In this work, we investigate the multifractal properties of eye movement dynamics of children with infantile nystagmus, particularly the fluctuations of its velocity. The eye movements of three children and one adult with infantile nystagmus were evaluated in a simple task in comparison with 28 children with no ocular pathologies. Four indices emerge from the analysis: the classical Hurst exponent, the singularity strength corresponding to the maximum of the singularity spectrum, the asymmetry of the singularity spectrum, and the multifractal strength, each of which characterizes a particular aspect of eye movement dynamics. Our findings indicate that, when compared to children with no ocular pathologies, patients with infantile nystagmus present lower values of all indices. Except for the multifractal strength, the difference in the remaining indices is statistically significant. To test whether the characterization of patients with infantile nystagmus in terms of multifractality indices allows them to be distinguished from children without ocular pathologies, we performed an unsupervised clustering analysis and classified the subjects using supervised clustering techniques. The results indicate that these indices do, indeed, distinctively characterize the eye movements of patients with infantile nystagmus.

1.
A.
Duchowski
, “
A breadth-first survey of eye-tracking applications
,”
Behav. Res. Methods Instrum. Comput.
34
(
4
),
455
470
(
2002
).
2.
M.
Horsley
,
M.
Eliot
,
B. A.
Knight
, and
R.
Reilly
,
Current Trends in Eye Tracking Research
(
Springer
,
Cham
,
2014
).
3.
J.
Otero-Millan
,
X. G.
Troncoso
,
S. L.
Macknik
,
I.
Serrano-Pedraza
, and
S.
Martinez-Conde
, “
Saccades and microsaccades during visual fixation, exploration, and search: Foundations for a common saccadic generator
,”
J. Vision
8
(
14
),
21
(
2008
).
4.
M. D.
Crutcher
,
R.
Calhoun-Haney
,
C. M.
Manzanares
,
J. J.
Lah
,
A. I.
Levey
, and
S. M.
Zola
, “
Eye tracking during a visual paired comparison task as a predictor of early dementia
,”
Am. J. Alzheimer’s Dis. Other Dementias
24
(
3
),
258
266
(
2009
).
5.
B.
Poletti
,
L.
Carelli
,
F.
Solca
,
A.
Lafronza
,
E.
Pedroni
,
A.
Faini
,
S.
Zago
,
N.
Ticozzi
,
A.
Ciammola
,
C.
Morelli
,
P.
Meriggi
,
P.
Cipresso
,
D.
Lulé
,
A. C.
Ludolph
,
G.
Riva
, and
V.
Silani
, “
An eye-tracking controlled neuropsychological battery for cognitive assessment in neurological diseases
,”
Neurol. Sci.
38
(
4
),
595
603
(
2017
).
6.
A. C. A.
Silva
and
C. A.
Varanda
, “
Eye-tracking technique as an instrument in the diagnosis of autism spectrum disorder
,”
Austin J. Autism Relat. Disab.
3
(
3
),
1047
(
2017
), see https://austinpublishinggroup.com/autism/fulltext/autism-v3-id1047.pdf.
7.
E.
Papageorgiou
,
R. J.
McLean
, and
I.
Gottlob
, “
Nystagmus in childhood
,”
Pediatr. Neonatol.
55
(
5
),
341
351
(
2014
).
8.
B. J.
West
, “
Fractal physiology and the fractional calculus: A perspective
,”
Front. Physiol.
1
,
12
(
2010
).
9.
D. J.
Aks
,
G. J.
Zelinsky
, and
J. C.
Sprott
, “
Memory across eye-movements: 1/f dynamics in vision search
,”
Nonlinear Dyn. Psychol. Life Sci.
6
,
1
25
(
2002
).
10.
C.
Stan
,
C.
Astefanoaei
,
E.
Pretegiani
,
L.
Optican
,
D.
Creanga
,
A.
Rufa
, and
C. P.
Cristescu
, “
Nonlinear analysis of saccade speed fluctuations during combined action and perception tasks
,”
J. Neurosci. Methods
232
,
102
109
(
2014
).
11.
E.
Bakalis
,
H.
Fujie
,
F.
Zerbetto
, and
Y.
Tanaka
, “
Multifractal structure of microscopic eye–head coordination
,”
Physica A
512
,
945
953
(
2018
).
12.
M.
Sharifi
,
H.
Farahani
,
F.
Shahbazi
,
M.
Sharifi
,
C. T.
Kello
, and
M.
Zare
, “
Multifractality and non-Gaussianity of eye fixation duration time series in reading Persian texts
,”
Physica A
514
,
549
562
(
2019
).
13.
D. G.
Stephen
and
D.
Mirman
, “
Interactions dominate the dynamics of visual cognition
,”
Cognition
115
,
154
165
(
2010
).
14.
D.
Mirman
,
J. R.
Irwin
, and
D. G.
Stephen
, “
Eye movement dynamics and cognitive self-organization in typical and atypical development
,”
Cognit. Neurodyn.
6
(
1
),
61
73
(
2012
).
15.
M. L.
Freije
,
A. A.
Jiménez Gandica
,
J. I.
Specht
,
G.
Gasaneo
,
C. A.
Delrieux
,
B.
Stosic
,
T.
Stosic
, and
R.
de Luis-Garcia
, “Multifractal detrended fluctuation analysis of eye-tracking data,” in VipIMAGE 2017. ECCOMAS 2017, Lecture Notes in Computational Vision and Biomechanics, edited by J. Tavares and R. N. Jorge (International Publishing AG, 2017), pp. 476–484.
16.
K.
Harezlak
and
P.
Kasprowski
, “
Understanding eye movement signal characteristics based on their dynamical and fractal features
,”
Sensors
19
(
3
),
626
(
2019
).
17.
F.
Avila
,
C.
Delrieux
, and
G.
Gasaneo
, “
Complexity analysis of eye-tracking trajectories
,”
Eur. Phys. J. B
92
(
273
),
273
(
2019
).
18.
F. R.
Iaconis
,
A. A.
Jiménez Gandica
,
J. A.
Del Punta
,
C. A.
Delrieux
, and
G.
Gasaneo
, “
Information-theoretic characterization of eye-tracking signals with relation to cognitive tasks
,”
Chaos
31
(
3
),
033107
(
2021
).
19.
M. M.
Meo
,
F. R.
Iaconis
,
J. A.
Del Punta
,
C. A.
Delrieux
, and
G.
Gasaneo
, “
Multifractal information on reading eye tracking data
,”
Physica A
638
,
129625
(
2024
).
20.
J.
Gómez-Gómez
,
R.
Carmona-Cabezas
,
A. B.
Ariza-Villaverde
,
E. Gutiérrez
de Ravé
, and
F. J.
Jiménez-Hornero
, “
Multifractal detrended fluctuation analysis of temperature in Spain (1960–2019)
,”
Physica A
578
,
126118
(
2021
).
21.
J. L.
Morales Martínez
,
I.
Segovia-Domínguez
,
I.
Quiros Rodríguez
,
F. A.
Horta-Rangel
, and
G.
Sosa-Gómez
, “
A modified multifractal detrended fluctuation analysis (MFDFA) approach for multifractal analysis of precipitation
,”
Physica A
565
,
125611
(
2021
).
22.
X.
Zhang
,
M.
Zeng
, and
Q.
Meng
, “
Multivariate multifractal detrended fluctuation analysis of 3D wind field signals
,”
Physica A
490
,
513
523
(
2018
).
23.
Y.
Wang
,
L.
Liu
, and
R.
Gu
, “
Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis
,”
Int. Rev. Financ. Anal.
18
(
5
),
271
276
(
2009
).
24.
G.
Lim
,
S. Y.
Kim
,
H.
Lee
,
K.
Kim
, and
D.
Lee
, “
Multifractal detrended fluctuation analysis of derivative and spot markets
,”
Physica A
386
(
1
),
259
266
(
2007
).
25.
A. K.
Tiwari
,
C. T.
Albulescu
, and
S.
Yoon
, “
A multifractal detrended fluctuation analysis of financial market efficiency: Comparison using Dow Jones sector ETF indices
,”
Physica A
483
,
182
192
(
2017
).
26.
A. K.
Maity
,
R.
Pratihar
,
A.
Mitra
,
S.
Dey
,
V.
Agrawal
,
S.
Sanyal
,
A.
Banerjee
,
R.
Sengupta
, and
D.
Ghosh
, “
Multifractal detrended fluctuation analysis of alpha and theta EEG rhythms with musical stimuli
,”
Chaos, Soliton. Fract.
81
(Part A),
52
67
(
2015
).
27.
L. F.
Dell’Osso
and
J. B.
Jacobs
, “
An expanded nystagmus acuity function: Intra- and intersubject prediction of best-corrected visual acuity
,”
Doc. Ophthalmol.
104
(
3
),
249
276
(
2002
).
28.
D.
Giordano
,
C.
Pino
,
C.
Spampinato
,
M.
Di Pietro
, and
A.
Reibaldi
, “Eye tracker based method for quantitative analysis of pathological nystagmus,” in
2011 24th International Symposium on Computer-Based Medical Systems (CBMS)
, Bristol, UK, 1–6 2011.
29.
J.
Felius
,
V. L. N.
Fu
,
E. E.
Birch
,
R. W.
Hertle
,
R. M.
Jost
, and
V.
Subramanian
, “
Quantifying nystagmus in infants and young children: Relation between foveation and visual acuity deficit
,”
Invest. Ophthalmol. Vis. Sci.
52
(
12
),
8724
8731
(
2011
).
30.
W.
Rosengren
,
M.
Nyström
,
B.
Hammar
,
M.
Rahne
,
L.
Sjödahl
, and
M.
Stridh
, “
Modeling and quality assessment of nystagmus eye movements recorded using an eye-tracker
,”
Behav. Res. Methods
52
(
4
),
1729
1743
(
2020
).
31.
M.
Meo
,
J. A.
Del Punta
,
I.
Sánchez Pavón
,
G.
Gasaneo
,
R.
Martín Herranz
, and
R.
de Luis-Garcia
, “
A dynamical method to objectively assess infantile nystagmus based on eye tracking—A pilot study
,”
J. Optom.
16
(
3
),
221
228
(
2023
).
32.
Y.
Elgammal
,
M.
Zahran
, and
M.
Mohamed Abdelsalam
, “
A new strategy for the early detection of Alzheimer disease stages using multifractal geometry analysis based on K-nearest neighbor algorithm
,”
Sci. Rep.
12
,
22381
(
2022
).
33.
J.
Lim
,
J.
Mountstephens
, and
J.
Teo
, “
Eye-tracking feature extraction for biometric machine learning
,”
Front. Neurorob.
15
,
796895
(
2022
).
34.
S.
Woo
and
H. E.
Bedell
, “
Beating the beat: Reading can be faster than the frequency of eye movements in persons with congenital nystagmus
,”
Optom. Vis. Sci.
83
(
8
),
E559
E571
(
2006
).
35.
M. G.
Thomas
,
I.
Gottlob
,
R. J.
McLean
,
G.
Maconachie
,
A.
Kumar
, and
F. A.
Proudlock
, “
Reading strategies in infantile nystagmus syndrome
,”
Invest. Ophthalmol. Vis. Sci.
52
(
11
),
8156
8165
(
2011
).
36.
J.
Feder
,
Fractals
(
Plenum Press
,
New York
,
1988
).
37.
J. W.
Kantelhardt
,
S. A.
Zschiegner
,
E.
Koscielny-Bunde
,
S.
Havlin
,
A.
Bunde
, and
H.
Stanley
, “
Multifractal detrended fluctuation analysis of nonstationary time series
,”
Physica A
316
(
1-4
),
87
114
(
2002
).
38.
E. A. F.
Ihlen
, “
Introduction to multifractal detrended fluctuation analysis in Matlab
,”
Front. Physiol.
3
(
141
),
1
18
(
2012
).
39.
Y.
Shimizu
,
S.
Thurner
, and
K.
Ehrenberger
, “
Multifractal spectra as a measure of complexity in human posture
,”
Fractals
10
(
1
),
103
116
(
2002
).
40.
I.
Vajs
,
G.
Kvascev
,
T.
Papic
, and
M.
Janković
, “
Eye-tracking image encoding: Autoencoders for the crossing of language boundaries in developmental dyslexia detection
,”
IEEE Access
11
,
3024
3033
(
2023
).
41.
D.
Belete
and
M.
Huchaiah
, “
Grid search in hyperparameter optimization of machine learning models for prediction of HIV/AIDS test results
,”
Int. J. Comput. Appl.
44
(9),
875
886
(
2022
).
42.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
, “
Scikit-learn: Machine learning in Python
,”
J. Mach. Learn. Res.
12
,
2825
2830
(
2011
), see https://www.jmlr.org/papers/volume12/pedregosa11a/pedregosa11a.pdf.
You do not currently have access to this content.