PCA of waveforms and functional PCA: A primer for biomechanics

Area of Science:

• Biomechanics
• Statistics
• Functional Data Analysis (FDA)

Background:

• Principal Components Analysis (PCA) and Functional PCA (fPCA) are statistical methods for analyzing biomechanical curve data.
• fPCA is an established method within the Functional Data Analysis (FDA) framework.
• Understanding the relationship between PCA and fPCA is crucial for advanced data exploration.

Purpose of the Study:

• To demonstrate that PCA of waveforms is a rudimentary form of FDA.
• To rationalize PCA within the broader FDA statistical framework.
• To highlight the benefits of fPCA over PCA, particularly regarding smoothing control in functional principal components.

Main Methods:

• Mathematical proofing to demonstrate the relationship between PCA and fPCA.
• Application of both PCA and fPCA techniques to biomechanical curve data.
• Utilizing an open-access motion sickness dataset to illustrate fPCA's advantages.

Main Results:

• PCA can be understood as a basic form of FDA.
• fPCA provides greater control over smoothing of functional principal components compared to basic PCA.
• The study provides practical demonstrations and open-access software for implementing these methods.

Conclusions:

• PCA is a foundational element within the FDA framework.
• fPCA offers enhanced analytical capabilities for biomechanical data, especially when precise control over smoothing is needed.
• The provided open-access software aims to facilitate the adoption of FDA methods in biomechanics research.