# Identifying Autism Gaze Patterns in Five-Second Data Records

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Benchmark1: Standard Eye-Tracking Metrics

- The average of the log-velocity ${\mu}_{F}$ over the ${N}_{F}$ data points that are labeled as fixations:$${\mu}_{F}=\frac{{\sum}_{1}^{{N}_{F}}log\left(v\left(t\right)\right)}{{N}_{F}}\phantom{\rule{0.166667em}{0ex}}.$$
- The standard deviation of the log-velocity ${\sigma}_{F}$ over the ${N}_{F}$ data points that are labeled as fixations:$${\sigma}_{F}=\frac{\sqrt{{\sum}_{1}^{{N}_{F}}{(log\left(v\left(t\right)\right)-{\mu}_{F})}^{2}}}{{N}_{F}}\phantom{\rule{0.166667em}{0ex}}.$$
- The average of the log-velocity ${\mu}_{S}$ over the ${N}_{S}$ data points that are labeled as fixations:$${\mu}_{S}=\frac{{\sum}_{1}^{{N}_{S}}log\left(v\left(t\right)\right)}{{N}_{S}}\phantom{\rule{0.166667em}{0ex}}.$$
- The standard deviation of the log-velocity ${\sigma}_{S}$ over the ${N}_{S}$ data points that are labeled as saccades:$${\sigma}_{S}=\frac{\sqrt{{\sum}_{1}^{{N}_{S}}log\left(v\left(t\right)\right)-{\mu}_{S}{)}^{2}}}{{N}_{S}}\phantom{\rule{0.166667em}{0ex}}.$$
- The probability ${P}_{FS}$ of the saccade-labeled point following a fixation labeled one:
- The probability of a fixation-labeled point following a saccade-labeled one: ${P}_{SF}$.

**Table 1.**Mean of each parameter plotted in Figure 3 for both ASD and TD groups alongside the p-value of the Student’s t test. From this table, it is clear that ${\mu}_{F}$, ${\sigma}_{S}$, ${P}_{FS}$ and $\mathsf{\Lambda}$ are statistically significant at $95\%$ confidence level. It is unclear if ${\mu}_{S}$ is different between groups, and no difference was found in ${\sigma}_{S}$ and ${P}_{SF}$.

Param. | Mean TD | Mean ASD | t Test |
---|---|---|---|

${\mathbf{\mu}}_{\mathbf{F}}$ | $1.04$ | $1.20$ | $4.3\times {10}^{-3}$ |

${\sigma}_{F}$ | $4.37\times {10}^{-1}$ | $4.29\times {10}^{-1}$ | $3.1\times {10}^{-1}$ |

${\mu}_{S}$ | $2.13$ | $2.16$ | $3.2\times {10}^{-2}$ |

${\mathbf{\sigma}}_{\mathbf{S}}$ | $7.08\times {10}^{-1}$ | $6.21\times {10}^{-1}$ | $1.2\times {10}^{-4}$ |

${\mathbf{P}}_{\mathbf{FS}}$ | $5.02\times {10}^{-2}$ | $6.17\times {10}^{-2}$ | $2.2\times {10}^{-2}$ |

${P}_{SF}$ | $3.58\times {10}^{-1}$ | $3.25\times {10}^{-1}$ | $2.7\times {10}^{-1}$ |

$\mathsf{\Lambda}$ | $32.8$ | $36.2$ | $9.4\times {10}^{-12}$ |

#### 2.2. Benchmark2: AI Classification Algorithm

#### 2.3. A New 5 s Exploratory Metric

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ASD | Autism Spectrum Disorder |

TD | Typically developed |

## References

- Center of Diseases Control and Prevention. Open Source Database. Available online: https://www.cdc.gov/autism/publications/adults-living-with-autism-spectrum-disorder.html?CDC_AAref_Val=https://www.cdc.gov/ncbddd/autism/features/adults-living-with-autism-spectrum-disorder.html (accessed on 10 May 2023).
- Braukmann, R.; Ward, E.; Hessels, R.S.; Bekkering, H.; Buitelaar, J.K.; Hunnius, S. Action prediction in 10-month-old infants at high and low familial risk for Autism Spectrum Disorder. Res. Autism Spectr. Disord.
**2018**, 49, 34–46. [Google Scholar] [CrossRef] - Vacas, J.; Antolí, A.; Sánchez-Raya, A.; Pérez-Dueñas, C.; Cuadrado, F. Social attention and autism in early childhood: Evidence on behavioral markers based on visual scanning of emotional faces with eye-tracking methodology. Res. Autism Spectr. Disord.
**2022**, 93, 101930. [Google Scholar] [CrossRef] - Cuve, H.C.; Gao, Y.; Fuse, A. Is it avoidance or hypoarousal? A systematic review of emotion recognition, eye-tracking, and psychophysiological studies in young adults with autism spectrum conditions. Res. Autism Spectr. Disord.
**2018**, 55, 1–13. [Google Scholar] [CrossRef] - Wan, G.; Kong, X.; Sun, B.; Yu, S.; Tu, Y.; Park, J.; Lang, C.; Koh, M.; Wei, Z.; Feng, Z.; et al. Applying eye tracking to identify autism spectrum disorder in children. J. Autism Dev. Disord.
**2019**, 49, 209–215. [Google Scholar] [CrossRef] [PubMed] - Schmitt, L.M.; Cook, E.H.; Sweeney, J.A.; Mosconi, M.W. Saccadic eye movement abnormalities in autism spectrum disorder indicate dysfunctions in cerebellum and brainstem. Mol. Autism
**2014**, 5, 47. [Google Scholar] [CrossRef] [PubMed] - Kovarski, K.; Siwiaszczyk, M.; Malvy, J.; Batty, M.; Latinus, M. Faster eye movements in children with autism spectrum disorder. Autism Res.
**2019**, 12, 212–224. [Google Scholar] [CrossRef] [PubMed] - Takarae, Y.; Minshew, N.J.; Luna, B.; Krisky, C.M.; Sweeney, J.A. Pursuit eye movement deficits in autism. Brain
**2004**, 127, 2584–2594. [Google Scholar] [CrossRef] [PubMed] - Yaneva, V.; Eraslan, S.; Yesilada, Y.; Mitkov, R. Detecting high-functioning autism in adults using eye tracking and machine learning. IEEE Trans. Neural Syst. Rehabil. Eng.
**2020**, 28, 1254–1261. [Google Scholar] [CrossRef] [PubMed] - Yaneva, V.; Ha, L.A.; Eraslan, S.; Yesilada, Y.; Mitkov, R. Detecting autism based on eye-tracking data from web searching tasks. In Proceedings of the 15th International Web for All Conference, Lyon, France, 23–25 April 2018; pp. 1–10. [Google Scholar]
- Jeyarani, R.A.; Senthilkumar, R. Eye Tracking Biomarkers for Autism Spectrum Disorder Detection using Machine Learning and Deep Learning Techniques. Res. Autism Spectr. Disord.
**2023**, 108, 102228. [Google Scholar] [CrossRef] - Carette, R.; Elbattah, M.; Cilia, F.; Dequen, G.; Guerin, J.L.; Bosche, J. Learning to Predict Autism Spectrum Disorder based on the Visual Patterns of Eye-tracking Scanpaths. In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies BIOSTEC, Prague, Czech Republic, 22–24 February 2019; pp. 103–112. [Google Scholar]
- Kollias, K.F.; Syriopoulou-Delli, C.K.; Sarigiannidis, P.; Fragulis, G.F. The Contribution of Machine Learning and Eye-Tracking Technology in Autism Spectrum Disorder Research: A Systematic Review. Electronics
**2021**, 10, 2982. [Google Scholar] [CrossRef] - Çetintaş, D.; Tuncer, T.; Çınar, A. Detection of autism spectrum disorder from changing of pupil diameter using multi-modal feature fusion based hybrid CNN model. J. Ambient. Intell. Humaniz. Comput.
**2023**, 14, 11273–11284. [Google Scholar] [CrossRef] - Cilia, F.; Carette, R.; Elbattah, M.; Guérin, J.L.; Dequen, G. Eye-Tracking Dataset to Support the Research on Autism Spectrum Disorder. In Proceedings of the 1st Workshop on Scarce Data in Artificial Intelligence for Healthcare, Vienna, Austria, 25 July 2022. [Google Scholar]
- Schopler, E. L’échelle D’évaluation de L’autisme Infantile (CARS); Université de Mons-Hainaut: Mons, Belgium, 1989. [Google Scholar]
- Guidetti, M.; Tourrette, C. Evaluation de la Communication Sociale Précoce; EAP: Paris, France, 1993. [Google Scholar]
- Lencastre, P.; Raischel, F.; Rogers, T.; Lind, P. From empirical data to time-inhomogeneous continuous Markov processes. Phys. Rev. E
**2016**, 93, 032135. [Google Scholar] [CrossRef] [PubMed] - Komogortsev, O.V.; Gobert, D.V.; Jayarathna, S.; Gowda, S.M. Standardization of automated analyses of oculomotor fixation and saccadic behaviors. IEEE Trans. Biomed. Eng.
**2010**, 57, 2635–2645. [Google Scholar] [CrossRef] [PubMed] - Birawo, B.; Kasprowski, P. Review and evaluation of eye movement event detection algorithms. Sensors
**2022**, 22, 8810. [Google Scholar] [CrossRef] - Ismail Fawaz, H.; Lucas, B.; Forestier, G.; Pelletier, C.; Schmidt, D.F.; Weber, J.; Webb, G.I.; Idoumghar, L.; Muller, P.A.; Petitjean, F. Inceptiontime: Finding alexnet for time series classification. Data Min. Knowl. Discov.
**2020**, 34, 1936–1962. [Google Scholar] [CrossRef] - Oguiza, I. Tsai—A State-of-the-Art Deep Learning Library for Time Series and Sequential Data; Github: San Francisco, CA, USA, 2023. [Google Scholar]
- Pesarin, F.; Salmaso, L. Permutation Tests for Complex Data: Theory, Applications and Software; John Wiley & Sons: Hoboken, NJ, USA, 2010. [Google Scholar]
- Zhang, Z. Improved adam optimizer for deep neural networks. In Proceedings of the 2018 IEEE/ACM 26th International Symposium on Quality of Service (IWQoS), Banff, AB, Canada, 4–6 June 2018; IEEE: Piscataway, NJ, USA, 2018; pp. 1–2. [Google Scholar]
- Riby, D.M.; Doherty, M.J. Tracking eye movements proves informative for the study of gaze direction detection in autism. Res. Autism Spectr. Disord.
**2009**, 3, 723–733. [Google Scholar] [CrossRef] - Wass, S.V.; Jones, E.J.; Gliga, T.; Smith, T.J.; Charman, T.; Johnson, M.H.; BASIS Team. Shorter spontaneous fixation durations in infants with later emerging autism. Sci. Rep.
**2015**, 5, 8284. [Google Scholar] [CrossRef] - Bast, N.; Mason, L.; Freitag, C.M.; Smith, T.; Portugal, A.M.; Poustka, L.; Banaschewski, T.; Johnson, M.; Group, E.A.L. Saccade dysmetria indicates attenuated visual exploration in autism spectrum disorder. J. Child Psychol. Psychiatry
**2021**, 62, 149–159. [Google Scholar] [CrossRef] - Unema, P.J.; Pannasch, S.; Joos, M.; Velichkovsky, B.M. Time course of information processing during scene perception: The relationship between saccade amplitude and fixation duration. Vis. Cogn.
**2005**, 12, 473–494. [Google Scholar] [CrossRef] - Valliappan, N.; Dai, N.; Steinberg, E.; He, J.; Rogers, K.; Ramachandran, V.; Xu, P.; Shojaeizadeh, M.; Guo, L.; Kohlhoff, K.; et al. Accelerating eye movement research via accurate and affordable smartphone eye tracking. Nat. Commun.
**2020**, 11, 4553. [Google Scholar] [CrossRef] - Hooge, I.T.; Niehorster, D.C.; Nyström, M.; Andersson, R.; Hessels, R.S. Is human classification by experienced untrained observers a gold standard in fixation detection? Behav. Res. Methods
**2018**, 50, 1864–1881. [Google Scholar] [CrossRef] [PubMed] - Papanikolaou, C.; Sharma, A.; Lind, P.G.; Lencastre, P. Lévy-flight model of gaze trajectories to improve ADHD diagnoses. Entropy
**2024**, 26, 392. [Google Scholar] [CrossRef] - Lencastre, P.; Gjersdal, M.; Gorjão, L.R.; Yazidi, A.; Lind, P.G. Modern AI versus century-old mathematical models: How far can we go with generative adversarial networks to reproduce stochastic processes? Phys. D Nonlinear Phenom.
**2023**, 453, 133831. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of the first 300 data points (corresponding to 5 s) from four gaze trajectories, two of them belonging to TD children (

**top**) and two to children with ASD (

**bottom**). All gaze points are marked as blue circumferences, while the parts of the saccade labeled gaze trajectory are represented as red lines. The borders of the computer screen at which the children were looking are marked with black lines.

**Figure 2.**(

**a**) Log-velocity distribution of TD children and children with ASD. (

**b**) Illustration of a 2-state process where the states F (Fixation) and S (Saccade) are characterized by the averages ${\mu}_{F}$ and ${\mu}_{S}$ and standard deviations ${\sigma}_{F}$ and ${\sigma}_{S}$, respectively, corresponding to the log-velocity of fixations (respectively, saccades). These states alternate throughout time with probabilities ${P}_{FS}$ if the transition is from saccade to fixation, or ${P}_{SF}$ if from fixation to saccade. (

**c**) Illustration of the visited area A. The areas marked with “1” represent the areas of the image visited in the considered time period. In this case, A was calculated for the first 300 data points and, for illustration purposes, the area of each grid’s square was enhanced to around 10 degrees of visual angle in each axis.

**Figure 3.**Probability density functions (pdf) for each quantity analyzed here for ASD (blue) and TD (orange) children. In the top row, we have the pdfs of the fixation and saccade parameters (${\mu}_{F}$,${\sigma}_{F}$, ${\mu}_{S}$,${\sigma}_{S}$) across all participants. On the bottom row, we have the pdfs of the parameters ${P}_{FS}$, ${P}_{SF}$, and $\mathsf{\Lambda}$. From visual inspection, we observe that this latter variable is the one where the difference in distribution is the starkest. This can be verified in Table 1.

**Figure 4.**Values of $\mathsf{\Lambda}(\tau ,N)$ for different values of $N\Delta \tau $, corresponding to the amount of time considered to compute this metric. We observe that for different multiples of $\tau $, the values of $\mathsf{\Lambda}$ are statistically significant across groups. The symbols indicate the average value of $\Gamma $ over all participants, and the error bars represent the corresponding standard deviation.

**Figure 5.**Confusion matrices relative to the classification results for the two benchmark models as well as the classification using the $\mathsf{\Lambda}$ metric. Besides needing fewer data, we observe that the quantity $\mathsf{\Lambda}$ has a higher accuracy $93.9\%$ compared to $72.5\%$ and $86.8\%$ of benchmark1 and benchmark2 respectively. Relative to the other measures, the $\mathsf{\Lambda}$ classification also outperforms the benchmarks, with sensitivity, specificity and precision values of $95.1\%$, $93.1\%$ and $89.6\%$ respectively, compared to the values of $68.9\%$$74.4\%$, $59.0\%$ for the same metrics for benchmark1 and $82.5\%$$89.9\%$, $85.7\%$ for benchmark2.

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**MDPI and ACS Style**

Lencastre, P.; Lotfigolian, M.; Lind, P.G.
Identifying Autism Gaze Patterns in Five-Second Data Records. *Diagnostics* **2024**, *14*, 1047.
https://doi.org/10.3390/diagnostics14101047

**AMA Style**

Lencastre P, Lotfigolian M, Lind PG.
Identifying Autism Gaze Patterns in Five-Second Data Records. *Diagnostics*. 2024; 14(10):1047.
https://doi.org/10.3390/diagnostics14101047

**Chicago/Turabian Style**

Lencastre, Pedro, Maryam Lotfigolian, and Pedro G. Lind.
2024. "Identifying Autism Gaze Patterns in Five-Second Data Records" *Diagnostics* 14, no. 10: 1047.
https://doi.org/10.3390/diagnostics14101047