, 2026
MATHEMATICAL FEATURE REPRESENTATIONS OF MOUSE DYNAMICS FOR CONTINUOUS USER AUTHENTICATION
Continuous authentication on endpoint devices requires behavioural representations that are accurate, compact and suitable for real-time use. This paper investigates mathematical feature representations for modelling user behaviour from mouse-dynamics data. Three feature families are proposed: path signatures derived from rough path theory, differential-geometric descriptors of cursor trajectories and optimal-control residuals based on human motor-control models. The proposed features are evaluated on the Balabit and SapiMouse datasets and compared with a 142-feature reference bank from existing mouse-dynamics literature. All feature sets are tested under the same one-class Mahalanobis protocol to isolate the contribution of the features themselves. The results show that optimal-control features provide the best compact representation, achieving competitive performance with only 23 features. Feature fusion further improves accuracy, while cross-dataset experiments highlight the importance of robustness across long and short session regimes (13-27).
Keywords: Mouse dynamics, Behavioural biometrics, Continuous authentication, Path signatures, Differential geometry, Optimal control
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