Analysis of High-Dimensional Coordination in Human Movement Using Variance Spectrum Scaling and Intrinsic Dimensionality

Area of Science:

• Biomechanics
• Movement Science
• Dynamical Systems Theory

Background:

• Full-body movement analysis traditionally uses one-dimensional data, limiting understanding of complex coordination.
• High-density recording and data sharing advancements necessitate new theoretical frameworks for biomechanical degrees of freedom and variability.
• Existing methods often up-dimensionalize data, while dimensionality reduction is crucial for understanding low-dimensional manifolds within high-dimensional kinematic spaces.

Purpose of the Study:

• To present a novel approach for quantifying the smoothness and dimensionality of the kinematic manifold in full-body movements.
• To establish a method for inferring manifold properties from the variance spectrum of embedding dimensions.
• To investigate the relationship between manifold properties and gait impairment.

Main Methods:

• Developed a method using principal component analysis of embedding dimensions to analyze the variance spectrum.
• Calculated the power law scaling exponent of the variance spectrum as a measure of manifold smoothness and dimensionality.
• Validated the approach with the Kuramoto model for synchronization and applied it to a full-body motion capture dataset of gait trials.

Main Results:

• The power law scaling exponent effectively quantifies manifold smoothness and dimensionality, with a threshold indicating non-differentiability.
• Variance scaling was highest in healthy individuals, intermediate in osteoarthritis patients post-surgery, and lowest pre-surgery.
• Intrinsic dimensionality increased while fractal dimension decreased with improved gait, suggesting a more compact yet complex manifold in healthy individuals.

Conclusions:

• The proposed method provides a robust way to analyze the complexity of full-body movement manifolds.
• Manifold dimensionality and smoothness are sensitive indicators of gait impairment.
• This framework can inform classical problems in movement science and the study of full-body biomechanics.