Table 4
Investigated heuristic features – the argument and value at minimum derivative of the transient
functions
# Features Formal definition
1 x10 x10 min h1' (m)
m [ 0, M ]
2 x11 x11 arg min h (m) 1
'
m [ 0, M ]
3 x12 x12 min h2' (m, m)
m [ 0, M ]
4 x13 x13 arg min h2' (m, m)
m [ 0, M ]
5 x14 x14 min h (m, m, m)
'
3
m [ 0, M ]
6 x15 x15 arg min h3' (m, m, m)
m [ 0, M ]
Table 5
Investigated heuristic features – the argument and value at the maximum transient response
# Features Formal definition
1 x16 x16 max h1 (m)
m [ 0, M ]
2 x17 x17 arg max h1 (m)
m [ 0, M ]
3 x18 x18 max h2 (m, m)
m [ 0, M ]
4 x19 x19 arg max h2 (m, m)
m [ 0, M ]
5 x20 x20 max h3 (m, m, m)
m [ 0, M ]
6 x21 x21 arg max h3 (m, m, m)
mm [ 0 , M ]
Gaussian classifier of a person’s fatigue state in a two-dimensional feature space is provided with
the maximum recognition reliability (P = 0.9375) with combinations of the following features:
M
x3 h3 (m, m, m) & x12 min h2' (m, m) , (10)
m 0 m [ 0, M ]
or
M
x3 h3 (m, m, m) & x14 min h3' (m, m, m) , (11)
m 0 m [ 0, M ]
or
x8 max h3' (m, m, m) & x6 max h2' (m, m) , (12)
m [ 0, M ] m [ 0, M ]
or
x9 arg max h3' (m, m, m) & x6 max h2' (m, m) , (13)
m [ 0, M ] m [ 0, M ]
or
x13 arg min h2' (m, m) & x6 max h2' (m, m) , (14)
m [ 0, M ] m [ 0, M ]
or
x14 min h3' (m, m, m) & x12 min h2' (m, m) . (15)
m [ 0, M ] m [ 0, M ]
Separately, the PCR features: x9 or x13 – P = 0,625; x3 or x8 – P = 0,6875; x12 – P = 0,75; x6 or x14 –
P = 0,8125.
6. Conclusion
Instrumental algorithmic and software tools for building a nonparametric dynamic model of the
human oculomotor system taking into account its inertial and nonlinear properties based on the data
of experimental studies "input-output" using technology tracking are developed. The Volterra model
is used in the form of multidimensional transition functions.
The following tasks are solved:
1. The application of the OMS identification method based on the Volterra model in the form of
multidimensional transition functions using test visual stimuli with different distances from the
starting position - step functions of different amplitude is substantiated.
2. The information technology of obtaining experimental data for the identification of OMS with
the help of test visual stimuli and the use of eye tracking to track the corresponding eye movements
has been developed.
3. Developed in the Matlab system software for the identification of OMS based on Volterra
polynomials in the form of multidimensional transient functions according to eye tracking.
4. Experimental studies of OMS were performed with the help of eye tracking technology and the
transitional functions of the first, second and third orders were determined on the basis of
oculographic studies. Studies of local self-government with the help of the obtained transient
functions by means of computer modeling confirm the adequacy of the constructed approximation
model to the real system.
5. Classifiers of human cognitive states are built on the basis of the studied heuristic features that
are resistant to computational errors. The features were calculated on multidimensional transient
functions obtained from the integral Volterra models of human OMS within a new approach to
diagnosing human conditions.
The analysis of variability of transient functions corresponding to different psychophysiological
states of the individual (states of fatigue) is carried out. It is established that the diagonal intersections
of the transient functions of the second and third order with respect to the transient functions of the
first order for fatigue states change significantly in magnitude. Thus, they can be used as a data source
in the formation of spaces of diagnostic features for the construction of classifiers of human
psychophysiological states.
7. References
[1] Y. Wamain, X. Corveleyn, L. Ott, Y. Coello, “Does the motor system contribute to the
perception of changes in objects visual attributes? The neural dynamics of sensory binding by
action,” Neuropsychologia, 132, 2019. 107121.doi.org/10.1016/j.neuropsychologia.2019.107121
[2] M. Daoudi, M. Coello, P. Desrosiers, L. Ott, “A New Computational Approach to Identify
Human Social Intention in Action,” In the 13th IEEE International Conference on Automatic
Face & Gesture Recognition, FG 2018, Xi'an, China on May 15-19. (2018).
[3] F. Quesque, A. Mignon, Y. Coello, “Cooperative and competitive contexts do not modify the
effect of social intention on motor action. Consciousness and Cognition. doi: 10.1016/j.concog,”
2017, 06.011.
[4] L. Lanata, Sebastian, F. Di Gruttola, S. Di Modica, E.P. Scilingo and A. Greco1 “Nonlinear
Analysis of Eye-Tracking Information for Motor Imagery Assessments. Frontiers in
Neuroscience”, 2020, 13:1431 DOI: 10.3389/fnins.2019.01431.
[5] N. Gueugneau, L.Crognier, and C. Papaxanthis, “The influence of eye movements on the
temporal features of executed and imagined arm movements,” Brain Research, 1187, 2008, pp.
95–102.
[6] A. Guillot, C. Collet, “Duration of mentally simulated movement: A review,” Journal of Motor
Behaviour, 2005, 37, pp.10-20.
[7] A. Guillot, C. Collet, “Construction of the motor imagery integrative model in sport: A review
and theoretical investigation of motor imagery use,” International Review of Sport and Exercise
Psychology, 1, 2008, pp. 32–44.
[8] A. Guillot, C. Collet, V. A. Nguyen, F. Malouin, C.Richards, and J.Doyon, “Functional
neuroanatomical networks associated with expertise in motor imagery ability,” Neuroimage, 41,
2008, pp. 1471–1483.
[9] A. Guillot, M. Louis, and C. Collet, “Neurophysiological substrates of motor imagery ability,” In
A. Guillot and C. Collet (Eds). The neurophysiological foundations of mental and motor
imagery, 2010, pp. 109–124, Oxford University Press.
[10] M. El Haj, Y. Coello, D. Kapogiannis, K. Gallouj, P. Antoine, “Negative prospective memory in
Alzheimer’s Disease: do not perform that action”, Journal of Alzheimer's Disease, 2018, 61(2),
pp. 663-672, doi: 10.3233/JAD-170807.
[11] X. Corveleyn, J. Blampain, L. Ott, I. Lavenu, C. Delayen, A. Di Pastena, Y. Coello, “Body-
centred and object-centred motor imagery in Alzheimer disease”, 2018, Current Alzheimer
Research, 15 (3), doe: 10.2174/156720 504666171030105720.
[12] D Jansson, A. Medvedev, H. Axelson and D. Nyholm “Stochastic anomaly detection in eye
tracking data for quantification of motor symptoms in Parkinson's disease”, Advances in
Experimental Medicine and Biology, 2015, 823 pp. 63-82.
[13] D. Jansson, O. Rosén and A. Medvedev, “Parametric and nonparametric analysis of eye-tracking
data by anomaly detection,” IEEE Transaction control system technology, 23, 2015, pp. 1578-
1586.
[14] V. Bro and A. Medvedev “Nonlinear dynamics of the human smooth pursuit system in health
and disease: model structure and parameter estimation”, IEEE 56th Annual Conference on
Decision and Control, (Melbourne) 4692-4697, 2017.
[15] F. J. Doyle, R. K. Pearson, and B.A. Ogunnaike “Identification and control using Volterra
models,” Germany: Springer Publ, 2002, 314 p.
[16] V. Pavlenko, S. Pavlenko and V. Speranskyy “Identification of Systems using Volterra Model in
Time and Frequency Domain,” In book V. Haasz and K. Madani (Eds.). Advanced Data
Acquisition and Intelligent Data Processing, River Publishers, 2014, pp. 233-270.
[17] V. Pavlenko and S. Pavlenko “Deterministic identification methods for nonlinear dynamical
systems based on the Volterra model,” Applied Aspects оf Information Technology, 2018, No
01(01), pp. 9-29.
[18] V.D. Pavlenko, M. Milosz and M. Dzienkowski, “Identification of the oculo-motor system based
on the Volterra model using eye tracking technology,” 4th Int. Conf. on Applied Physics,
Simulation and Computing (APSAC 2020) 23-25 May 2020, Rome, Italy, Journal of Physics:
Conference Series, Volume 1603, 2020 , IOP Publishing, 2020, pp. 1-8, doi:10.1088/1742-
6596/1603/1/012011.
[19] V. Pavlenko, D. Salata, M. Dombrovskyi and Y. Maksymenko, “Estimation of the
multidimensional transient functions oculo-motor system of human,” Mathematical Methods and
Computational Techniques in Science and Engineering: AIP Conf. Proc. MMCTSE, UK,
Cambridge, 2017, Vol. 1872, Melville, New York, 2017, pp. 110-117.
[20] V. Pavlenko, I. Ivanov, and E. Kravchenko, “Estimation of the multidimensional dynamical
characteristic eye-motor system,” Proceedings of the 9th IEEE International Conference on
Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications,
(Bucharest), 2, 2017, pp. 645-650.
[21] A. Tikhonov, A. Goncharsky, V. Stepanov, and A. Yagola, “Numerical Methods for the Solution
of Ill-Posed Problems,” Netherlands: Springer Netherlands. Retrieved 9 August 2018. ISBN
079233583X
[22] V. Vapnik, “The Nature of Statistical Learning Theory.” Springer-Verlag New York Inc., 2010.