Prediction of Grade, Gender, and Academic Performance of Children and Teenagers from Handwriting Using the Sigma-Lognormal Model

Adrian Iste; Kazuki Nishizawa; Chisa Tanaka; Andrew Vargo; Anna Scius-Bertrand; Andreas Fischer; Koichi Kise

cs.HCMar 12, 2026

Prediction of Grade, Gender, and Academic Performance of Children and Teenagers from Handwriting Using the Sigma-Lognormal Model

Authors: Adrian Iste, Kazuki Nishizawa, Chisa Tanaka, Andrew Vargo, Anna Scius-Bertrand, Andreas Fischer, Koichi Kise

Organizations: Osaka Metropolitan University, Osaka, Japan · University of Applied Sciences and Arts Western Switzerland, Fribourg, Switzerland · University of Fribourg, Fribourg, Switzerland · German Research Center for Artiﬁcial Intelligence, Japan Laboratory, Osaka, Japan

Abstract

Digital handwriting acquisition enables the capture of detailed temporal and kinematic signals reflecting the motor processes underlying writing behavior. While handwriting analysis has been extensively explored in clinical or adult populations, its potential for studying developmental and educational characteristics in children remains less investigated. In this work, we examine whether handwriting dynamics encode information related to student characteristics using a large-scale online dataset collected from Japanese students from elementary school to junior high school. We systematically compare three families of handwriting-derived features: basic statistical descriptors of kinematic signals, entropy-based measures of variability, and parameters obtained from the sigma-lognormal model. Although the dataset contains dense stroke-level recordings, features are aggregated at the student level to enable a controlled comparison between representations. These features are evaluated across three prediction tasks: grade prediction, gender classification, and academic performance classification, using Linear or Logistic Regression and Random Forest models under consistent experimental settings. The results show that handwriting dynamics contain measurable signals related to developmental stage and individual differences, especially for the grade prediction task. These findings highlight the potential of kinematic handwriting analysis and confirm that through their development, children's handwriting evolves toward a lognormal motor organization.

Figures & tables

Figure 1: Distribution of the ages of the students in Wacom dataset.

Grade	Boys	Girls	Total
1	27	23	50
2	24	26	50
3	23	27	50
4	17	30	47
5	22	28	50
6	30	20	50

Table 1: Distribution of students across grades.

Panel of Figure 2 — Figure 2: Examples of drills from subject “Japanese language” for grade 1 to 9.

Figure 3: Distribution of number of questions in the drills of the subject Japanese language.

Panel of Figure 4 — Figure 4: Score distributions analysis in Wacome dataset

Feature	Description
Number of Lognormal Components ( $C$ )	The number of lognormal components required to model each stroke. This parameter reflects the degree of motor segmentation.
Velocity Profile Signal-to-Noise Ratio (SNR)	Signal-to-noise ratio of the velocity profile, which quantifies how well the reconstructed lognormal model explains the observed kinematic signal.
Normalized SNR (SNR/ $C$ )	Signal-to-noise ratio divided by the number of lognormal components, normalizing reconstruction quality by model complexity.
Time Dispersion ( $D$ )	The lognormal time dispersion parameter controlling the temporal spread of each motor impulse. It is associated with the duration and fluidity of the movement.
Time Delay ( $t_{0}$ )	The onset timing of motor commands within the stroke sequence.
Location Parameter ( $\mu$ )	Determines the temporal positioning of each motor impulse within the stroke.

Table 2: Description of Lognormal Stroke Features

Panel of Figure 5 — Figure 5: Prediction of the grade for each set of feature using Linear Regression (left) and Random Forest (right) using 5-fold cross validation. One point corresponds to a prediction of a point from the test fold.

Figure 6: Box plot of the signal-to-noise ratio over the number of lognormal components across all grades.

Panel of Figure 7 — Figure 7: Confusion matrix of the gender classification for each set of feature using Logistic Regression (top) and Random Forest (bottom) with 5-fold cross validation.

Feature Set	Logistic Regression			Random Forest			Majority-class baseline
	ACC	F1	AUC	ACC	F1	AUC	Majority ACC
Base	0.611	0.535	0.626	0.600	0.551	0.625	0.537
Entropy	0.552	0.445	0.574	0.552	0.493	0.595	0.537
Sigma-lognormal	0.653	0.604	0.725	0.658	0.614	0.693	0.537

Table 3: Gender classification performance over all grades using 5-fold cross validation for all sets of feature compared to a majority-class baseline.

Panel of Figure 8 — Figure 8: Confusion matrix of the prediction of the academic performance of a student for each set of feature using Logistic Regression (top) and Random Forest (bottom) with 5-fold cross validation.

Feature Set	Logistic Regression			Random Forest			Baseline
	ACC	F1	AUC	ACC	F1	AUC	Majority ACC
Base	0.596	0.569	0.645	0.579	0.540	0.624	0.526
Entropy	0.607	0.583	0.642	0.592	0.560	0.641	0.526
Sigma-lognormal	0.628	0.607	0.673	0.615	0.579	0.665	0.526

Table 4: Classification results over all grades of the overall academic performance of a student using 5-fold cross validation for all sets of feature compared to a “always majority” model.

Educational Assessment

Educational assessment measures what learners know and can do, using tests, rubrics, and learning evidence to guide decisions.

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From Pen Strokes to Sleep States: Detecting Low-Recovery Days Using Sigma-Lognormal Handwriting Features

Chisa Tanaka, Andrew Vargo, Anna Scius-Bertrand, Andreas Fischer+1

Osaka Metropolitan University, Osaka, Japan · University of Applied Sciences and Arts Western Switzerland, Fribourg, Switzerland · University of Fribourg, Fribourg, Switzerland+1

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While handwriting has traditionally been studied for character recognition and disease classification, its potential to reflect day-to-day physiological fluctuations in healthy individuals remains unexplored. This study examines whether daily variations in sleep-related recovery states can be inferred from online handwriting dynamics. % We propose a personalized binary classification framework that detects low-recovery days using features derived from the Sigma-Lognormal model, which captures the neuromotor generation process of pen strokes. In a 28-day in-the-wild study involving 13 university students, handwriting was recorded three times daily, and nocturnal cardiac indicators were measured using a wearable ring. For each participant, the lowest (or highest) quartile of four sleep-related metrics -- HRV, lowest heart rate, average heart rate, and total sleep duration -- defined the positive class. Leave-One-Day-Out cross-validation showed that PR-AUC significantly exceeded the baseline (0.25) for all four variables after FDR correction, with the strongest performance observed for cardiac-related variables. Importantly, classification performance did not differ significantly across task types or recording timings, indicating that recovery-related signals are embedded in general movement dynamics. These results demonstrate that subtle within-person autonomic recovery fluctuations can be detected from everyday handwriting, opening a new direction for non-invasive, device-independent health monitoring.

Abstract

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