Dynamic signatures: a mathematical approach to analysis

Abstract

This study evaluates mathematical tools (principal component analysis, dynamic time warping, and the Kolmogorov-Smirnov hypothesis test) to analyse global and local data from dynamic signatures to reduce subjectivity and increase the reproducibility of handwriting examination using a two-step approach. A dataset composed of 1 800 genuine signature samples, 870 simulated signatures, and 60 disguises (30 formally similar or "autosimulated" and 30 random but different from usual) provided by 30 volunteers was collected. The first step involved global data analysis using principal component analysis and a hypothesis test performed for 62 global characteristics, and associations of these characteristics were analysed through calculations of multivariate distance followed by a hypothesis test. The second step involved the analysis of local characteristics including vertical and horizontal positions, speed, pressure gradient, acceleration, and jerk point-to-point, by using dynamic time warping followed by a hypothesis test. Optimization of sensitivity and specificity metrics of the hypothesis test was explored by varying its stringency and observing accuracy rates for the simulated and genuine groups. A P-value threshold of 1 × 10^-10 was found to be optimal, making the test more restrictive and yielding accuracy rates of 96.7% for genuine global data and 88.9% for simulated data. The same cut-off value for local characteristics provided an average accuracy rate of 95.4% for genuine samples and 94.7% for simulated samples, demonstrating high accuracy for both simulated and genuine samples. However, the method did not offer reasonable accuracy rates for disguises, consistent with observations in traditional handwriting examination. Our approach provided satisfactory results for forensic examination use. The visualization of graphs and signatures and analysis of all identifying elements of handwriting by the examining expert are still essential. In future studies, we plan to perform blind tests to validate our approach and propose a rigorous methodology.

Keywords: data analysis; digitally captured signatures; dynamic signature; dynamic time warping; forensic handwriting examination.

Figure 1

An example of principal component analysis (PCA) clustering for one subject. D_form: formal disguise (circle); D_rand: free disguise (diamond); N: natural signatures from the pattern (square), and S: simulation (X symbol).