Impulsivity Analysis Module

Overview

The Impulsivity module captures the burst-like, impulsive quality of a movement pattern. It conceptually pairs spatial abruptly-changing metrics with temporal suddenness metrics to define a singular 'Impulse'.

Theoretical Interpretation

• Input Requirements: Expects a 3D tensor of positional motion data over time. It internally routes this data to sub-features.
• Value Interpretation:
  • A high impulsivity index indicates a movement that is both spatially sharp (a sudden tight turn or change in geometric direction) and temporally sudden (a spike in velocity characteristic of a heavy-tailed distribution).
  • If the movement is entirely predictable or smooth (not sudden), impulsivity strictly evaluates to 0.0.

Algorithm Details & Mathematics

Impulsivity is fundamentally computed as the cross-product of spatial Direction Change (specifically its cosine similarity metric) and temporal Suddenness.

Let \(D_{cos} \in [0, 1]\) be the cosine similarity score representing the sharpness of the trajectory's angle (derived from the DirectionChange module). Let \(S_{binary} \in \{0, 1\}\) be the boolean classification natively returned by the Suddenness module (where \(1\) denotes a sudden movement phase, and \(0\) denotes continuous).

The impulsive index \(I\) is calculated as the simple scalar multiplier:

This ensures that high spatial curvature without temporal acceleration (e.g., slowly tracing a sharp corner) safely scores zero impulsivity.

References